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

[Philip Thrift]

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.

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.

“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

[Brent Meeker]

On 2/19/2019 5:10 PM, agrayson2...@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."

Brent

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Advanced LIGO

[John Clark]

LIGO should get back online and start detecting gravitational waves again
in about a month after being upgraded, and now they're talking about the
upgrades that will come after that. By 2022 they expect to be able to
detect one Black Hole merger a month and by 2025 one per hour. The quality
of the observations will go up too, they'll be able to tell how fast the
holes were spinning even before they merged.

LIGO to spot one black-hole merger per hour



John K Clark

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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: When Did Consciousness Begin?

[Brent Meeker]

On 2/17/2019 2:10 AM, Bruno Marchal wrote:

But the machine itself will not believe us, or understand this.

Why not?  It can't prove what algorithm it is, but it can know that we 
know...so why would it disbelieve us.

Tha machine becomes inconsistent if it assumes its consistency (cf Rogers’s 
sentence). The machine can assume a sort of consistency of its past belief, 
like PA can add the axioms that PA is consistent, (or that PA is inconsistent) 
without losing its consistency, but in that case it becomes a new machine, with 
a similar theology in shape, but a different content/meaning for the box. She 
has changed her own code (as we do every second instinctively).


I think this is misleading.  When you say it becomes inconsistent if it 
assumes it's consistency, you mean that if it uses its consistency as an 
axiom it can lead to proving "false".   But in fact everyone assumes 
that their beliefs are consistent, they just don't take it as an axiom 
and neither do they take it as an axiom that they are inconsistent.  If 
I'm creating an AI I see no reason to have it make any assumption or 
inference about it's consistency in the sense of Goedel.  It need only 
be consistent in the sense of avoiding ex quod libet.


Brent

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Re: When Did Consciousness Begin?

[Bruno Marchal]

> On 15 Feb 2019, at 19:50, Brent Meeker  wrote:
> 
> 
> 
> On 2/14/2019 3:14 AM, Bruno Marchal wrote:
>>> On 14 Feb 2019, at 06:44, Brent Meeker  wrote:
>>> 
>>> 
>>> 
>>> On 2/12/2019 5:34 AM, Bruno Marchal wrote:
 If we could knew which machine we are, we could define consciousness, or 
 at least our personal current consciousness, as it would be defined by the 
 combinator realising us. But that is impossible, and it defines only 
 mechanism and the choice we might make for our substitution level.
>>> But when we build AI's we will know which machine they are.
>>> 
>> In theory yes, and we can be sure of its theology if the machine is sensibly 
>> less complex than us.
> 
> I don't understand that.  "We" in the collective sense build lots of things 
> that no one of us understands (e.g. Boeing 747), but "we" understand it.


The point is that a machine cannot prove its own consistency, or define its own 
notion of truth/god, but she  *can* prove that IF she is consistent, then she 
cannot prove its own consistency. At that stage, its living or experience of 
its inability to prove its consistency can be abductively explained by the fact 
she *might* be consistent. Something similar happens with soundness, and all 
its limitation. 
The key here is that machine can prove their own conditional incompleteness, 
and experience things (by the qualitative difference brought by the difference 
of the logic of G ([]p) and S4Grz ([]p & p).

For the Boeing 747, even the 787!, machine understand it eventually, it is pure 
3p, even if it is 1p-plural, after assuming compuytationalism, but it is 
entirely explainable in 3p terms. Not so for the proper theology of the 
machine: the (G* minus G) points on things which have to be above them, when 
the box “[]” refers to their beliefs (as assumed by mechanism where “[]” 
describes their correct level of substitution). But all machine can do the 
theology of the simpler machine, and see “empirically” if that is confirmed, in 
the experiential (1p) way, and in some first person plural way (1p-plural, 
locally 3p).







> 
>> But the machine itself will not believe us, or understand this.
> 
> Why not?  It can't prove what algorithm it is, but it can know that we 
> know...so why would it disbelieve us.


Tha machine becomes inconsistent if it assumes its consistency (cf Rogers’s 
sentence). The machine can assume a sort of consistency of its past belief, 
like PA can add the axioms that PA is consistent, (or that PA is inconsistent) 
without losing its consistency, but in that case it becomes a new machine, with 
a similar theology in shape, but a different content/meaning for the box. She 
has changed her own code (as we do every second instinctively).




> 
>> Then in practice, the machine will transform itself very quickly,
> 
> Wild speculation.  We don't "transform ourselves very quickly”.

