Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 6:46:49 PM UTC-6, Brent wrote:
>
>
>
> On 4/24/2019 4:17 PM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 24, 2019 at 5:11:13 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/21/2019 7:35 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: 



 On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:

 *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says 
 the metric tensor is a Kronecker delta function. But I could swear that 
 the 
 diagonal of -1,1,1,1 represents flat space in SR. AG??*


 What's odd about that??? Flat space is just special case of curved 
 space in which the curvature is zero.

 Brent

>>>
>>> *Sure, but he seems to be saying that the Kronecker delta is the metric 
>>> tensor for curved space. Isn't that how you interpret his comment?*
>>>
>>>
>>> No.?? After he goes thru the derivation with delta function in it, then 
>>> he says it's different for a curve?? space.
>>>
>>> Brent
>>>
>>
>> *I just reviewed it again. That's not my reading. In any event, it's not 
>> clear what he means, and using Bruno's suggestion, t' --> it,?? doesn't 
>> really help either since you end up with the Lorentz metric which is far 
>> from Euclidean intuition for demonstrating deviations from flatness. 
>> Further, there are transformations that keep spacetime flat with NON-zero 
>> off diagonal elements, such as a simple rotation. AG??*
>>
>
>
> *Using the Lorentz metric, how is "flat" spacetime defined mathematically? 
> AG *
>
>
> The general definition is that the Riemann tensor is zero.?? This is 
> independent of what coordinate system is used.?? 
> https://en.wikipedia.org/wiki/Riemann_curvature_tensor
>
> If the Lorentz metric applies globally the space is flat.
>
> Brent
>

Are the double question marks significant in some way, or typos? AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 6:04:43 PM UTC-6, Brent wrote:
>
>
>
> On 4/24/2019 4:11 PM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/21/2019 7:35 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:
>>>
>>> *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says 
>>> the metric tensor is a Kronecker delta function. But I could swear that the 
>>> diagonal of -1,1,1,1 represents flat space in SR. AG??*
>>>
>>>
>>> What's odd about that??? Flat space is just special case of curved space 
>>> in which the curvature is zero.
>>>
>>> Brent
>>>
>>
>> *Sure, but he seems to be saying that the Kronecker delta is the metric 
>> tensor for curved space. Isn't that how you interpret his comment?*
>>
>>
>> No.?? After he goes thru the derivation with delta function in it, then 
>> he says it's different for a curve?? space.
>>
>> Brent
>>
>
> *I just reviewed it again. That's not my reading. In any event, it's not 
> clear what he means, and using Bruno's suggestion, t' --> it,?? doesn't 
> really help either since you end up with the Lorentz metric which is far 
> from Euclidean intuition for demonstrating deviations from flatness. *
>
>
> It was NOT demonstrating deviation from flatness.??
>

*I know. He just offered a final comment that deviations from flatness 
corresponds to non-zero off diagonal elements, so it got me wondering how 
flatness is mathematically defined for a Lorentz metric. I agree I should 
focus on the reference I posted. AG*
 

> I don't know what the guy was intending to demonstrate but he started with 
> assuming flatness, got a metric, and then remarked that it's different for 
> curve space.?? So what's your problem??? Read
>
> arXiv:1608.05752v1 [physics.hist-ph] 19 Aug 2016
>
> and stop fussing about some video.
>
> Brent
>
> *Further, there are transformations that keep spacetime flat with NON-zero 
> off diagonal elements, such as a simple rotation. AG??*
> -- 
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>
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 5:11:13 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/21/2019 7:35 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:
>>>
>>> *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says 
>>> the metric tensor is a Kronecker delta function. But I could swear that the 
>>> diagonal of -1,1,1,1 represents flat space in SR. AG??*
>>>
>>>
>>> What's odd about that??? Flat space is just special case of curved space 
>>> in which the curvature is zero.
>>>
>>> Brent
>>>
>>
>> *Sure, but he seems to be saying that the Kronecker delta is the metric 
>> tensor for curved space. Isn't that how you interpret his comment?*
>>
>>
>> No.?? After he goes thru the derivation with delta function in it, then 
>> he says it's different for a curve?? space.
>>
>> Brent
>>
>
> *I just reviewed it again. That's not my reading. In any event, it's not 
> clear what he means, and using Bruno's suggestion, t' --> it,  doesn't 
> really help either since you end up with the Lorentz metric which is far 
> from Euclidean intuition for demonstrating deviations from flatness. 
> Further, there are transformations that keep spacetime flat with NON-zero 
> off diagonal elements, such as a simple rotation. AG *
>

*Using the Lorentz metric, how is "flat" spacetime defined mathematically? 
AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote:
>
>
>
> On 4/21/2019 7:35 PM, agrays...@gmail.com  wrote:
>
>
>
> On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:
>>
>> *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says the 
>> metric tensor is a Kronecker delta function. But I could swear that the 
>> diagonal of -1,1,1,1 represents flat space in SR. AG??*
>>
>>
>> What's odd about that??? Flat space is just special case of curved space 
>> in which the curvature is zero.
>>
>> Brent
>>
>
> *Sure, but he seems to be saying that the Kronecker delta is the metric 
> tensor for curved space. Isn't that how you interpret his comment?*
>
>
> No.?? After he goes thru the derivation with delta function in it, then he 
> says it's different for a curve?? space.
>
> Brent
>

*I just reviewed it again. That's not my reading. In any event, it's not 
clear what he means, and using Bruno's suggestion, t' --> it,  doesn't 
really help either since you end up with the Lorentz metric which is far 
from Euclidean intuition for demonstrating deviations from flatness. 
Further, there are transformations that keep spacetime flat with NON-zero 
off diagonal elements, such as a simple rotation. AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 11:29:36 AM UTC-6, agrays...@gmail.com 
wrote:
>
>
>
> On Wednesday, April 24, 2019 at 11:06:10 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 23 Apr 2019, at 13:39, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 23, 2019 at 4:00:26 AM UTC-6, Bruno Marchal wrote:
>>>
>>>
>>> On 20 Apr 2019, at 23:14, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:


 On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote:



 On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>
> Sorry, I don't remember what, if anything, I intended to text.
>
> I'm not expert on how Einstein arrived at his famous field equations.  
> I know that he insisted on them being tensor equations so that they would 
> have the same form in all coordinate systems.  That may sound like a 
> mathematical technicality, but it is really to ensure that the things in 
> the equation, the tensors, could have a physical interpretation.  He also 
> limited himself to second order differentials, probably as a matter of 
> simplicity.  And he excluded torsion, but I don't know why.  And of 
> course 
> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>
> Brent
>

 Here's a link which might help;

  https://arxiv.org/pdf/1608.05752.pdf



 Yes. That is helpful.

 The following (long!) video can also help (well, it did help me)

 https://www.youtube.com/watch?v=foRPKAKZWx8


 Bruno

>>>
>>> *I've been viewing this video. I don't see how he established that the 
>>> metric tensor is a correction for curved spacetime. AG *
>>>
>>>
>>> ds^2 = dx^2 + dy^2 is Pythagorus theorem, in the plane. The “g_mu,nu” 
>>> are the coefficients needed to ensure un non-planner (curved) metric, and 
>>> they can be use to define the curvature.
>>>
>>> Bruno 
>>>
>>
>> *Thanks for your time, but I don't think you have a clue what the issues 
>> are here. And, as a alleged expert in logic, it puts your other claims in 
>> jeopardy. Firstly, in the video you offered, the presenter has a Kronecker 
>> delta as the leading multiplicative factor in his definition of the Metric 
>> Tensor, which implies all off diagonal terms are zero. And even if that 
>> term were omitted, your reference to Pythagorus leaves much to be desired. 
>> In SR we're dealing with a 4 dim space with the Lorentz metric, not a 
>> Euclidean space where the Pythagorean theorem applies. How does a diagonal 
>> signature of -1,1,1,1 imply flat space? Why would non-zero off diagonal 
>> elements have anything to do with a departure from flat space under 
>> Lorentz's metric? AG *
>>
>>
>>
>> Oops sorry. Since long I do relativity only in its euclidian form, 
>> through the transformation t' := it. (I being the square root of -1). This 
>> makes Minkowski euclidean again. I should have mentioned this.
>>
>> Bruno
>>
>
>  
> *How does it make Minkowski euclidean if you're not dealing with 
> spacetime. Euclidean and departures from flat require real coordinates. AG*
>

*Using transformation t' --> it  yields a pseudo-Euclidean or 
pseudo-Minkowski space, and can't be used to explain the off-diagonal 
elements of the metric tensor as indicative of lack of Euclidean flatness. 
AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 11:06:10 AM UTC-6, Bruno Marchal wrote:
>
>
> On 23 Apr 2019, at 13:39, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 23, 2019 at 4:00:26 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 20 Apr 2019, at 23:14, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
>>>
>>>
>>> On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:

 Sorry, I don't remember what, if anything, I intended to text.

 I'm not expert on how Einstein arrived at his famous field equations.  
 I know that he insisted on them being tensor equations so that they would 
 have the same form in all coordinate systems.  That may sound like a 
 mathematical technicality, but it is really to ensure that the things in 
 the equation, the tensors, could have a physical interpretation.  He also 
 limited himself to second order differentials, probably as a matter of 
 simplicity.  And he excluded torsion, but I don't know why.  And of course 
 he knew it had to reproduce Newtonian gravity in the weak/slow limit.

 Brent

>>>
>>> Here's a link which might help;
>>>
>>>  https://arxiv.org/pdf/1608.05752.pdf
>>>
>>>
>>>
>>> Yes. That is helpful.
>>>
>>> The following (long!) video can also help (well, it did help me)
>>>
>>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>>
>>>
>>> Bruno
>>>
>>
>> *I've been viewing this video. I don't see how he established that the 
>> metric tensor is a correction for curved spacetime. AG *
>>
>>
>> ds^2 = dx^2 + dy^2 is Pythagorus theorem, in the plane. The “g_mu,nu” are 
>> the coefficients needed to ensure un non-planner (curved) metric, and they 
>> can be use to define the curvature.
>>
>> Bruno 
>>
>
> *Thanks for your time, but I don't think you have a clue what the issues 
> are here. And, as a alleged expert in logic, it puts your other claims in 
> jeopardy. Firstly, in the video you offered, the presenter has a Kronecker 
> delta as the leading multiplicative factor in his definition of the Metric 
> Tensor, which implies all off diagonal terms are zero. And even if that 
> term were omitted, your reference to Pythagorus leaves much to be desired. 
> In SR we're dealing with a 4 dim space with the Lorentz metric, not a 
> Euclidean space where the Pythagorean theorem applies. How does a diagonal 
> signature of -1,1,1,1 imply flat space? Why would non-zero off diagonal 
> elements have anything to do with a departure from flat space under 
> Lorentz's metric? AG *
>
>
>
> Oops sorry. Since long I do relativity only in its euclidian form, through 
> the transformation t' := it. (I being the square root of -1). This makes 
> Minkowski euclidean again. I should have mentioned this.
>
> Bruno
>

 
*How does it make Minkowski euclidean if you're not dealing with spacetime. 
Euclidean and departures from flat require real coordinates. AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 23, 2019 at 4:00:26 AM UTC-6, Bruno Marchal wrote:
>
>
> On 20 Apr 2019, at 23:14, agrays...@gmail.com  wrote:
>
>
>
> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>>>
>>> Sorry, I don't remember what, if anything, I intended to text.
>>>
>>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>>> know that he insisted on them being tensor equations so that they would 
>>> have the same form in all coordinate systems.  That may sound like a 
>>> mathematical technicality, but it is really to ensure that the things in 
>>> the equation, the tensors, could have a physical interpretation.  He also 
>>> limited himself to second order differentials, probably as a matter of 
>>> simplicity.  And he excluded torsion, but I don't know why.  And of course 
>>> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>>>
>>> Brent
>>>
>>
>> Here's a link which might help;
>>
>>  https://arxiv.org/pdf/1608.05752.pdf
>>
>>
>>
>> Yes. That is helpful.
>>
>> The following (long!) video can also help (well, it did help me)
>>
>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>
>>
>> Bruno
>>
>
> *I've been viewing this video. I don't see how he established that the 
> metric tensor is a correction for curved spacetime. AG *
>
>
> ds^2 = dx^2 + dy^2 is Pythagorus theorem, in the plane. The “g_mu,nu” are 
> the coefficients needed to ensure un non-planner (curved) metric, and they 
> can be use to define the curvature.
>
> Bruno 
>

*Thanks for your time, but I don't think you have a clue what the issues 
are here. And, as a alleged expert in logic, it puts your other claims in 
jeopardy. Firstly, in the video you offered, the presenter has a Kronecker 
delta as the leading multiplicative factor in his definition of the Metric 
Tensor, which implies all off diagonal terms are zero. And even if that 
term were omitted, your reference to Pythagorus leaves much to be desired. 
In SR we're dealing with a 4 dim space with the Lorentz metric, not a 
Euclidean space where the Pythagorean theorem applies. How does a diagonal 
signature of -1,1,1,1 imply flat space? Why would non-zero off diagonal 
elements have anything to do with a departure from flat space under 
Lorentz's metric? AG *

>
>
>
>
>
>
>>
>>
>>
>> AG
>>
>>>
>>> On 4/18/2019 7:59 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com 
>>> wrote: 

 *I see no new text in this message. AG*

>>>  
>>> Brent; if you have time, please reproduce the text you intended. 
>>>
>>> I recall reading that before Einstein published his GR paper, he used a 
>>> trial and error method to determine the final field equations (as he raced 
>>> for the correct ones in competition with Hilbert, who may have arrived at 
>>> them first).  So it's hard to imagine a mathematical methodology which 
>>> produces them. If you have any articles that attempt to explain how the 
>>> field equations are derived, I'd really like to explore this aspect of GR 
>>> and get some "satisfaction". I can see how he arrived at some principles, 
>>> such as geodesic motion, by applying the Least Action Principle, or how he 
>>> might have intuited that matter/energy effects the geometry of spacetime, 
>>> but from these principles it's baffling how he arrived at the field 
>>> equations. 
>>>
>>> AG
>>>


 On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote: 
>
>
>
> On 4/17/2019 5:20 PM, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 



 On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:



 On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
 wrote: 
>
>
>
> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, 
>>> agrays...@gmail.com wrote: 



 On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote:
>
>
>
> On 4/21/2019 6:31 PM, agrays...@gmail.com  wrote:
>
> *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says the 
> metric tensor is a Kronecker delta function. But I could swear that the 
> diagonal of -1,1,1,1 represents flat space in SR. AG *
>
>
> What's odd about that?  Flat space is just special case of curved space in 
> which the curvature is zero.
>
> Brent
>

*Sure, but he seems to be saying that the Kronecker delta is the metric 
tensor for curved space. Isn't that how you interpret his comment? AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, April 21, 2019 at 5:59:25 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Sunday, April 21, 2019 at 5:54:33 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/21/2019 2:20 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, April 20, 2019 at 9:51:13 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/20/2019 2:14 PM, agrays...@gmail.com wrote:
>>>
>>> The following (long!) video can also help (well, it did help me)

 https://www.youtube.com/watch?v=foRPKAKZWx8


 Bruno

>>>
>>> *I've been viewing this video. I don't see how he established that the 
>>> metric tensor is a correction for curved spacetime. AG *
>>>
>>>
>>> The metric tensor is the quantified embodiment of curved spacetime.  But 
>>> How else would you define curvature, if not with the metric?
>>>
>>> Brent
>>>
>>
>> *At 49:42 he defines the metric tensor. It has a Kronecker delta as the 
>> leading term. So all cross terms will be zero in its matrix representation. 
>> *
>>
>>
>> But then he says that in a curved space g_mn must be something else, that 
>> does have cross terms.   I don't find his presentation very enlightening.  
>> He ends up wit ds^2 = g_m_n dx^r dx^sHe doesn't even have the indices 
>> match as in Einstein's summation forumula.
>>
>> Brent
>>
>
> Thanks. I'm going on to Susskind's lectures on GR.  AG
>

*Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says the 
metric tensor is a Kronecker delta function. But I could swear that the 
diagonal of -1,1,1,1 represents flat space in SR. AG *

>
>> *Listen; this is pure mathematics. If what he calls the metric tensor is 
>> the general correction for curved spacetime, it can be proven 
>> mathematically, strictly by mathematics. What I see is a hand-waving 
>> argument at best! Ball in your court. AG *
>> -- 
>> You received this message because you are subscribed to the Google Groups 
>> "Everything List" group.
>> To unsubscribe from this group and stop receiving emails from it, send an 
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>>
>>
>>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, April 21, 2019 at 5:54:33 PM UTC-6, Brent wrote:
>
>
>
> On 4/21/2019 2:20 AM, agrays...@gmail.com  wrote:
>
>
>
> On Saturday, April 20, 2019 at 9:51:13 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/20/2019 2:14 PM, agrays...@gmail.com wrote:
>>
>> The following (long!) video can also help (well, it did help me)
>>>
>>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>>
>>>
>>> Bruno
>>>
>>
>> *I've been viewing this video. I don't see how he established that the 
>> metric tensor is a correction for curved spacetime. AG *
>>
>>
>> The metric tensor is the quantified embodiment of curved spacetime.  But 
>> How else would you define curvature, if not with the metric?
>>
>> Brent
>>
>
> *At 49:42 he defines the metric tensor. It has a Kronecker delta as the 
> leading term. So all cross terms will be zero in its matrix representation. 
> *
>
>
> But then he says that in a curved space g_mn must be something else, that 
> does have cross terms.   I don't find his presentation very enlightening.  
> He ends up wit ds^2 = g_m_n dx^r dx^sHe doesn't even have the indices 
> match as in Einstein's summation forumula.
>
> Bren
>

Thanks. I'm going on to Susskind's lectures on GR.  AG

>
> *Listen; this is pure mathematics. If what he calls the metric tensor is 
> the general correction for curved spacetime, it can be proven 
> mathematically, strictly by mathematics. What I see is a hand-waving 
> argument at best! Ball in your court. AG *
> -- 
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>
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, April 21, 2019 at 12:07:07 AM UTC-6, Philip Thrift wrote:
>
>
>
> On Saturday, April 20, 2019 at 4:14:27 PM UTC-5, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
>>>
>>>
>>> On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:

 Sorry, I don't remember what, if anything, I intended to text.

 I'm not expert on how Einstein arrived at his famous field equations.  
 I know that he insisted on them being tensor equations so that they would 
 have the same form in all coordinate systems.  That may sound like a 
 mathematical technicality, but it is really to ensure that the things in 
 the equation, the tensors, could have a physical interpretation.  He also 
 limited himself to second order differentials, probably as a matter of 
 simplicity.  And he excluded torsion, but I don't know why.  And of course 
 he knew it had to reproduce Newtonian gravity in the weak/slow limit.

 Brent

>>>
>>> Here's a link which might help;
>>>
>>>  https://arxiv.org/pdf/1608.05752.pdf
>>>
>>>
>>>
>>> Yes. That is helpful.
>>>
>>> The following (long!) video can also help (well, it did help me)
>>>
>>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>>
>>>
>>> Bruno
>>>
>>
>> *I've been viewing this video. I don't see how he established that the 
>> metric tensor is a correction for curved spacetime. AG *
>>
>>>
>>>
>
>
> The physicists' vocabulary can be baffling (at least it is to me).
>
> I think the basic thing though is that the Einstein Field Equations (EFE) 
> is not - in a sense - absolute. EFE is relative.
>
> Once one has established a coordinate system/metric (c-sys1) for "the 
> world" independently, then EFE(c-sys1) provides a recipe for making 
> predictions within c-sys1. Change c-sys1 to c-sys2, and EFE(c-sys2) 
> calculates predictions in c-sys2.
>
> There is no absolute c-sys for "the world".
>
> - pt
>

I don't follow your argument. GR satisfies the Principle of General 
Covariance since it's written in tensor form, and tensors transform 
covariantly. Whether the video shows what is alleged as the metric tensor 
is truly a representation of departure from flatness is an entirely 
different matter, as I explained to Brent. AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Saturday, April 20, 2019 at 9:51:13 PM UTC-6, Brent wrote:
>
>
>
> On 4/20/2019 2:14 PM, agrays...@gmail.com  wrote:
>
> The following (long!) video can also help (well, it did help me)
>>
>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>
>>
>> Bruno
>>
>
> *I've been viewing this video. I don't see how he established that the 
> metric tensor is a correction for curved spacetime. AG *
>
>
> The metric tensor is the quantified embodiment of curved spacetime.  How 
> else would you define curvature, if not with the metric?
>
> Brent
>

*At 49:42 he defines the metric tensor. It has a Kronecker delta as the 
leading term. So all cross terms will be zero in its matrix representation. 
Listen; this is pure mathematics. If what he calls the metric tensor is the 
general correction for curved spacetime, it can be proven mathematically, 
strictly by mathematics. What I see is a hand-waving argument at best! Ball 
in your court. AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
>
>
> On 19 Apr 2019, at 04:08, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>>
>> Sorry, I don't remember what, if anything, I intended to text.
>>
>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>> know that he insisted on them being tensor equations so that they would 
>> have the same form in all coordinate systems.  That may sound like a 
>> mathematical technicality, but it is really to ensure that the things in 
>> the equation, the tensors, could have a physical interpretation.  He also 
>> limited himself to second order differentials, probably as a matter of 
>> simplicity.  And he excluded torsion, but I don't know why.  And of course 
>> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>>
>> Brent
>>
>
> Here's a link which might help;
>
>  https://arxiv.org/pdf/1608.05752.pdf
>
>
>
> Yes. That is helpful.
>
> The following (long!) video can also help (well, it did help me)
>
> https://www.youtube.com/watch?v=foRPKAKZWx8
>
>
> Bruno
>

*I've been viewing this video. I don't see how he established that the 
metric tensor is a correction for curved spacetime. AG *

>
>
>
>
> AG
>
>>
>> On 4/18/2019 7:59 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>> *I see no new text in this message. AG*
>>>
>>  
>> Brent; if you have time, please reproduce the text you intended. 
>>
>> I recall reading that before Einstein published his GR paper, he used a 
>> trial and error method to determine the final field equations (as he raced 
>> for the correct ones in competition with Hilbert, who may have arrived at 
>> them first).  So it's hard to imagine a mathematical methodology which 
>> produces them. If you have any articles that attempt to explain how the 
>> field equations are derived, I'd really like to explore this aspect of GR 
>> and get some "satisfaction". I can see how he arrived at some principles, 
>> such as geodesic motion, by applying the Least Action Principle, or how he 
>> might have intuited that matter/energy effects the geometry of spacetime, 
>> but from these principles it's baffling how he arrived at the field 
>> equations. 
>>
>> AG
>>
>>>
>>>
>>> On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote: 



 On 4/17/2019 5:20 PM, agrays...@gmail.com wrote:



 On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: 
>
>
>
> On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
>>> wrote: 



 On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>
>
>
> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>
>
>
> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, 
>> agrays...@gmail.com wrote: 
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 



 On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>
>>

>>> He might have been referring to a transformation to a 
>>> tangent space where the metric tensor is diagonalized and its 
>>> derivative at 
>>> that point in spacetime is zero. Does this make any sense? 
>>>
>>>
>>> Sort of.  
>>>
>>
>>
>> Yeah, that's what he's doing. He's assuming a given 
>> coordinate system and some arbitrary point in a non-empty 
>> spacetime. So 
>> spacetime has a non zero curvature and the derivative of the 
>> metric tensor 
>> is 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 18, 2019 at 9:20:36 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 18, 2019 at 8:08:58 PM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>>>
>>> Sorry, I don't remember what, if anything, I intended to text.
>>>
>>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>>> know that he insisted on them being tensor equations so that they would 
>>> have the same form in all coordinate systems.  That may sound like a 
>>> mathematical technicality, but it is really to ensure that the things in 
>>> the equation, the tensors, could have a physical interpretation.  He also 
>>> limited himself to second order differentials, probably as a matter of 
>>> simplicity.  And he excluded torsion, but I don't know why.  And of course 
>>> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>>>
>>> Brent
>>>
>>
>> Here's a link which might help;
>>
>>  https://arxiv.org/pdf/1608.05752.pdf
>>
>> AG
>>
>
> I'm coming to the view that what I have been seeking these many years - 
> namely, a mathematical derivation of Einstein's field equations, somewhat 
> like a mathematical theorem -- doesn't exist. It's more a case of a set of 
> highly subtle physical intuitions about how the universe functions, which, 
> when cobbled together, result in the field equations. For this reason, most 
> alleged explanations of GR involve, at some point, essentially pulling the 
> field equations out of the proverbial hat.  As with the Principle of 
> Relativity and the Least Action Principle, the latter say applied to 
> asserting geodesic motion for freely falling bodies, they're not provable 
> as "true", but assuming them "false" would be a dead-end for physics and 
> would, as well, make our lives miserable. AG
>

One possible exception to the above is the Einstein-Hilbert Principle of 
Least Action, from which, it is alleges, Einstein's field equations can be 
derived.

 https://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action

But what it is, and how it would work, is above my pay grade. Maybe someone 
here can shed some light on this topic. 

AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 18, 2019 at 8:08:58 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>>
>> Sorry, I don't remember what, if anything, I intended to text.
>>
>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>> know that he insisted on them being tensor equations so that they would 
>> have the same form in all coordinate systems.  That may sound like a 
>> mathematical technicality, but it is really to ensure that the things in 
>> the equation, the tensors, could have a physical interpretation.  He also 
>> limited himself to second order differentials, probably as a matter of 
>> simplicity.  And he excluded torsion, but I don't know why.  And of course 
>> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>>
>> Brent
>>
>
> Here's a link which might help;
>
>  https://arxiv.org/pdf/1608.05752.pdf
>
> AG
>

I'm coming to the view that what I have been seeking these many years - 
namely, a mathematical derivation of Einstein's field equations, somewhat 
like a mathematical theorem -- doesn't exist. It's more a case of a set of 
highly subtle physical intuitions about how the universe functions, which, 
when cobbled together, result in the field equations. For this reason, most 
alleged explanations of GR involve, at some point, essentially pulling the 
field equations out of the proverbial hat.  As with the Principle of 
Relativity and the Least Action Principle, the latter say applied to 
asserting geodesic motion for freely falling bodies, they're not provable 
as "true", but assuming them "false" would be a dead-end for physics and 
would, as well, make our lives miserable. AG

-- 
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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>
> Sorry, I don't remember what, if anything, I intended to text.
>
> I'm not expert on how Einstein arrived at his famous field equations.  I 
> know that he insisted on them being tensor equations so that they would 
> have the same form in all coordinate systems.  That may sound like a 
> mathematical technicality, but it is really to ensure that the things in 
> the equation, the tensors, could have a physical interpretation.  He also 
> limited himself to second order differentials, probably as a matter of 
> simplicity.  And he excluded torsion, but I don't know why.  And of course 
> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>
> Brent
>

Here's a link which might help;

 https://arxiv.org/pdf/1608.05752.pdf

AG

>
> On 4/18/2019 7:59 AM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>> *I see no new text in this message. AG*
>>
>  
> Brent; if you have time, please reproduce the text you intended. 
>
> I recall reading that before Einstein published his GR paper, he used a 
> trial and error method to determine the final field equations (as he raced 
> for the correct ones in competition with Hilbert, who may have arrived at 
> them first).  So it's hard to imagine a mathematical methodology which 
> produces them. If you have any articles that attempt to explain how the 
> field equations are derived, I'd really like to explore this aspect of GR 
> and get some "satisfaction". I can see how he arrived at some principles, 
> such as geodesic motion, by applying the Least Action Principle, or how he 
> might have intuited that matter/energy effects the geometry of spacetime, 
> but from these principles it's baffling how he arrived at the field 
> equations. 
>
> AG
>
>>
>>
>> On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/17/2019 5:20 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: 



 On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:



 On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 
>
>
>
> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 



 On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:



 On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>
>
>
> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>
>
>
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 



 On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent 
>> space where the metric tensor is diagonalized and its derivative 
>> at that 
>> point in spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate 
> system and some arbitrary point in a non-empty spacetime. So 
> spacetime has 
> a non zero curvature and the derivative of the metric tensor is 
> generally 
> non-zero at that arbitrary point, however small we assume the 
> region around 
> that point. But applying the EEP, we can transform to the tangent 
> space at 
> that point to diagonalize the metric tensor and have its 
> derivative as zero 
> at that point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a 
> Riemannian space.
>
> Brent
>

 But isn't it weird 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com wrote:
>
> *I see no new text in this message. AG*
>
 
Brent; if you have time, please reproduce the text you intended. 

I recall reading that before Einstein published his GR paper, he used a 
trial and error method to determine the final field equations (as he raced 
for the correct ones in competition with Hilbert, who may have arrived at 
them first).  So it's hard to imagine a mathematical methodology which 
produces them. If you have any articles that attempt to explain how the 
field equations are derived, I'd really like to explore this aspect of GR 
and get some "satisfaction". I can see how he arrived at some principles, 
such as geodesic motion, by applying the Least Action Principle, or how he 
might have intuited that matter/energy effects the geometry of spacetime, 
but from these principles it's baffling how he arrived at the field 
equations. 

AG

>
>
> On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/17/2019 5:20 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 



 On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:



 On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 
>
>
>
> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 



 On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:



 On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
 wrote: 
>
>
>
> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 



 On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:


>>
> He might have been referring to a transformation to a tangent 
> space where the metric tensor is diagonalized and its derivative 
> at that 
> point in spacetime is zero. Does this make any sense? 
>
>
> Sort of.  
>


 Yeah, that's what he's doing. He's assuming a given coordinate 
 system and some arbitrary point in a non-empty spacetime. So 
 spacetime has 
 a non zero curvature and the derivative of the metric tensor is 
 generally 
 non-zero at that arbitrary point, however small we assume the 
 region around 
 that point. But applying the EEP, we can transform to the tangent 
 space at 
 that point to diagonalize the metric tensor and have its 
 derivative as zero 
 at that point. Does THIS make sense? AG


 Yep.  That's pretty much the defining characteristic of a 
 Riemannian space.

 Brent

>>>
>>> But isn't it weird that changing labels on spacetime points by 
>>> transforming coordinates has the result of putting the test 
>>> particle in 
>>> local free fall, when it wasn't prior to the transformation? AG 
>>>
>>> It doesn't put it in free-fall.  If the particle has EM forces 
>>> on it, it will deviate from the geodesic in the tangent space 
>>> coordinates.  
>>> The transformation is just adapting the coordinates to the local 
>>> free-fall 
>>> which removes gravity as a force...but not other forces.
>>>
>>> Brent
>>>
>>
>> In both cases, with and without non-gravitational forces acting 
>> on test particle, I assume the trajectory appears identical to an 
>> external 
>> observer, before and after coordinate transformation to the tangent 
>> plane 
>> at some point; all that's changed are the labels of spacetime 
>> points. If 
>> this is true, it's 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

*I see no new text in this message. AG*

On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote:
>
>
>
> On 4/17/2019 5:20 PM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 



 On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:



 On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
 wrote: 
>
>
>
> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>>> wrote: 



 On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>>
>>>
>
 He might have been referring to a transformation to a tangent 
 space where the metric tensor is diagonalized and its derivative 
 at that 
 point in spacetime is zero. Does this make any sense? 


 Sort of.  

>>>
>>>
>>> Yeah, that's what he's doing. He's assuming a given coordinate 
>>> system and some arbitrary point in a non-empty spacetime. So 
>>> spacetime has 
>>> a non zero curvature and the derivative of the metric tensor is 
>>> generally 
>>> non-zero at that arbitrary point, however small we assume the 
>>> region around 
>>> that point. But applying the EEP, we can transform to the tangent 
>>> space at 
>>> that point to diagonalize the metric tensor and have its derivative 
>>> as zero 
>>> at that point. Does THIS make sense? AG
>>>
>>>
>>> Yep.  That's pretty much the defining characteristic of a 
>>> Riemannian space.
>>>
>>> Brent
>>>
>>
>> But isn't it weird that changing labels on spacetime points by 
>> transforming coordinates has the result of putting the test particle 
>> in 
>> local free fall, when it wasn't prior to the transformation? AG 
>>
>> It doesn't put it in free-fall.  If the particle has EM forces on 
>> it, it will deviate from the geodesic in the tangent space 
>> coordinates.  
>> The transformation is just adapting the coordinates to the local 
>> free-fall 
>> which removes gravity as a force...but not other forces.
>>
>> Brent
>>
>
> In both cases, with and without non-gravitational forces acting on 
> test particle, I assume the trajectory appears identical to an 
> external 
> observer, before and after coordinate transformation to the tangent 
> plane 
> at some point; all that's changed are the labels of spacetime points. 
> If 
> this is true, it's still hard to see why changing labels can remove 
> the 
> gravitational forces. And what does this buy us? AG
>
>
> You're looking at it the wrong way around.  There never were any 
> gravitational forces, just your choice of coordinate system made 
> fictitious 
> forces appear; just like when you use a merry-go-round as your 
> reference 
> frame you get coriolis forces.  
>

 If gravity is a fictitious force produced by the choice of 
 coordinate system, in its absence (due to a change in coordinate 
 system) 
 how does GR explain motion? Test particles move on geodesics in the 
 absence 
 of non-gravitational forces, but why do they move at all? AG

>>>
>>> Maybe GR assumes motion but doesn't explain it. AG 
>>>
>>>
>>> The sciences do not try to explain, they hardly even try to  
>>> interpret, they mainly make models. By a model is meant a  mathematical 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote:
>
>
>
> On 4/17/2019 12:36 PM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
>>> wrote: 



 On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>
>
>
> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>
>
>
> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 



 On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>
>>

>>> He might have been referring to a transformation to a tangent 
>>> space where the metric tensor is diagonalized and its derivative at 
>>> that 
>>> point in spacetime is zero. Does this make any sense? 
>>>
>>>
>>> Sort of.  
>>>
>>
>>
>> Yeah, that's what he's doing. He's assuming a given coordinate 
>> system and some arbitrary point in a non-empty spacetime. So 
>> spacetime has 
>> a non zero curvature and the derivative of the metric tensor is 
>> generally 
>> non-zero at that arbitrary point, however small we assume the region 
>> around 
>> that point. But applying the EEP, we can transform to the tangent 
>> space at 
>> that point to diagonalize the metric tensor and have its derivative 
>> as zero 
>> at that point. Does THIS make sense? AG
>>
>>
>> Yep.  That's pretty much the defining characteristic of a 
>> Riemannian space.
>>
>> Brent
>>
>
> But isn't it weird that changing labels on spacetime points by 
> transforming coordinates has the result of putting the test particle 
> in 
> local free fall, when it wasn't prior to the transformation? AG 
>
> It doesn't put it in free-fall.  If the particle has EM forces on 
> it, it will deviate from the geodesic in the tangent space 
> coordinates.  
> The transformation is just adapting the coordinates to the local 
> free-fall 
> which removes gravity as a force...but not other forces.
>
> Brent
>

 In both cases, with and without non-gravitational forces acting on 
 test particle, I assume the trajectory appears identical to an 
 external 
 observer, before and after coordinate transformation to the tangent 
 plane 
 at some point; all that's changed are the labels of spacetime points. 
 If 
 this is true, it's still hard to see why changing labels can remove 
 the 
 gravitational forces. And what does this buy us? AG


 You're looking at it the wrong way around.  There never were any 
 gravitational forces, just your choice of coordinate system made 
 fictitious 
 forces appear; just like when you use a merry-go-round as your 
 reference 
 frame you get coriolis forces.  

>>>
>>> If gravity is a fictitious force produced by the choice of 
>>> coordinate system, in its absence (due to a change in coordinate 
>>> system) 
>>> how does GR explain motion? Test particles move on geodesics in the 
>>> absence 
>>> of non-gravitational forces, but why do they move at all? AG
>>>
>>
>> Maybe GR assumes motion but doesn't explain it. AG 
>>
>>
>> The sciences do not try to explain, they hardly even try to  
>> interpret, they mainly make models. By a model is meant a  mathematical 
>> construct which, with the addition of certain verbal  interpretations, 
>> describes observed phenomena. The justification of  such a mathematical 
>> construct is solely and precisely that it is  expected to work.
>> --—John von Neumann
>>
>>
>>> Another problem is the inconsistency 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote:
>
>
>
> On 4/17/2019 7:37 AM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 



 On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:



 On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>
>
>
> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>
>
>
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 



 On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent 
>> space where the metric tensor is diagonalized and its derivative at 
>> that 
>> point in spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate 
> system and some arbitrary point in a non-empty spacetime. So 
> spacetime has 
> a non zero curvature and the derivative of the metric tensor is 
> generally 
> non-zero at that arbitrary point, however small we assume the region 
> around 
> that point. But applying the EEP, we can transform to the tangent 
> space at 
> that point to diagonalize the metric tensor and have its derivative 
> as zero 
> at that point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a 
> Riemannian space.
>
> Brent
>

 But isn't it weird that changing labels on spacetime points by 
 transforming coordinates has the result of putting the test particle 
 in 
 local free fall, when it wasn't prior to the transformation? AG 

 It doesn't put it in free-fall.  If the particle has EM forces on 
 it, it will deviate from the geodesic in the tangent space 
 coordinates.  
 The transformation is just adapting the coordinates to the local 
 free-fall 
 which removes gravity as a force...but not other forces.

 Brent

>>>
>>> In both cases, with and without non-gravitational forces acting on 
>>> test particle, I assume the trajectory appears identical to an external 
>>> observer, before and after coordinate transformation to the tangent 
>>> plane 
>>> at some point; all that's changed are the labels of spacetime points. 
>>> If 
>>> this is true, it's still hard to see why changing labels can remove the 
>>> gravitational forces. And what does this buy us? AG
>>>
>>>
>>> You're looking at it the wrong way around.  There never were any 
>>> gravitational forces, just your choice of coordinate system made 
>>> fictitious 
>>> forces appear; just like when you use a merry-go-round as your 
>>> reference 
>>> frame you get coriolis forces.  
>>>
>>
>> If gravity is a fictitious force produced by the choice of coordinate 
>> system, in its absence (due to a change in coordinate system) how does 
>> GR 
>> explain motion? Test particles move on geodesics in the absence of 
>> non-gravitational forces, but why do they move at all? AG
>>
>
> Maybe GR assumes motion but doesn't explain it. AG 
>
>
> The sciences do not try to explain, they hardly even try to  
> interpret, they mainly make models. By a model is meant a  mathematical 
> construct which, with the addition of certain verbal  interpretations, 
> describes observed phenomena. The justification of  such a mathematical 
> construct is solely and precisely that it is  expected to work.
> --—John von Neumann
>
>
>> Another problem is the inconsistency of the fictitious gravitational 
>> force, and how the other forces function; EM, Strong, and Weak, which 
>> apparently can't be removed by changes in coordinates systems. AG
>>
>
> It's said that consistency is the hobgoblin of small minds. I am 
> merely pointing out the 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2019 6:14 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 



 On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:



 On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
 wrote: 
>
>
>
> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 



 On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:


>>
> He might have been referring to a transformation to a tangent 
> space where the metric tensor is diagonalized and its derivative at 
> that 
> point in spacetime is zero. Does this make any sense? 
>
>
> Sort of.  
>


 Yeah, that's what he's doing. He's assuming a given coordinate 
 system and some arbitrary point in a non-empty spacetime. So spacetime 
 has 
 a non zero curvature and the derivative of the metric tensor is 
 generally 
 non-zero at that arbitrary point, however small we assume the region 
 around 
 that point. But applying the EEP, we can transform to the tangent 
 space at 
 that point to diagonalize the metric tensor and have its derivative as 
 zero 
 at that point. Does THIS make sense? AG


 Yep.  That's pretty much the defining characteristic of a 
 Riemannian space.

 Brent

>>>
>>> But isn't it weird that changing labels on spacetime points by 
>>> transforming coordinates has the result of putting the test particle in 
>>> local free fall, when it wasn't prior to the transformation? AG 
>>>
>>> It doesn't put it in free-fall.  If the particle has EM forces on 
>>> it, it will deviate from the geodesic in the tangent space coordinates. 
>>>  
>>> The transformation is just adapting the coordinates to the local 
>>> free-fall 
>>> which removes gravity as a force...but not other forces.
>>>
>>> Brent
>>>
>>
>> In both cases, with and without non-gravitational forces acting on 
>> test particle, I assume the trajectory appears identical to an external 
>> observer, before and after coordinate transformation to the tangent 
>> plane 
>> at some point; all that's changed are the labels of spacetime points. If 
>> this is true, it's still hard to see why changing labels can remove the 
>> gravitational forces. And what does this buy us? AG
>>
>>
>> You're looking at it the wrong way around.  There never were any 
>> gravitational forces, just your choice of coordinate system made 
>> fictitious 
>> forces appear; just like when you use a merry-go-round as your reference 
>> frame you get coriolis forces.  
>>
>
> If gravity is a fictitious force produced by the choice of coordinate 
> system, in its absence (due to a change in coordinate system) how does GR 
> explain motion? Test particles move on geodesics in the absence of 
> non-gravitational forces, but why do they move at all? AG
>

 Maybe GR assumes motion but doesn't explain it. AG 


 The sciences do not try to explain, they hardly even try to  interpret, 
 they mainly make models. By a model is meant a  mathematical construct 
 which, with the addition of certain verbal  interpretations, describes 
 observed phenomena. The justification of  such a mathematical construct is 
 solely and precisely that it is  expected to work.
 --—John von Neumann


> Another problem is the inconsistency of the fictitious gravitational 
> force, and how the other forces function; EM, Strong, and Weak, which 
> apparently can't be removed by changes in coordinates systems. AG
>

 It's said that consistency is the hobgoblin of small minds. I am merely 
 pointing out the inconsistency of the gravitational force with the other 
 forces. Maybe gravity is just different. AG 


 That's one possibility, e.g entropic gravity.


>  
>
>> What is gets you is it enforces and explains the equivalence 
>> principle.  And of course Einstein's theory 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 9:21:32 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2019 6:25 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 16, 2019 at 5:41:35 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/16/2019 7:56 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>>> wrote: 

 ...
 If gravity is a fictitious force produced by the choice of coordinate 
 system, in its absence (due to a change in coordinate system)* how 
 does GR explain motion?* Test particles move on geodesics in the 
 absence of non-gravitational forces, but * why do they move at all?* AG

>>>
>>> Maybe GR assumes motion but doesn't explain it. AG 
>>>
>>>
>>> The sciences do not try to explain, they hardly even try to  interpret, 
>>> they mainly make models. By a model is meant a  mathematical construct 
>>> which, with the addition of certain verbal  interpretations, describes 
>>> observed phenomena. The justification of  such a mathematical construct is 
>>> solely and precisely that it is  expected to work.
>>> --—John von Neumann
>>>
>>
>> *This is straight out of the "shut up and calculate" school, and I don't 
>> completely buy it. E.g., the Principle of Relativity and Least Action 
>> Principle give strong indications of not only how the universe works, but 
>> why. That is, they're somewhat explanatory in nature. AG*
>>
>>
>> Fine, then take them as explanations.  But to ask that they be explained 
>> is to misunderstand their status.  It's possible that they could be 
>> explained; but only by finding a more fundamental theory that includes them 
>> as consequences or special cases.  Whatever theory is fundamental cannot 
>> have an explanation in the sense you want because then it would not be 
>> fundamental.
>>
>> Brent
>>
>
> *I don't think I asked them to be explained, and I don't think*
> * I misunderstand their status. In the examples I gave, the principles are 
> pretty fundamental and nonetheless seem to explain something substantive 
> about the universe even though they're not part of a deeper theory. AG *
>
>
> You wrote, "...how does GR explain motion? Test particles move on 
> geodesics in the absence of non-gravitational forces, but why do they move 
> at all?"
>
> GR hypothesizes that force-free motion of test particles is along 
> geodesics.  In 4-space they "move" because there is a time coordinate and a 
> particle is by definition something that persists in time (in contrast to 
> an "event").
>
> Brent
>

*Yes, I asked for an explanation of motion in the context of GR, but my 
response to Von Neumann was NOT meant in that context; namely, that physics 
sometimes DOES give explanations in what we could consider fundamental 
theories. But particles can hypothetically persist at a fixed time and 
still be particles. I don't think GR says anything about WHY test particles 
move, other than to postulate HOW they move; along geodesics. By 
distinction, our other force theories do IMO explain WHY particles move. 
AG *

> -- 
> You received this message because you are subscribed to the Google Groups 
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> To post to this group, send email to everyth...@googlegroups.com 
> .
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> For more options, visit https://groups.google.com/d/optout.
>
>
>

-- 
You received this message because you are subscribed to the Google Groups 
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For more options, visit https://groups.google.com/d/optout.

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2019 6:14 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 



 On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:



 On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
 wrote: 
>
>
>
> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 



 On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:


>>
> He might have been referring to a transformation to a tangent 
> space where the metric tensor is diagonalized and its derivative at 
> that 
> point in spacetime is zero. Does this make any sense? 
>
>
> Sort of.  
>


 Yeah, that's what he's doing. He's assuming a given coordinate 
 system and some arbitrary point in a non-empty spacetime. So spacetime 
 has 
 a non zero curvature and the derivative of the metric tensor is 
 generally 
 non-zero at that arbitrary point, however small we assume the region 
 around 
 that point. But applying the EEP, we can transform to the tangent 
 space at 
 that point to diagonalize the metric tensor and have its derivative as 
 zero 
 at that point. Does THIS make sense? AG


 Yep.  That's pretty much the defining characteristic of a 
 Riemannian space.

 Brent

>>>
>>> But isn't it weird that changing labels on spacetime points by 
>>> transforming coordinates has the result of putting the test particle in 
>>> local free fall, when it wasn't prior to the transformation? AG 
>>>
>>> It doesn't put it in free-fall.  If the particle has EM forces on 
>>> it, it will deviate from the geodesic in the tangent space coordinates. 
>>>  
>>> The transformation is just adapting the coordinates to the local 
>>> free-fall 
>>> which removes gravity as a force...but not other forces.
>>>
>>> Brent
>>>
>>
>> In both cases, with and without non-gravitational forces acting on 
>> test particle, I assume the trajectory appears identical to an external 
>> observer, before and after coordinate transformation to the tangent 
>> plane 
>> at some point; all that's changed are the labels of spacetime points. If 
>> this is true, it's still hard to see why changing labels can remove the 
>> gravitational forces. And what does this buy us? AG
>>
>>
>> You're looking at it the wrong way around.  There never were any 
>> gravitational forces, just your choice of coordinate system made 
>> fictitious 
>> forces appear; just like when you use a merry-go-round as your reference 
>> frame you get coriolis forces.  
>>
>
> If gravity is a fictitious force produced by the choice of coordinate 
> system, in its absence (due to a change in coordinate system) how does GR 
> explain motion? Test particles move on geodesics in the absence of 
> non-gravitational forces, but why do they move at all? AG
>

 Maybe GR assumes motion but doesn't explain it. AG 


 The sciences do not try to explain, they hardly even try to  interpret, 
 they mainly make models. By a model is meant a  mathematical construct 
 which, with the addition of certain verbal  interpretations, describes 
 observed phenomena. The justification of  such a mathematical construct is 
 solely and precisely that it is  expected to work.
 --—John von Neumann


> Another problem is the inconsistency of the fictitious gravitational 
> force, and how the other forces function; EM, Strong, and Weak, which 
> apparently can't be removed by changes in coordinates systems. AG
>

 It's said that consistency is the hobgoblin of small minds. I am merely 
 pointing out the inconsistency of the gravitational force with the other 
 forces. Maybe gravity is just different. AG 


 That's one possibility, e.g entropic gravity.


>  
>
>> What is gets you is it enforces and explains the equivalence 
>> principle.  And of course Einstein's theory 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 5:41:35 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2019 7:56 AM, agrays...@gmail.com  wrote:
>
>
>
> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 



 On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>
>>

>>> He might have been referring to a transformation to a tangent space 
>>> where the metric tensor is diagonalized and its derivative at that 
>>> point in 
>>> spacetime is zero. Does this make any sense? 
>>>
>>>
>>> Sort of.  
>>>
>>
>>
>> Yeah, that's what he's doing. He's assuming a given coordinate system 
>> and some arbitrary point in a non-empty spacetime. So spacetime has a 
>> non 
>> zero curvature and the derivative of the metric tensor is generally 
>> non-zero at that arbitrary point, however small we assume the region 
>> around 
>> that point. But applying the EEP, we can transform to the tangent space 
>> at 
>> that point to diagonalize the metric tensor and have its derivative as 
>> zero 
>> at that point. Does THIS make sense? AG
>>
>>
>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>> space.
>>
>> Brent
>>
>
> But isn't it weird that changing labels on spacetime points by 
> transforming coordinates has the result of putting the test particle in 
> local free fall, when it wasn't prior to the transformation? AG 
>
> It doesn't put it in free-fall.  If the particle has EM forces on it, 
> it will deviate from the geodesic in the tangent space coordinates.  The 
> transformation is just adapting the coordinates to the local free-fall 
> which removes gravity as a force...but not other forces.
>
> Brent
>

 In both cases, with and without non-gravitational forces acting on test 
 particle, I assume the trajectory appears identical to an external 
 observer, before and after coordinate transformation to the tangent plane 
 at some point; all that's changed are the labels of spacetime points. If 
 this is true, it's still hard to see why changing labels can remove the 
 gravitational forces. And what does this buy us? AG


 You're looking at it the wrong way around.  There never were any 
 gravitational forces, just your choice of coordinate system made 
 fictitious 
 forces appear; just like when you use a merry-go-round as your reference 
 frame you get coriolis forces.  

>>>
>>> If gravity is a fictitious force produced by the choice of coordinate 
>>> system, in its absence (due to a change in coordinate system) how does GR 
>>> explain motion? Test particles move on geodesics in the absence of 
>>> non-gravitational forces, but why do they move at all? AG
>>>
>>
>> Maybe GR assumes motion but doesn't explain it. AG 
>>
>>
>> The sciences do not try to explain, they hardly even try to  interpret, 
>> they mainly make models. By a model is meant a  mathematical construct 
>> which, with the addition of certain verbal  interpretations, describes 
>> observed phenomena. The justification of  such a mathematical construct is 
>> solely and precisely that it is  expected to work.
>> --—John von Neumann
>>
>
> *This is straight out of the "shut up and calculate" school, and I don't 
> completely buy it. E.g., the Principle of Relativity and Least Action 
> Principle give strong indications of not only how the universe works, but 
> why. That is, they're somewhat explanatory in nature. AG*
>
>
> Fine, then take them as explanations.  But to ask that they be explained 
> is to misunderstand their status.  It's possible that they could be 
> explained; but only by finding a more fundamental theory that includes them 
> as consequences or special cases.  Whatever theory is fundamental cannot 
> have an explanation in the sense you want because then it would not be 
> fundamental.
>
> Brent
>

*I don't think I asked them to be explained, and I don't think** I 
misunderstand their status. In the examples I gave, the principles are 
pretty fundamental and nonetheless seem to explain something substantive 
about the universe even though they're not part of a deeper theory. AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>>> wrote: 



 On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>>
>>>
>
 He might have been referring to a transformation to a tangent space 
 where the metric tensor is diagonalized and its derivative at that 
 point in 
 spacetime is zero. Does this make any sense? 


 Sort of.  

