🚀 go-pugleaf

> > 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. 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."
>
> 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."
>
> Sooner or later Einsteinians will have to answer the simple question:
> The gravitational redshift factor 1+phi/c^2 experimentally confirmed
> by Pound and Rebka is consistent with:
>
> (A) Einstein's 1911 equation c'=c(1+phi/c^2) given by Newton's
> emission theory of light?
>
> (B) Einstein's 1955 equation c'=c(1+2phi/c^2)?
>
> Then Einsteinians will have to explain why they have been so silent
> about this simple problem for so long.

Jean Eisenstaedt is relatively honest here:

http://www.amazon.com/gp/product/1402012845
JEAN EISENSTAEDT
THE PREHISTORY OF RELATIVITY
Jean Eisenstaedt: "In 1907, Einstein was already working on what were
to become his two favorite concepts: light and gravitation. In 1911,
his paper published in Annalen der Physik was chiefly concerned with
the question of influence of gravitation on the propagation of light.
During the summer 1913 he wrote to Erwin Finlay-Freundlich who aimed
at observing the bending of light by different techniques: "that the
idea of the bending of light rays appeared at the time of the theory
of emission [was] rather natural..." Actually it happens that the
bending of light in a Newtonian context is explicitly discussed in
Bernstein, a popular handbook that Einstein read in his youth."

Jean Eisenstaedt honest again, but at the end he gets slightly
dishonest (just in case):

http://www.mfo.de/programme/schedule/2006/08c/OWR_2006_10.pdf
Jean Eisenstaedt: "At the end of the 18th century, a natural extension
of Newton's dynamics to light was developed but immediately forgotten.
A body of works completed the Principia with a relativistic optics of
moving bodies, the discovery of the Doppler-Fizeau effect some sixty
years before Doppler, and many other effects and ideas which represent
a fascinating preamble to Einstein relativities. It was simply
supposed that 'a body-light', as Newton named it, was subject to the
whole dynamics of the Principia in much the same way as were material
particles; thus it was subject to the Galilean relativity and its
velocity was supposed to be variable. Of course it was subject to the
short range 'refringent' force of the corpuscular theory of light --
which is part of the Principia-- but also to the long range force of
gravitation which induces Newton's theory of gravitation. The fact
that the 'mass' of a corpuscle of light was not known did not
constitute a problem since it does not appear in the Newtonian (or
Einsteinian) equations of motion. It was precisely what John Michell
(1724-1793), Robert Blair (1748-1828), Johann G. von Soldner
(1776-1833) and Fran¸cois Arago (1786-1853) were to do at the end of
the 18th century and the beginning the 19th century in the context of
Newton's dynamics. Actually this 'completed' Newtonian theory of light
and material corpuscle seems to have been implicitly accepted at the
time. In such a Newtonian context, not only Soldner's calculation of
the deviation of light in a gravitational field was understood, but
also dark bodies (cousins of black holes). A natural (Galilean and
thus relativistic) optics of moving bodies was also developed which
easily explained aberration and implied as well the essence of what we
call today the Doppler effect. Moreover, at the same time the
structure of -- but also the questions raised by-- the Michelson
experiment was understood. Most of this corpus has long been
forgotten. The Michell-Blair-Arago effect, prior to Doppler's effect,
is entirely unknown to physicists and historians. As to the influence
of gravitation on light, the story was very superficially known but
had never been studied in any detail. Moreover, the existence of a
theory dealing with light, relativity and gravitation, embedded in
Newton's Principia was completely ignored by physicists and by
historians as well. But it was a simple and natural way to deal with
the question of light, relativity (and gravitation) in a Newtonian
context. EINSTEIN HIMSELF DID NOT KNOW OF THIS NEWTONIAN THEORY OF
LIGHT AND HE DID NOT RELY ON IT IN HIS OWN RESEARCH."

Pentcho Valev
pvalev@yahoo.com