Of course we do. For example, you just change yourself into a new “Brent” with 
the axiom: I just read Bruno saying “Of course we do.” In a mail from 17 
February 2019. You kept your persona identity, because we have define the 
identity of the person through their inclusive memories. 

Bruno




> 
> Brent
> 
>> and we will also not known which machine she is, except that we will know 
>> some bound on its substitution level: by construction indeed. Once as much 
>> complex than us, even in that case, we will lost the information (except for 
>> the substitution level again).
>> 
>> All (sound) machine can develop the whole theology of a simpler machine, 
>> although not algorithmically in the first person modal logic. But the 
>> propositional theology is just G*, and provably so if we can prove that the 
>> machine is arithmetically sound (like we tend to believe for machine like PA 
>> and ZF).
>> 
>> Bruno
>> 
>> 
>> 
>>> Brent
>>> 
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Re: When Did Consciousness Begin?

[Bruno Marchal]

> On 15 Feb 2019, at 20:37, John Clark  wrote:
> 
> On Fri, Feb 15, 2019 at 1:15 PM Bruno Marchal  > wrote:
> 
> > I will do a personal confession: I have never believe in matter, 
> 
> Matter doesn't care if you believe in it or not, it will just continue doing 
> what it does.

Assuming it exists. But in that case you have to explain what is primary 
matter, and how it makes some computations (going through your mind state) in 
arithmetic more real than others. That assumption makes things more complex, 
and without any evidence for it. So it looks like making things only more 
complex without any evidence for it. Assuming matter makes it primitive, 
without reason.




> 
> > because I have never seen any evidence for it. 
> 
> That's OK, I don't think matter has ever seen any evidence for you either.

Nor for your consciousness, but you cannot eliminate it, as you say in your 
critics on Dennett (with which I agree).



> 
> > Matter is like God, 
> 
> Matter is nothing like God, one is amenable to the scientific method and one 
> is not, that is to say one is bullshit and one is not.

I should have written “Assumed Matter” or “Primitive Matter”. It is like a 
creator God, instead of “God made it”, you accept/assume its existence, which 
is equivalent to abandoning the idea of explains it from simpler principles. It 
is the common “Aristotle's mistake” of reifying a metaphysical notion, to avoid 
explains it. To say “because matter is” is not a progress from “because A God 
made it”. 




> 
> > in the sense of the greeks
> 
> Yes in the sense of the ancient Greeks, in other words in the sense of people 
> with less scientific literacy than a bright fourth grader.

No, in theology Wie have regressed a lot, after the theology-science has been 
stolen by Churches and Tempes to control and manipulate people. Most people are 
even ignorant of the work of the neopythagorean and the neoplatonist. They 
ignore that the science of physics, mathematics, and even mathematical logic 
are all born from that scientific theology of the ancient greeks. It is just 
that after 529 in Occident, and after1248 (Al Ghazali) in the Middle-East, the 
field has been made taboo or mocked by people who use dogma instead.



> Why oh why do you keep talking about those ignoramuses? 

Because in theology, to put it roughly, we have imposed inconsistent theories 
since long.




> 
> > which means that it is something that we have to explain,
> 
> And then we have to explain the explanation and then explain the explanation 
> of the explanation and then…

… and then we explains everything, including the necessary presence of some 
unexplainable experiences and realms, just from elementary addition and 
multiplication, without assuming anything more than Mechanism and accepting the 
standard definitions in the fields of epistemology and ancient theology.
Mechanism explains the conscious appearance and the sharable and non sharable 
part of the physical reality, without committing itself in strong ontological 
assumption. 

Bruno





> 
>  John K Clark
> 
> 
> 
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Re: When Did Consciousness Begin?

[Bruno Marchal]

> On 15 Feb 2019, at 19:53, Brent Meeker  wrote:
> 
> 
> 
> On 2/14/2019 3:26 AM, Bruno Marchal wrote:
>> Don’t hesitate to find some argument in favour of primitive materials, but 
>> in my opinion, this is highly speculative, and never used in physics.
> 
> But the non-material primitive is never used either. 

Assuming matter! But even a physicist will prefer to assume numbers, as he 
needs to record the results of its experiment and develop its theory, than to 
derive the notion of numbers from, say the strings (and not the string 
*theory*, which assumes some number or equivalent Turing-complete base.



> Insofar as I know, no scientist ever worries about what is primitive;

I agree. That is the case since 1500 years. Metaphysics/theology have been 
taken away from science. 