>>>
>>>
>>> Yeah, that's what he's doing. He's assuming a given coordinate 
>>> system and some arbitrary point in a non-empty spacetime. So spacetime 
>>> has 
>>> a non zero curvature and the derivative of the metric tensor is 
>>> generally 
>>> non-zero at that arbitrary point, however small we assume the region 
>>> around 
>>> that point. But applying the EEP, we can transform to the tangent space 
>>> at 
>>> that point to diagonalize the metric tensor and have its derivative as 
>>> zero 
>>> at that point. Does THIS make sense? AG
>>>
>>>
>>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>>> space.
>>>
>>> Brent
>>>
>>
>> But isn't it weird that changing labels on spacetime points by 
>> transforming coordinates has the result of putting the test particle in 
>> local free fall, when it wasn't prior to the transformation? AG 
>>
>> It doesn't put it in free-fall.  If the particle has EM forces on it, 
>> it will deviate from the geodesic in the tangent space coordinates.  The 
>> transformation is just adapting the coordinates to the local free-fall 
>> which removes gravity as a force...but not other forces.
>>
>> Brent
>>
>
> In both cases, with and without non-gravitational forces acting on 
> test particle, I assume the trajectory appears identical to an external 
> observer, before and after coordinate transformation to the tangent plane 
> at some point; all that's changed are the labels of spacetime points. If 
> this is true, it's still hard to see why changing labels can remove the 
> gravitational forces. And what does this buy us? AG
>
>
> You're looking at it the wrong way around.  There never were any 
> gravitational forces, just your choice of coordinate system made 
> fictitious 
> forces appear; just like when you use a merry-go-round as your reference 
> frame you get coriolis forces.  
>

 If gravity is a fictitious force produced by the choice of coordinate 
 system, in its absence (due to a change in coordinate system) how does GR 
 explain motion? Test particles move on geodesics in the absence of 
 non-gravitational forces, but why do they move at all? AG

>>>
>>> Maybe GR assumes motion but doesn't explain it. AG 
>>>
>>>
>>> The sciences do not try to explain, they hardly even try to  interpret, 
>>> they mainly make models. By a model is meant a  mathematical construct 
>>> which, with the addition of certain verbal  interpretations, describes 
>>> observed phenomena. The justification of  such a mathematical construct is 
>>> solely and precisely that it is  expected to work.
>>> --—John von Neumann
>>>
>>>
 Another problem is the inconsistency of the fictitious gravitational 
 force, and how the other forces function; EM, Strong, and Weak, which 
 apparently can't be removed by changes in coordinates systems. AG

>>>
>>> It's said that consistency is the hobgoblin of small minds. I am merely 
>>> pointing out the inconsistency of the gravitational force with the other 
>>> forces. Maybe gravity is just different. AG 
>>>
>>>
>>> That's one possibility, e.g entropic gravity.
>>>
>>>
  

> What is gets you is it enforces and explains the equivalence 
> principle.  And of course Einstein's theory also correctly predicted the 
> bending of light, gravitational waves, time dilation and the precession 
> of 
> the perhelion of Mercury.
>

 I was referring earlier just to the transformation to the tangent 
 space; what specifically does it buy us; why would we want 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2019 11:41 AM, agrays...@gmail.com  wrote:
>
>
>
> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 



 On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>
>>

>>> He might have been referring to a transformation to a tangent space 
>>> where the metric tensor is diagonalized and its derivative at that 
>>> point in 
>>> spacetime is zero. Does this make any sense? 
>>>
>>>
>>> Sort of.  
>>>
>>
>>
>> Yeah, that's what he's doing. He's assuming a given coordinate system 
>> and some arbitrary point in a non-empty spacetime. So spacetime has a 
>> non 
>> zero curvature and the derivative of the metric tensor is generally 
>> non-zero at that arbitrary point, however small we assume the region 
>> around 
>> that point. But applying the EEP, we can transform to the tangent space 
>> at 
>> that point to diagonalize the metric tensor and have its derivative as 
>> zero 
>> at that point. Does THIS make sense? AG
>>
>>
>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>> space.
>>
>> Brent
>>
>
> But isn't it weird that changing labels on spacetime points by 
> transforming coordinates has the result of putting the test particle in 
> local free fall, when it wasn't prior to the transformation? AG 
>
> It doesn't put it in free-fall.  If the particle has EM forces on it, 
> it will deviate from the geodesic in the tangent space coordinates.  The 
> transformation is just adapting the coordinates to the local free-fall 
> which removes gravity as a force...but not other forces.
>
> Brent
>

 In both cases, with and without non-gravitational forces acting on test 
 particle, I assume the trajectory appears identical to an external 
 observer, before and after coordinate transformation to the tangent plane 
 at some point; all that's changed are the labels of spacetime points. If 
 this is true, it's still hard to see why changing labels can remove the 
 gravitational forces. And what does this buy us? AG


 You're looking at it the wrong way around.  There never were any 
 gravitational forces, just your choice of coordinate system made 
 fictitious 
 forces appear; just like when you use a merry-go-round as your reference 
 frame you get coriolis forces.  

>>>
>>> If gravity is a fictitious force produced by the choice of coordinate 
>>> system, in its absence (due to a change in coordinate system) how does GR 
>>> explain motion? Test particles move on geodesics in the absence of 
>>> non-gravitational forces, but why do they move at all? AG
>>>
>>
>> Maybe GR assumes motion but doesn't explain it. AG 
>>
>>
>> The sciences do not try to explain, they hardly even try to  interpret, 
>> they mainly make models. By a model is meant a  mathematical construct 
>> which, with the addition of certain verbal  interpretations, describes 
>> observed phenomena. The justification of  such a mathematical construct is 
>> solely and precisely that it is  expected to work.
>> --—John von Neumann
>>
>>
>>> Another problem is the inconsistency of the fictitious gravitational 
>>> force, and how the other forces function; EM, Strong, and Weak, which 
>>> apparently can't be removed by changes in coordinates systems. AG
>>>
>>
>> It's said that consistency is the hobgoblin of small minds. I am merely 
>> pointing out the inconsistency of the gravitational force with the other 
>> forces. Maybe gravity is just different. AG 
>>
>>
>> That's one possibility, e.g entropic gravity.
>>
>>
>>>  
>>>
 What is gets you is it enforces and explains the equivalence 
 principle.  And of course Einstein's theory also correctly predicted the 
 bending of light, gravitational waves, time dilation and the precession of 
 the perhelion of Mercury.

>>>
>>> I was referring earlier just to the transformation to the tangent space; 
>>> what specifically does it buy us; why would we want to execute this 
>>> particular transformation? AG 
>>>
>>
>> For one thing, you know the acceleration due to non-gravitational forces 
>> in this frame.  
>>
>
> *IIUC, the tangent space is a vector space which has elements with 
> 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
>
>
>
> On 4/15/2019 7:14 PM, agrays...@gmail.com  wrote:
>
>
>
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com wrote: 
>>
>>
>>
>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 



 On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent space 
>> where the metric tensor is diagonalized and its derivative at that point 
>> in 
>> spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate system 
> and some arbitrary point in a non-empty spacetime. So spacetime has a non 
> zero curvature and the derivative of the metric tensor is generally 
> non-zero at that arbitrary point, however small we assume the region 
> around 
> that point. But applying the EEP, we can transform to the tangent space 
> at 
> that point to diagonalize the metric tensor and have its derivative as 
> zero 
> at that point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a Riemannian 
> space.
>
> Brent
>

 But isn't it weird that changing labels on spacetime points by 
 transforming coordinates has the result of putting the test particle in 
 local free fall, when it wasn't prior to the transformation? AG 

 It doesn't put it in free-fall.  If the particle has EM forces on it, 
 it will deviate from the geodesic in the tangent space coordinates.  The 
 transformation is just adapting the coordinates to the local free-fall 
 which removes gravity as a force...but not other forces.

 Brent

>>>
>>> In both cases, with and without non-gravitational forces acting on test 
>>> particle, I assume the trajectory appears identical to an external 
>>> observer, before and after coordinate transformation to the tangent plane 
>>> at some point; all that's changed are the labels of spacetime points. If 
>>> this is true, it's still hard to see why changing labels can remove the 
>>> gravitational forces. And what does this buy us? AG
>>>
>>>
>>> You're looking at it the wrong way around.  There never were any 
>>> gravitational forces, just your choice of coordinate system made fictitious 
>>> forces appear; just like when you use a merry-go-round as your reference 
>>> frame you get coriolis forces.  
>>>
>>
>> If gravity is a fictitious force produced by the choice of coordinate 
>> system, in its absence (due to a change in coordinate system) how does GR 
>> explain motion? Test particles move on geodesics in the absence of 
>> non-gravitational forces, but why do they move at all? AG
>>
>
> Maybe GR assumes motion but doesn't explain it. AG 
>
>
> The sciences do not try to explain, they hardly even try to  interpret, 
> they mainly make models. By a model is meant a  mathematical construct 
> which, with the addition of certain verbal  interpretations, describes 
> observed phenomena. The justification of  such a mathematical construct is 
> solely and precisely that it is  expected to work.
> --—John von Neumann
>
>
>> Another problem is the inconsistency of the fictitious gravitational 
>> force, and how the other forces function; EM, Strong, and Weak, which 
>> apparently can't be removed by changes in coordinates systems. AG
>>
>
> It's said that consistency is the hobgoblin of small minds. I am merely 
> pointing out the inconsistency of the gravitational force with the other 
> forces. Maybe gravity is just different. AG 
>
>
> That's one possibility, e.g entropic gravity.
>
>
>>  
>>
>>> What is gets you is it enforces and explains the equivalence principle.  
>>> And of course Einstein's theory also correctly predicted the bending of 
>>> light, gravitational waves, time dilation and the precession of the 
>>> perhelion of Mercury.
>>>
>>
>> I was referring earlier just to the transformation to the tangent space; 
>> what specifically does it buy us; why would we want to execute this 
>> particular transformation? AG 
>>
>
> For one thing, you know the acceleration due to non-gravitational forces 
> in this frame.  
>

*IIUC, the tangent space is a vector space which has elements with constant 
t.  So its elements are linear combinations of t, x, y, and z. How do you 
get accelerations from such sums (even if t is not constant)? AG*

So you can transform to it, put in the accelerations, and transform back. 
>

*I see no way to put the accelerations into the tangent space 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
>
>
>
> On 4/15/2019 7:14 PM, agrays...@gmail.com  wrote:
>
>
>
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com wrote: 
>>
>>
>>
>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 



 On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent space 
>> where the metric tensor is diagonalized and its derivative at that point 
>> in 
>> spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate system 
> and some arbitrary point in a non-empty spacetime. So spacetime has a non 
> zero curvature and the derivative of the metric tensor is generally 
> non-zero at that arbitrary point, however small we assume the region 
> around 
> that point. But applying the EEP, we can transform to the tangent space 
> at 
> that point to diagonalize the metric tensor and have its derivative as 
> zero 
> at that point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a Riemannian 
> space.
>
> Brent
>

 But isn't it weird that changing labels on spacetime points by 
 transforming coordinates has the result of putting the test particle in 
 local free fall, when it wasn't prior to the transformation? AG 

 It doesn't put it in free-fall.  If the particle has EM forces on it, 
 it will deviate from the geodesic in the tangent space coordinates.  The 
 transformation is just adapting the coordinates to the local free-fall 
 which removes gravity as a force...but not other forces.

 Brent

>>>
>>> In both cases, with and without non-gravitational forces acting on test 
>>> particle, I assume the trajectory appears identical to an external 
>>> observer, before and after coordinate transformation to the tangent plane 
>>> at some point; all that's changed are the labels of spacetime points. If 
>>> this is true, it's still hard to see why changing labels can remove the 
>>> gravitational forces. And what does this buy us? AG
>>>
>>>
>>> You're looking at it the wrong way around.  There never were any 
>>> gravitational forces, just your choice of coordinate system made fictitious 
>>> forces appear; just like when you use a merry-go-round as your reference 
>>> frame you get coriolis forces.  
>>>
>>
>> If gravity is a fictitious force produced by the choice of coordinate 
>> system, in its absence (due to a change in coordinate system) how does GR 
>> explain motion? Test particles move on geodesics in the absence of 
>> non-gravitational forces, but why do they move at all? AG
>>
>
> Maybe GR assumes motion but doesn't explain it. AG 
>
>
> The sciences do not try to explain, they hardly even try to  interpret, 
> they mainly make models. By a model is meant a  mathematical construct 
> which, with the addition of certain verbal  interpretations, describes 
> observed phenomena. The justification of  such a mathematical construct is 
> solely and precisely that it is  expected to work.
> --—John von Neumann
>

*This is straight out of the "shut up and calculate" school, and I don't 
completely buy it. E.g., the Principle of Relativity and Least Action 
Principle give strong indications of not only how the universe works, but 
why. That is, they're somewhat explanatory in nature. AG*
  

>
>
>> Another problem is the inconsistency of the fictitious gravitational 
>> force, and how the other forces function; EM, Strong, and Weak, which 
>> apparently can't be removed by changes in coordinates systems. AG
>>
>
> It's said that consistency is the hobgoblin of small minds. I am merely 
> pointing out the inconsistency of the gravitational force with the other 
> forces. Maybe gravity is just different. AG 
>
>
> That's one possibility, e.g entropic gravity.
>
>
>>  
>>
>>> What is gets you is it enforces and explains the equivalence principle.  
>>> And of course Einstein's theory also correctly predicted the bending of 
>>> light, gravitational waves, time dilation and the precession of the 
>>> perhelion of Mercury.
>>>
>>
>> I was referring earlier just to the transformation to the tangent space; 
>> what specifically does it buy us; why would we want to execute this 
>> particular transformation? AG 
>>
>
> For one thing, you know the acceleration due to non-gravitational forces 
> in this frame.  So you can transform to it, put in the accelerations, and 
> transform back.  

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Monday, April 15, 2019 at 8:14:35 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:
>>>
>>>
>>>
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 



 On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent space 
>> where the metric tensor is diagonalized and its derivative at that point 
>> in 
>> spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate system 
> and some arbitrary point in a non-empty spacetime. So spacetime has a non 
> zero curvature and the derivative of the metric tensor is generally 
> non-zero at that arbitrary point, however small we assume the region 
> around 
> that point. But applying the EEP, we can transform to the tangent space 
> at 
> that point to diagonalize the metric tensor and have its derivative as 
> zero 
> at that point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a Riemannian 
> space.
>
> Brent
>

 But isn't it weird that changing labels on spacetime points by 
 transforming coordinates has the result of putting the test particle in 
 local free fall, when it wasn't prior to the transformation? AG 

 It doesn't put it in free-fall.  If the particle has EM forces on it, 
 it will deviate from the geodesic in the tangent space coordinates.  The 
 transformation is just adapting the coordinates to the local free-fall 
 which removes gravity as a force...but not other forces.

 Brent

>>>
>>> In both cases, with and without non-gravitational forces acting on test 
>>> particle, I assume the trajectory appears identical to an external 
>>> observer, before and after coordinate transformation to the tangent plane 
>>> at some point; all that's changed are the labels of spacetime points. If 
>>> this is true, it's still hard to see why changing labels can remove the 
>>> gravitational forces. And what does this buy us? AG
>>>
>>>
>>> You're looking at it the wrong way around.  There never were any 
>>> gravitational forces, just your choice of coordinate system made fictitious 
>>> forces appear; just like when you use a merry-go-round as your reference 
>>> frame you get coriolis forces.  
>>>
>>
>> If gravity is a fictitious force produced by the choice of coordinate 
>> system, in its absence (due to a change in coordinate system) how does GR 
>> explain motion? Test particles move on geodesics in the absence of 
>> non-gravitational forces, but why do they move at all? AG
>>
>
> Maybe GR assumes motion but doesn't explain it. AG 
>
>>
>> Another problem is the inconsistency of the fictitious gravitational 
>> force, and how the other forces function; EM, Strong, and Weak, which 
>> apparently can't be removed by changes in coordinates systems. AG
>>
>
> It's said that consistency is the hobgoblin of small minds. I am merely 
> pointing out the inconsistency of the gravitational force with the other 
> forces. Maybe gravity is just different. AG 
>
>>
>>  
>>
>>> What is gets you is it enforces and explains the equivalence principle.  
>>> And of course Einstein's theory also correctly predicted the bending of 
>>> light, gravitational waves, time dilation and the precession of the 
>>> perhelion of Mercury.
>>>
>>
>> I was referring earlier just to the transformation to the tangent space; 
>> what specifically does it buy us; why would we want to execute this 
>> particular transformation? AG 
>>
>>>
>>> Brent
>>>
>>
*I could be mistaken, I usually am, but ISTM that labeling all points in 
spacetime as (t, x, y, z) makes no sense since there is no universal clock 
in GR. Each observer has his own clock in GR. No "Bird's Eye" observer GR. 
So what could the same t for all spatial points mean, or increasing t's as 
time evolves? AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 



 On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:


>>
> He might have been referring to a transformation to a tangent space 
> where the metric tensor is diagonalized and its derivative at that point 
> in 
> spacetime is zero. Does this make any sense? 
>
>
> Sort of.  
>


 Yeah, that's what he's doing. He's assuming a given coordinate system 
 and some arbitrary point in a non-empty spacetime. So spacetime has a non 
 zero curvature and the derivative of the metric tensor is generally 
 non-zero at that arbitrary point, however small we assume the region 
 around 
 that point. But applying the EEP, we can transform to the tangent space at 
 that point to diagonalize the metric tensor and have its derivative as 
 zero 
 at that point. Does THIS make sense? AG


 Yep.  That's pretty much the defining characteristic of a Riemannian 
 space.

 Brent

>>>
>>> But isn't it weird that changing labels on spacetime points by 
>>> transforming coordinates has the result of putting the test particle in 
>>> local free fall, when it wasn't prior to the transformation? AG 
>>>
>>> It doesn't put it in free-fall.  If the particle has EM forces on it, it 
>>> will deviate from the geodesic in the tangent space coordinates.  The 
>>> transformation is just adapting the coordinates to the local free-fall 
>>> which removes gravity as a force...but not other forces.
>>>
>>> Brent
>>>
>>
>> In both cases, with and without non-gravitational forces acting on test 
>> particle, I assume the trajectory appears identical to an external 
>> observer, before and after coordinate transformation to the tangent plane 
>> at some point; all that's changed are the labels of spacetime points. If 
>> this is true, it's still hard to see why changing labels can remove the 
>> gravitational forces. And what does this buy us? AG
>>
>>
>> You're looking at it the wrong way around.  There never were any 
>> gravitational forces, just your choice of coordinate system made fictitious 
>> forces appear; just like when you use a merry-go-round as your reference 
>> frame you get coriolis forces.  
>>
>
> If gravity is a fictitious force produced by the choice of coordinate 
> system, in its absence (due to a change in coordinate system) how does GR 
> explain motion? Test particles move on geodesics in the absence of 
> non-gravitational forces, but why do they move at all? AG
>

Maybe GR assumes motion but doesn't explain it. AG 

>
> Another problem is the inconsistency of the fictitious gravitational 
> force, and how the other forces function; EM, Strong, and Weak, which 
> apparently can't be removed by changes in coordinates systems. AG
>

It's said that consistency is the hobgoblin of small minds. I am merely 
pointing out the inconsistency of the gravitational force with the other 
forces. Maybe gravity is just different. AG 

>
>  
>
>> What is gets you is it enforces and explains the equivalence principle.  
>> And of course Einstein's theory also correctly predicted the bending of 
>> light, gravitational waves, time dilation and the precession of the 
>> perhelion of Mercury.
>>
>
> I was referring earlier just to the transformation to the tangent space; 
> what specifically does it buy us; why would we want to execute this 
> particular transformation? AG 
>
>>
>> Brent
>>
>

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How does one make a topic UNREAD?

[agrayson2000]

I only see an option to make all topics READ. TIA. AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:
>
>
>
> On 4/11/2019 9:33 PM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>>
>>>
>
 He might have been referring to a transformation to a tangent space 
 where the metric tensor is diagonalized and its derivative at that point 
 in 
 spacetime is zero. Does this make any sense? 


 Sort of.  

>>>
>>>
>>> Yeah, that's what he's doing. He's assuming a given coordinate system 
>>> and some arbitrary point in a non-empty spacetime. So spacetime has a non 
>>> zero curvature and the derivative of the metric tensor is generally 
>>> non-zero at that arbitrary point, however small we assume the region around 
>>> that point. But applying the EEP, we can transform to the tangent space at 
>>> that point to diagonalize the metric tensor and have its derivative as zero 
>>> at that point. Does THIS make sense? AG
>>>
>>>
>>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>>> space.
>>>
>>> Brent
>>>
>>
>> But isn't it weird that changing labels on spacetime points by 
>> transforming coordinates has the result of putting the test particle in 
>> local free fall, when it wasn't prior to the transformation? AG 
>>
>> It doesn't put it in free-fall.  If the particle has EM forces on it, it 
>> will deviate from the geodesic in the tangent space coordinates.  The 
>> transformation is just adapting the coordinates to the local free-fall 
>> which removes gravity as a force...but not other forces.
>>
>> Brent
>>
>
> In both cases, with and without non-gravitational forces acting on test 
> particle, I assume the trajectory appears identical to an external 
> observer, before and after coordinate transformation to the tangent plane 
> at some point; all that's changed are the labels of spacetime points. If 
> this is true, it's still hard to see why changing labels can remove the 
> gravitational forces. And what does this buy us? AG
>
>
> You're looking at it the wrong way around.  There never were any 
> gravitational forces, just your choice of coordinate system made fictitious 
> forces appear; just like when you use a merry-go-round as your reference 
> frame you get coriolis forces.  
>

If gravity is a fictitious force produced by the choice of coordinate 
system, in its absence (due to a change in coordinate system) how does GR 
explain motion? Test particles move on geodesics in the absence of 
non-gravitational forces, but why do they move at all? AG

Another problem is the inconsistency of the fictitious gravitational force, 
and how the other forces function; EM, Strong, and Weak, which apparently 
can't be removed by changes in coordinates systems. AG

 

> What is gets you is it enforces and explains the equivalence principle.  
> And of course Einstein's theory also correctly predicted the bending of 
> light, gravitational waves, time dilation and the precession of the 
> perhelion of Mercury.
>

I was referring earlier just to the transformation to the tangent space; 
what specifically does it buy us; why would we want to execute this 
particular transformation? AG 

>
> Brent
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote:
>
>
>
> On 4/11/2019 4:53 PM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>
>>

>>> He might have been referring to a transformation to a tangent space 
>>> where the metric tensor is diagonalized and its derivative at that point in 
>>> spacetime is zero. Does this make any sense? 
>>>
>>>
>>> Sort of.  
>>>
>>
>>
>> Yeah, that's what he's doing. He's assuming a given coordinate system and 
>> some arbitrary point in a non-empty spacetime. So spacetime has a non zero 
>> curvature and the derivative of the metric tensor is generally non-zero at 
>> that arbitrary point, however small we assume the region around that point. 
>> But applying the EEP, we can transform to the tangent space at that point 
>> to diagonalize the metric tensor and have its derivative as zero at that 
>> point. Does THIS make sense? AG
>>
>>
>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>> space.
>>
>> Brent
>>
>
> But isn't it weird that changing labels on spacetime points by 
> transforming coordinates has the result of putting the test particle in 
> local free fall, when it wasn't prior to the transformation? AG 
>
> It doesn't put it in free-fall.  If the particle has EM forces on it, it 
> will deviate from the geodesic in the tangent space coordinates.  The 
> transformation is just adapting the coordinates to the local free-fall 
> which removes gravity as a force...but not other forces.
>
> Brent
>

In both cases, with and without non-gravitational forces acting on test 
particle, I assume the trajectory appears identical to an external 
observer, before and after coordinate transformation to the tangent plane 
at some point; all that's changed are the labels of spacetime points. If 
this is true, it's still hard to see why changing labels can remove the 
gravitational forces. And what does this buy us? AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote:
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com  wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent space where 
>> the metric tensor is diagonalized and its derivative at that point in 
>> spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate system and 
> some arbitrary point in a non-empty spacetime. So spacetime has a non zero 
> curvature and the derivative of the metric tensor is generally non-zero at 
> that arbitrary point, however small we assume the region around that point. 
> But applying the EEP, we can transform to the tangent space at that point 
> to diagonalize the metric tensor and have its derivative as zero at that 
> point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a Riemannian space.
>
> Brent
>

But isn't it weird that changing labels on spacetime points by transforming 
coordinates has the result of putting the test particle in local free fall, 
when it wasn't prior to the transformation? AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 9, 2019 at 11:09:36 PM UTC-6, Brent wrote:
>
>
>
> On 4/9/2019 6:52 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 9, 2019 at 6:41:52 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/9/2019 5:20 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 9, 2019 at 2:40:16 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/9/2019 12:47 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote: 



 On 4/9/2019 11:55 AM, agrays...@gmail.com wrote:



 On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote: 
>
>
>
> On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:
>
>
>
> On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>> In GR, is there a distinction between coordinate systems and frames 
>> of reference? AG??
>>
>
> Here's the problem; there's a GR expert known to some members of this 
> list, who claims GR does NOT distinguish coordinate systems from frames 
> of 
> reference. He also claims that given an arbitrary coordinate system on a 
> manifold, and any given point in space-time, it's possible to find a 
> transformation from the given coordinate system (and using Einstein's 
> Equivalence Principle), to another coordinate system which is locally 
> flat 
> at the arbitrarily given point in space-time. This implies that a test 
> particle is in free fall at that point in space-time. But how can 
> changing 
> labels on space-time points, change the physical properties of a test 
> particle at some arbitrarily chosen point in space-time? I believe that 
> such a transformation implies a DIFFERENT frame of reference, in motion, 
> possibly accelerated, from the original frame or coordinate system. Am I 
> correct? TIA, AG
>
>
> You're right that a coordinate system is just a function for labeling 
> points and, while is may make the equations messy or simple, it doesn't 
> change the physics.?? If you have two different coordinate systems the 
> transformation between them may be arbitrarily complicated.?? But your 
> last 
> sentence referring to motion as distinguishing a coordinate transform 
> from 
> a reference frame seems to have slipped into a 3D picture.?? In a 4D 
> spacetime, block universe there's no difference between an accelerated 
> reference frame and one defined by coordinates that are not geodesic.
>
> Brent
>

 Suppose the test particle is on a geodesic path in one coordinate 
 system, but in another it's on an approximately flat 4D surface at some 
 point in the transformed coordinate system. 


