🚀 go-pugleaf

Koobee Wublee schrieb:
> On Jan 22, 8:38 am, Dieter Heidorn wrote:
> 
>>Koobee Wublee schrieb:
> 
>>>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.
> 
> Do you have a link to this article in the yearbook of radio and
> electronics even if it is in German?
> 

I only know where to find the original work - also leider auf Deutsch:

http://www.soso.ch/wissen/hist/SRT/E-1907.pdf

>>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".
> 
> Pais declared Poincare to be a vegetable that could not even
> understand the basics of special relativity.  Pais' account cannot be
> any accurate.
> 

It's not a question of account but a question of historical sources, for
instance:
* the correspondence between Einstein and Grossmann before 1912,
   when Einstein returned to Z�rich and started working with Grossmann,
* the papers published by Einstein before 1912.
Grossmann has nothing to do with Einstein's works before 1912.

>>* 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
> 
> These are not experimentations on deflection but measurements in speed
> delay or rather gravitational time delay.  <shrug>
> 

These _are_ experiments on light deflection. Please have a look at

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

pages 33 - 35.

>>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
> 
> Please note the constant '2' arises due to the round trip condition.
> 

That's why I wrote "round-trip travel time".

>>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
> 
> G = 6.7e-11 in MKS system
> M = Mass of the sun = 2.0e30 Kg
> R = Radius of the sun = 1.4e9 m
>

In Europe we are told that the radius of the sun is

R = 6.96e8 m   :-)

> c = 3.0e8 m/Sec
> a_E = 1.5e11 m
> a_V = 1.1e11 m
> 
> delta t (round trip) = 100 k uSec
> 

Using the sun's european radius ;-) we obtain using the above equation
for delta t:

delta t (round trip) = k * 120 uSec

This agrees with the experimental value delta t ~ 240 uSec only if

k = 2

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

> I don't know where you get 240uSec of delay time from.  With k = 1, it
> agrees with all the calculations.  
>

Obviously not: for k = 1 you get

delta t (round trip) = 1 * 120 uSec

> http://en.wikipedia.org/wiki/Shapiro_effect
>

The equation given there:

delta t = -2 (GM / c^3) ln(1 - R.x)

is valid for one half of the round-trip. The factor in this equation  is 
  due to eq.(1916) - it's the k = 2.

> By the way, this type of measurement on the delay time requires you to
> know the accuracy of the distance involved.  You'd better know this
> accuracy from the earth to the Venus with a few centimeters or
> better.  Without an interferometer, how can you accept any
> experimental results on this subject without any question?
> 

The delta t (round trip) is equivalent to a seeming (virtual?
apparent?) increase of the distance between Earth and Venus of

c delta t / 2 = 36 km

It's not necessary to know the distance with an accuracy of centimeters.

The distance Earth - Venus when Venus stands between Earth and
Sun can be measured by measuring the travel time of reflected radar
signals. In combination with the data of Venus' orbit you get the
distance needed for the Shapiro-Experiment.

>>* 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)
> 

Your calculation concerning time delay:

> To derive the Shapiro time delay through gravitational time dilation,
> we have
> 
> T = 2 int[ds / c]  (from -a_E to a_V)
>   = 2 int[dx / sqrt(1 - 2 U)] / c
>   ~ 2 int[dx (1 + U)] / c
>   = 2 x / c + (G M / c^3) sinh^-1(x / R)
>   ~ 2 (a_E + a_V) / c + 2 (G M / c^3) ln(4 a_E a_V / R^2)
> 
> Where
> 
> **  U = G M / c^2 / r
> **  a_E >> R
> **  a_V >> R
> 
> This is the same derivation when we have the following 1911 equation
> 
> C(r) = c (1 - U)
> 

Your calculation is the same calculation as I have given - with a little
meaningful difference. Please compare:

[KW] T = 2 int[dx (1 + U)] / c   or:

      T = (2/c) int dx (1 -  V/c^2)

[DH] T = (2/c) int dx (1 - kV/c^2)

For the round trip we get:

[KW] delta t (round trip) = 2   (G M / c^3) ln(4 a_E a_V / R^2)

[DH] delta t (round trip) = 2 k (G M / c^3) ln(4 a_E a_V / R^2)

The values are as mentioned above:

[KW] delta t (round trip) ~ 120 uSec

[DH] delta t (round trip) ~ 240 uSec

240 uSec is in agreement with experimental data.

> The deflection must agree with time delay.
>

Starting with the equation

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

     k = 1: 1911
     k = 2: 1916

you can derive

1. light deflection angle:

    alpha = k * 2 GM / (c^2 R)

    Experiments show: k = 2.

2. time delay:

    delta t (round trip) =  k * (2 G M / c^3) ln(4 a_E a_V / R^2)

    Experiments show: k = 2

So eq.(1911) is disproved by experiment.

Dieter Heidorn