🚀 go-pugleaf

On Oct 30, 9:42 am, Pentcho Valev <pva...@yahoo.com> wrote:
> On Oct 21, 11:10 pm, carlip-nos...@physics.ucdavis.edu wrote in
> sci.physics:
>
> > In sci.physics Koobee Wublee <koobee.wub...@gmail.com> wrote:
>
> > [...]
>
> > > The 1919 expedition/experiment of solar eclipse carried out by
> > > Eddington was flawed right from the very start.  Since then, there
> > > have been no credible experiments done to prove the twice-the-
> > > Newtonian result in deflection of photons.
>
> > Shapiro et al., Phys. Rev. Lett. 92 (2004) 121101: 2500 24-hour
> >     observing sessions, involving 87 VLBI sites and 541 radio sources;
> >     GR deflection confirmed to .04%
>
> > Lebach et al., Phys. Rev. Lett. 75 (1995) 1439: VLBI measurements
> >     of two radio sources over a 10-day period;  GR deflection confirmed
> >     to .1%
>
> > Froeschle et al., Proceedings from the Hipparcos Venice ???97 Symposium
> >    (ESA, Noordwijk, Netherlands, 1997): optical measurements with the
> >    Hipparcos satellite; GR deflection confirmed to .3%
>
> > Would you like more?
>
> > Steve Carlip
>
> That's quite enough Honest Carlip but your brother Honest Tom Roberts
> did not answer an important question and now it is your turn. The
> problem is that Einstein has given two equations showing how the speed
> of light varies with the gravitational potential V: c'=c(1+V/c^2),
> Einstein's 1911 equation, and c'=c(1+2V/c^2), his final decision:
>
> http://www.mathpages.com/rr/s6-01/6-01.htm
> "In geometrical units we define c_0 = 1, so Einstein's 1911 formula
> can be written simply as c=1+phi. However, this formula for the speed
> of light (not to mention this whole approach to gravity) turned out to
> be incorrect, as Einstein realized during the years leading up to 1915
> and the completion of the general theory. In fact, the general theory
> of relativity doesn't give any equation for the speed of light at a
> particular location, because the effect of gravity cannot be
> represented by a simple scalar field of c values. Instead, the "speed
> of light" at a each point depends on the direction of the light ray
> through that point, as well as on the choice of coordinate systems, so
> we can't generally talk about the value of c at a given point in a non-
> vanishing gravitational field. However, if we consider just radial
> light rays near a spherically symmetrical (and non- rotating) mass,
> and if we agree to use a specific set of coordinates, namely those in
> which the metric coefficients are independent of t, then we can read a
> formula analogous to Einstein's 1911 formula directly from the
> Schwarzschild metric. (...) In the Newtonian limit the classical
> gravitational potential at a distance r from mass m is phi=-m/r, so if
> we let c_r = dr/dt denote the radial speed of light in Schwarzschild
> coordinates, we have c_r =1+2phi, which corresponds to Einstein's 1911
> equation, except that we have a factor of 2 instead of 1 on the
> potential term."
>
> Now, Honest Carlip, you will have to give a straightforward answer to
> the following question: Are the experimental results you refer to
> consistent with Einstein's 1911 equation c'=c(1+V/c^2) or are they
> consistent with Einstein's final equation c'=c(1+2V/c^2)?
>
> Einstein zombie world is desperately waiting for your answer Honest
> Carlip!

Honest Carlip I suggest the following solution to the problem:
Initially experimental results were consistent with Einstein's 1911
equation c'=c(1+V/c^2), then they became consistent with Einstein's
improved equation  c'=c(1+2V/c^2) but in the end experimental results
proved consistent with Einsteiniana's most breathtaking discovery that
the speed of light is constant in a gravitational field, that is, with
the equation c'=c. I think this solution to the problem, Honest
Carlip, is consistent with the following text of yours which is a
source of inspiration for young Einsteinians:

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
Steve Carlip: "Einstein went on to discover a more general theory of
relativity which explained gravity in terms of curved spacetime, and
he talked about the speed of light changing in this new theory. In the
1920 book "Relativity: the special and general theory" he wrote:
". . . according to the general theory of relativity, the law of the
constancy of the velocity of light in vacuo, which constitutes one of
the two fundamental assumptions in the special theory of relativity
[. . .] cannot claim any unlimited validity. A curvature of rays of
light can only take place when the velocity of propagation of light
varies with position." Since Einstein talks of velocity (a vector
quantity: speed with direction) rather than speed alone, it is not
clear that he meant the speed will change, but the reference to
special relativity suggests that he did mean so. This interpretation
is perfectly valid and makes good physical sense, but a more modern
interpretation is that the speed of light is constant in general
relativity."

Pentcho Valev
pvalev@yahoo.com