On Apr 19, 7:55 am, Tom Roberts wrote in sci.physics.relativity:
> Harry Wilson, DSc wrote:
> > If the first postulate requires NO universal frame, HOW and WHY can the second
> > postulate DEMAND that all starlight traveling in any one direction across space
> > does so at the same speed?
>
> First, you must learn to distinguish between a theory of physics and
> what happens in the world we inhabit. The former are MODELS of the
> latter, and can make no "demands" on physical phenomena.
>
> The resolution of your confusion about the speed of starlight, and why
> all starlight travels at the same speed, is resolved in SR by the
> geometry of spaceTIME. The universal speed c of the Lorentz transform
> has the property that it has the same value in every inertial frame. In
> the world we inhabit it "just so happens" that light travels at this
> speed. So in SR, light must travel according to the properties of this
> universal speed in every inertial frame, and must do so regardless of
> the motion of its source relative to any of those frames. This is the
> power of such a symmetry principle: at one fell swoop it explains a lot
> of seemingly-unrelated phenomena (independence of source velocity,
> universality in all inertial frames, isotropy of propagation in every
> inertial frame).
Honest Roberts why should the problem of variability/constancy of the speed of starlight be resolved "in SR"? There is always a gravitational potential difference between the light source (the star's surface) and the observer and therefore, if we put aside factors different from gravity, the speed of starlight coming to us is always lower than c (that is, starlight is always redshifted). As for the quantitative analysis, it is up to you to choose between Einstein's 1911 equation c'=c(1+V/c^2) given by Newton's emission theory of light and Einstein's 1915 (or 1955) "improved" equation c'=c(1+2V/c^2):
http://www.physlink.com/Education/AskExperts/ae13.cfm
"So, it is absolutely true that the speed of light is not constant in a gravitational field [which, by the equivalence principle, applies as well to accelerating (non-inertial) frames of reference]. If this were not so, there would be no bending of light by the gravitational field of stars....Indeed, this is exactly how Einstein did the calculation in: 'On the Influence of Gravitation on the Propagation of Light,' Annalen der Physik, 35, 1911. which predated the full formal development of general relativity by about four years. This paper is widely available in English. You can find a copy beginning on page 99 of the Dover book 'The Principle of Relativity.' 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 + V / c^2 )
where V is the gravitational potential relative to the point where the speed of light c0 is measured."
http://www.blazelabs.com/f-g-gcont.asp
"So, faced with this evidence most readers must be wondering why we learn about the importance of the constancy of speed of light. Did Einstein miss this? Sometimes I find out that what's written in our textbooks is just a biased version taken from the original work, so after searching within the original text of the theory of GR by Einstein, I found this quote: "In the second place our result shows that, 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 and to which we have already frequently referred, 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. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity ; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)." - Albert Einstein (1879-1955) - The General Theory of Relativity: Chapter 22 - A Few Inferences from the General Principle of Relativity-. Today we find that since the Special Theory of Relativity unfortunately became part of the so called mainstream science, it is considered a sacrilege to even suggest that the speed of light be anything other than a constant. This is somewhat surprising since even Einstein himself suggested in a paper "On the Influence of Gravitation on the Propagation of Light," Annalen der Physik, 35, 1911, that the speed of light might vary with the gravitational potential. Indeed, the variation of the speed of light in a vacuum or space is explicitly shown in Einstein's calculation for the angle at which light should bend upon the influence of gravity. One can find his calculation in his paper. The result is c'=c(1+V/c^2) where V is the gravitational potential relative to the point where the measurement is taken. 1+V/c^2 is also known as the GRAVITATIONAL REDSHIFT FACTOR."
http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German (download from:
http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1911_35_898-908.pdf). 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
"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."
Pentcho Valev
pvalev@yahoo.com