Instead of obeying to elementary Pltinian-like theology, whose recommend to 
never mention Its Name in any terrestrial effective matter, we do tolerate the 
blasphemy all the times. That explains why in the human science we are still in 
the superstition, idolatry, with a complacency to total lack of rigour. That 
explains (but not justifies) the Shoah, Rwanda, Wars, and the many lies we are 
given all the times in the human domain, the medical science included. Science 
has not yet begun, except somehow in between -500 (Pythagorus) and +500 
(Damascius, end of Plato’s Academy in Athen).

Science is neutral on metaphysics and theology, *especially* in scientific 
metaphysics/psychology/theology. You are right, I have never find a paper in 
physics which assumes ontological matter. Only in philosophy do many people do 
that assumption, which is not a problem if recognised as such, and not mixed 
with Digital Mechanism. But the empirical evidences sides more with Mechanism 
than Materialism.



> they only want to find a theory that is consilient, broad in scope, and 
> correct in predictions.

Yes, so let us do that with theology and metaphysics. 

Bruno




> 
> Brent
> 
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RE: When Did Consciousness Begin?

[Bruno Marchal]

Hi Philip,

I cannot answer in your text for reason of bad formatting. It looks hard to be 
sent too.

I comment here: when you say:

<<
Matter is everything that we can see, smell, touch, feel and even can't see.  
>>

I am OK with this definition. 

But when you add


<<
Everything is matter, there isn't anything that isn't matter.  
>>


That means you adopt Aristotle’s metaphysics, which is incompatible with the 
“Mechanist act of faith”.
Indeed, logic makes the Mechanist theory entitling that “seeing, smelling, 
touching, feeling” are phenomenological number attributes, and explains matter 
without making it primitive, which means really explain it, instead of 
populating at the outset.

If you believe that matter explains the numbers, you should provide the 
explanation, and of course, not assume the numbers, or anything 
Turing-equivalent, in the process. Existing theories in physics do assumes the 
numbers, and so cannot be used in this context.

Bruno

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

[Bruno Marchal]

> On 15 Feb 2019, at 20:43, Philip Thrift  wrote:
> 
> 
> 
> On Friday, February 15, 2019 at 12:01:26 PM UTC-6, Bruno Marchal wrote:
> 
>> On 15 Feb 2019, at 16:12, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Friday, February 15, 2019 at 5:35:02 AM UTC-6, Bruno Marchal wrote:
>> 
>>> On 15 Feb 2019, at 08:25, Philip Thrift > wrote:
>>> 
>>> On Wednesday, February 13, 2019 at 10:40:32 PM UTC-6, 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:
>>> 
>>> https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/
>>>  
>>> 
>>> 
>>> 
>>>  
>>> One can (sort of) write all "physics" in a couple of equations: the 
>>> Einstein Field Equation (EFE) and the Standard Model Equation (SME):
>>> 
>>> EFE: 
>>> https://upload.wikimedia.org/wikipedia/commons/thumb/4/45/EinsteinLeiden4.jpg/620px-EinsteinLeiden4.jpg
>>>  
>>> 
>>> +
>>> SME: 
>>> https://www.sciencealert.com/images/Screen_Shot_2016-08-03_at_3.20.12_pm.png
>>>  
>>> 
>>> 
>>> What caused this particular arrangement of expressions in these to be the 
>>> "law" of our universe I suppose can be "explained" by it's being one of any 
>>> number of possible arrangements.
>> 
>> 
>> The tiny (sigma_1) arithmetical reality contains all “combinations” of all 
>> programs, and your explanation is a bit like digital physics, where the 
>> physical universe would be one special universal number, say U. That is 
>> possible, but this can explain the origin of the physical laws, in a 
>> coherent way with respect to the mind-body problem (the hard problem of 
>> consciousness) only in presence of an explanation of why that program U is 
>> winning, that is how such U can “multiply” you so much in the relative way 
>> that the laws of physics get stabilised. Arithmetical self-reference 
>> explains consciousness “easily”, but at the price of forcing us to derive 
>> the physical laws from any universal machinery.
>> The physical reality is not a mathematical reality among others, it is the 
>> projective border of the universal mind, which is just the mind of the 
>> universal machine. It is a complex many-dreams structure, and its quantum 
>> aspects explain why negative amplitude of probability can play a role in 
>> making the aberrant histories relatively rare, despite them being also in 
>> that sigma_1 arithmetic.
>> 
>> With mechanism, the idea that there is anything more than the sigma_1 
>> arithmetical truth is absolutely undecidable. The sigma_1 truth emulates the 
>> sigma_n believers for all n, and beyond. If the physics which is in the head 
>> of the universal numbers departs too much from what we see, it will be time 
>> to suspect that there is indeed something more. But not only there are no 
>> evidence for that, but there are strong evidence for the completeness of the 
>> sigma_1 truth with respect to the metaphysical questions.
>> 
>> Bruno 
>> 
>> 
>> 
>> 
>> Whatever 

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

[John Clark]

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?


