Re: [Phys-L] Two questions on General Relativity

[Moses Fayngold <moshfarlan@yahoo.com>]

 On Saturday, March 26, 2022, 3:42:59 AM EDT, Antti Savinainen via Phys-l <phys-l@mail.phys-l.org> wrote:  
> "Does the modern interpretation of GR still > maintain that the speed of light depends on the gravitational potential 
> as stated by Einstein in 1911?" 

  This depends on what kind of speed of light we discuss. See below. 


> "A final note: Many sources seem to agree that "In GR the velocity of 
> light is only locally equal to c."

  This is true. Just as the principle of equivalence is universal only locally, the speed of light is universal constant only locally. The difference between local and nonlocal speed of light is most clearly seen in the experiments involving rotating RF which generate non-uniform gravitational field. The physical distinctions between local and global light speeds there can be even shown grapfically, which might be very instructive in the classroom. The details are described in my book "Special Relativity and How It Works", Wiley-VCH, 2008 (Section 8.4). It also discusses associated topic of the red shift (Sec. 13.2). Today I would write the book more concisely, but the essence would remain the same.  

Moses FayngoldNJIT

   
 On Saturday, March 26, 2022, 3:42:59 AM EDT, Antti Savinainen via Phys-l <phys-l@mail.phys-l.org> wrote:  
 
 Hi,

I read a book on Einstein's Legacy (in Finnish). It was an interesting 
tour through the predictions that Einstein made in physics. The author 
is an astronomer who has lectured general relativity at a university 
level. He starts each chapter by quoting an original article either by 
Einstein or some other researcher using Einstein's ideas and theories. 
This is the best overview of Einstein's scientific work I've read so far.

However, there are two claims in the book which surprised me (quotations 
translated by me).

1) "Nowadays the Equivalence Principle has mainly historical meaning."

This is because it's just an approximation of GR. The evidence offered 
is Einstein's paper in 1911 in which he calculated the bending of light 
due to the Sun, and got an answer which is only half of the measured 
value. The final prediction was made in his 1915 paper and this provided 
a correct value.

Is it really so that the Equivalence Principle, if correctly applied, 
fails to yield the correct value in the experiments carried out by 
Eddington and others? Has the Equivalence Principle only pedagogical 
value anymore, that is, is it virtually useless for research purposes?

2) "The speed of light is slowed down in a gravitational field."

The author cites Einstein's paper in 1911. In that paper, Einstein 
derived a formula indicating that the speed of light is a function of 
position in a gravitational field (that is, depends on the gravitational 
potential). The empirical evidence is provided by the Shapiro time delay 
experiments (https://en.wikipedia.org/wiki/Shapiro_time_delay). More 
recently, the Cassini spacecraft has produced a very precise 
confirmation of the time delay effect: 
https://www.nature.com/articles/nature01997.

My question is the following: Does the modern interpretation of GR still 
maintain that the speed of light depends on the gravitational potential 
as stated by Einstein in 1911? If so, wouldn't this mean that when light 
climbs from a gravitational well, it would experience both the 
gravitational redshift 
(https://astronomy.swin.edu.au/cosmos/g/Gravitational+Redshift) *and* 
the decrease in speed?

A final note: Many sources seem to agree that "In GR the velocity of 
light is only locally equal to c."

Regards,

Antti Savinainen, PhD

Kuopio Lyseo HS

Finland





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