 A geodesic is a physically defined path, one of extremal length.  It's 
 independent of coordinate systems and reference frames.  If a geodesic is 
 not a geodesic in your transformed coordinate system, then you've done 
 something wrong in transforming the metric.

 Brent

>>>
>>> It would clarify the situation if you would state the acceptable before 
>>> and after states of a coordinate transformation that puts the test particle 
>>> in a locally flat region for some chosen point in the transformed 
>>> coordinate system. AG 
>>>
>>>
>>> Like "geodesic" being "locally flat" is a physical characteristic of the 
>>> spacetime.  It's just part of being a Riemannian space that there is a 
>>> sufficiently small region around any point that is "flat".  This is the 
>>> mathematical correlate of Einstein's equivalence principle.  So it is not 
>>> the coordinate system or any transformation that "puts the particle in a 
>>> flat region".  It's just a property of the space being smooth and 
>>> differentiable so that even a curved spacetime at every point has a flat 
>>> tangent space.
>>>
>>> Brent
>>>
>>
>> What you're saying is pretty easy to understand. So I wonder why the 
>> "expert" I was discussing this with, claimed something about a 
>> transformation existing from one coordinate system to another, to make the 
>> particle to be locally in an inertial condition, when that's always the 
>> case?  Do you have any idea what he was referring to? AG
>>
>>
>> Well, it's not always the case.  There are other forces that can act on a 
>> particle besides gravity.  So the the fact that you can always transform to 
>> a free-falling local reference frame and eliminate "gravitational force" 
>> doesn't mean that a particle may not be accelerated by EM or other forces.
>>
>> Brent
>>
>
> He might have been referring to a transformation to a tangent space where 
> the metric tensor is diagonalized and its derivative at that point in 
> spacetime is zero. Does this make any sense? 
>
>
> Sort of.  
>


Yeah, that's what he's doing. He's assuming a given coordinate system and 
some arbitrary point in a non-empty spacetime. So spacetime 

Re: Notes from the Underground

[agrayson2000]

On Wednesday, April 10, 2019 at 1:32:30 PM UTC-6, spudb...@aol.com wrote:
>
> As a conspiracy-believer, I agree with Howard Hunt on this, sadly. I used 
> to believe that because Oswald was a communist, he was a tool of the KGB 
> and Cuban DGI/Castro, and they both had reasons to kill Kennedy. Kennedy 
> used CIA to kill Castro, and the Kremlin fail of the Cuban Missile Crisis 
> of 1962. I have since, looked at Hoover's spying on all politicians, His 
> blackmail of the Kennedy's, and their behavior, and Hoover &  Clive 
> Tolafson's, behavior, and find the Hoover thing to be the strongest case! 
> The Kennedy's spied on Hoover as well, when he and his bed mate Tolafson, 
> stayed at the Greenbrier Hotel. The Kennedy's used Boston and NY 
> detectives, who were once in the Army signal corps, to accomplish this. 
> There is a good book on what would have occured if Kennedy had lived in 
> 1963 and escaped assassination. The book is called "Surrounded by Enemies," 
> -good read. 
>

This is the key video to view if you want to see LBJ's motive for 
culpability in the assassination. He didn't plan the whole thing, but had 
one of his close associates orchestrate the event, his close personal 
attorney, as revealed by Barr McClellan, an attorney who joined that law 
firm in 1966 and learned of its inner workings. McClellan wrote a book 
about it in 2003, "Blood, Money & Power". His later book "The Verdict", 
written in 2015 is unavailable on Amazon, allegedly "Out of Print".  Bobby 
Kennedy was peripherally involved in that he was planning another invasion 
of Cuba, and/or the assassination of Castro. Apparently the assassins used 
the machinery he had set up, Mafia connections, etc., to have his brother 
murdered. This latter twist is not in this video, but can be found in 
others on this topic. AG

https://www.youtube.com/watch?v=nEq9tzPEW4I=PLKLMacl8yKNvAE2kKQ3AtTKTOIeZERpe3=10=261s

In the fall of 1963, an investigation by the DoJ was ordered by Kennedy to 
reveal felonious dealings associated with Department of Agriculture cotton 
subsidies in Texas. Maybe the name Billy Sol Estes will jog your memory. It 
was pretty certain that LBJ was on the take to the tune of millions of 
dollars in payoffs and kickbacks, and if that came to light JFK would have 
been forced to remove him from the ticket in the 1964 election. In fact, 
LBJ would likely have gone to prison, in addition to losing his place on 
the ticket. There was a guy named Marshall, in the TX department of 
Agriculture who couldn't be bought off, who was murdered with five shots to 
his stomach with his own 22 caliber rifle, and the death was ruling a 
"suicide". Involved in this was LBJ's personal assassin named Malcolm 
Wallace, whose fingerprint was later found on one of the cardboard boxes on 
the 6th floor the Texas School Book Depository immediately after the 
assassination. AG



> -Original Message-
> From: agrayson2000 >
> To: Everything List >
> Sent: Tue, Apr 9, 2019 10:11 pm
> Subject: Notes from the Underground
>
> Remember E. Howard Hunt, CIA agent and one of the Watergate burglars? He 
> passed away in 2007, and made a deathbed confession to his son that he was 
> aware of a conspiracy to assassinate JFK. I've been researching this 
> lately, as well as other issues, and it seems like LBJ was involved -- 
> something I previously didn't believe.
> -- 
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Notes from the Underground

[agrayson2000]

Remember E. Howard Hunt, CIA agent and one of the Watergate burglars? He 
passed away in 2007, and made a deathbed confession to his son that he was 
aware of a conspiracy to assassinate JFK. I've been researching this 
lately, as well as other issues, and it seems like LBJ was involved -- 
something I previously didn't believe.

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 9, 2019 at 6:41:52 PM UTC-6, Brent wrote:
>
>
>
> On 4/9/2019 5:20 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 9, 2019 at 2:40:16 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/9/2019 12:47 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/9/2019 11:55 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote: 



 On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:



 On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com 
 wrote: 
>
> In GR, is there a distinction between coordinate systems and frames of 
> reference? AG??
>

 Here's the problem; there's a GR expert known to some members of this 
 list, who claims GR does NOT distinguish coordinate systems from frames of 
 reference. He also claims that given an arbitrary coordinate system on a 
 manifold, and any given point in space-time, it's possible to find a 
 transformation from the given coordinate system (and using Einstein's 
 Equivalence Principle), to another coordinate system which is locally flat 
 at the arbitrarily given point in space-time. This implies that a test 
 particle is in free fall at that point in space-time. But how can changing 
 labels on space-time points, change the physical properties of a test 
 particle at some arbitrarily chosen point in space-time? I believe that 
 such a transformation implies a DIFFERENT frame of reference, in motion, 
 possibly accelerated, from the original frame or coordinate system. Am I 
 correct? TIA, AG


 You're right that a coordinate system is just a function for labeling 
 points and, while is may make the equations messy or simple, it doesn't 
 change the physics.?? If you have two different coordinate systems the 
 transformation between them may be arbitrarily complicated.?? But your 
 last 
 sentence referring to motion as distinguishing a coordinate transform from 
 a reference frame seems to have slipped into a 3D picture.?? In a 4D 
 spacetime, block universe there's no difference between an accelerated 
 reference frame and one defined by coordinates that are not geodesic.

 Brent

>>>
>>> Suppose the test particle is on a geodesic path in one coordinate 
>>> system, but in another it's on an approximately flat 4D surface at some 
>>> point in the transformed coordinate system. 
>>>
>>>
>>> A geodesic is a physically defined path, one of extremal length.  It's 
>>> independent of coordinate systems and reference frames.  If a geodesic is 
>>> not a geodesic in your transformed coordinate system, then you've done 
>>> something wrong in transforming the metric.
>>>
>>> Brent
>>>
>>
>> It would clarify the situation if you would state the acceptable before 
>> and after states of a coordinate transformation that puts the test particle 
>> in a locally flat region for some chosen point in the transformed 
>> coordinate system. AG 
>>
>>
>> Like "geodesic" being "locally flat" is a physical characteristic of the 
>> spacetime.  It's just part of being a Riemannian space that there is a 
>> sufficiently small region around any point that is "flat".  This is the 
>> mathematical correlate of Einstein's equivalence principle.  So it is not 
>> the coordinate system or any transformation that "puts the particle in a 
>> flat region".  It's just a property of the space being smooth and 
>> differentiable so that even a curved spacetime at every point has a flat 
>> tangent space.
>>
>> Brent
>>
>
> What you're saying is pretty easy to understand. So I wonder why the 
> "expert" I was discussing this with, claimed something about a 
> transformation existing from one coordinate system to another, to make the 
> particle to be locally in an inertial condition, when that's always the 
> case?  Do you have any idea what he was referring to? AG
>
>
> Well, it's not always the case.  There are other forces that can act on a 
> particle besides gravity.  So the the fact that you can always transform to 
> a free-falling local reference frame and eliminate "gravitational force" 
> doesn't mean that a particle may not be accelerated by EM or other forces.
>
> Brent
>

He might have been referring to a transformation to a tangent space where 
the metric tensor is diagonalized and its derivative at that point in 
spacetime is zero. Does this make any sense? I am not sure what initial 
conditions he assumed for the test particle, whether or not it was under 
the influence of non gravitational forces. AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 9, 2019 at 2:40:16 PM UTC-6, Brent wrote:
>
>
>
> On 4/9/2019 12:47 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/9/2019 11:55 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com 
>>> wrote: 

 In GR, is there a distinction between coordinate systems and frames of 
 reference? AG??

>>>
>>> Here's the problem; there's a GR expert known to some members of this 
>>> list, who claims GR does NOT distinguish coordinate systems from frames of 
>>> reference. He also claims that given an arbitrary coordinate system on a 
>>> manifold, and any given point in space-time, it's possible to find a 
>>> transformation from the given coordinate system (and using Einstein's 
>>> Equivalence Principle), to another coordinate system which is locally flat 
>>> at the arbitrarily given point in space-time. This implies that a test 
>>> particle is in free fall at that point in space-time. But how can changing 
>>> labels on space-time points, change the physical properties of a test 
>>> particle at some arbitrarily chosen point in space-time? I believe that 
>>> such a transformation implies a DIFFERENT frame of reference, in motion, 
>>> possibly accelerated, from the original frame or coordinate system. Am I 
>>> correct? TIA, AG
>>>
>>>
>>> You're right that a coordinate system is just a function for labeling 
>>> points and, while is may make the equations messy or simple, it doesn't 
>>> change the physics.?? If you have two different coordinate systems the 
>>> transformation between them may be arbitrarily complicated.?? But your last 
>>> sentence referring to motion as distinguishing a coordinate transform from 
>>> a reference frame seems to have slipped into a 3D picture.?? In a 4D 
>>> spacetime, block universe there's no difference between an accelerated 
>>> reference frame and one defined by coordinates that are not geodesic.
>>>
>>> Brent
>>>
>>
>> Suppose the test particle is on a geodesic path in one coordinate system, 
>> but in another it's on an approximately flat 4D surface at some point in 
>> the transformed coordinate system. 
>>
>>
>> A geodesic is a physically defined path, one of extremal length.  It's 
>> independent of coordinate systems and reference frames.  If a geodesic is 
>> not a geodesic in your transformed coordinate system, then you've done 
>> something wrong in transforming the metric.
>>
>> Brent
>>
>
> It would clarify the situation if you would state the acceptable before 
> and after states of a coordinate transformation that puts the test particle 
> in a locally flat region for some chosen point in the transformed 
> coordinate system. AG 
>
>
> Like "geodesic" being "locally flat" is a physical characteristic of the 
> spacetime.  It's just part of being a Riemannian space that there is a 
> sufficiently small region around any point that is "flat".  This is the 
> mathematical correlate of Einstein's equivalence principle.  So it is not 
> the coordinate system or any transformation that "puts the particle in a 
> flat region".  It's just a property of the space being smooth and 
> differentiable so that even a curved spacetime at every point has a flat 
> tangent space.
>
> Brent
>

What you're saying is pretty easy to understand. So I wonder why the 
"expert" I was discussing this with, claimed something about a 
transformation existing from one coordinate system to another, to make the 
particle to be locally in an inertial condition, when that's always the 
case?  Do you have any idea what he was referring to? AG

>
>
>> Doesn't this represent a change in the physics via a change in labeling 
>> the space-time points?  How is this possible without a change in the frame 
>> of reference, and if so, how would that be described if not by 
>> acceleration? AG
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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote:
>
>
>
> On 4/9/2019 11:55 AM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>> In GR, is there a distinction between coordinate systems and frames of 
>>> reference? AG??
>>>
>>
>> Here's the problem; there's a GR expert known to some members of this 
>> list, who claims GR does NOT distinguish coordinate systems from frames of 
>> reference. He also claims that given an arbitrary coordinate system on a 
>> manifold, and any given point in space-time, it's possible to find a 
>> transformation from the given coordinate system (and using Einstein's 
>> Equivalence Principle), to another coordinate system which is locally flat 
>> at the arbitrarily given point in space-time. This implies that a test 
>> particle is in free fall at that point in space-time. But how can changing 
>> labels on space-time points, change the physical properties of a test 
>> particle at some arbitrarily chosen point in space-time? I believe that 
>> such a transformation implies a DIFFERENT frame of reference, in motion, 
>> possibly accelerated, from the original frame or coordinate system. Am I 
>> correct? TIA, AG
>>
>>
>> You're right that a coordinate system is just a function for labeling 
>> points and, while is may make the equations messy or simple, it doesn't 
>> change the physics.?? If you have two different coordinate systems the 
>> transformation between them may be arbitrarily complicated.?? But your last 
>> sentence referring to motion as distinguishing a coordinate transform from 
>> a reference frame seems to have slipped into a 3D picture.?? In a 4D 
>> spacetime, block universe there's no difference between an accelerated 
>> reference frame and one defined by coordinates that are not geodesic.
>>
>> Brent
>>
>
> Suppose the test particle is on a geodesic path in one coordinate system, 
> but in another it's on an approximately flat 4D surface at some point in 
> the transformed coordinate system. 
>
>
> A geodesic is a physically defined path, one of extremal length.  It's 
> independent of coordinate systems and reference frames.  If a geodesic is 
> not a geodesic in your transformed coordinate system, then you've done 
> something wrong in transforming the metric.
>
> Brent
>

It would clarify the situation if you would state the acceptable before and 
after states of a coordinate transformation that puts the test particle in 
a locally flat region for some chosen point in the transformed coordinate 
system. AG 

>
> Doesn't this represent a change in the physics via a change in labeling 
> the space-time points?  How is this possible without a change in the frame 
> of reference, and if so, how would that be described if not by 
> acceleration? AG
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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote:
>
>
>
> On 4/9/2019 7:52 AM, agrays...@gmail.com  wrote:
>
>
>
> On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com wrote: 
>>
>> In GR, is there a distinction between coordinate systems and frames of 
>> reference? AG??
>>
>
> Here's the problem; there's a GR expert known to some members of this 
> list, who claims GR does NOT distinguish coordinate systems from frames of 
> reference. He also claims that given an arbitrary coordinate system on a 
> manifold, and any given point in space-time, it's possible to find a 
> transformation from the given coordinate system (and using Einstein's 
> Equivalence Principle), to another coordinate system which is locally flat 
> at the arbitrarily given point in space-time. This implies that a test 
> particle is in free fall at that point in space-time. But how can changing 
> labels on space-time points, change the physical properties of a test 
> particle at some arbitrarily chosen point in space-time? I believe that 
> such a transformation implies a DIFFERENT frame of reference, in motion, 
> possibly accelerated, from the original frame or coordinate system. Am I 
> correct? TIA, AG
>
>
> You're right that a coordinate system is just a function for labeling 
> points and, while is may make the equations messy or simple, it doesn't 
> change the physics.?? If you have two different coordinate systems the 
> transformation between them may be arbitrarily complicated.?? But your last 
> sentence referring to motion as distinguishing a coordinate transform from 
> a reference frame seems to have slipped into a 3D picture.?? In a 4D 
> spacetime, block universe there's no difference between an accelerated 
> reference frame and one defined by coordinates that are not geodesic.
>
> Brent
>

Suppose the test particle is on a geodesic path in one coordinate system, 
but in another it's on an approximately flat 4D surface at some point in 
the transformed coordinate system. Doesn't this represent a change in the 
physics via a change in labeling the space-time points?  How is this 
possible without a change in the frame of reference, and if so, how would 
that be described if not by acceleration? AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com wrote:
>
> In GR, is there a distinction between coordinate systems and frames of 
> reference? AG 
>

Here's the problem; there's a GR expert known to some members of this list, 
who claims GR does NOT distinguish coordinate systems from frames of 
reference. He also claims that given an arbitrary coordinate system on a 
manifold, and any given point in space-time, it's possible to find a 
transformation from the given coordinate system (and using Einstein's 
Equivalence Principle), to another coordinate system which is locally flat 
at the arbitrarily given point in space-time. This implies that a test 
particle is in free fall at that point in space-time. But how can changing 
labels on space-time points, change the physical properties of a test 
particle at some arbitrarily chosen point in space-time? I believe that 
such a transformation implies a DIFFERENT frame of reference, in motion, 
possibly accelerated, from the original frame or coordinate system. Am I 
correct? TIA, AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

In GR, is there a distinction between coordinate systems and frames of 
reference? AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 5:08:15 PM UTC-6, smitra wrote:
>
> On 26-03-2019 20:29, agrays...@gmail.com  wrote: 
> > On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote: 
> > 
> >> On Tue, Mar 26, 2019 at 1:14 PM  wrote: 
> >> 
> >>> _> How do the mathematicians prove it?_ 
> >> 
> >> Mathematicians can't prove that a physical theory is correct, all 
> >> they can do is show that changing the coordinate system (for example 
> >> by rotating the X and Y axis) does not result in different physical 
> >> predictions. Only exparament can tell you if the predictions is 
> >> right, or at least mostly right. 
> >> 
> >> John K Clark 
> > 
> > I'm not asking if GR is correct; rather, whether it is covariant. 
> > Moreover, for SR we can prove covariance, since under the LT, the law 
> > of physics don't change and the SoL is c in any inertial frame. ME are 
> > also invariant under the LT.  AG 
> > 
>
> There are many ways one can do this, the most elegant way is to start 
> with a Lagrangian of a field theory and then demand that it be invariant 
> under general coordinate transforms, which requires factors of the 
> square root of the determinant of the metric tensor to be inserted to 
> compensate for the Jacobian of a coordinate transform. This seemingly 
> rather trivial insertion, will yield the field equations of GR as far as 
> the coupling with the fields desribed by the field theory are concerned. 
>
> Compare this with the way you can derive the Maxwell equations from 
> scratch. You start of a scalar field theory, that is invariant under 
> global gauge transforms phi ---> exp(i alpha) phi. And then you make the 
> constant alpha an arbitrary function of space-time, which destroys the 
> invariance due to derivatives generating additional terms. But you can 
> compensate for these derivatives by including a gauge potential. This 
> then yields the coupling of the scalar field to a new field that we can 
> call the electromagnetic field, and this field will have its own gauge 
> invariant term proportional to the field strength tensor squared. 
>
> So, as Paul Davies puts it, in principle mathematically gifted cave men 
> who had never done any experiments involving electromagnetism and 
> gravity could have deduced the Maxwell equations and the Einstein 
> equations of GR from scratch based only on mathematical elegance. 
>
> Saibal 
>

*As I just told Brent, I think I should spend more time reading relevant 
articles, *
*than asking questions. With that objective, please post some links 
describing *
*the methods you reference above, and the article with Davies quote. TIA, 
AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 7:58:11 PM UTC-6, Brent wrote:
>
>
>
> On 3/26/2019 12:29 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote: 
>>
>> On Tue, Mar 26, 2019 at 1:14 PM  wrote:
>>
>> *> How do the mathematicians prove it?*
>>
>>
>> Mathematicians can't prove that a physical theory is correct, all they 
>> can do is show that changing the coordinate system (for example by rotating 
>> the X and Y axis) does not result in different physical predictions. Only 
>> exparament can tell you if the predictions is right, or at least mostly 
>> right.  
>>
>> John K Clark
>>
>
> I'm not asking if GR is correct; rather, whether it is covariant. 
> Moreover, for SR we can prove covariance, since under the LT, the law of 
> physics don't change and the SoL is c in any inertial frame. ME are also 
> invariant under the LT.  AG
>
>
> Look at the paper by Gupta and Padmanabhan that I linked to.  
>


*I looked through your posts here and do not find these papers. Please post 
the links. I want to spend more time reading relevant articles, than asking 
questions. AG*
 

> The equations are written a manifestly covariant form, so no "proof" is 
> relevant.  
>

*That's what I need to grasp; what is a covariant form and why it's 
sufficient to establish covariance, or frame independence of the laws of 
physics. AG *

But the equations are local, partial differential equations.  So when you 
> want to calculate something that involves radiation (and accelerating a 
> mass produced gravitational radiation), even though the local equations are 
> covariant the solution depends on an integral equation over the past motion 
> of the body.  Since that motion can be, ex hypothesi, arbitrary, there's no 
> general transformation between two reference systems that have gone through 
> arbitrary motions in the past.
>
> Brent 
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote:
>
> On Tue, Mar 26, 2019 at 1:14 PM > wrote:
>
> *> How do the mathematicians prove it?*
>
>
> Mathematicians can't prove that a physical theory is correct, all they can 
> do is show that changing the coordinate system (for example by rotating the 
> X and Y axis) does not result in different physical predictions. Only 
> exparament can tell you if the predictions is right, or at least mostly 
> right.  
>
> John K Clark
>

I'm not asking if GR is correct; rather, whether it is covariant. Moreover, 
for SR we can prove covariance, since under the LT, the law of physics 
don't change and the SoL is c in any inertial frame. ME are also invariant 
under the LT.  AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 10:36:03 AM UTC-6, John Clark wrote:
>
> By the way, just  2 weeks ago the best test ever made of Einstein's 
> Equivalence Principle was performed in a gravitational field one million 
> times greater than Earth's and Einstein passed the test with flying 
> colors.  
>
> Test of the Einstein Equivalence Principle near the Galactic Center 
> Supermassive Black Hole 
>   
>
> John K Clark
>

I read an article about that yesterday. AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 9:35:41 AM UTC-6, John Clark wrote:
>
> On Tue, Mar 26, 2019 at 9:14 AM > wrote:
>
> *>* *although the field equations are claimed to be the same in all 
>> frames, accelerating or not, how does one prove that*
>>
>
> Mathematicians prove things Physicists don't. Physicists show that some 
> ideas are less wrong than others and they do that by determining how 
> closely the idea conforms with experimental observation. So far at least 
> General Relativity has conformed very very well. 
>
>  John K Clark
>

Thanks, but that's very far removed from a viable explanation of covariance 
as a property of the GR field equations. How do the mathematicians prove 
it? You know, Einstein worked with the best of them, such as Grossman and 
Hilbert. They must have been very satisfied that covariance was an 
established, provable property. Do you have a clue how that might be done 
-- to establish covariance? AG 

>
>  
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 6:28:18 AM UTC-6, John Clark wrote:
>
> On Tue, Mar 26, 2019 at 4:40 AM > wrote:
>
> >>>Einstein never said everything is relative. Unlike velocity there is 
 such a thing as absolute acceleration, if that were not true the Twin 
 Paradox could not be resolved.

