🚀 go-pugleaf

Koobee Wublee schrieb:
> On Jan 20, 9:11 am, Dieter Heidorn <d.heid...@t-online.de> wrote:
> 
>>Koobee Wublee schrieb:
> 
>>>Einstein did not derive anything.  In this case, he merely stated
>>>them.  <shrug>
>>
>>A look in his 1911 work will show you that this is not correct. This
>>work is available in english (see the repeated postings of Pentcho Valev):
>>" 'On the Influence of Gravitation on the Propagation of
>>Light,' Annalen der Physik, 35, 1911. You can find a copy beginning on
>>page 99 of the Dover book 'The Principle of Relativity.' "
> 
> But, it is all Grossmann's work.  <shrug>
> 

The 1911 work is based on an article Einstein published 1907 in 
"Jahrbuch der Radioaktivit�t und Elektronik" 4,411(1907)
Here the relation

c' = c(1 + V/c^2)

is derived for the first time.

Einstein and Grossmann worked together in 1912/1913. In their common 
work, Grossmann contributed Riemannian Geometry and tensor calculus as 
convenient mathematical frame for the development of GR. The physical 
part is completely due to Einstein. For historical details see for 
instance A.Pais: " 'Subtle is the Lord...' The Science and the Life of 
Albert Einstein".

>>   In local inertial frames of reference the speed of light is constant,
>>   and local measurements always result in
>>
>>   c ~ 3e8 m/s
> 
> There is no mathematics that says c should be 3e8m/Sec.  <shrug>
> 

I didn't claim that the value of c could be derived mathematically... I 
just mentioned that local measurements always result in this value.

>>* [speed of light at A] measured by the observer at B:
>>
>>   ds^2 = 0
>>
>>   (1 + 2V/c^2) c^2dt^2 = (1 - 2V/c^2) dx^2
>>
>>   c (1 + V/c^2) dt = (1 - V/c^2) dx
>>
>>   c_A(measured at B) = dx/dt = c (1 + V/c^2) / (1 - V/c^2)
>>
>>   c_A(measured at B) = c (1 + 2V/c^2)
>>
>>Clearly the observer at A cannot use c_A = (1 + 2V/c^2), and of course
>>he will not measure a local variability of c in his local frame of
>>reference.
> 
> OK, but since an observer always observe the speed of light to be c
>

...locally...

> whatever the square root of the product of the permeability and the
> permittivity in free space happens to be, the speed of light as a
> function of the Newtonian gravitational potential does not reflect the
> observed.  What you have written down represents the
>

non-local

> actual speed of
> light at that point in space even if you have observed the

local

> speed of
> light in accordance to c.
> 

The difference between local and non-local must always be kept in mind.

>>The difference between
>>
>>c_A = c (1 + 2V/c^2)  (1916)
>>
>>and
>>
>>c_A = c (1 + V/c^2)   (1911)
>>
>>is the factor 2 with the gravitational potential. Equation (1916) is
>>confirmed by experiment, for instance by:
>>
>>* light deflection
>>   (using eq.(1916) Einstein calculates the correct deflection angle
>>    alpha = 4 GM / (c^2 R))
> 
> Theoretically, yes.  However, the only experiment (the 1919 expedition
> of Eddington) on is flawed.  <shrug>
> 

"Eddington" was just the first experiment. Further experiments with 
improved accuracy were carried out, for instance:

* measurements using radio-interferometery
* VLBI measurements on quasistellar radio sources
* observations made by the Hipparcos optical astrometry satellite

VLBI light deflection measurements have reached agreement with GR to 
0.02 percent.

For references see

http://arxiv.org/abs/gr-qc/0510072

>>* radar time delay (Shapiro experiment)
> 
> If you have followed through the mathematics, this actually supports
> the 1911 result after establishing the following relationship.
> 
> dt / c = dTau / C
> 
> Where
> 
> **  dt = Observer's own flow of time
> **  dTau = Flow of time at a particular point in space
> **  c = Observer's own speed of light
> **  C = Speed of light at that particular point in space
> 

Let's see.

c' = c (1 + kV/c^2)

    k = 1: 1911
    k = 2: 1916

Round-trip travel time for a light-ray started on earth (position -a_E), 
passing near the sun (position 0, radius R), reaching Venus (position 
a_V) and returning to earth:

t = 2 int dx/c'  (from -a_E to a_V)

   ~ 2 int (1 - kV/c^2) dx/c

   = 2 int dx/c - 2 int kV/c^3 dx

   =    t_N   + delta t

The first term is the Newtonian travel time, the second term is the 
relativistic deviation from the Newtonian result.

delta t = 2 kGM/c^3 int dx/r

         = 2 kGM/c^3 int dx/sqrt(R^2 + x^2)

delta t ~ 2 kGM/c^3 ln(4 a_E a_V / R^2)

         ~ k * 120e-6 s

This agrees with the experimental value delta t ~ 240e-6 s only if

k = 2

Thus eq.(1916) c' = c (1 + 2V/c^2) is confirmed.

>>So eq.(1911) is disproved by experiment.
> 
> No, not really.  There has been no experiment that disproves the 1911
> equation.  
>

* All time delay measurements like the Shapiro-experiment (Venus)
   disprove the 1911 equation:

   - Mercury
   - Mariner 6 and 7
   - Viking Mars landers and orbiters
   - Cassini spacecraft to Saturn

   For references see http://arxiv.org/abs/gr-qc/0510072

* All experiments on the deflection of light disprove the 1911
   equation, because this equation leads to the wrong deflection angle

   alpha = 2 GM / (c^2 R)   (1911)

> In fact, the 1916 equation is very absurd, for it does not
> agree with the gravitational redshift or with the gravitational time
> delay.
> 

There's no reason why eq.(1916) should agree with gravitational 
redshift, because in GR gravitational redshift depends on the curved 
space-time, not on variable speed of light. The agreement with 
gravitational time delay was just shown.

Dieter Heidorn