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EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD



 
 
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  #1  
Old November 3rd 11, 07:12 AM posted to sci.astro,sci.math
Pentcho Valev
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Default EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD

Divine Albert 1911: If clocks OF IDENTICAL CONSTITUTION are used, the
speed of light will not be measured to vary with the gravitational
potential:

http://www.relativitybook.com/resour...n_gravity.html
Albert Einstein 1911: "For if we measure the velocity of light at
different places in the accelerated, gravitation-free system K',
employing clocks U of identical constitution we obtain the same
magnitude at all these places. The same holds good, by our fundamental
assumption, for the system K [a stationary system in a homogeneous
gravitational field] as well."

Divine Albert 1915: If clocks OF IDENTICAL CONSTITUTION are used, the
speed of light will be measured to vary with the gravitational
potential two times faster than the speed of cannonballs:

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German. 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
"Around 1911 Einstein proposed to incorporate gravitation into a
modified version of special relativity by allowing the speed of light
to vary as a scalar from place to place in Euclidean space as a
function of the gravitational potential. This "scalar c field" is
remarkably similar to a simple refractive medium, in which the speed
of light varies as a function of the density. Fermat's principle of
least time can then be applied to define the paths of light rays as
geodesics in the spacetime manifold (as discussed in Section 8.4).
Specifically, Einstein wrote in 1911 that the speed of light at a
place with the gravitational potential phi would be c(1+phi/c^2),
where c is the nominal speed of light in the absence of gravity. In
geometrical units we define c=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. (...) ...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."

The truth: If clocks OF IDENTICAL CONSTITUTION are used, the speed of
light will be measured to vary with the gravitational potential
exactly as the speed of cannonballs does. The variation obeys the
equation c'=c(1+phi/c^2) given by Newton's emission theory of light.

Pentcho Valev

  #2  
Old November 3rd 11, 01:03 PM posted to sci.astro,sci.math
Pentcho Valev
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Posts: 8,078
Default EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD

The Feynman Lectures on Physics, Volume 2, Chapter 42-6:
"Suppose we put a clock at the "head" of the rocket ship - that is, at
the front end - and we put another identical clock at the "tail," as
in fig. 42-16. Let's call the two clocks A and B. If we compare these
two clocks when the ship is accelerating, the clock at the head seems
to run fast relative to the one at the tail. To see that, imagine that
the front clock emits a flash of light each second, and that you are
sitting at the tail comparing the arival of the light flashes with the
ticks of clock B. (...) The first flash travels the distance L1 and
the second flash travels the shorter distance L2. It is a shorter
distance because the ship is acelerating and has a higher speed at the
time of the second flash. You can see, then, that if the two flashes
were emitted from clock A one second apart, they would arrive at clock
B with a separation somewhat less than one second, since the second
flash doesn't spend as much time on the way."

Einsteiniana's idiocies can confuse any mind, even Richard Feynman's
one! If the acceleration is uniform, it is obvious that L1=L2.

The problem has an easy solution. The observer (sitting at the tail)
measures the frequency of light to have increased. Then, by taking
into account the formula:

(frequency) = (speed of light)/(wavelength)

he concludes that either the speed of light (relative to the observer)
has increased (then Einstein's 1905 light postulate is false) or the
wavelength has decreased. Einsteinians believe that the wavelength
somehow varies with the speed of the observer:

http://www.pitt.edu/~jdnorton/teachi...ang/index.html
John Norton: "Here's a light wave and an observer. If the observer
were to hurry towards the source of the light, the observer would now
pass wavecrests more frequently than the resting observer. That would
mean that moving observer would find the frequency of the light to
have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE
BETWEEN CRESTS - TO HAVE DECREASED)."

Pentcho Valev

  #3  
Old November 3rd 11, 02:37 PM posted to sci.astro,sci.math
Pentcho Valev
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Posts: 8,078
Default EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD

The Feynman Lectures on Physics, Volume 1, Chapter 15-1:
"Suppose we are riding in a car that is going at a speed u, and light
from the rear is going past the car with speed c. Differentiating the
first equation in (15.2) gives dx'/dt=dx/dt-u, which means that
according to the Galilean transformation the apparent speed of the
passing light, as we measure it in the car, should not be c but should
be c-u."

