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IS THE SPEED OF LIGHT A CONSTANT IN THE UNIVERSE?



 
 
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Old October 4th 11, 10:08 AM posted to sci.astro,sci.math
Pentcho Valev
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Default IS THE SPEED OF LIGHT A CONSTANT IN THE UNIVERSE?

http://juneauempire.com/opinion/2011...einstein-wrong
"If the speed of light is a constant in the universe, as Albert
Einstein famously predicted..."

Actually he did not predict that. The speed of light varies with the
gravitational potential either in accordance with the equation
c'=c(1+phi/c^2) given by Newton's emission theory of light or in
accordance with the equation c'=c(1+2phi/c^2) given by general
relativity:

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German. It predated the full
formal development of general relativity by about four years. You can
find an English translation of this paper in the Dover book 'The
Principle of Relativity' beginning on page 99; you will find in
section 3 of that paper Einstein's derivation of the variable speed of
light in a gravitational potential, eqn (3). The result is:
c'=c0(1+phi/c^2) where phi is the gravitational potential relative to
the point where the speed of light co is measured......You can find a
more sophisticated derivation later by Einstein (1955) from the full
theory of general relativity in the weak field approximation....For
the 1955 results but not in coordinates see page 93, eqn (6.28):
c(r)=[1+2phi(r)/c^2]c. Namely the 1955 approximation shows a variation
in km/sec twice as much as first predicted in 1911."

http://www.mathpages.com/rr/s6-01/6-01.htm
"Around 1911 Einstein proposed to incorporate gravitation into a
modified version of special relativity by allowing the speed of light
to vary as a scalar from place to place in Euclidean space as a
function of the gravitational potential. This "scalar c field" is
remarkably similar to a simple refractive medium, in which the speed
of light varies as a function of the density. Fermat's principle of
least time can then be applied to define the paths of light rays as
geodesics in the spacetime manifold (as discussed in Section 8.4).
Specifically, Einstein wrote in 1911 that the speed of light at a
place with the gravitational potential phi would be c(1+phi/c^2),
where c is the nominal speed of light in the absence of gravity. In
geometrical units we define c=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. (...) ...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."

CONCLUSION: Light leaving the gravitational field of the emitter
continues its journey with speed c' lower than c. The lower the speed
of light, the higher the redshift.

Pentcho Valev

 




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