>>>
>>> *>> But in GR don't the field equations take the same form in all 
>>> frames, including accelerating frames, which if I understand correctly, IS 
>>> the Principle of Relativity? TIA, AG*
>>>
>>
>> *> Clark, how about an answer?*
>>
>
> *Sir yes sir!* Saying the field equations are the same form in all 
> reference frames is just another way of saying the fundamental laws of 
> physics are the same everywhere, and if they weren't the same 
> everywhere General Relativity would be a very bad theory. It took Einstein 
> 10 years to find equations that fit these invariant requirements so that in 
> every reference frame the spacetime distance between 2 events is the same, 
> and in every reference frame absolute acceleration exists but absolute 
> motion does not, and every frame is accelerating except for one moving 
> through flat spacetime (aka a zero gravitational field) in a straight path, 
> and for every curved spacetime path there must be a force being applied 
> unless that particular spacetime curve happens to be a geodesic. 
>
> John K Clark
>

*TY! But what still puzzles me is that, according to Brent, there is no 
general transformation from one accelerating frame to another accelerating 
frame (only a local LT). So, although the field equations are claimed to be 
the same in all frames, accelerating or not, how does one prove that 
without applying a general (non existent!) transformation? TIA, AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 20, 2019 at 11:13:06 PM UTC-6, agrays...@gmail.com 
wrote:
>
>
>
> On Wednesday, March 20, 2019 at 10:08:53 AM UTC-6, John Clark wrote:
>>
>> On Wed, Mar 20, 2019 at 9:16 AM  wrote:
>>
>> * > how does GR establish the Principle of Relativity (for accelerating 
>>> frames)? AG *
>>>
>>
>> It doesn't, Einstein never said everything is relative. Unlike velocity 
>> there is such a thing as absolute acceleration, if that were not true the 
>> Twin Paradox could not be resolved.
>>
>> John K Clark
>>
>
> But in GR don't the field equations take the same form in all frames, 
> including accelerating frames, which if I understand correctly,* IS* the 
> Principle of Relativity? TIA, AG
>

*Clark, how about an answer? If the GR field equations have the same form 
in all frames, including accelerating frames, isn't this what we call the 
Principle of Relativity? AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Saturday, March 23, 2019 at 2:19:39 PM UTC-6, Brent wrote:
>
>
>
> On 3/23/2019 5:45 AM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, March 21, 2019 at 12:40:13 AM UTC-6, smitra wrote: 
>>
>> On 21-03-2019 06:21, agrays...@gmail.com wrote: 
>> > On Wednesday, March 20, 2019 at 12:51:18 PM UTC-6, Brent wrote: 
>> > 
>> >> On 3/20/2019 3:07 AM, agrays...@gmail.com wrote: 
>> >> 
>> >> On Tuesday, March 19, 2019 at 7:23:29 PM UTC-6, Brent wrote: 
>> >> 
>> >> On 3/19/2019 9:32 AM, John Clark wrote: 
>> >> 
>> >> On Tue, Mar 19, 2019 at 4:50 AM  wrote: 
>> >> 
>> >>> I SUPPOSE EINSTEIN STARTED WITH THE MOTIVATION OF FINDING A 
>> >> GENERAL TRANSFORMATION FROM ONE ACCELERATING FRAME TO ANOTHER, AND 
>> >> LATER GAVE UP ON THIS PROJECT AND SETTLED FOR A THEORY OF GRAVITY. 
>> >> IS THIS TRUE? TIA, AG 
>> >> 
>> >> Einstein's breakthrough, what he called "the happiest thought of my 
>> >> life" was when he realized a man in a falling elevator will not feel 
>> >> gravity but a man in a accelerating elevator will. In other words an 
>> >> accelerating frame and gravity are the same thing, that's why it's 
>> >> called the Equivalence Principle. 
>> > 
>> >  I wonder if Einstein ever considered whether a charged particle in 
>> > the falling radiate would radiate? 
>> > 
>> >  Brent 
>> > 
>> > Because of your typos, at first I thought you were joking. Well, maybe 
>> > it was a joke, but for me it sounds like a damned good question. I 
>> > surmise that a charged particle accelerating due to gravity does NOT 
>> > radiate energy, but why? AG 
>> > 
>> >  Sorry about the typos.   Yes, it does seem paradoxical.  Here's a 
>> > paper that purports to solve the problem. 
>> > 
>> > THE RADIATION OF A UNIFORMLY ACCELERATED CHARGE IS BEYOND THE HORIZON: 
>> > A SIMPLE DERIVATION 
>> > 
>> > Camila de Almeida [1], Alberto Saa [2] 
>> > (Submitted on 6 Jun 2005 (v1 [3]), last revised 2 Dec 2005 (this 
>> > version, v5)) 
>> > 
>> >> We show, by exploring some elementary consequences of the covariance 
>> >> of Maxwell's equations under general coordinate transformations, 
>> >> that, despite inertial observers can indeed detect electromagnetic 
>> >> radiation emitted from a uniformly accelerated charge, comoving 
>> >> observers will see only a static electric field. This simple 
>> >> analysis can help understanding one of the most celebrated paradoxes 
>> >> of last century. 
>> > 
>> >  Comments: 
>> >  Revtex, 6 pages, 2 figures. v2: Some small 
>> corrections. v3: 
>> > Citation of a earlier paper included. v4: Some stylistic changes. v5: 
>> > Final version to appear in AJP 
>> > 
>> >  Subjects: 
>> >  Classical Physics (physics.class-ph); General 
>> Relativity and 
>> > Quantum Cosmology (gr-qc) 
>> > 
>> >  Journal reference: 
>> >  Am.J.Phys. 74 (2006) 154-158 
>> > 
>> >  DOI: 
>> >  10.1119/1.2162548 [4] 
>> > 
>> >  Cite as: 
>> >  arXiv:physics/0506049 [5] [physics.class-ph] 
>> > 
>> >  (or arXiv:physics/0506049v5 [6] [physics.class-ph] for 
>> this 
>> > version) 
>> > 
>> >  And another paper that looks at possible experimental evidence. 
>> > 
>> > ELECTRICAL CHARGES IN GRAVITATIONAL FIELDS, AND EINSTEINS 
>> > EQUIVALENCE PRINCIPLE 
>> > 
>> > Gerold Gründler [7] 
>> > (Submitted on 14 Sep 2015 (v1 [8]), last revised 12 Oct 2015 (this 
>> > version, v3)) 
>> > 
>> >> According to Larmor's formula, accelerated electric charges radiate 
>> >> electromagnetic waves. Hence charges should radiate, if they are in 
>> >> free fall in gravitational fields, and they should not radiate if 
>> >> they are supported at rest in gravitational fields. But according to 
>> >> Einstein's equivalence principle, charges in free fall should not 
>> >> radiate, while charges supported at rest in gravitational fields 
>> >> should radiate. In this article we point out indirect experimental 
>> >> evidence, indicating that the equivalence principle is correct, 
>> >> while the traditional interpretation of Larmor's formula must be 
>> >> amended. 
>> > 
>> >  Subjects: 
>> >  General Physics (physics.gen-ph) 
>> > 
>> >  Cite as: 
>> >  arXiv:1509.08757 [9] [physics.gen-ph] 
>> > 
>> >  (or arXiv:1509.08757v3 [10] [physics.gen-ph] for this 
>> version) 
>> > 
>> >  However, I don't find them entirely convincing.  We know that double 
>> > stars, which are orbiting one another in free-fall, radiate 
>> > gravitational waves.  Are we to suppose that if one or both of them 
>> > had an electrical charge that there would be no EM radiation? 
>> > 
>> >  Brent 
>> > 
>> > IF WE GO BACK TO CLASSICAL E, WHERE DOES THE EM RADIATION COME FROM 
>> > WHICH IS EMITTED FOR ACCELERATING PARTICLES? IT CANT COME FROM 
>> > THE SELF FIELD OF, SAY, AN ELECTRON, SINCE THAT WOULD 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 20, 2019 at 10:08:53 AM UTC-6, John Clark wrote:
>
> On Wed, Mar 20, 2019 at 9:16 AM > wrote:
>
> * > how does GR establish the Principle of Relativity (for accelerating 
>> frames)? AG *
>>
>
> It doesn't, Einstein never said everything is relative. Unlike velocity 
> there is such a thing as absolute acceleration, if that were not true the 
> Twin Paradox could not be resolved.
>
> John K Clark
>

In the TP we're comparing an inertial frame with an accelerating frame; not 
the general case I was referring to for accelerating frames. But I'm 
confused, again. Don't Einstein's field equations take the same form in all 
frames, and isn't this the Principle of Relativity for gravity? AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, March 21, 2019 at 12:40:13 AM UTC-6, smitra wrote:
>
> On 21-03-2019 06:21, agrays...@gmail.com  wrote: 
> > On Wednesday, March 20, 2019 at 12:51:18 PM UTC-6, Brent wrote: 
> > 
> >> On 3/20/2019 3:07 AM, agrays...@gmail.com wrote: 
> >> 
> >> On Tuesday, March 19, 2019 at 7:23:29 PM UTC-6, Brent wrote: 
> >> 
> >> On 3/19/2019 9:32 AM, John Clark wrote: 
> >> 
> >> On Tue, Mar 19, 2019 at 4:50 AM  wrote: 
> >> 
> >>> I SUPPOSE EINSTEIN STARTED WITH THE MOTIVATION OF FINDING A 
> >> GENERAL TRANSFORMATION FROM ONE ACCELERATING FRAME TO ANOTHER, AND 
> >> LATER GAVE UP ON THIS PROJECT AND SETTLED FOR A THEORY OF GRAVITY. 
> >> IS THIS TRUE? TIA, AG 
> >> 
> >> Einstein's breakthrough, what he called "the happiest thought of my 
> >> life" was when he realized a man in a falling elevator will not feel 
> >> gravity but a man in a accelerating elevator will. In other words an 
> >> accelerating frame and gravity are the same thing, that's why it's 
> >> called the Equivalence Principle. 
> > 
> >  I wonder if Einstein ever considered whether a charged particle in 
> > the falling radiate would radiate? 
> > 
> >  Brent 
> > 
> > Because of your typos, at first I thought you were joking. Well, maybe 
> > it was a joke, but for me it sounds like a damned good question. I 
> > surmise that a charged particle accelerating due to gravity does NOT 
> > radiate energy, but why? AG 
> > 
> >  Sorry about the typos.   Yes, it does seem paradoxical.  Here's a 
> > paper that purports to solve the problem. 
> > 
> > THE RADIATION OF A UNIFORMLY ACCELERATED CHARGE IS BEYOND THE HORIZON: 
> > A SIMPLE DERIVATION 
> > 
> > Camila de Almeida [1], Alberto Saa [2] 
> > (Submitted on 6 Jun 2005 (v1 [3]), last revised 2 Dec 2005 (this 
> > version, v5)) 
> > 
> >> We show, by exploring some elementary consequences of the covariance 
> >> of Maxwell's equations under general coordinate transformations, 
> >> that, despite inertial observers can indeed detect electromagnetic 
> >> radiation emitted from a uniformly accelerated charge, comoving 
> >> observers will see only a static electric field. This simple 
> >> analysis can help understanding one of the most celebrated paradoxes 
> >> of last century. 
> > 
> >  Comments: 
> >  Revtex, 6 pages, 2 figures. v2: Some small corrections. 
> v3: 
> > Citation of a earlier paper included. v4: Some stylistic changes. v5: 
> > Final version to appear in AJP 
> > 
> >  Subjects: 
> >  Classical Physics (physics.class-ph); General 
> Relativity and 
> > Quantum Cosmology (gr-qc) 
> > 
> >  Journal reference: 
> >  Am.J.Phys. 74 (2006) 154-158 
> > 
> >  DOI: 
> >  10.1119/1.2162548 [4] 
> > 
> >  Cite as: 
> >  arXiv:physics/0506049 [5] [physics.class-ph] 
> > 
> >  (or arXiv:physics/0506049v5 [6] [physics.class-ph] for 
> this 
> > version) 
> > 
> >  And another paper that looks at possible experimental evidence. 
> > 
> > ELECTRICAL CHARGES IN GRAVITATIONAL FIELDS, AND EINSTEINS 
> > EQUIVALENCE PRINCIPLE 
> > 
> > Gerold Gründler [7] 
> > (Submitted on 14 Sep 2015 (v1 [8]), last revised 12 Oct 2015 (this 
> > version, v3)) 
> > 
> >> According to Larmor's formula, accelerated electric charges radiate 
> >> electromagnetic waves. Hence charges should radiate, if they are in 
> >> free fall in gravitational fields, and they should not radiate if 
> >> they are supported at rest in gravitational fields. But according to 
> >> Einstein's equivalence principle, charges in free fall should not 
> >> radiate, while charges supported at rest in gravitational fields 
> >> should radiate. In this article we point out indirect experimental 
> >> evidence, indicating that the equivalence principle is correct, 
> >> while the traditional interpretation of Larmor's formula must be 
> >> amended. 
> > 
> >  Subjects: 
> >  General Physics (physics.gen-ph) 
> > 
> >  Cite as: 
> >  arXiv:1509.08757 [9] [physics.gen-ph] 
> > 
> >  (or arXiv:1509.08757v3 [10] [physics.gen-ph] for this 
> version) 
> > 
> >  However, I don't find them entirely convincing.  We know that double 
> > stars, which are orbiting one another in free-fall, radiate 
> > gravitational waves.  Are we to suppose that if one or both of them 
> > had an electrical charge that there would be no EM radiation? 
> > 
> >  Brent 
> > 
> > IF WE GO BACK TO CLASSICAL E, WHERE DOES THE EM RADIATION COME FROM 
> > WHICH IS EMITTED FOR ACCELERATING PARTICLES? IT CANT COME FROM 
> > THE SELF FIELD OF, SAY, AN ELECTRON, SINCE THAT WOULD IMPLY LOSS OF 
> > MASS OR CHARGE OF THE ELECTRON, WHICH IS NEVER CLAIMED. SO IT MUST 
> > COME FROM THE EM FIELD CAUSING THE ACCELERATION. NOW IF WE GO TO THE 
> > CASE OF GRAVITY WITHOUT ANY EM SOURCE FIELDS, AND WE STILL GET EM 
> > 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 20, 2019 at 12:51:18 PM UTC-6, Brent wrote:
>
>
>
> On 3/20/2019 3:07 AM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, March 19, 2019 at 7:23:29 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 3/19/2019 9:32 AM, John Clark wrote:
>>
>> On Tue, Mar 19, 2019 at 4:50 AM  wrote:
>>
>> * > I suppose Einstein started with the motivation of finding a general 
>>> transformation from one accelerating frame to another, and later gave up on 
>>> this project and settled for a theory of gravity. Is this true? TIA, AG*
>>
>>
>> Einstein's breakthrough, what he called "the happiest thought of my life" 
>> was when he realized a man in a falling elevator will not feel gravity but 
>> a man in a accelerating elevator will. In other words an accelerating frame 
>> and gravity are the same thing, that's why it's called the Equivalence 
>> Principle.
>>
>>
>> I wonder if Einstein ever considered whether a charged particle in the 
>> falling radiate would radiate?
>>
>> Brent
>>
>
> Because of your typos, at first I thought you were joking. Well, maybe it 
> was a joke, but for me it sounds like a damned good question. I surmise 
> that a charged particle accelerating due to gravity does NOT radiate 
> energy, but why? AG 
>
>
> Sorry about the typos.   Yes, it does seem paradoxical.  Here's a paper 
> that purports to solve the problem.
>
> The radiation of a uniformly accelerated charge is beyond the horizon: a 
> simple derivation 
> Camila de Almeida 
> 
> , Alberto Saa 
> 
> (Submitted on 6 Jun 2005 (v1 ), 
> last revised 2 Dec 2005 (this version, v5))
>
> We show, by exploring some elementary consequences of the covariance of 
> Maxwell's equations under general coordinate transformations, that, despite 
> inertial observers can indeed detect electromagnetic radiation emitted from 
> a uniformly accelerated charge, comoving observers will see only a static 
> electric field. This simple analysis can help understanding one of the most 
> celebrated paradoxes of last century.
>
> Comments: Revtex, 6 pages, 2 figures. v2: Some small corrections. v3: 
> Citation of a earlier paper included. v4: Some stylistic changes. v5: Final 
> version to appear in AJP 
> Subjects: Classical Physics (physics.class-ph); General Relativity and 
> Quantum Cosmology (gr-qc) 
> Journal reference: Am.J.Phys. 74 (2006) 154-158 
> DOI: 10.1119/1.2162548 
> 
>  
> Cite as: arXiv:physics/0506049  
> [physics.class-ph] 
>   (or arXiv:physics/0506049v5  
> [physics.class-ph] for this version) 
> And another paper that looks at possible experimental evidence.
>
> Electrical charges in gravitational fields, and Einstein's equivalence 
> principle 
> Gerold Gründler 
> 
> (Submitted on 14 Sep 2015 (v1 ), last 
> revised 12 Oct 2015 (this version, v3))
>
> According to Larmor's formula, accelerated electric charges radiate 
> electromagnetic waves. Hence charges should radiate, if they are in free 
> fall in gravitational fields, and they should not radiate if they are 
> supported at rest in gravitational fields. But according to Einstein's 
> equivalence principle, charges in free fall should not radiate, while 
> charges supported at rest in gravitational fields should radiate. In this 
> article we point out indirect experimental evidence, indicating that the 
> equivalence principle is correct, while the traditional interpretation of 
> Larmor's formula must be amended.
>
> Subjects: General Physics (physics.gen-ph) 
> Cite as: arXiv:1509.08757  
> [physics.gen-ph] 
>   (or arXiv:1509.08757v3  
> [physics.gen-ph] for this version) 
> However, I don't find them entirely convincing.  We know that double 
> stars, which are orbiting one another in free-fall, radiate gravitational 
> waves.  Are we to suppose that if one or both of them had an electrical 
> charge that there would be no EM radiation?
>
> Brent
>

*If we go back to classical E, where does the EM radiation come from 
which is emitted for accelerating particles? It can't come from the self 
field of, say, an electron, since that would imply loss of mass or charge 
of the electron, which is never claimed. So it must come from the EM field 
causing the acceleration. Now if we go to the case of gravity without any 
EM source fields, and we still get EM radiation due to the acceleration, 
where does it come from? AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 20, 2019 at 10:08:53 AM UTC-6, John Clark wrote:
>
> On Wed, Mar 20, 2019 at 9:16 AM > wrote:
>
> * > how does GR establish the Principle of Relativity (for accelerating 
>> frames)? AG *
>>
>
> It doesn't, Einstein never said everything is relative. Unlike velocity 
> there is such a thing as absolute acceleration, if that were not true the 
> Twin Paradox could not be resolved.
>
> John K Clark
>

But in GR don't the field equations take the same form in all frames, 
including accelerating frames, which if I understand correctly,* IS* the 
Principle of Relativity? TIA, AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 20, 2019 at 7:03:48 AM UTC-6, John Clark wrote:
>
> On Tue, Mar 19, 2019 at 7:54 PM > wrote:
>
> >> Einstein's breakthrough, what he called "the happiest thought of my 
>>> life" was when he realized a man in a falling elevator will not feel 
>>> gravity but a man in a accelerating elevator will. In other words an 
>>> accelerating frame and gravity are the same thing, that's why it's called 
>>> the Equivalence Principle.
>>>
>>
>> > 
>> *I think your claim, in response to my question, is that if you have a 
>> theory of gravity, then via the EP you also have a general theory of how to 
>> transform from one accelerating frame to another which obeys the Principle 
>> of Relativity. I tend not to believe this since gravity is only locally 
>> equivalent to acceleration. AG *
>>
>
> Einstein was certainly aware  that the EP was only true for regions that 
> were very small compared to the curvature of the gravitational field, in 
> fact working out the consequences of tidal effects was one of the reasons 
> it took him nearly a full decade of grueling work to go from "the happiest 
> thought of my life" to a fully developed theory of General Relativity. 
> Einstein had to master how 4D Tensors work in Non-Euclidean space and was 
> so obsessed and worked so hard it nearly killed him. When he finished he 
> lost nearly 50 pounds felt weak and expected to die soon, but fortunately 
> didn't. 
>
> John K Clark
>

But getting back to my original question a few messages ago; if there is no 
general transformation from one accelerating frame to another (except 
locally), how does GR establish the Principle of Relativity (for 
accelerating frames)? AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 19, 2019 at 7:23:29 PM UTC-6, Brent wrote:
>
>
>
> On 3/19/2019 9:32 AM, John Clark wrote:
>
> On Tue, Mar 19, 2019 at 4:50 AM > wrote:
>
> * > I suppose Einstein started with the motivation of finding a general 
>> transformation from one accelerating frame to another, and later gave up on 
>> this project and settled for a theory of gravity. Is this true? TIA, AG*
>
>
> Einstein's breakthrough, what he called "the happiest thought of my life" 
> was when he realized a man in a falling elevator will not feel gravity but 
> a man in a accelerating elevator will. In other words an accelerating frame 
> and gravity are the same thing, that's why it's called the Equivalence 
> Principle.
>
>
> I wonder if Einstein ever considered whether a charged particle in the 
> falling radiate would radiate?
>
> Brent
>

Because of your typos, at first I thought you were joking. Well, maybe it 
was a joke, but for me it sounds like a damned good question. I surmise 
that a charged particle accelerating due to gravity does NOT radiate 
energy, but why? AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 19, 2019 at 10:33:35 AM UTC-6, John Clark wrote:
>
> On Tue, Mar 19, 2019 at 4:50 AM > wrote:
>
> * > I suppose Einstein started with the motivation of finding a general 
>> transformation from one accelerating frame to another, and later gave up on 
>> this project and settled for a theory of gravity. Is this true? TIA, AG*
>
>
> Einstein's breakthrough, what he called "the happiest thought of my life" 
> was when he realized a man in a falling elevator will not feel gravity but 
> a man in a accelerating elevator will. In other words an accelerating frame 
> and gravity are the same thing, that's why it's called the Equivalence 
> Principle.
>
> John K Clark
>
> I think your claim, in response to my question, is that if you have a 
theory of gravity, then via the EP you *also* have a general theory of how 
to transform from one accelerating frame to another which obeys the 
Principle of Relativity. I tend *not* to believe this since gravity is only* 
locally* equivalent to acceleration. AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 12, 2019 at 4:05:04 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Thursday, March 7, 2019 at 3:19:39 AM UTC-7, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, March 6, 2019 at 11:42:33 AM UTC-7, Brent wrote:
>>>
>>>
>>>
>>> On 3/6/2019 1:27 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, March 6, 2019 at 1:03:16 AM UTC-7, Brent wrote: 



 On 3/5/2019 10:02 PM, agrays...@gmail.com wrote:



 On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, agrays...@gmail.com 
 wrote: 
>
>
>
> On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agray...@gmail.com 
> wrote: 
>>
>>
>>
>> On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote: 



 On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:

 *Are you assuming uniqueness to tensors; that only tensors can 
 produce covariance in 4-space? Is that established or a mathematical 
 speculation? TIA, AG *


 That's looking at it the wrong way around.  Anything that 
 transforms as an object in space, must be representable by tensors. 
 The 
 informal definition of a tensor is something that transforms like an 
 object, i.e. in three space it's something that has a location and an 
 orientation and three extensions.  Something that doesn't transform as 
 a 
 tensor under coordinate system changes is something that depends on 
 the 
 arbitrary choice of coordinate system and so cannot be a fundamental 
 physical object.

 Brent

>>>
>>> 1) Is it correct to say that tensors in E's field equations can be 
>>> represented as 4x4 matrices which have different representations 
>>> depending 
>>> on the coordinate system being used, but represent the same object? 
>>>
>>>
>>> That's right as far as it goes.   Tensors can be of any order.  The 
>>> curvature tensor is 4x4x4x4.
>>>
>>> 2) In SR we use the LT to transform from one* non-accelerating* 
>>> frame to another. In GR, what is the transformation for going from one 
>>> *accelerating* frame to another? 
>>>
>>>
>>> The Lorentz transform, but only in a local patch.
>>>
>>
>> *That's what I thought you would say. But how does this advance 
>> Einstein's presumed project of finding how the laws of physics are 
>> invariant for accelerating frames? How did it morph into a theory of 
>> gravity? TIA, AG *
>>
>
> *Or suppose, using GR, that two frames are NOT within the same local 
> patch.  If we can't use the LT, how can we transform from one frame to 
> the 
> other? TIA, AG *
>
> *Or suppose we have two arbitrary accelerating frames, again NOT 
> within the same local patch, is it true that Maxwell's Equations are 
> covariant under some transformation, and what is that transformation? 
> TIA, 
> AG*
>


 *I think I can simplify my issue here, if indeed there is an issue: did 
 Einstein, or anyone, ever prove what I will call the General Principle of 
 Relativity, namely that the laws of physics are invariant for accelerating 
 frames? If the answer is affirmative, is there a transformation equation 
 for Maxwell's Equations which leaves them unchanged for arbitrary 
 accelerating frames? TIA, AG *


 Your question isn't clear.  If you're simply asking about the equations 
 describing physics* as expressed* in an accelerating (e.g. rotating) 
 reference frame, that's pretty trivial.  You write the equations in 
 whatever reference frame is convenient (usually an inertial one) and then 
 transform the coordinates to the accelerated frame coordinates.   But if 
 you're asking about what equations describe some physical system while it 
 is being accelerated as compared to it not being accelerated, that's more 
 complicated. 