Needless to say, Feynman rejects the equation c'=c-u (it is
incompatible with Einstein's special relativity) but:

1. According to Maxwell's theory, the equation c'=c-u is correct (u is
the speed of the car relative to the ether).

2. According to Newton's emission theory of light, the equation c'=c-u
is correct (u is the speed of the car relative to the emitter).

3. In the absence of ad hoc auxiliary hypotheses (Lorentz-FitzGerald's
length contraction), the Michelson-Morley experiment unequivocally
confirms the equation c'=c-u and refutes the alternative equation c'=c
compatible with Einstein's special relativity.

Pentcho Valev

  #4  
Old November 3rd 11, 03:11 PM posted to sci.astro,sci.math
Pentcho Valev
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Posts: 8,078
Default EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD

Einsteinians compelled to stick to Newton's emission theory of light:

A light source on top of a tower of height h emits light with
frequency f and speed c (relative to the source). The light reaches an
observer on the ground with frequency f' and speed c' (relative to the
observer).

Equivalently, a light source at the front end of an accelerating
rocket of length h and accelaration g emits light with frequency f and
speed c (relative to the source). The light reaches an observer at the
back end with frequency f' and speed c' (relative to the observer).

Consider equations (13.2) on p. 3 in David Morin's text:

http://student.fizika.org/~jsisko/Kn...Morin/CH13.PDF
f' = f(1 + v/c) = f(1 + gh/c^2) (13.2)

where v is the relative speed of the light source (at the moment of
emission) and the observer (at the moment of reception) in the rocket
scenario. By combining these equations with:

(frequency) = (speed of light)/(wavelength)

one obtains the fundamental equations of Newton's emission theory of
light:

c' = c + v = c(1 + gh/c^2)

In the absence of ad hoc auxiliary hypotheses the Pound-Rebka
experiment, just like the Michelson-Morley experiment, unequivocally
confirms the fundamental equations of Newton's emission theory of
light and refutes the principle of constancy of the speed of light:

http://student.fizika.org/~jsisko/Kn...Morin/CH13.PDF
David Morin (p. 4): "This GR time-dilation effect was first measured
at Harvard by Pound and Rebka in 1960. They sent gamma rays up a 20m
tower and measured the redshift (that is, the decrease in frequency)
at the top. This was a notable feat indeed, considering that they were
able to measure a frequency shift of gh/c^2 (which is only a few parts
in 10^15) to within 1% accuracy."

David Morin's text referred to above reappears as Chapter 14 in:

http://www.people.fas.harvard.edu/~djmorin/book.html
Introduction to Classical Mechanics With Problems and Solutions, David
Morin, Cambridge University Press

Pentcho Valev

  #5  
Old November 3rd 11, 09:48 PM posted to sci.astro,sci.math
Pentcho Valev
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Posts: 8,078
Default EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD

Einsteiniana's priests shock believers:

http://www.logosjournal.com/issue_4.3/smolin.htm
Lee Smolin: "Special relativity was the result of 10 years of
intellectual struggle, yet Einstein had convinced himself it was wrong
within two years of publishing it."

Believers are baffled. What could have happened in 1907? "Wrong" is a
wrong word perhaps? Did Smolin mean "incomplete"? An hour of silence
but then again the wind carries the tunes of "Divine Einstein" and
"Yes we all believe in relativity, relativity, relativity" all over
the world.

Then John Norton shocks believers by providing the second moiety of
the story:

http://www.pitt.edu/~jdnorton/papers...UP_TimesNR.pdf
John Norton: "Already in 1907, a mere two years after the completion
of the special theory, he [Einstein] had concluded that the speed of
light is variable in the presence of a gravitational field."

Believers are baffled again. Variable?!?! This is more serious and the
silence lasts for two days. On the third day Steve Carlip restores the
serenity in Einsteiniana's schizophrenic world by explaining to
believers that, even though the speed of light may have been variable
in 1907, now it is constant and that's it:

http://math.ucr.edu/home/baez/physic..._of_light.html
Steve Carlip: "Einstein went on to discover a more general theory of
relativity which explained gravity in terms of curved spacetime, and
he talked about the speed of light changing in this new theory. In the
1920 book "Relativity: the special and general theory" he wrote:
"...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
[...] 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." Since Einstein talks of velocity (a vector
quantity: speed with direction) rather than speed alone, it is not
clear that he meant the speed will change, but the reference to
special relativity suggests that he did mean so. This interpretation
is perfectly valid and makes good physical sense, but a more modern
interpretation is that the speed of light is constant in general
relativity."

