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Article #5756

Re: Fermat's principle and curved spacetime

#5756
From: Eric Gisse
Date: Fri, 25 Jan 2008 17:51
154 lines
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On Jan 24, 10:31 pm, Koobee Wublee <koobee.wub...@gmail.com> wrote:
> On Jan 23, 1:09 pm, Dieter Heidorn schrieb:
>
> > Koobee Wublee schrieb:
> > > 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
>
> Danke.  It is going to take some time for me to sort through it.
>
> > > 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:
>
> Yes, indeed.  However, the modern historic sources are from the
> usurpers like Pais who tried to write his own account of history.
> <shrug>
>
> > * the correspondence between Einstein and Grossmann before 1912,
> >    when Einstein returned to ZΓΌrich and started working with Grossmann,
>
> > * the papers published by Einstein before 1912.
> > Grossmann has nothing to do with Einstein's works before 1912.
>
> OK, from all the references I have uncovered all have claimed Einstein-
> Grossmann cooperation began in 1912.
>
> > > 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.
>
> Have you not noticed that there are all claims and no specific
> experiments shown with analyzable data given?
>
> > > 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   :-)
>
> OK, it is my mistake to use the diameter instead of the radius.
>
> > > 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
>
> What does this 36Km have anything to do with anything?
>
> > It's not necessary to know the distance with an accuracy of centimeters.
>
> Why?
>
> > 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.
>
> I am still not convinced this 240uSec is qualified.  There is no
> interferometer to detect such a minute difference in signal.  There is
> no way to nail down the distance from the earth to Venus to an
> accuracy of mere centimeters.  There is no reference signal to be
> compared with.
>
>
>
> > > 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.
>
> Well, I see my mistake.  Thank you for pointing that out.  There is an
> extra curvature in the r direction.  Thus, according to the
> Schwarzschild metric, we have the round trip time derived as the
> following.
>
> T = 2 int[ds / sqrt(1 - 2 U) / sqrt(1 - 2 U)] (from -a_E to a_V)
>   = 2 int[dx / (1 - 2 U)] / c
>   ~ 2 int[dx (1 + 2 U)] / c
>   = 2 x / c + (4 G M / c^3) sinh^-1(x / R)
>   ~ 2 (a_E + a_V) / c + (4 G M / c^3) ln(4 a_E a_V / R^2)
>
> Thus, the delay time is
>
> dt = (4 G M / c^3) ln(4 a_E a_V / R^2)
>
> > Starting with the equation
>
> > c' = c (1 + kV/c^2)
>
> >      k = 1: 1911
> >      k = 2: 1916
>
> However, this does not mean
>
> C(r) = c (1 + 2 U), k = 2
>
> Or
>
> C(r) = c (1 + U), k = 1
>
> Under the concept of GR, the speed of light must be the same
> everywhere.  That is

No, persistent idiot, the local speed of light is the same everywhere.
GR makes no claims about the global speed.

>
> C(r) = c
>
> It is the gravitational time dilation and the curvature in space that
> seems to affect the speed of light in an experiment.
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From: Eric Gisse <jowr.pi@gmail.com>
Newsgroups: sci.physics.relativity, sci.physics, sci.astro, fr.sci.physique, 
 fr.sci.maths
Subject: Re: Fermat's principle and curved spacetime
Date: Fri, 25 Jan 2008 09:51:39 -0800 (PST)
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