>>>
>>> *Thanks, but I wasn't referring to either of those cases; rather, the 
>>> case of transforming from one accelerating frame to another accelerating 
>>> frame, and whether the laws of physics are invariant. *
>>>
>>>
>>> For simplicity consider just flat Minkowski space time.  If you know the 
>>> motion of a particle in reference frame, whether the reference frame is 
>>> accelerated or not, you can determine its motion in any other reference 
>>> frame.  As for the particle path through spacetime, that's just some 
>>> geometric path and you're changing from describing it in one coordinate 
>>> system to describing it in another system...no physics is changing, just 
>>> the description.  If the reference 

Re: CMBR

[agrayson2000]

On Sunday, March 17, 2019 at 2:49:43 AM UTC-6, Bruce wrote:
>
> On Sun, Mar 17, 2019 at 7:38 PM > wrote:
>
>>
>>
>> On Thursday, March 14, 2019 at 8:27:58 PM UTC-6, agrays...@gmail.com 
>> wrote:
>>>
>>> IIUC, the combined mass of an electron and proton is larger than the 
>>> hydrogen atom they form at recombination time. Thus, I would expect a very 
>>> narrow pulse of energy as a result when recombination occurs. This 
>>> apparently being the case, why does the CMBR have a black body distribution 
>>> and not a pulse with a very narrow spread? TIA, AG
>>>
>>
>> Is this a really dumb question and the reason for zero replies; or is it 
>> because no one here has the answer? Or maybe just no interest in another 
>> puzzle? AG
>>
>
> Dumb question. CMB is thermal radiation, not the recombination energy. It 
> reflects the temperature at the time the universe became transparent to 
> radiation of all wavelengths -- because the electron-proton plasma 
> recombined to form less reactive hydrogen.
>
> Bruce 
>

FWIW, the origin of the "dumb question" was my impression, from texts I 
have read, that the CMBR* originated *with recombination, in which case it 
should be totally a function of that recombination. In fact, it is just the 
black body radiation of the universe projected forward in time, with the 
hydrogen absorption lines imposed. Then I made a second error in forgetting 
that hydrogen has a countably infinite set of energy states, not simply a 
single one.  Anyway, now I see my errors, and thank everyone for their 
indulgence. AG

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Re: CMBR

[agrayson2000]

On Monday, March 18, 2019 at 11:36:24 AM UTC-6, Brent wrote:
>
>
>
> On 3/18/2019 2:34 AM, agrays...@gmail.com  wrote: 
> > If that's the case, then there's no visible remnant of the 
> > recombination in the observed CMBR, and what we observe is simply the 
> > cooled BB radiation of pre-combination times. So what does the CMBR 
> > tell us? AG 
>
> It tells us it was hot.  So those lines were smeared out by doppler 
> shifts due the motion of the particles. 
>
> Brent 
>

More important IMO, is that it tells us that the cosmological red shift is 
due to an expanding universe, not, say, to "tired light". AG 

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Re: CMBR

[agrayson2000]

On Sunday, March 17, 2019 at 6:17:01 PM UTC-6, Lawrence Crowell wrote:
>
> On Sunday, March 17, 2019 at 1:36:22 PM UTC-6, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, March 17, 2019 at 12:12:58 PM UTC-6, Brent wrote:
>>>
>>>
>>>
>>> On 3/17/2019 4:50 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, March 17, 2019 at 3:05:14 AM UTC-6, agrays...@gmail.com 
>>> wrote: 



 On Sunday, March 17, 2019 at 2:49:43 AM UTC-6, Bruce wrote: 
>
> On Sun, Mar 17, 2019 at 7:38 PM  wrote:
>
>>
>>
>> On Thursday, March 14, 2019 at 8:27:58 PM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>> IIUC, the combined mass of an electron and proton is larger than the 
>>> hydrogen atom they form at recombination time. Thus, I would expect a 
>>> very 
>>> narrow pulse of energy as a result when recombination occurs. This 
>>> apparently being the case, why does the CMBR have a black body 
>>> distribution 
>>> and not a pulse with a very narrow spread? TIA, AG
>>>
>>
>> Is this a really dumb question and the reason for zero replies; or is 
>> it because no one here has the answer? Or maybe just no interest in 
>> another 
>> puzzle? AG
>>
>
> Dumb question. CMB is thermal radiation, not the recombination energy. 
> It reflects the temperature at the time the universe became transparent 
> to 
> radiation of all wavelengths -- because the electron-proton plasma 
> recombined to form less reactive hydrogen.
>
> Bruce 
>

 But the recombination energy must be part of the mix at recombination 
 time and this is never mentioned in the texts I have read. I suppose this 
 is another dumb question. AG 

>>>
>>> What this thread shows is that I don't understand the CMBR. Maybe no one 
>>> does. ISTM that the universe was cooling *prior* to recombination time 
>>> and therefore must have had a thermal spectrum *independent* of the 
>>> recombination. Yet the going assumption, AFAICT, is that the CMBR *comes 
>>> into existence* at recombination time, but is independent of the 
>>> physical recombination which is never included or mentioned as part of the 
>>> observed spectrum.  Can anyone explain what is actually going on in this 
>>> model? TIA, AG
>>>
>>>
>>> Your mistake is assuming that this recombination is one big jump from 
>>> complete dissociation to bound hydrogen atom.  A hydrogen atom has lots of 
>>> energy states and, as the plasma cooled due to expansion, there would be a 
>>> continuous shift of energy from the proton/electron to the gamma rays.
>>>
>>> Brent
>>>
>>
>> In fact, hydrogen has a countably infinite set of energy states, which I 
>> forgot. Is it correct to say that these recombination states form the 
>> thermal signature which is observed (in which case Bruce's explanation is 
>> misleading)? AG  
>>
>
> I am presuming you are raising the prospect of there being absorption 
> lines in the spectrum, just as we see the same with the sun. There were 
> such lines for the hydrogen atom after recombination that would have been 
> visible. However, with red shifting by z = 1100 and spectral broadening 
> they have been smeared out. 
>
> LC
>

If that's the case, then there's no visible remnant of the recombination in 
the observed CMBR, and what we observe is simply the cooled BB radiation of 
pre-combination times. So what does the CMBR tell us? AG  

>
> [image: spectrum of the sun.jpg]
>  
>

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Re: CMBR

[agrayson2000]

On Sunday, March 17, 2019 at 12:12:58 PM UTC-6, Brent wrote:
>
>
>
> On 3/17/2019 4:50 AM, agrays...@gmail.com  wrote:
>
>
>
> On Sunday, March 17, 2019 at 3:05:14 AM UTC-6, agrays...@gmail.com wrote: 
>>
>>
>>
>> On Sunday, March 17, 2019 at 2:49:43 AM UTC-6, Bruce wrote: 
>>>
>>> On Sun, Mar 17, 2019 at 7:38 PM  wrote:
>>>


 On Thursday, March 14, 2019 at 8:27:58 PM UTC-6, agrays...@gmail.com 
 wrote: 
>
> IIUC, the combined mass of an electron and proton is larger than the 
> hydrogen atom they form at recombination time. Thus, I would expect a 
> very 
> narrow pulse of energy as a result when recombination occurs. This 
> apparently being the case, why does the CMBR have a black body 
> distribution 
> and not a pulse with a very narrow spread? TIA, AG
>

 Is this a really dumb question and the reason for zero replies; or is 
 it because no one here has the answer? Or maybe just no interest in 
 another 
 puzzle? AG

>>>
>>> Dumb question. CMB is thermal radiation, not the recombination energy. 
>>> It reflects the temperature at the time the universe became transparent to 
>>> radiation of all wavelengths -- because the electron-proton plasma 
>>> recombined to form less reactive hydrogen.
>>>
>>> Bruce 
>>>
>>
>> But the recombination energy must be part of the mix at recombination 
>> time and this is never mentioned in the texts I have read. I suppose this 
>> is another dumb question. AG 
>>
>
> What this thread shows is that I don't understand the CMBR. Maybe no one 
> does. ISTM that the universe was cooling *prior* to recombination time 
> and therefore must have had a thermal spectrum *independent* of the 
> recombination. Yet the going assumption, AFAICT, is that the CMBR *comes 
> into existence* at recombination time, but is independent of the physical 
> recombination which is never included or mentioned as part of the observed 
> spectrum.  Can anyone explain what is actually going on in this model? TIA, 
> AG
>
>
> Your mistake is assuming that this recombination is one big jump from 
> complete dissociation to bound hydrogen atom.  A hydrogen atom has lots of 
> energy states and, as the plasma cooled due to expansion, there would be a 
> continuous shift of energy from the proton/electron to the gamma rays.
>
> Brent
>

In fact, hydrogen has a countably infinite set of energy states, which I 
forgot. Is it correct to say that these recombination states form the 
thermal signature which is observed (in which case Bruce's explanation is 
misleading)? AG  

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Re: CMBR

[agrayson2000]

On Sunday, March 17, 2019 at 3:05:14 AM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Sunday, March 17, 2019 at 2:49:43 AM UTC-6, Bruce wrote:
>>
>> On Sun, Mar 17, 2019 at 7:38 PM  wrote:
>>
>>>
>>>
>>> On Thursday, March 14, 2019 at 8:27:58 PM UTC-6, agrays...@gmail.com 
>>> wrote:

 IIUC, the combined mass of an electron and proton is larger than the 
 hydrogen atom they form at recombination time. Thus, I would expect a very 
 narrow pulse of energy as a result when recombination occurs. This 
 apparently being the case, why does the CMBR have a black body 
 distribution 
 and not a pulse with a very narrow spread? TIA, AG

>>>
>>> Is this a really dumb question and the reason for zero replies; or is it 
>>> because no one here has the answer? Or maybe just no interest in another 
>>> puzzle? AG
>>>
>>
>> Dumb question. CMB is thermal radiation, not the recombination energy. It 
>> reflects the temperature at the time the universe became transparent to 
>> radiation of all wavelengths -- because the electron-proton plasma 
>> recombined to form less reactive hydrogen.
>>
>> Bruce 
>>
>
> But the recombination energy must be part of the mix at recombination time 
> and this is never mentioned in the texts I have read. I suppose this is 
> another dumb question. AG 
>

What this thread shows is that I don't understand the CMBR. Maybe no one 
does. ISTM that the universe was cooling *prior* to recombination time and 
therefore must have had a thermal spectrum *independent* of the 
recombination. Yet the going assumption, AFAICT, is that the CMBR *comes 
into existence* at recombination time, but is independent of the physical 
recombination which is never included or mentioned as part of the observed 
spectrum.  Can anyone explain what is actually going on in this model? TIA, 
AG

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Re: CMBR

[agrayson2000]

On Sunday, March 17, 2019 at 2:49:43 AM UTC-6, Bruce wrote:
>
> On Sun, Mar 17, 2019 at 7:38 PM > wrote:
>
>>
>>
>> On Thursday, March 14, 2019 at 8:27:58 PM UTC-6, agrays...@gmail.com 
>> wrote:
>>>
>>> IIUC, the combined mass of an electron and proton is larger than the 
>>> hydrogen atom they form at recombination time. Thus, I would expect a very 
>>> narrow pulse of energy as a result when recombination occurs. This 
>>> apparently being the case, why does the CMBR have a black body distribution 
>>> and not a pulse with a very narrow spread? TIA, AG
>>>
>>
>> Is this a really dumb question and the reason for zero replies; or is it 
>> because no one here has the answer? Or maybe just no interest in another 
>> puzzle? AG
>>
>
> Dumb question. CMB is thermal radiation, not the recombination energy. It 
> reflects the temperature at the time the universe became transparent to 
> radiation of all wavelengths -- because the electron-proton plasma 
> recombined to form less reactive hydrogen.
>
> Bruce 
>

But the recombination energy must be part of the mix at recombination time 
and this is never mentioned in the texts I have read. I suppose this is 
another dumb question. AG 

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Re: CMBR

[agrayson2000]

On Thursday, March 14, 2019 at 8:27:58 PM UTC-6, agrays...@gmail.com wrote:
>
> IIUC, the combined mass of an electron and proton is larger than the 
> hydrogen atom they form at recombination time. Thus, I would expect a very 
> narrow pulse of energy as a result when recombination occurs. This 
> apparently being the case, why does the CMBR have a black body distribution 
> and not a pulse with a very narrow spread? TIA, AG
>

Is this a really dumb question and the reason for zero replies; or is it 
because no one here has the answer? Or maybe just no interest in another 
puzzle? AG

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CMBR

[agrayson2000]

IIUC, the combined mass of an electron and proton is larger than the 
hydrogen atom they form at recombination time. Thus, I would expect a very 
narrow pulse of energy as a result when recombination occurs. This 
apparently being the case, why does the CMBR have a black body distribution 
and not a pulse with a very narrow spread? TIA, AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, March 7, 2019 at 3:19:39 AM UTC-7, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, March 6, 2019 at 11:42:33 AM UTC-7, Brent wrote:
>>
>>
>>
>> On 3/6/2019 1:27 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, March 6, 2019 at 1:03:16 AM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 3/5/2019 10:02 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, agrays...@gmail.com 
>>> wrote: 



 On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agray...@gmail.com 
 wrote: 
>
>
>
> On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:
>>>
>>> *Are you assuming uniqueness to tensors; that only tensors can 
>>> produce covariance in 4-space? Is that established or a mathematical 
>>> speculation? TIA, AG *
>>>
>>>
>>> That's looking at it the wrong way around.  Anything that transforms 
>>> as an object in space, must be representable by tensors. The informal 
>>> definition of a tensor is something that transforms like an object, 
>>> i.e. in 
>>> three space it's something that has a location and an orientation and 
>>> three 
>>> extensions.  Something that doesn't transform as a tensor under 
>>> coordinate 
>>> system changes is something that depends on the arbitrary choice of 
>>> coordinate system and so cannot be a fundamental physical object.
>>>
>>> Brent
>>>
>>
>> 1) Is it correct to say that tensors in E's field equations can be 
>> represented as 4x4 matrices which have different representations 
>> depending 
>> on the coordinate system being used, but represent the same object? 
>>
>>
>> That's right as far as it goes.   Tensors can be of any order.  The 
>> curvature tensor is 4x4x4x4.
>>
>> 2) In SR we use the LT to transform from one* non-accelerating* 
>> frame to another. In GR, what is the transformation for going from one 
>> *accelerating* frame to another? 
>>
>>
>> The Lorentz transform, but only in a local patch.
>>
>
> *That's what I thought you would say. But how does this advance 
> Einstein's presumed project of finding how the laws of physics are 
> invariant for accelerating frames? How did it morph into a theory of 
> gravity? TIA, AG *
>

 *Or suppose, using GR, that two frames are NOT within the same local 
 patch.  If we can't use the LT, how can we transform from one frame to the 
 other? TIA, AG *

 *Or suppose we have two arbitrary accelerating frames, again NOT within 
 the same local patch, is it true that Maxwell's Equations are covariant 
 under some transformation, and what is that transformation? TIA, AG*

>>>
>>>
>>> *I think I can simplify my issue here, if indeed there is an issue: did 
>>> Einstein, or anyone, ever prove what I will call the General Principle of 
>>> Relativity, namely that the laws of physics are invariant for accelerating 
>>> frames? If the answer is affirmative, is there a transformation equation 
>>> for Maxwell's Equations which leaves them unchanged for arbitrary 
>>> accelerating frames? TIA, AG *
>>>
>>>
>>> Your question isn't clear.  If you're simply asking about the equations 
>>> describing physics* as expressed* in an accelerating (e.g. rotating) 
>>> reference frame, that's pretty trivial.  You write the equations in 
>>> whatever reference frame is convenient (usually an inertial one) and then 
>>> transform the coordinates to the accelerated frame coordinates.   But if 
>>> you're asking about what equations describe some physical system while it 
>>> is being accelerated as compared to it not being accelerated, that's more 
>>> complicated. 
>>>
>>
>> *Thanks, but I wasn't referring to either of those cases; rather, the 
>> case of transforming from one accelerating frame to another accelerating 
>> frame, and whether the laws of physics are invariant. *
>>
>>
>> For simplicity consider just flat Minkowski space time.  If you know the 
>> motion of a particle in reference frame, whether the reference frame is 
>> accelerated or not, you can determine its motion in any other reference 
>> frame.  As for the particle path through spacetime, that's just some 
>> geometric path and you're changing from describing it in one coordinate 
>> system to describing it in another system...no physics is changing, just 
>> the description.  If the reference frames are accelerated you get extra 
>> terms in this description, like "centrifugal acceleration" which are just 
>> artifacts of the frame choice. This is the same as in Newtonian mechanics.  
>>
>> But if the particle is actually 

Re: Black holes and the information paradox

[agrayson2000]

On Tuesday, March 12, 2019 at 12:18:51 PM UTC-6, Bruno Marchal wrote:
>
>
> On 11 Mar 2019, at 03:16, agrays...@gmail.com  wrote:
>
> They say if information is lost, determination is toast. 
>
>
> That is not correct. If information is lost, reversibility is toast, but 
> determination can be conserved.
>

*If reversibility is lost, how can determinism be preserved? It can't, and 
this is the position Hawking took IIUC. What's your definition of 
determinism? Doesn't it require the laws of physics to be time reversible? 
AG *

>
> Typically the Kestrek bird K is irreversible, as it eliminates information 
> Kxy = x. From KSI you get S, but from S, even knowing it comes from the 
> application of K, you cannot retrieve I. Similarly with addition and 
> multiplication in arithmetic. From 18 you can’t guess it cames from 7 and 
> 11. Erasing information is common.
>
> Some does not tolerate that, so Church works in the base {I, B, W, C}, 
> where I is [x]x, B is [x][y][z] x(yz), etc. 
>
> That base is not combinatorial complete, but is still Turing complete, 
> illustrating that we can do computation without eliminating any 
> information. (None of I, B, C and X eliminates information)
>
> But the quantum eliminates even the combinator W (Wxy = xyy), or the lamda 
> expression [x][y]. xyy. That is, we cannot eliminate information, but we 
> cannot duplicate it either!
>
> Now, the problem is that the BCI combinator algebra are not 
> Turing-complete. It is the core of the physical reality, and Turing 
> universality needs the addition of modal “combinators”.
>

*I have no idea what you're referring to. AG *

>
>
>
>
> But doesn't QM inherently affirm information loss? I mean, although, say, 
> the SWE can be run backward in time to reconstruct any wf it describes, we 
> can never reconstruct or play backward Born's rule, in the sense of knowing 
> what original particular state gave a particular outcome. That is, there is 
> no rule in QM to predict a particular outcome, so how can we expect, that 
> given some outcome, we can know from whence it arose? AG
>
>
>
> You can run backward by discarding information. Born rule, or the 
> projection inherent in the measurement discard information, when you 
> abandon the collapse postulate. That is why “fusing” histories can be done 
> by relative amnesia, and also that is how Church emulate “local kestrels” 
> capable to “apparently eliminate information”, but only with selected 
> objects, like the numbers. K *n* *m* = *n* 
>
> A quantum computer (essentially irreversible during the processing) is 
> Turing complete, and so can simulate all classical computers discarding 
> information all the times, but in the details, everything is locally 
> determinist and reversible.
>
> Bruno
>
>
>
>
>
>
> -- 
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Re: Black holes and the information paradox

[agrayson2000]

On Tuesday, March 12, 2019 at 12:18:50 PM UTC-6, Bruno Marchal wrote:
>
>
> On 11 Mar 2019, at 09:54, agrays...@gmail.com  wrote:
>
>
>
> On Monday, March 11, 2019 at 1:43:05 AM UTC-6, Liz R wrote:
>>
>> I thought QM was deterministic, at least mathematically - and I guess in 
>> the MWI?
>>
>
> *QM is deterministic, but only as far as reconstructing wf's as time is 
> reversed, but it can't reconstruct individual events which are without 
> ostensible cause. As for the MWI, I don't think it's deterministic since 
> the different branches are never in causal contact. AG *
>
>
> It has to be. 
>

*So If I am in one world of many, how can I time reverse my outcome to 
reconstruct something from another world, the one that gave rise to the 
many worlds? AG*
 

> Without wave collapse the evolution is “just” a unitary transformation. It 
> is a vector rotating in some (Hilbert) space. Only the wave collapse 
> postulate bring 3p-indterminacy. In Everett the indeterminacy is explained 
> like in arithmetic, or combinator, with the digital mechanistic hypothesis 
> (in the cognitive science, not in physics).. 
>

*Can't we keep your theory out of this? AG *

>
> Bruno
>
>
>
>
>> I mean everyone can't have forgotten quantum indeterminacy when 
>> discussing the BHIP, surely?
>>
>
>  
>
> -- 
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>
>
>

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Re: Black holes and the information paradox

[agrayson2000]

On Monday, March 11, 2019 at 2:41:13 PM UTC-6, John Clark wrote:
>
>
> On Mon, Mar 11, 2019 at 12:18 PM > 
> wrote:
>
> >>We can calculate the wave function exactly but the wave function does 
>>> not determine exactly how matter will behave. 
>>>
>>
>> *That's precisely my point. If we can't determine exactly how matter will 
>> behave, how can we go back in time to reconstruct the original state for 
>> single trials. If we can't do that, then QM inherently contradicts 
>> determinism, so why make an issue about BH information loss? AG*
>>
>
>
> Schrodinger says If you know what the wave function of a particle is now 
> then you can predict what the wave function will be tomorrow and determine 
> what it was yesterday. Even more important Schrodinger says his function is 
> unitary, that means probabilities are conserved, but that can only happen 
> if information is conserved. 
>
> For the very idea of probability to make sense everything must add up to 
> exactly 1; if you calculate there is a 70% chance an electron will curve to 
> the left and a 40% chance it will curve to the right then you'll know 
> you've calculated nonsense. Black Holes seem to destroy information but if 
> so then the Schrodinger Wave Function can't be unitary and thus is total 
> nonsense, but it has been tested many many times and it always works so 
> it can't be total nonsense. That is the paradox.
>

*How is information preserved in usual QM? If a particle bends in one 
direction, and you play the wf back in time, how do you recover a particle 
which will bend in the same direction, exactly? AG *

>
> If all this confused you welcome to the club, nobody knows how to resolve 
> this paradox but when they do they'll probably resolve the conflict between 
> General Relativity and Quantum Mechanics too.  
>
> John K Clark
>
>
>>

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Re: Black holes and the information paradox

[agrayson2000]

On Monday, March 11, 2019 at 7:40:59 AM UTC-6, John Clark wrote:
>
> On Mon, Mar 11, 2019 at 4:54 AM > wrote:
>
> *> QM is deterministic, but only as far as reconstructing wf's*
>>
>
> We can calculate the wave function exactly but the wave function does not 
> determine exactly how matter will behave. 
>

*That's precisely my point. If we can't determine exactly how matter will 
behave, how can we go back in time to reconstruct the original state for 
single trials. If we can't do that, then QM inherently contradicts 
determinism, so why make an issue about BH information loss? AG*
 

> As far as the Black Hole information paradox goes solving that is one of 
> the deepest problems in cutting edge physics. It all boils down to the fact 
> that General Relativity and Quantum Mechanics, although both work great on 
> their own, don't work well together. 
>
>  John K Clark
>
>

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Re: Black holes and the information paradox

[agrayson2000]

On Monday, March 11, 2019 at 1:43:05 AM UTC-6, Liz R wrote:
>
> I thought QM was deterministic, at least mathematically - and I guess in 
> the MWI?
>

*QM is deterministic, but only as far as reconstructing wf's as time is 
reversed, but it can't reconstruct individual events which are without 
ostensible cause. As for the MWI, I don't think it's deterministic since 
the different branches are never in causal contact. AG *

>
> I mean everyone can't have forgotten quantum indeterminacy when discussing 
> the BHIP, surely?
>

 

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Black holes and the information paradox

[agrayson2000]

They say if information is lost, determination is toast. But doesn't QM 
inherently affirm information loss? I mean, although, say, the SWE can be 
run backward in time to reconstruct any wf it describes, we can never 
reconstruct or play backward Born's rule, in the sense of knowing what 
original particular state gave a particular outcome. That is, there is no 
rule in QM to predict a particular outcome, so how can we expect, that 
given some outcome, we can know from whence it arose? AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 6, 2019 at 11:42:33 AM UTC-7, Brent wrote:
>
>
>
> On 3/6/2019 1:27 AM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, March 6, 2019 at 1:03:16 AM UTC-7, Brent wrote: 
>>
>>
>>
>> On 3/5/2019 10:02 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agray...@gmail.com 
>>> wrote: 



 On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote: 
>
>
>
> On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:
>>
>> *Are you assuming uniqueness to tensors; that only tensors can 
>> produce covariance in 4-space? Is that established or a mathematical 
>> speculation? TIA, AG *
>>
>>
>> That's looking at it the wrong way around.  Anything that transforms 
>> as an object in space, must be representable by tensors. The informal 
>> definition of a tensor is something that transforms like an object, i.e. 
>> in 
>> three space it's something that has a location and an orientation and 
>> three 
>> extensions.  Something that doesn't transform as a tensor under 
>> coordinate 
>> system changes is something that depends on the arbitrary choice of 
>> coordinate system and so cannot be a fundamental physical object.
>>
>> Brent
>>
>
> 1) Is it correct to say that tensors in E's field equations can be 
> represented as 4x4 matrices which have different representations 
> depending 
> on the coordinate system being used, but represent the same object? 
>
>
> That's right as far as it goes.   Tensors can be of any order.  The 
> curvature tensor is 4x4x4x4.
>
> 2) In SR we use the LT to transform from one* non-accelerating* frame 
> to another. In GR, what is the transformation for going from one 
> *accelerating* frame to another? 
>
>
> The Lorentz transform, but only in a local patch.
>

 *That's what I thought you would say. But how does this advance 
 Einstein's presumed project of finding how the laws of physics are 
 invariant for accelerating frames? How did it morph into a theory of 
 gravity? TIA, AG *

>>>
>>> *Or suppose, using GR, that two frames are NOT within the same local 
>>> patch.  If we can't use the LT, how can we transform from one frame to the 
>>> other? TIA, AG *
>>>
>>> *Or suppose we have two arbitrary accelerating frames, again NOT within 
>>> the same local patch, is it true that Maxwell's Equations are covariant 
>>> under some transformation, and what is that transformation? TIA, AG*
>>>
>>
>>
>> *I think I can simplify my issue here, if indeed there is an issue: did 
>> Einstein, or anyone, ever prove what I will call the General Principle of 
>> Relativity, namely that the laws of physics are invariant for accelerating 
>> frames? If the answer is affirmative, is there a transformation equation 
>> for Maxwell's Equations which leaves them unchanged for arbitrary 
>> accelerating frames? TIA, AG *
>>
>>
>> Your question isn't clear.  If you're simply asking about the equations 
>> describing physics* as expressed* in an accelerating (e.g. rotating) 
>> reference frame, that's pretty trivial.  You write the equations in 
>> whatever reference frame is convenient (usually an inertial one) and then 
>> transform the coordinates to the accelerated frame coordinates.   But if 
>> you're asking about what equations describe some physical system while it 
>> is being accelerated as compared to it not being accelerated, that's more 
>> complicated. 
>>
>
> *Thanks, but I wasn't referring to either of those cases; rather, the case 
> of transforming from one accelerating frame to another accelerating frame, 
> and whether the laws of physics are invariant. *
>
>
> For simplicity consider just flat Minkowski space time.  If you know the 
> motion of a particle in reference frame, whether the reference frame is 
> accelerated or not, you can determine its motion in any other reference 
> frame.  As for the particle path through spacetime, that's just some 
> geometric path and you're changing from describing it in one coordinate 
> system to describing it in another system...no physics is changing, just 
> the description.  If the reference frames are accelerated you get extra 
> terms in this description, like "centrifugal acceleration" which are just 
> artifacts of the frame choice. This is the same as in Newtonian mechanics.  
>
> But if the particle is actually accelerated, then there may be more to the 
> problem than just it's world line through spacetime.  For example, if the 
> particle has an electric charge, then it will radiate when accelerated and 
> there will be a 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 6, 2019 at 7:18:04 AM UTC-7, John Clark wrote:
>
>
> On Wed, Mar 6, 2019 at 1:02 AM > wrote:
>
> *> did Einstein, or anyone, ever prove what I will call the General 
>> Principle of Relativity, namely that the laws of physics are invariant for 
>> accelerating frames? If the answer is affirmative, is there a 
>> transformation equation for Maxwell's Equations which leaves them unchanged 
>> for arbitrary accelerating frames? *
>
>
> Mathematicians prove things Physicists don't, they find theories that are 
> less wrong than previous ideas, but Maxwell's original equations already 
> did what you ask for, 
>

*I don't think so. ME's are invariant under the LT. AFAIK, this applies to 
inertial frames, not accelerating frames, which is what I was asking about. 
AG*
  

> they enabled you to calculate the speed of light and they indicated the 
> speed was the same for any reference frame.  In fact this was the reason 
> Einstein suspected Newtonian physics didn't tell the entire story and is 
> why he started working on Relativity in the first place. Maxwell needs 
> modification to be consistent with Quantum Mechanics but with Special or 
> General Relativity no change is required.
>
>  John K Clark
>
>

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Re: Are there real numbers that cannot be defined?