Pentcho Valev

  #6  
Old December 3rd 11, 10:06 AM posted to sci.astro,sci.math
Pentcho Valev
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Posts: 8,078
Default EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD

Implicit references to Halton Arp's "intrinsic redshift" in
Einsteiniana's schizophrenic world:

http://www.wired.com/wiredscience/20...in-relativity/
"The researchers, led by Radek Wojtak of the Niels Bohr Institute at
the University of Copenhagen, set out to test a classic prediction of
general relativity: that light will lose energy as it is escaping a
gravitational field. The stronger the field, the greater the energy
loss suffered by the light. As a result, photons emitted from the
center of a galaxy cluster - a massive object containing thousands of
galaxies - should lose more energy than photons coming from the edge
of the cluster because gravity is strongest in the center."

"Light will lose energy as it is escaping a gravitational field" is a
euphemism. In fact, general relativity predicts that light will lose
SPEED. The speed of light varies with the gravitational potential,
phi, either in accordance with the equation c'=c(1+phi/c^2) given by
Newton's emission theory of light or in accordance with the equation
c'=c(1+2phi/c^2) given by general relativity:

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German. 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

  #7  
Old December 5th 11, 07:17 PM posted to sci.astro,sci.math
Pentcho Valev
external usenet poster
 
Posts: 8,078
Default EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD

Truth in Einsteiniana's schizophrenic world: Einsteinians show that
the speed of light varies with gh, the gravitational potential, in
accordance with the equation c'=c(1+gh/c^2) (an equation given by
Newton's emission theory of light):

http://www.youtube.com/watch?v=FJ2SVPahBzg
Relativity 3 - gravity and light

Of course, this truth is unnoticeable since two blatant lies are
officially taught: that the speed of light is constant in a
gravitational field (for beginners) and that it varies with the
gravitational potential in accordance with the equation c'=c(1+2gh/
c^2) (for advanced Einsteinians):

http://www.amazon.com/Brief-History-.../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 Newton's 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...)"

http://www.mathpages.com/rr/s6-01/6-01.htm
"Around 1911 Einstein proposed to incorporate gravitation into a
modified version of special relativity by allowing the speed of light
to vary as a scalar from place to place in Euclidean space as a
function of the gravitational potential. This "scalar c field" is
remarkably similar to a simple refractive medium, in which the speed
of light varies as a function of the density. Fermat's principle of
least time can then be applied to define the paths of light rays as
geodesics in the spacetime manifold (as discussed in Section 8.4).
Specifically, Einstein wrote in 1911 that the speed of light at a
place with the gravitational potential phi would be c(1+phi/c^2),
where c is the nominal speed of light in the absence of gravity. In
geometrical units we define c=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. (...) ...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

  #8  
Old December 12th 11, 12:09 AM posted to sci.astro,sci.math
Pentcho Valev
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Posts: 8,078
Default EINSTEINIANA: SPEED OF LIGHT IN A GRAVITATIONAL FIELD

Irwin Shapiro incidentally hears "something about the speed depending
on the gravitational potential" and realizes that the speed of light
is obviously variable:

http://www.hep.yorku.ca/menary/cours...relativity.pdf
Irwin Shapiro: "...I attended an afternoon of presentations c.
1961-1962 by MIT staff on their progress on various research projects,
conducted under joint services (DOD) sponsorship. One was on speed-of-
light measurements by George Stroke who mentioned something about the
speed depending on the gravitational potential. This remark surprised
me and I pursued it via "brushing up" on my knowledge of general
relativity and realized the obvious: whereas the speed of light
measured locally in an inertial frame will have the same value
everywhere, save for measurement errors, the propagation time of light
along some path will depend on the gravitational potential along that
path."

Of course, although Shapiro and Stroke are free to discuss anything,
even the variation of the speed of light, believers are not. They
should just sing, as fiercely as possible, "Divine Einstein" and "Yes
we all believe in relativity, relativity, relativity".

Pentcho Valev

 




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