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

['Brent Meeker' via Everything List]

On 3/26/2019 12:29 PM, agrayson2...@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.  The 
equations are written a manifestly covariant form, so no "proof" is 
relevant.  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

['Brent Meeker' via Everything List]

On 3/26/2019 6:14 AM, agrayson2...@gmail.com wrote:



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

*


Look at Appendix C of this very nice paper arXiv:physics/9710036v1 It 
derives the covariant equations for the field of an arbitrarily moving 
charge.


Brent

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

[smitra]

On 26-03-2019 20:29, agrayson2...@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

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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

[John Clark]

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






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>

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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

[John Clark]

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

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

[John Clark]

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

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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

[John Clark]

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

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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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