[agrayson2000]

On Monday, March 4, 2019 at 3:35:55 AM UTC-7, Lawrence Crowell wrote:
>
> On Saturday, March 2, 2019 at 8:28:01 PM UTC-6, John Clark wrote:
>>
>>
>> On Fri, Mar 1, 2019 at 4:23 PM Lawrence Crowell  
>> wrote:
>>
>> > There are numbers that have no description in a practical sense. The 
>>> numbers 10^{10^{10^{10}}} and 10^{10^{10^{10^{10 have a vast number of 
>>> numbers that have no description with any information theoretic sense.
>>>
>>
>> The 8000th Busy Beaver Number can be named but not calculated even 
>> theoretically, but most Real Numbers can't even be uniquely named with 
>> ASCII characters, not even with an infinite number of them.   
>>
>> John K Clark
>>
>
> There exists an uncountably infinite number of reals in the interval (0, 
> 1), and they exhaust all possible information theoretic description. Some 
> mathematicians have argued this means they do not in some ways exist. Most 
> mathematicians disagree with that by arguing computational tractability is 
> not equivalent to mathematical existence. 
>

FWIW, that's my view. Since there's no way to describe irrational numbers, 
with a few exceptions such as pi and e, one can prove they exist, but 
they're impossible to calculate. AG 

>
> LC 
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 6, 2019 at 1:03:16 AM UTC-7, Brent wrote:
>
>
>
> On 3/5/2019 10:02 PM, agrays...@gmail.com  wrote:
>
>
>
> On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agray...@gmail.com wrote: 
>>>
>>>
>>>
>>> On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote: 



 On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:



 On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote: 
>
>
>
> On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:
>
> *Are you assuming uniqueness to tensors; that only tensors can produce 
> covariance in 4-space? Is that established or a mathematical speculation? 
> TIA, AG *
>
>
> That's looking at it the wrong way around.  Anything that transforms 
> as an object in space, must be representable by tensors. The informal 
> definition of a tensor is something that transforms like an object, i.e. 
> in 
> three space it's something that has a location and an orientation and 
> three 
> extensions.  Something that doesn't transform as a tensor under 
> coordinate 
> system changes is something that depends on the arbitrary choice of 
> coordinate system and so cannot be a fundamental physical object.
>
> Brent
>

 1) Is it correct to say that tensors in E's field equations can be 
 represented as 4x4 matrices which have different representations depending 
 on the coordinate system being used, but represent the same object? 


 That's right as far as it goes.   Tensors can be of any order.  The 
 curvature tensor is 4x4x4x4.

 2) In SR we use the LT to transform from one* non-accelerating* frame 
 to another. In GR, what is the transformation for going from one 
 *accelerating* frame to another? 


 The Lorentz transform, but only in a local patch.

>>>
>>> *That's what I thought you would say. But how does this advance 
>>> Einstein's presumed project of finding how the laws of physics are 
>>> invariant for accelerating frames? How did it morph into a theory of 
>>> gravity? TIA, AG *
>>>
>>
>> *Or suppose, using GR, that two frames are NOT within the same local 
>> patch.  If we can't use the LT, how can we transform from one frame to the 
>> other? TIA, AG *
>>
>> *Or suppose we have two arbitrary accelerating frames, again NOT within 
>> the same local patch, is it true that Maxwell's Equations are covariant 
>> under some transformation, and what is that transformation? TIA, AG*
>>
>
>
> *I think I can simplify my issue here, if indeed there is an issue: did 
> Einstein, or anyone, ever prove what I will call the General Principle of 
> Relativity, namely that the laws of physics are invariant for accelerating 
> frames? If the answer is affirmative, is there a transformation equation 
> for Maxwell's Equations which leaves them unchanged for arbitrary 
> accelerating frames? TIA, AG *
>
>
> Your question isn't clear.  If you're simply asking about the equations 
> describing physics* as expressed* in an accelerating (e.g. rotating) 
> reference frame, that's pretty trivial.  You write the equations in 
> whatever reference frame is convenient (usually an inertial one) and then 
> transform the coordinates to the accelerated frame coordinates.   But if 
> you're asking about what equations describe some physical system while it 
> is being accelerated as compared to it not being accelerated, that's more 
> complicated. 
>

*Thanks, but I wasn't referring to either of those cases; rather, the case 
of transforming from one accelerating frame to another accelerating frame, 
and whether the laws of physics are invariant. Here the "laws" could be ME 
or Mechanics. It seem as if GR is a special case for gravity, but I was 
asking whether invariance, or covariance, has been generally established. 
Also, if the LT works locally in GR, how do we transform between non-local 
frames? TIA, AG*
 

> Maxwell's equations apply to the description of the EM field of an 
> accelerating charged particle and show that the particle loses energy to an 
> EM wave, but how the particle interacts with it's own field when 
> accelerated produces unrealistic results which were superceded by quantum 
> field theory.  Bill Unruh showed that the accelerated system interacts with 
> the vacuum as though the vacuum is hot.  
>
> Brent
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, agrays...@gmail.com wrote:
>
>
>
> On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote:
>>>
>>>
>>>
>>> On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote: 



 On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:

 *Are you assuming uniqueness to tensors; that only tensors can produce 
 covariance in 4-space? Is that established or a mathematical speculation? 
 TIA, AG *


 That's looking at it the wrong way around.  Anything that transforms as 
 an object in space, must be representable by tensors. The informal 
 definition of a tensor is something that transforms like an object, i.e. 
 in 
 three space it's something that has a location and an orientation and 
 three 
 extensions.  Something that doesn't transform as a tensor under coordinate 
 system changes is something that depends on the arbitrary choice of 
 coordinate system and so cannot be a fundamental physical object.

 Brent

>>>
>>> 1) Is it correct to say that tensors in E's field equations can be 
>>> represented as 4x4 matrices which have different representations depending 
>>> on the coordinate system being used, but represent the same object? 
>>>
>>>
>>> That's right as far as it goes.   Tensors can be of any order.  The 
>>> curvature tensor is 4x4x4x4.
>>>
>>> 2) In SR we use the LT to transform from one* non-accelerating* frame 
>>> to another. In GR, what is the transformation for going from one 
>>> *accelerating* frame to another? 
>>>
>>>
>>> The Lorentz transform, but only in a local patch.
>>>
>>
>> *That's what I thought you would say. But how does this advance 
>> Einstein's presumed project of finding how the laws of physics are 
>> invariant for accelerating frames? How did it morph into a theory of 
>> gravity? TIA, AG *
>>
>
> *Or suppose, using GR, that two frames are NOT within the same local 
> patch.  If we can't use the LT, how can we transform from one frame to the 
> other? TIA, AG *
>
> *Or suppose we have two arbitrary accelerating frames, again NOT within 
> the same local patch, is it true that Maxwell's Equations are covariant 
> under some transformation, and what is that transformation? TIA, AG*
>

*I think I can simplify my issue here, if indeed there is an issue: did 
Einstein, or anyone, ever prove what I will call the General Principle of 
Relativity, namely that the laws of physics are invariant for accelerating 
frames? If the answer is affirmative, is there a transformation equation 
for Maxwell's Equations which leaves them unchanged for arbitrary 
accelerating frames? TIA, AG *

>
>>> Brent
>>>
>>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agrays...@gmail.com wrote:
>
>
>
> On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote:
>>
>>
>>
>> On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:
>>>
>>> *Are you assuming uniqueness to tensors; that only tensors can produce 
>>> covariance in 4-space? Is that established or a mathematical speculation? 
>>> TIA, AG *
>>>
>>>
>>> That's looking at it the wrong way around.  Anything that transforms as 
>>> an object in space, must be representable by tensors. The informal 
>>> definition of a tensor is something that transforms like an object, i.e. in 
>>> three space it's something that has a location and an orientation and three 
>>> extensions.  Something that doesn't transform as a tensor under coordinate 
>>> system changes is something that depends on the arbitrary choice of 
>>> coordinate system and so cannot be a fundamental physical object.
>>>
>>> Brent
>>>
>>
>> 1) Is it correct to say that tensors in E's field equations can be 
>> represented as 4x4 matrices which have different representations depending 
>> on the coordinate system being used, but represent the same object? 
>>
>>
>> That's right as far as it goes.   Tensors can be of any order.  The 
>> curvature tensor is 4x4x4x4.
>>
>> 2) In SR we use the LT to transform from one* non-accelerating* frame to 
>> another. In GR, what is the transformation for going from one 
>> *accelerating* frame to another? 
>>
>>
>> The Lorentz transform, but only in a local patch.
>>
>
> *That's what I thought you would say. But how does this advance Einstein's 
> presumed project of finding how the laws of physics are invariant for 
> accelerating frames? How did it morph into a theory of gravity? TIA, AG *
>

*Or suppose, using GR, that two frames are NOT within the same local 
patch.  If we can't use the LT, how can we transform from one frame to the 
other? TIA, AG *

*Or suppose we have two arbitrary accelerating frames, again NOT within the 
same local patch, is it true that Maxwell's Equations are covariant under 
some transformation, and what is that transformation? TIA, AG*

>
>> Brent
>>
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote:
>
>
>
> On 2/28/2019 4:07 AM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:
>>
>> *Are you assuming uniqueness to tensors; that only tensors can produce 
>> covariance in 4-space? Is that established or a mathematical speculation? 
>> TIA, AG *
>>
>>
>> That's looking at it the wrong way around.  Anything that transforms as 
>> an object in space, must be representable by tensors. The informal 
>> definition of a tensor is something that transforms like an object, i.e. in 
>> three space it's something that has a location and an orientation and three 
>> extensions.  Something that doesn't transform as a tensor under coordinate 
>> system changes is something that depends on the arbitrary choice of 
>> coordinate system and so cannot be a fundamental physical object.
>>
>> Brent
>>
>
> 1) Is it correct to say that tensors in E's field equations can be 
> represented as 4x4 matrices which have different representations depending 
> on the coordinate system being used, but represent the same object? 
>
>
> That's right as far as it goes.   Tensors can be of any order.  The 
> curvature tensor is 4x4x4x4.
>
> 2) In SR we use the LT to transform from one* non-accelerating* frame to 
> another. In GR, what is the transformation for going from one 
> *accelerating* frame to another? 
>
>
> The Lorentz transform, but only in a local patch.
>

*That's what I thought you would say. But how does this advance Einstein's 
presumed project of finding how the laws of physics are invariant for 
accelerating frames? How did it morph into a theory of gravity? TIA, AG *

>
> Brent
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote:
>
>
>
> On 2/27/2019 4:58 PM, agrays...@gmail.com  wrote:
>
> *Are you assuming uniqueness to tensors; that only tensors can produce 
> covariance in 4-space? Is that established or a mathematical speculation? 
> TIA, AG *
>
>
> That's looking at it the wrong way around.  Anything that transforms as an 
> object in space, must be representable by tensors. The informal definition 
> of a tensor is something that transforms like an object, i.e. in three 
> space it's something that has a location and an orientation and three 
> extensions.  Something that doesn't transform as a tensor under coordinate 
> system changes is something that depends on the arbitrary choice of 
> coordinate system and so cannot be a fundamental physical object.
>
> Brent
>

1) Is it correct to say that tensors in E's field equations can be 
represented as 4x4 matrices which have different representations depending 
on the coordinate system being used, but represent the same object? 
2) In SR we use the LT to transform from one* non-accelerating* frame to 
another. In GR, what is the transformation for going from one *accelerating* 
frame to another? 
AG

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Re: Recommend this article, Even just for the Wheeler quote near the end

[agrayson2000]

On Wednesday, February 13, 2019 at 9:40:32 PM UTC-7, cdemorsella wrote:
>
> Two fascinating (and very different) approaches are presented to derive 
> Quantim Mechanics main practical tool (e.g. Born's rule). Wonder what some 
> of the physicists on here think about this research?
>
> I find the argument that no laws is the fundamental law... and that the 
> universe and its laws are emergent guided by subtle mathematical 
> statistical phenomena, at the same time both alluring and annoying it 
> is somehow unsatisfactory like being served a quite empty plate with 
> nice garnish for dinner.
>
> One example of emergence from chaotic conditions is how traffic jams (aka 
> density waves) can emerge from chaotic initial conditions, becoming self 
> re-enforcing within local domains of influence... for those unlucky to be 
> stuck in them. Density wave emergence is seen across scale, for example the 
> spiral arms of galaxies can be explained as giant gravitational pile ups 
> with some fundamentally similar parallels to say a rush hour traffic jam, 
> except on vastly different scales of course and due to other different 
> factors, in the galactic case the emergent effects of a vast number of 
> gravitational inter-actions as stars migrate through these arms on their 
> grand voyages around the galactic core.
>
> This paired with the corollary argument that any attempt to discover a 
> fundamental law seems doomed to the infinite regression of then needing to 
> explain what this foundation itself rests upon leading to the "it's 
> turtles all the way down" hall of mirrors carnival house... head-banger. 
>
> Perhaps, as Wheeler argued, the world is a self-synthesizing system, and 
> the seeming order we observe, is emergent... a law without law.
>
> Here is the link to the article:
>
>
>
> The Born Rule Has Been Derived From Simple Physical Principles | Quanta 
> Magazine 
> 
> The Born Rule Has Been Derived From Simple Physical Principles | Quanta 
> Magazine 
>
> The new work promises to give researchers a better grip on the core 
> mystery of quantum mechanics.
>
> 
>  
>
>  

> *Is there consensus that Born's rule can be, and has been derived from 
> physical principles, and/or the other postulates of QM? TIA, AG*
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, February 24, 2019 at 4:49:45 PM UTC-7, Lawrence Crowell wrote:
>
> On Sunday, February 24, 2019 at 5:31:35 PM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Sunday, February 24, 2019 at 6:41:00 AM UTC-7, Lawrence Crowell wrote:
>>>
>>> On Friday, February 22, 2019 at 4:40:31 PM UTC-6, agrays...@gmail.com 
>>> wrote:



 On Friday, February 22, 2019 at 1:34:31 PM UTC-7, Brent wrote:
>
>
>
> On 2/21/2019 10:47 PM, agrays...@gmail.com wrote:
>
>
>>
> *Even if gravitons are detected, and they account for "force" 
> consistent with the other three forces, wouldn't there remain the task of 
> changing the form of gravity to make it covariant? AG*
>
>
> Gravitons, as quanta of the metric field, are already relativistic 
> particles and covariant.
>

 *I thought it's the equations of motion for the particular force, not 
 the mediating particles, that must be covariant. On a related topic for 
 this thread, where does GR depart from Mach's principle? That is, what did 
 Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG *

>
> *Would that require tensors? AG*
>
>
>>> General relativity is covariant, and curvature is expressed according to 
>>> Riemann tensors. 
>>>
>>> LC
>>>
>>
>> *Thanks, but I think you missed the thrust of my question; namely, if a 
>> theory using gravitons is independent of GR, since it would have to be 
>> covariant, could that be done without tenors, or are tensors nevertheless 
>> necessary.  AG*
>>
>
> Tensors transform homogeneously with the Lorentz group and are thus 
> covariant. Yep you need tensors. 
>
> LC 
>

*Are you assuming uniqueness to tensors; that only tensors can produce 
covariance in 4-space? Is that established or a mathematical speculation? 
TIA, AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, February 24, 2019 at 6:52:50 AM UTC-7, Philip Thrift wrote:
>
>
>
> On Saturday, February 23, 2019 at 6:04:15 PM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Saturday, February 23, 2019 at 6:53:09 AM UTC-7, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Saturday, February 23, 2019 at 7:25:21 AM UTC-6, John Clark wrote:

 On Fri, Feb 22, 2019 at 11:08 PM  wrote:

 > *In GR, the paths are determined by geometry in the absence of 
> forces, not by mediating particles.*


 Yes, that's because General Relativity is a classical theory that is 
 not quantized, it has so far passed every experimental test posed to it 
 with flying colors but we know it can't be entirely correct because when 
 we 
 ask it what happens when things become very small and very massive, such 
 as 
 in the center of Black Holes, it gives the absurd answer of infinity. 
 Neither Quantum Mechanics or General Relativity works when things get 
 massive and small, perhaps quantizing General Relativity will fix this or 
 maybe there is some other way to do so. Nobody knows.

  > *I could be mistaken, but I see gravitons as being part of a 
> distinct theory of gravity, which might give the same results as GR,*

  
 Nobody has ever experimentally detected a graviton and it's extremely 
 unlikely anybody ever will, so if they make the same predictions as 
 standard General Relativity there would be no point in introducing the 
 idea. 

  John K Clark


>>>
>>> If all experiments proposed to determine if gravity is quantized* fail*
>>>
>>>  Such measurements, they say, could enable them to uncover the quantum 
>>> nature of gravity and determine whether or not gravity is quantized.
>>>
>>>
>>>
>>> https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.122.071101
>>>
>>>
>>> that is: the search for a quantized gravity is a wild goose chase
>>>
>>> what do theorists do then?
>>>
>>> (I asked Hossenfelder. No answer.)
>>>
>>> - pt 
>>>
>>
>> *The article you cite indicates increasing hypothetical sensitivity for 
>> measuring gravity for tiny effects. If gravity can be quantized, what 
>> exactly would be quantized? Bruce says that gravity waves would involve 
>> gravitons under a quantized theory. Is that all? AG *
>>
>
>
>
>
> I suppose it needs to defined *what an experiment would be* that would 
> determine that gravity is quantized in a measurable way.
>
> Theories disconnected from experiments are mere math games.
>

*A good theory gives pointers on what to measure and how. AG *

>
> - pt
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, February 24, 2019 at 6:41:00 AM UTC-7, Lawrence Crowell wrote:
>
> On Friday, February 22, 2019 at 4:40:31 PM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Friday, February 22, 2019 at 1:34:31 PM UTC-7, Brent wrote:
>>>
>>>
>>>
>>> On 2/21/2019 10:47 PM, agrays...@gmail.com wrote:
>>>
>>>

>>> *Even if gravitons are detected, and they account for "force" consistent 
>>> with the other three forces, wouldn't there remain the task of changing the 
>>> form of gravity to make it covariant? AG*
>>>
>>>
>>> Gravitons, as quanta of the metric field, are already relativistic 
>>> particles and covariant.
>>>
>>
>> *I thought it's the equations of motion for the particular force, not the 
>> mediating particles, that must be covariant. On a related topic for this 
>> thread, where does GR depart from Mach's principle? That is, what did 
>> Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG *
>>
>>>
>>> *Would that require tensors? AG*
>>>
>>>
> General relativity is covariant, and curvature is expressed according to 
> Riemann tensors. 
>
> LC
>

*Thanks, but I think you missed the thrust of my question; namely, if a 
theory using gravitons is independent of GR, since it would have to be 
covariant, could that be done without tenors, or are tensors nevertheless 
necessary.  AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Saturday, February 23, 2019 at 6:53:09 AM UTC-7, Philip Thrift wrote:
>
>
>
> On Saturday, February 23, 2019 at 7:25:21 AM UTC-6, John Clark wrote:
>>
>> On Fri, Feb 22, 2019 at 11:08 PM  wrote:
>>
>> > *In GR, the paths are determined by geometry in the absence of forces, 
>>> not by mediating particles.*
>>
>>
>> Yes, that's because General Relativity is a classical theory that is not 
>> quantized, it has so far passed every experimental test posed to it with 
>> flying colors but we know it can't be entirely correct because when we ask 
>> it what happens when things become very small and very massive, such as in 
>> the center of Black Holes, it gives the absurd answer of infinity. Neither 
>> Quantum Mechanics or General Relativity works when things get massive and 
>> small, perhaps quantizing General Relativity will fix this or maybe there 
>> is some other way to do so. Nobody knows.
>>
>>  > *I could be mistaken, but I see gravitons as being part of a distinct 
>>> theory of gravity, which might give the same results as GR,*
>>
>>  
>> Nobody has ever experimentally detected a graviton and it's extremely 
>> unlikely anybody ever will, so if they make the same predictions as 
>> standard General Relativity there would be no point in introducing the 
>> idea. 
>>
>>  John K Clark
>>
>>
>
> If all experiments proposed to determine if gravity is quantized* fail*
>
>  Such measurements, they say, could enable them to uncover the quantum 
> nature of gravity and determine whether or not gravity is quantized.
>
>
>
> https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.122.071101
>
>
> that is: the search for a quantized gravity is a wild goose chase
>
> what do theorists do then?
>
> (I asked Hossenfelder. No answer.)
>
> - pt 
>

*The article you cite indicates increasing hypothetical sensitivity for 
measuring gravity for tiny effects. If gravity can be quantized, what 
exactly would be quantized? Bruce says that gravity waves would involve 
gravitons under a quantized theory. Is that all? AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Friday, February 22, 2019 at 9:12:02 PM UTC-7, Bruce wrote:
>
> On Sat, Feb 23, 2019 at 3:08 PM > wrote:
>
>> On Friday, February 22, 2019 at 8:13:21 PM UTC-7, Brent wrote:
>>>
>>> On 2/22/2019 6:04 PM, agrays...@gmail.com wrote:
>>>
>>> On Friday, February 22, 2019 at 4:55:41 PM UTC-7, Brent wrote: 



 On 2/22/2019 2:40 PM, agrays...@gmail.com wrote:

 Gravitons, as quanta of the metric field, are already relativistic 
> particles and covariant.
>

 *I thought it's the equations of motion for the particular force, not 
 the mediating particles, that must be covariant. On a related topic for 
 this thread, where does GR depart from Mach's principle? That is, what did 
 Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG *


 Einstein thought he would develop a theory that satisfied Mach's 
 principle, but as it turned out GR doesn't. For example the metric of 
 spacetime is a dynamic field and transmit momentum and energy, as shown by 
 LIGO.  Mach's idea of spacetime as purely a relation between material 
 events couldn't do that.

 Brent

>>>
>>> *Were you inferring covariance simply because the mediating particle for 
>>> gravity, the graviton, travels at the SoL? *
>>>
>>>
>>> GR is a covariant theory.  So it's quanta, gravitons, are covariant.
>>>
>>
>> *I could be mistaken, but I see gravitons as being part of a distinct 
>> theory of gravity, which might give the same results as GR. In GR, the 
>> paths are determined by geometry in the absence of forces, not by mediating 
>> particles. AG *
>>
>
> GR, as a theory, implies the existence of gravity waves. Wave, when 
> quantised, give particles: these are the gravitons of the theory. Exchange 
> of such gravitons does not necessarily have anything to do with the forces 
> in the theory, or the formation of geodesics.
>
> Bruce 
>

*Very clarifying. Then, since gravitational waves have been detected, it 
must be that gravitons exist, but too low in energy to be detected. AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Friday, February 22, 2019 at 8:13:21 PM UTC-7, Brent wrote:
>
>
>
> On 2/22/2019 6:04 PM, agrays...@gmail.com  wrote:
>
>
>
> On Friday, February 22, 2019 at 4:55:41 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 2/22/2019 2:40 PM, agrays...@gmail.com wrote:
>>
>> Gravitons, as quanta of the metric field, are already relativistic 
>>> particles and covariant.
>>>
>>
>> *I thought it's the equations of motion for the particular force, not the 
>> mediating particles, that must be covariant. On a related topic for this 
>> thread, where does GR depart from Mach's principle? That is, what did 
>> Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG *
>>
>>
>> Einstein thought he would develop a theory that satisfied Mach's 
>> principle, but as it turned out GR doesn't. For example the metric of 
>> spacetime is a dynamic field and transmit momentum and energy, as shown by 
>> LIGO.  Mach's idea of spacetime as purely a relation between material 
>> events couldn't do that.
>>
>> Brent
>>
>
> *Were you inferring covariance simply because the mediating particle for 
> gravity, the graviton, travels at the SoL? *
>
>
> GR is a covariant theory.  So it's quanta, gravitons, are covariant.
>

*I could be mistaken, but I see gravitons as being part of a distinct 
theory of gravity, which might give the same results as GR. In GR, the 
paths are determined by geometry in the absence of forces, not by mediating 
particles. AG *

>
> *I thought it's the equations of motion for the particular force, not the 
> mediating particles, that must be covariant.  Do we have equations of 
> motions for strong and weak forces, which are covariant? AG*
>
>
> Forces are mediated by exchange of bosons.  Those bosons appear in the 
> Standard Model Lagrangian, from which equations of motion can be derived.
>
>
> https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model
>
> Brent
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Friday, February 22, 2019 at 4:55:41 PM UTC-7, Brent wrote:
>
>
>
> On 2/22/2019 2:40 PM, agrays...@gmail.com  wrote:
>
> Gravitons, as quanta of the metric field, are already relativistic 
>> particles and covariant.
>>
>
> *I thought it's the equations of motion for the particular force, not the 
> mediating particles, that must be covariant. On a related topic for this 
> thread, where does GR depart from Mach's principle? That is, what did 
> Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG *
>
>
> Einstein thought he would develop a theory that satisfied Mach's 
> principle, but as it turned out GR doesn't. For example the metric of 
> spacetime is a dynamic field and transmit momentum and energy, as shown by 
> LIGO.  Mach's idea of spacetime as purely a relation between material 
> events couldn't do that.
>
> Brent
>

*Were you inferring covariance simply because the mediating particle for 
gravity, the graviton, travels at the SoL? I thought it's the equations of 
motion for the particular force, not the mediating particles, that must be 
covariant.  Do we have equations of motions for strong and weak forces, 
which are covariant? AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Friday, February 22, 2019 at 1:34:31 PM UTC-7, Brent wrote:
>
>
>
> On 2/21/2019 10:47 PM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, February 21, 2019 at 8:38:12 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 2/21/2019 4:05 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, February 21, 2019 at 1:35:17 PM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 2/21/2019 5:27 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, February 20, 2019 at 7:50:51 PM UTC-7, Brent wrote: 



 On 2/20/2019 1:23 PM, agrays...@gmail.com wrote:



 On Wednesday, February 20, 2019 at 12:16:31 PM UTC-7, Brent wrote: 
>
>
>
> On 2/20/2019 8:42 AM, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote: 
>>
>>
>> >* Newton "explained" *
>>
>>
>> Why did you put explained in quotation marks? If you can predict what 
>> something is going to do then you've explained it, the better the 
>> prediction the better the explanation. I don't know what else the word 
>> could possibly mean. And in science no explanation is perfect, but some 
>> are 
>> less wrong than others.
>>
>
> *QM better illustrates the justification for quotes. Many 
> interpretations that make the same predictions. AG *
>
>>
>> *> why a body at "rest" can start moving, via the application of 
>>> "force"*
>>
>>
>> And Einstein explained that a body moving in a geodesic through 4D 
>> spacetime will take a path that is not a geodesic if a force is applied. 
>> The Earth is moving in a straight line (aka a geodesic) through curved 
>> spacetime; the reason Earth's orbit looks elliptical to us is due to map 
>> distortion, the same reason that in a flat map of the curved surface of 
>> the 
>> Earth Greenland looks larger than South America and is almost as large 
>> as 
>> Africa. Except that it's even worse, in one we're projecting the 2 D 
>> curved surface of the Earth into the flat 2D surface of the map, but 
>> with 
>> Einstein we're projecting a curved 4D volume into a flat 3D volume. 
>>
>> *> What does "rest" mean in GR *
>>
>>
>> In General Relativity moving in a geodesic is as close as you can 
>> get to the traditional idea of rest, but as long as time passes you're 
>> going to be moving through 4D spacetime.
>>
>
>
> *If you're at spatial rest in spacetime in the presence of a 
> gravitational source, how does GR explain the subsequent spatial motion? 
> AG 
> *
>
>
> When you were at "spatial rest" you had a force applied to you.  
> Removing it allowed you to follow a geodesics path through 
> spacetimealso known as "falling".
>
> Brent
>
>

 *So it seems that GR doesn't explain motion; rather, it assumes motion 
 is a natural state of things. AG *


 So called "standing still" is just motion in the time direction 
 only...in Newtonian and special relativity as well. Just as there is no 
 absolute motion, there's no absolution motionless either...it's called 
 "relativity" for a reason.

