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The Sirius B fraud is now forgotten but an analogous test (involving
measuring the gravitational redshift) performed in 1960 by Pound and
Rebka is still being hailed as the third historical test (apart from
the 1919 eclipse fraud and the procrusteanization of general
relativity equations into conformity with Mercury's anomalous
perihelion advance) that has gloriously confirmed Divine Albert's
Divine Theory. Pound and Rebka correctly measured the gravitational
redshift factor to be 1+V/c^2; the problem is that this value is
consistent with either Einstein's 1911 equation c'=c(1+V/c^2) given by
Newton's emission theory of light, or Einstein's 1915 equation
c'=c(1+2V/c^2), or Hawking's equation c'=c. Of all the Einsteinians,
not one could think of a reason why this problem should be discussed:

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.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."

http://www.amazon.com/Brief-History-Time-Stephen-Hawking/dp/0553380168
Stephen Hawking, "A Brief History of Time", Chapter 6:
"Under the theory that light is made up of waves, it was not clear how
it would respond to gravity. But if light is composed of particles,
one might expect them to be affected by gravity in the same way that
cannonballs, rockets, and planets are.....In fact, it is not really
consistent to treat light like cannonballs in Newtons theory of
gravity because the speed of light is fixed. (A cannonball fired
upward from the earth will be slowed down by gravity and will
eventually stop and fall back; a photon, however, must continue upward
at a constant speed...)"

Pentcho Valev wrote:

http://www.upd.aas.org/had/meetings/2010Abstracts.html
Open Questions Regarding the 1925 Measurement of the Gravitational
Redshift of Sirius B
Jay B. Holberg Univ. of Arizona.
"In January 1924 Arthur Eddington wrote to Walter S. Adams at the Mt.
Wilson Observatory suggesting a measurement of the "Einstein shift" in
Sirius B and providing an estimate of its magnitude. Adams' 1925
published results agreed remarkably well with Eddington's estimate.
Initially this achievement was hailed as the third empirical test of
General Relativity (after Mercury's anomalous perihelion advance and
the 1919 measurement of the deflection of starlight). IT HAS BEEN
KNOWN FOR SOME TIME THAT BOTH EDDINGTON'S ESTIMATE AND ADAMS'
MEASUREMENT UNDERESTIMATED THE TRUE SIRIUS B GRAVITATIONAL REDSHIFT BY
A FACTOR OF FOUR."

http://www.cieletespace.fr/evenement/relativit-les-preuves-taient-fausses
Jean-Marc Bonnet Bidaud: "Autour de l'étoile brillante Sirius, on
découvre une petite étoile, Sirius B, à la fois très chaude et très
faiblement lumineuse. Pour expliquer ces deux particularités, il faut
supposer que l'étoile est aussi massive que le Soleil et aussi petite
qu'une planète comme la Terre. C'est Eddington lui-même qui aboutit à
cette conclusion dont il voit vite l'intérêt : avec de telles
caractéristiques, ces naines blanches sont extrêmement denses et leur
gravité très puissante. Le décalage vers le rouge de la gravitation
est donc 100 fois plus élevé que sur le Soleil. Une occasion inespérée
pour mesurer enfin quelque chose dappréciable. Eddington s'adresse
aussitôt à Walter Adams, directeur de l'observatoire du mont Wilson,
en Californie, afin que le télescope de 2,5 m de diamètre Hooker
entreprenne les vérifications. Selon ses estimations, basées sur une
température de 8 000 degrés de Sirius B, mesurée par Adams lui-même,
le décalage vers le rouge prédit par la relativité, en s'élevant à 20
km/s, devrait être facilement mesurable. Adams mobilise d'urgence le
grand télescope et expose 28 plaques photographiques pour réaliser la
mesure. Son rapport, publié le 18 mai 1925, est très confus car il
mesure des vitesses allant de 2 à 33 km/s. Mais, par le jeu de
corrections arbitraires dont personne ne comprendra jamais la logique,
le décalage passe finalement à 21 km/s, plus tard corrigé à 19 km/s,
et Eddington de conclure : "Les résultats peuvent être considérés
comme fournissant une preuve directe de la validité du troisième test
de la théorie de la relativité générale." Adams et Eddington se
congratulent, ils viennent encore de "prouver" Einstein. Ce résultat,
pourtant faux, ne sera pas remis en cause avant 1971. Manque de chance
effectivement, la première mesure de température de Sirius B était
largement inexacte : au lieu des 8 000 degrés envisagés par Eddington,
l'étoile fait en réalité près de 30 000 degrés. Elle est donc beaucoup
plus petite, sa gravité est plus intense et le décalage vers le rouge
mesurable est de 89 km/s. C'est ce qu'aurait dû trouver Adams sur ses
plaques s'il n'avait pas été "influencé" par le calcul erroné
d'Eddington. L'écart est tellement flagrant que la suspicion de fraude
a bien été envisagée."

Pentcho Valev
pvalev@yahoo.com