🚀 go-pugleaf

On Jan 20, 9:11 am, Dieter Heidorn <d.heid...@t-online.de> wrote:
> Koobee Wublee schrieb:
>
> > On Jan 19, 5:46 am, Dieter Heidorn wrote:
>
> >>Koobee Wublee schrieb:
>
> >>>The equation [c = c_0 (1 + V/c^2)] is correct for gravitational redshift.
>
> >>Of course, because Einstein derived the c-equation in his 1911 work from
> >>the correct equation for gravitational red-shift.
>
> > 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.' "
>
>
>
> >>>> [variable speed of light in GR:   c_A = c ( 1 + 2 V/c^2)]
>
> >>>This equation will lead to a wrong value of the gravitational
> >>>redshift.  This is another example where GR is contradictory of itself
> >>>because it does not agree with the metric derivation as you have shown
> >>>above.
>
> >>You can take this as contradiction only, if gravitational red-shift
> >>would depend on a variable speed of light. In fact this is not correct
> >>in GR.
> >>The gravitational red-shift depends on the metric:
>
> >>    nu_B / nu_A = sqrt(g_00(r_A)/g_00(r_B))
>
> >>In weak fields the following approximation holds:
>
> >>    nu_B / nu_A = 1 + Delta V/c^2
>
> > 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
>
> 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:
>
> >>Die Grundlage der allgemeinen Relativitätstheorie.
> >>AdP 49, 769 (1916)
>
> > Sorry, ich lese nicht Deutsch.
>
> But you can write it - fine :-)
>
> 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
>
> * 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.
>
> 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))
> * radar time delay (Shapiro experiment)
>
> So eq.(1911) is disproved by experiment. It's consistency with
> gravitational redshift is based on the fact, that it was derived from
> the correct equation for the frequency shift - however it's wrong
> because it was derived using flat space instead of curved space-time.
>
> The connections can (very) simplified be illustrated by the following
> diagram:
>
>             equivalence principle
>               |                |
>               | 1911           | 1916
>               |                |
> frequency shift <---------- metric ds^2
>                                |
>                             variable speed of light (non-local)
>                                |
>                             light deflection
>
> Dieter Heidorn

Dieter's answer is about as good as it gets.
We should have an FAQ for SP.relativity, and
put his post there, to save typing.
Regards
Ken S. Tucker