 Brent

>>>
>>>
>>> *Other than gravity, the remaining known forces are moderated, or shall 
>>> we say "caused by" particles. Doesn't GR remain an exception; that is, 
>>> wouldn't it preclude the existence of a graviton? TIA, AG *
>>>
>>>
>>> Gravitons, the weak-field limit quanta of the gravitational field, 
>>> aren't precluded.  They are implicit in string-theory; which is why string 
>>> theory is a candidate for the quantum theory of gravity.  The problem is 
>>> there's no mathematically consistent way to extend the graviton, weak 
>>> field, picture to the strong field limit and predict what happens in a 
>>> black hole where GR predicts a singularity.
>>>
>>> Brent
>>>
>>
>> *ISTM that gravitons would be inconsistent with GR, which derives 
>> gravitating motion from geometry, not mediating particles.  AG*
>>
>>
>> It is conceptually inconsistent, just as GR is conceptually inconsistent 
>> with Newtonian gravity.  But that doesn't mean the theories make detectably 
>> different predictions in the domain where we can test them.  Notice how 
>> difficult it was to test GR vs Newton.
>>
>> Brent
>>
>
> *Even if gravitons are detected, and they account for "force" consistent 
> with the other three forces, wouldn't there remain the task of changing the 
> form of gravity to make it covariant? AG*
>
>
> Gravitons, as quanta of the metric field, are already relativistic 
> particles and covariant.
>

*I thought it's the equations of motion for the particular force, not the 
mediating particles, that must be covariant. On a related topic for this 
thread, where does GR depart from Mach's principle? That is, what did 
Einstein implicitly (or explicitly) deny about Mach's 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, February 21, 2019 at 8:38:12 PM UTC-7, Brent wrote:
>
>
>
> On 2/21/2019 4:05 PM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, February 21, 2019 at 1:35:17 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 2/21/2019 5:27 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, February 20, 2019 at 7:50:51 PM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 2/20/2019 1:23 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, February 20, 2019 at 12:16:31 PM UTC-7, Brent wrote: 



 On 2/20/2019 8:42 AM, agrays...@gmail.com wrote:



 On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote: 
>
>
> >* Newton "explained" *
>
>
> Why did you put explained in quotation marks? If you can predict what 
> something is going to do then you've explained it, the better the 
> prediction the better the explanation. I don't know what else the word 
> could possibly mean. And in science no explanation is perfect, but some 
> are 
> less wrong than others.
>

 *QM better illustrates the justification for quotes. Many 
 interpretations that make the same predictions. AG *

>
> *> why a body at "rest" can start moving, via the application of 
>> "force"*
>
>
> And Einstein explained that a body moving in a geodesic through 4D 
> spacetime will take a path that is not a geodesic if a force is applied. 
> The Earth is moving in a straight line (aka a geodesic) through curved 
> spacetime; the reason Earth's orbit looks elliptical to us is due to map 
> distortion, the same reason that in a flat map of the curved surface of 
> the 
> Earth Greenland looks larger than South America and is almost as large as 
> Africa. Except that it's even worse, in one we're projecting the 2 D 
> curved surface of the Earth into the flat 2D surface of the map, but with 
> Einstein we're projecting a curved 4D volume into a flat 3D volume. 
>
> *> What does "rest" mean in GR *
>
>
> In General Relativity moving in a geodesic is as close as you can get 
> to the traditional idea of rest, but as long as time passes you're going 
> to 
> be moving through 4D spacetime.
>


 *If you're at spatial rest in spacetime in the presence of a 
 gravitational source, how does GR explain the subsequent spatial motion? 
 AG 
 *


 When you were at "spatial rest" you had a force applied to you.  
 Removing it allowed you to follow a geodesics path through 
 spacetimealso known as "falling".

 Brent


>>>
>>> *So it seems that GR doesn't explain motion; rather, it assumes motion 
>>> is a natural state of things. AG *
>>>
>>>
>>> So called "standing still" is just motion in the time direction 
>>> only...in Newtonian and special relativity as well. Just as there is no 
>>> absolute motion, there's no absolution motionless either...it's called 
>>> "relativity" for a reason.
>>>
>>> Brent
>>>
>>
>>
>> *Other than gravity, the remaining known forces are moderated, or shall 
>> we say "caused by" particles. Doesn't GR remain an exception; that is, 
>> wouldn't it preclude the existence of a graviton? TIA, AG *
>>
>>
>> Gravitons, the weak-field limit quanta of the gravitational field, aren't 
>> precluded.  They are implicit in string-theory; which is why string theory 
>> is a candidate for the quantum theory of gravity.  The problem is there's 
>> no mathematically consistent way to extend the graviton, weak field, 
>> picture to the strong field limit and predict what happens in a black hole 
>> where GR predicts a singularity.
>>
>> Brent
>>
>
> *ISTM that gravitons would be inconsistent with GR, which derives 
> gravitating motion from geometry, not mediating particles.  AG*
>
>
> It is conceptually inconsistent, just as GR is conceptually inconsistent 
> with Newtonian gravity.  But that doesn't mean the theories make detectably 
> different predictions in the domain where we can test them.  Notice how 
> difficult it was to test GR vs Newton.
>
> Brent
>

*Even if gravitons are detected, and they account for "force" consistent 
with the other three forces, wouldn't there remain the task of changing the 
form of gravity to make it covariant? Would that require tensors? AG*

-- 
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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, February 21, 2019 at 1:35:17 PM UTC-7, Brent wrote:
>
>
>
> On 2/21/2019 5:27 AM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, February 20, 2019 at 7:50:51 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 2/20/2019 1:23 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, February 20, 2019 at 12:16:31 PM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 2/20/2019 8:42 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote: 


 >* Newton "explained" *


 Why did you put explained in quotation marks? If you can predict what 
 something is going to do then you've explained it, the better the 
 prediction the better the explanation. I don't know what else the word 
 could possibly mean. And in science no explanation is perfect, but some 
 are 
 less wrong than others.

>>>
>>> *QM better illustrates the justification for quotes. Many 
>>> interpretations that make the same predictions. AG *
>>>

 *> why a body at "rest" can start moving, via the application of 
> "force"*


 And Einstein explained that a body moving in a geodesic through 4D 
 spacetime will take a path that is not a geodesic if a force is applied. 
 The Earth is moving in a straight line (aka a geodesic) through curved 
 spacetime; the reason Earth's orbit looks elliptical to us is due to map 
 distortion, the same reason that in a flat map of the curved surface of 
 the 
 Earth Greenland looks larger than South America and is almost as large as 
 Africa. Except that it's even worse, in one we're projecting the 2 D 
 curved surface of the Earth into the flat 2D surface of the map, but with 
 Einstein we're projecting a curved 4D volume into a flat 3D volume. 

 *> What does "rest" mean in GR *


 In General Relativity moving in a geodesic is as close as you can get 
 to the traditional idea of rest, but as long as time passes you're going 
 to 
 be moving through 4D spacetime.

>>>
>>>
>>> *If you're at spatial rest in spacetime in the presence of a 
>>> gravitational source, how does GR explain the subsequent spatial motion? AG 
>>> *
>>>
>>>
>>> When you were at "spatial rest" you had a force applied to you.  
>>> Removing it allowed you to follow a geodesics path through 
>>> spacetimealso known as "falling".
>>>
>>> Brent
>>>
>>>
>>
>> *So it seems that GR doesn't explain motion; rather, it assumes motion is 
>> a natural state of things. AG *
>>
>>
>> So called "standing still" is just motion in the time direction only...in 
>> Newtonian and special relativity as well. Just as there is no absolute 
>> motion, there's no absolution motionless either...it's called "relativity" 
>> for a reason.
>>
>> Brent
>>
>
>
> *Other than gravity, the remaining known forces are moderated, or shall we 
> say "caused by" particles. Doesn't GR remain an exception; that is, 
> wouldn't it preclude the existence of a graviton? TIA, AG *
>
>
> Gravitons, the weak-field limit quanta of the gravitational field, aren't 
> precluded.  They are implicit in string-theory; which is why string theory 
> is a candidate for the quantum theory of gravity.  The problem is there's 
> no mathematically consistent way to extend the graviton, weak field, 
> picture to the strong field limit and predict what happens in a black hole 
> where GR predicts a singularity.
>
> Brent
>

*ISTM that gravitons would be inconsistent with GR, which derives 
gravitating motion from geometry, not mediating particles.  AG*

>
>
>
>>
>>
 *>  what causes "motion" from that pov?*


 Force, same as with Newton.

 John K Clark

>>> -- 
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>>>
>>>
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>>
>> -- 
> You received this message because you are subscribed to the Google Groups 
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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, February 20, 2019 at 7:50:51 PM UTC-7, Brent wrote:
>
>
>
> On 2/20/2019 1:23 PM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, February 20, 2019 at 12:16:31 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 2/20/2019 8:42 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote: 
>>>
>>>
>>> >* Newton "explained" *
>>>
>>>
>>> Why did you put explained in quotation marks? If you can predict what 
>>> something is going to do then you've explained it, the better the 
>>> prediction the better the explanation. I don't know what else the word 
>>> could possibly mean. And in science no explanation is perfect, but some are 
>>> less wrong than others.
>>>
>>
>> *QM better illustrates the justification for quotes. Many interpretations 
>> that make the same predictions. AG *
>>
>>>
>>> *> why a body at "rest" can start moving, via the application of "force"*
>>>
>>>
>>> And Einstein explained that a body moving in a geodesic through 4D 
>>> spacetime will take a path that is not a geodesic if a force is applied. 
>>> The Earth is moving in a straight line (aka a geodesic) through curved 
>>> spacetime; the reason Earth's orbit looks elliptical to us is due to map 
>>> distortion, the same reason that in a flat map of the curved surface of the 
>>> Earth Greenland looks larger than South America and is almost as large as 
>>> Africa. Except that it's even worse, in one we're projecting the 2 D 
>>> curved surface of the Earth into the flat 2D surface of the map, but with 
>>> Einstein we're projecting a curved 4D volume into a flat 3D volume. 
>>>
>>> *> What does "rest" mean in GR *
>>>
>>>
>>> In General Relativity moving in a geodesic is as close as you can get 
>>> to the traditional idea of rest, but as long as time passes you're going to 
>>> be moving through 4D spacetime.
>>>
>>
>>
>> *If you're at spatial rest in spacetime in the presence of a 
>> gravitational source, how does GR explain the subsequent spatial motion? AG 
>> *
>>
>>
>> When you were at "spatial rest" you had a force applied to you.  Removing 
>> it allowed you to follow a geodesics path through spacetimealso known 
>> as "falling".
>>
>> Brent
>>
>>
>
> *So it seems that GR doesn't explain motion; rather, it assumes motion is 
> a natural state of things. AG *
>
>
> So called "standing still" is just motion in the time direction only...in 
> Newtonian and special relativity as well. Just as there is no absolute 
> motion, there's no absolution motionless either...it's called "relativity" 
> for a reason.
>
> Brent
>

*Other than gravity, the remaining known forces are moderated, or shall we 
say "caused by" particles. Doesn't GR remain an exception; that is, 
wouldn't it preclude the existence of a graviton? TIA, AG *

>
>
>
>>> *>  what causes "motion" from that pov?*
>>>
>>>
>>> Force, same as with Newton.
>>>
>>> John K Clark
>>>
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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, February 20, 2019 at 12:16:31 PM UTC-7, Brent wrote:
>
>
>
> On 2/20/2019 8:42 AM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote: 
>>
>>
>> >* Newton "explained" *
>>
>>
>> Why did you put explained in quotation marks? If you can predict what 
>> something is going to do then you've explained it, the better the 
>> prediction the better the explanation. I don't know what else the word 
>> could possibly mean. And in science no explanation is perfect, but some are 
>> less wrong than others.
>>
>
> *QM better illustrates the justification for quotes. Many interpretations 
> that make the same predictions. AG *
>
>>
>> *> why a body at "rest" can start moving, via the application of "force"*
>>
>>
>> And Einstein explained that a body moving in a geodesic through 4D 
>> spacetime will take a path that is not a geodesic if a force is applied. 
>> The Earth is moving in a straight line (aka a geodesic) through curved 
>> spacetime; the reason Earth's orbit looks elliptical to us is due to map 
>> distortion, the same reason that in a flat map of the curved surface of the 
>> Earth Greenland looks larger than South America and is almost as large as 
>> Africa. Except that it's even worse, in one we're projecting the 2 D 
>> curved surface of the Earth into the flat 2D surface of the map, but with 
>> Einstein we're projecting a curved 4D volume into a flat 3D volume. 
>>
>> *> What does "rest" mean in GR *
>>
>>
>> In General Relativity moving in a geodesic is as close as you can get to 
>> the traditional idea of rest, but as long as time passes you're going to be 
>> moving through 4D spacetime.
>>
>
>
> *If you're at spatial rest in spacetime in the presence of a gravitational 
> source, how does GR explain the subsequent spatial motion? AG *
>
>
> When you were at "spatial rest" you had a force applied to you.  Removing 
> it allowed you to follow a geodesics path through spacetimealso known 
> as "falling".
>
> Brent
>
>
*So it seems that GR doesn't explain motion; rather, it assumes motion is a 
natural state of things. AG *

>
>> *>  what causes "motion" from that pov?*
>>
>>
>> Force, same as with Newton.
>>
>> John K Clark
>>
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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote:
>
>
> >* Newton "explained" *
>
>
> Why did you put explained in quotation marks? If you can predict what 
> something is going to do then you've explained it, the better the 
> prediction the better the explanation. I don't know what else the word 
> could possibly mean. And in science no explanation is perfect, but some are 
> less wrong than others.
>

*QM better illustrates the justification for quotes. Many interpretations 
that make the same predictions. AG *

>
> *> why a body at "rest" can start moving, via the application of "force"*
>
>
> And Einstein explained that a body moving in a geodesic through 4D 
> spacetime will take a path that is not a geodesic if a force is applied. 
> The Earth is moving in a straight line (aka a geodesic) through curved 
> spacetime; the reason Earth's orbit looks elliptical to us is due to map 
> distortion, the same reason that in a flat map of the curved surface of the 
> Earth Greenland looks larger than South America and is almost as large as 
> Africa. 
> Except that it's even worse, in one we're projecting the 2 D curved surface 
> of the Earth into the flat 2D surface of the map, but with Einstein we're 
> projecting a curved 4D volume into a flat 3D volume. 
>
> *> What does "rest" mean in GR *
>
>
> In General Relativity moving in a geodesic is as close as you can get to 
> the traditional idea of rest, but as long as time passes you're going to be 
> moving through 4D spacetime.
>

*If you're at spatial rest in spacetime in the presence of a gravitational 
source, how does GR explain the subsequent spatial motion? AG *

>
> *>  what causes "motion" from that pov?*
>
>
> Force, same as with Newton.
>
> John K Clark
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, February 20, 2019 at 12:30:01 AM UTC-7, Philip Thrift wrote:
>
>
>
> On Wednesday, February 20, 2019 at 1:06:25 AM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Tuesday, February 19, 2019 at 8:16:51 PM UTC-7, Brent wrote:
>>>
>>>
>>>
>>> On 2/19/2019 5:10 PM, agrays...@gmail.com wrote:
>>>
>>>
>>> *What you wrote makes no sense. It fails to explain why motion occurs in 
>>> the absence of force. AG *
>>>
>>>
>>> So did Newton: "A body in motion will remain in motion."
>>>
>>
>> *Right, but Newton "explained" why a body at "rest" can start moving, via 
>> the application of "force".  What does "rest" mean in GR and what causes 
>> "motion" from that pov? Incidentally, when I posed the question of why 
>> space and time must be fused in relativity. I didn't know the answer. I 
>> came to a partial explanation by posing the question. AG*
>>
>>>
>>>
>
> Physics doesn't really explain anything. It only creates expressions in 
> different mathematical dialects that we interpret.
>

*Right. That's why I put the quotes around *explained*. AG *

>
>
> https://www.newyorker.com/science/elements/a-different-kind-of-theory-of-everything
>  
>
>
> In 1964, during a lecture at Cornell University, the physicist Richard 
> Feynman articulated a profound mystery about the physical world. He told 
> his listeners to imagine two objects, each gravitationally attracted to the 
> other. How, he asked, should we predict their movements? Feynman identified 
> three approaches, each invoking a different belief about the world. The 
> first approach used Newton’s law of gravity, according to which the objects 
> exert a pull on each other. The second imagined a gravitational field 
> extending through space, which the objects distort. The third applied the 
> principle of least action, which holds that each object moves by following 
> the path that takes the least energy in the least time. All three 
> approaches produced the same, correct prediction. They were three equally 
> useful descriptions of how gravity works.
>

*Except that it's wrong to put Newton's gravity theory on the same level as 
Einstein's. Also, I think we can dispense with the Principle of Least 
Action and just use the geodesic hypothesis as a postulate of GR.  We could 
say that God preferred a unique path, the extremal, rather than having to 
choose among an uncountable set of paths for each path between distinct 
events in the manifold. AG*

>
> “One of the amazing characteristics of nature is this variety of 
> interpretational schemes,” Feynman said. ... “If you modify the laws much, 
> you find you can only write them in fewer ways,” Feynman said. “I always 
> found that mysterious, and I do not know the reason why it is that the 
> correct laws of physics are expressible in such a tremendous variety of 
> ways. They seem to be able to get through several wickets at the same time.”
>
> ...
>
> - pt
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, February 19, 2019 at 8:16:51 PM UTC-7, Brent wrote:
>
>
>
> On 2/19/2019 5:10 PM, agrays...@gmail.com  wrote:
>
>
> *What you wrote makes no sense. It fails to explain why motion occurs in 
> the absence of force. AG *
>
>
> So did Newton: "A body in motion will remain in motion."
>

*Right, but Newton "explained" why a body at "rest" can start moving, via 
the application of "force".  What does "rest" mean in GR and what causes 
"motion" from that pov? Incidentally, when I posed the question of why 
space and time must be fused in relativity. I didn't know the answer. I 
came to a partial explanation by posing the question. AG*

>
> Brent
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, February 19, 2019 at 2:50:42 PM UTC-7, John Clark wrote:
>
>
>
> On Tue, Feb 19, 2019 at 1:28 PM > wrote:
>
>>
>>
> >> If you want to meet me in Manhattan you're going to have to give me 4 
>>> numbers (aka dimensions); 2 of them will give me the street corner, another 
>>> one will tell me what floor to get off the elevator,  and the fourth will 
>>> give me the time of the meeting.
>>>
>>
>> *> You seem to have a firm grasp of the obvious. *
>>
>
> Is there any particular reason you always feel the need to be a dick even 
> to one who is trying his best to answer your questions?
>

*I apologize. I really do. But seriously, your explanation for merging 
space and time is hugely simplistic, and in fact not right. They have to be 
merged in order to create curvature in 4 dimensions. Otherwise, if only 
space is involved, we can't even define a Lorentzian metric. AG *

>  
>
>> *> Perhaps the reason space and time must be merged is for a much deeper 
>> reason; namely, only by merging them can we get a curvature of the result. 
>> AG  *
>>
>
>
> Talk about a firm grasp of the obvious!  You can't have a curve without 
> at least 2 dimensions.
>

*I explained at least one of the requirements for going to 4 dimensions. 
AG *

>
>  
>
>> *>> Also, why is it that Newton's law of gravity is not Lorentz 
 invariant, yet it seems to work in all inertial frames? TIA, AG *

>>>
>>> Newton's law of gravity only approximately works, although the 
>>> approximation is quite good provided the speeds involved are not too large 
>>> and the spacetime curvature (aka gravity) is not too great.  Newton's world 
>>> was not Lorentz invariant because there was no limit on how fast you could 
>>> go, so the laws of physics would look different depending on how fast you 
>>> were going; if you could move at the speed of light in a closed elevator 
>>> you could tell you were moving because a  beam of light would look frozen 
>>> in violation of Maxwell's Equations which says light always moves at the 
>>> same speed. Therefore if things are Lorentz invariant you can't move at the 
>>> speed of light in a closed elevator.
>>>
>>> By the way, when Maxwell came up with his theory some thought the one 
>>> flaw in the idea was that the speed of light that the theory produced with 
>>> did not say the speed relative to what. But Einstein realized that 
>>> Maxwell's greatest flaw was really his greatest triumph. 
>>>
>>
>> *> Can you cite any statement by Einstein to this effect? AG *
>>
>
> I could, but it would be obvious.
>  
>
>> >>Motion is how a change in time relates to a change in space,  if 
>>> spacetime is flat a given instance in time corresponds to a particular 
>>> point in space,  if spacetime is curved that same instance in time would 
>>> correspond to a different point in space.
>>>
>>
>> *> Please elaborate.*
>>
>
> No, why should I?
>  
>
>> * > I don't understand*
>>
>
> I'm not surprised.
>

*What you wrote makes no sense. It fails to explain why motion occurs in 
the absence of force. AG *

>
> John K Clark
>
>
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, February 19, 2019 at 6:41:52 AM UTC-7, John Clark wrote:
>
> On Mon, Feb 18, 2019 at 5:30 PM > wrote:
>
> *> Sure, but why does this obvious fact force us to merge space and time 
>> in one concept, aka a manifold?*
>>
>
> If you want to meet me in Manhattan you're going to have to give me 4 
> numbers (aka dimensions); 2 of them will give me the street corner, another 
> one will tell me what floor to get off the elevator,  and the fourth will 
> give me the time of the meeting.
>

*You seem to have a firm grasp of the obvious. Perhaps the reason space and 
time must be merged is for a much deeper reason; namely, only by merging 
them can we get a curvature of the result. AG  *

>  
>
>> *> Also, why is it that Newton's law of gravity is not Lorentz invariant, 
>> yet it seems to work in all inertial frames? TIA, AG *
>>
>
> Newton's law of gravity only approximately works, although the 
> approximation is quite good provided the speeds involved are not too large 
> and the spacetime curvature (aka gravity) is not too great.  Newton's world 
> was not Lorentz invariant because there was no limit on how fast you could 
> go, so the laws of physics would look different depending on how fast you 
> were going; if you could move at the speed of light in a closed elevator 
> you could tell you were moving because a  beam of light would look frozen 
> in violation of Maxwell's Equations which says light always moves at the 
> same speed. Therefore if things are Lorentz invariant you can't move at the 
> speed of light in a closed elevator.
>
> By the way, when Maxwell came up with his theory some thought the one flaw 
> in the idea was that the speed of light that the theory produced with did 
> not say the speed relative to what. But Einstein realized that Maxwell's 
> greatest flaw was really his greatest triumph. 
>

*Can you cite any statement by Einstein to this effect? AG *

>
>
> *> So how does GR explain motion? That is, how does curvature of 
>> space-time result in motion? AG*
>>
>
> Motion is how a change in time relates to a change in space,  if spacetime 
> is flat a given instance in time corresponds to a particular point in 
> space,  if spacetime is curved that same instance in time would correspond 
> to a different point in space.
>

*Please elaborate. I don't understand how curvature in itself produces 
accelerated motion. AG *

>
> *> What would baseball look like without that tiny curvature? AG *
>>
>
> Imagine a baseball game played on the International Space Station.
>

*It's strange that such a small change in curvature, produces such a hugely 
different result. AG *

>
> John K Clark
>
>

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