🚀 go-pugleaf

Einstein will rule longer than Big Brother because, in contrast with
Big Brother's world where two and two make five but 2+2=4 is forbidden
(that is, some consistency is sought), in Einstein's world both 2+2=5
and 2+2=4 are taught:

Teaching in the Department of Astronomy at the University of Florida:

http://www.astro.ufl.edu/~jt/teaching/ast1002/notes09/lecture_tan29.pdf
Jonathan C. Tan: "Americans Michelson and Morley (1887) - The speed of
light is the same no matter how fast the observer is moving:
EXPERIMENTAL RESULT.

Teaching in the Department of History and Philosophy of Science at the
University of Pittsburgh:

http://philsci-archive.pitt.edu/archive/00001743/02/Norton.pdf
John Norton: "Einstein regarded the Michelson-Morley experiment as
evidence for the principle of relativity, whereas later writers almost
universally use it as support for the light postulate of special
relativity......THE MICHELSON-MORLEY EXPERIMENT IS FULLY COMPATIBLE
WITH AN EMISSION THEORY OF LIGHT THAT CONTRADICTS THE LIGHT
POSTULATE."

Sometimes 2+2=3 is taught as well:

2+2=3: The speed of light does not vary with the gravitational
potential.

2+2=4: 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.

2+2=5: The speed of light varies with the gravitational potential V in
accordance with Einstein's 1915 equation c'=c(1+2V/c^2).

References:

http://www.astronomynotes.com/relativity/s4.htm
"Prediction: light escaping from a large mass should lose energy---the
wavelength must increase since the speed of light is constant.
Stronger surface gravity produces a greater increase in the
wavelength. This is a consequence of time dilation. Suppose person A
on the massive object decides to send light of a specific frequency f
to person B all of the time. So every second, f wave crests leave
person A. The same wave crests are received by person B in an interval
of time interval of (1+z) seconds. He receives the waves at a
frequency of f/(1+z). Remember that the speed of light c = (the
frequency f) (the wavelength L). If the frequency is reduced by (1+z)
times, the wavelength must INcrease by (1+z) times: L_atB = (1+z)
L_atA. In the doppler effect, this lengthening of the wavelength is
called a redshift. For gravity, the effect is called a gravitational
redshift."

http://helios.gsfc.nasa.gov/qa_sp_gr.html
"Is light affected by gravity? If so, how can the speed of light be
constant? Wouldn't the light coming off of the Sun be slower than the
light we make here? If not, why doesn't light escape a black hole?
Yes, light is affected by gravity, but not in its speed. General
Relativity (our best guess as to how the Universe works) gives two
effects of gravity on light. It can bend light (which includes effects
such as gravitational lensing), and it can change the energy of light.
But it changes the energy by shifting the frequency of the light
(gravitational redshift) not by changing light speed. Gravity bends
light by warping space so that what the light beam sees as "straight"
is not straight to an outside observer. The speed of light is still
constant." Dr. Eric Christian

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."

Pentcho Valev
pvalev@yahoo.com