🚀 go-pugleaf

On Sep 14, 12:43 am, Pentcho Valev <pva...@yahoo.com> wrote:
> On Sep 13, 10:18 pm, PD <thedraperfam...@gmail.com> wrote:
>
>
>
> > On Sep 13, 6:28 am, Pentcho Valev <pva...@yahoo.com> wrote:
>
> > > Premise: Einstein's equivalence principle
>
> > > Conclusions:
> > > If the speed of light varies with the gravitational potential V in
> > > accordance with Einstein's 1911 equation c'=c(1+V/c^2) given by
> > > Newton's emission theory of light, then the speed of light varies with
> > > the speed of the light source v in accordance with the equation c'=c+v
> > > given again by Newton's emission theory of light, that is, Einstein's
> > > 1905 light postulate is false.
>
> > > If the speed of light varies with the gravitational potential V in
> > > accordance with Einstein's 1915 equation c'=c(1+2V/c^2), then the
> > > speed of light varies with the speed of the light source v in
> > > accordance with the equation c'=c+2v, that is, Einstein's 1905 light
> > > postulate is false.
>
> > Nonsense, Pentcho. The variation of light speed as observed across a
> > gravitational potential is clearly a statement made in a non-inertial
> > frame.
> > The second postulate explicitly refers to the speed of light being
> > invariant in *inertial* reference frames.
>
> A light source on top of a tower of height h emits light with
> frequency f, speed c (relative to the source) and wavelength L. A
> receiver on the ground receives light with frequency f', speed
> c' (relative to the receiver) and wavelength L'. According to Newton's
> emission theory of light:
>
> f'=f(1+gh/c^2); c'=c(1+gh/c^2); L'=L
>
> A rocket of length h accelerates with acceleration g. A light source
> at the front end emits light with frequency f, speed c (relative to
> the source) and wavelength L. A receiver at the back end receives
> light with frequency f', speed c' (relative to the receiver) and
> wavelength L'. At the moment of reception, the receiver has speed v
> relative to the light source at the moment of emission. According to
> Newton's emission theory of light:
>
> f'=f(1+v/c); c'=c+v; L'=L
>
> Einstein did not offer any reasonable alternative to the variation of
> the speed of light in a gravitational field predicted by the emission
> theory.

Of course he did. It's in GR. Just because you don't understand any of
it doesn't make it unreasonable.

> Initially he was just using the equation c'=c(1+gh/c^2), then
> quite stupidly (or dishonestly) replaced it with c'=c(1+2gh/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.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
> pva...@yahoo.com