🚀 go-pugleaf

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>

> > In physics in general, we have
>
> > C = nu lambda
>
> > Where
>
> > **  nu = frequency
> > **  lambda = wavelength
>
> > There is no way you can get away with the red-shift not dependent on
> > the speed if the speed does indeed vary.  Thus, I stand by my
> > conclusion that the subject of gravitational redshift is one instance
> > where this interpretation to the field equations is contradicting
> > itself.  <shrug>
>
> In local inertial frames of reference the speed of light is constant.
> Thus local measurements always result in
>
> c ~ 3e8 m/s
>
> So a shifted frequency leads to a shifted wavelength and you have
>
> c = nu lambda = const

Well, if each point in space measures the speed of light to be 3e8m/
Sec, there would be serious problems in principle, but that is another
chapter of discussion.

> The variability of the speed of light in GR is not to be understood in
> the sense of  Einstein's 1911 work. That was preliminary.
> The meaning of the equation
>
> c_A = c ( 1 + 2 V/c^2)
>
> can be taken from Einstein's 1916 work:

We shall see.

> >>Die Grundlage der allgemeinen Relativitätstheorie.
> >>AdP 49, 769 (1916)
>
> > Sorry, ich lese nicht Deutsch.
>
> But you can write it - fine :-)

Danke.  Ich schreibe nicht zehr gut in Deutsch.

> If you're interested, here's an english textbook containing Einstein's
> four lectures given at Princeton University (1921) that gave an overview
> of his main ideas in his 1916 work:
>
> "The Meaning of Relativity (ISBN: 9780691120270)
>   University Presses of Ca."
>
> I try to give a short overview of the part concerning the variable speed
> of light in GR:
>
> An observer at a point B outside the gravitational field of a mass M
> (that means: in a sufficient great distance) uses a coordinate system CS
> with coordinates (x^mu) = (ct, x^i). Using his coordinates he measures
> the line element (or the metric)
>
> ds^2 = g_mu,nu dx^mu dx^nu
>
> In linear approximation for weak fields (V << c^2) the following
> equation holds:
>
> ds^2 = (1 + 2V/c^2) c^2dt^2 - (1 - 2V/c^2) dx^2
>
> Another observer is located at a Point A near the mass M. He uses a
> local frame of reference (at rest relative to CS) with coordinates
> (X^alpha) = (cT, X^i). Using local coordinates he measures the line element
>
> ds^2 = c^2 dT^2 - dX^2
>
> The speed of light at A results as follows:
>
> * measured by the observer at A:
>
>    ds^2 = 0
>
>    c^2 dT^2 = dX^2
>
>    c_A(measured at A) = dX/dT = c
>
>    That means as stated before:
>    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>

Your exercise was already claimed by Poincare that the speed of light
must be a scalar and constant to an observer.

> * 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
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 actual speed of
light at that point in space even if you have observed the speed of
light in accordance to c.

> 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>

> * 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

> So eq.(1911) is disproved by experiment.

No, not really.  There has been no experiment that disproves the 1911
equation.  In fact, the 1916 equation is very absurd, for it does not
agree with the gravitational redshift or with the gravitational time
delay.