🚀 go-pugleaf

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 Radioaktivität 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?

> 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.

> > 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.

Why would any one measure this value in the speed of light?  Have any
experiments been attempted to do just so at various places?

> * 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>

> > 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

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

> 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
c = 3.0e8 m/Sec
a_E = 1.5e11 m
a_V = 1.1e11 m

delta t (round trip) = 100 k uSec

> 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.

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

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

Thus, the 1916 equation is wrong.  As I mentioned below, this 1916
equation fails the necessary condition for the observed gravitational
time dilation and thus gravitational red shift.

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?

> > 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 seehttp://arxiv.org/abs/gr-qc/0510072

All of these involve the gravitational time dilation which is
basically the Shaprio delay as you have derived.

> * 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)

Only 1911 equation would predict the above quantity.  See the link I
gave you above.

> > 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.

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 / (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)

The deflection must agree with time delay.  Since in GR, the
deflection does not agree with time delay, GR has internal conflict.
This is not the only instance where an internal self-conflict occurs.
Thus, GR is a lousy interpretation to the very faulty set of field
equations, but this is not Einstein's fault because Einstein really
had nothing to do with the field equations and GR in general.

Would you accept this as the 'weltmaennisch' checkmate?