> *> 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.



> *>> 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.

John K Clark

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

[Brent Meeker]

On 2/19/2019 3:41 AM, agrayson2...@gmail.com wrote:
*I don't understand your comment. Curvature of space-time should be 
independent of coordinate systems, so how can there be different 
extremals for two fixed events in the manifold?  AG*


There can be a "hill" between the two events so that there are extremal 
paths around it, one on each side.  This how a galactic mass produces 
Einstein's ring.  A common test question is: There is a clock in low 
Earth orbit.  Another clock is launched straight up (assume non-rotating 
Earth) so that it just passes the orbiting clock on the way up and then 
it falls back such that it just passes the orbiting clock, one orbit 
later, on it's way down.  Between the two coincident events the clocks 
are in free fall, following geodesics.   Which one registers the longer 
interval between the coincident events?


Brent

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

[Brent Meeker]

On 2/19/2019 3:15 AM, agrayson2...@gmail.com wrote:



On Monday, February 18, 2019 at 3:37:19 PM UTC-7, Brent wrote:



On 2/18/2019 2:05 PM, agrays...@gmail.com  wrote:

*Is it correct to say that in 3-space with the Euclidian metric
the geodesic is the path determined by minimal distance between
two points, whereas in 4-space with the Lorentzian metric it's
the maximal distance? TIA, AG*


That's right as far as it goes.  "Geodesic" is a general term in
geometry, applying to curved spaces as well as flat and it refers
to paths that are extremal.  So in general relativity there can be
different geodesics between the same two events, each of which is
a local extremal.


*Do you mean the metric tensor differs, depending on the coordinate 
system? TIA, AG

*


No.  A tensor, like a vector, is a geometric object.  It has different 
representations depending on the coordinate system, but those 
representations transform like a real object that is independent of the 
coordinate system.


Brent

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

[John Clark]

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.


> *> 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.

*> 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.

*> What would baseball look like without that tiny curvature? AG *
>

Imagine a baseball game played on the International Space Station.

John K Clark

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

[agrayson2000]

On Tuesday, February 19, 2019 at 4:15:55 AM UTC-7, agrays...@gmail.com 
wrote:
>
>
>
> On Monday, February 18, 2019 at 3:37:19 PM UTC-7, Brent wrote:
>>
>>
>>
>> On 2/18/2019 2:05 PM, agrays...@gmail.com wrote:
>>
>> *Is it correct to say that in 3-space with the Euclidian metric the 
>> geodesic is the path determined by minimal distance between two points, 
>> whereas in 4-space with the Lorentzian metric it's the maximal distance? 
>> TIA, AG*
>>
>>
>> That's right as far as it goes.  "Geodesic" is a general term in 
>> geometry, applying to curved spaces as well as flat and it refers to paths 
>> that are extremal.  So in general relativity there can be different 
>> geodesics between the same two events, each of which is a local extremal.
>>
>
> *Do you mean the metric tensor differs, depending on the coordinate 
> system? TIA, AG *
>

*I don't understand your comment. Curvature of space-time should be 
independent of coordinate systems, so how can there be different extremals 
for two fixed events in the manifold?  AG*

>
>> Brent
>>
>

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

[agrayson2000]

On Monday, February 18, 2019 at 3:37:19 PM UTC-7, Brent wrote:
>
>
>
> On 2/18/2019 2:05 PM, agrays...@gmail.com  wrote:
>
> *Is it correct to say that in 3-space with the Euclidian metric the 
> geodesic is the path determined by minimal distance between two points, 
> whereas in 4-space with the Lorentzian metric it's the maximal distance? 
> TIA, AG*
>
>
> That's right as far as it goes.  "Geodesic" is a general term in geometry, 
> applying to curved spaces as well as flat and it refers to paths that are 
> extremal.  So in general relativity there can be different geodesics 
> between the same two events, each of which is a local extremal.
>

*Do you mean the metric tensor differs, depending on the coordinate system? 
TIA, AG *

>
> Brent
>

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