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RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS



 
 
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  #11  
Old May 19th 07 posted to sci.physics.relativity,sci.physics,sci.physics.cond-matter,sci.philosophy.tech,sci.astro
RP
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Posts: 2,224
Default RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS

On May 19, 11:43 am, The_Man wrote:
On May 19, 12:25 pm, RP wrote:





On May 19, 10:00 am, The_Man wrote:


On May 19, 9:31 am, RP wrote:


On May 18, 1:58 am, Pentcho Valev wrote:


http://groups.google.com/group/sci.p...hread/d28e668a...


On Oct 25, 1995, John Baez wrote in sci.physics:


"Nonetheless, it's a fact that a photon has a nonzero momentum."


A curious person asked:


"Are you therefore asserting that it has nonzero mass? If not, why
not?"


John Baez replied:


"You can see that I did not assert anything about the photon's mass. I
know what the photon's mass is, but I never talk about it around here
because the endless discussion of the photon's mass is boring, boring,
boring."


While I don't agree that the topic is boring, I do agree that it isn't
easy to understand, so I'll try to explain it. Photons don't exist.
Nothing that doesn't exist has mass.


You state as a fact what seems more like an opinion.


If special relativity is opinion, then I retract my statement


Photons have (spin) angular mometum. If photons "don't exist", the law
of conservation of angular momentum falls apart. Along with it, the
understanding of which electronic transitons occur, and how often they
occur (what we call "selection rules")


Photons don't have anything, because they don't exist. Momentum is
globally conserved, not locally conserved. The solution to the
radiation reaction problem is that there isn't a reaction, just an
action. Electrons are foward acting particles. The past light cone
contains events that influence the electron, the foward light cone
those events that it influences. There is no experimental evidence of
electron recoil under the influence of its own emitted radiation.
Before replying please note a distinction between a single electron
and an array of electrons, the latter of which produces feedback
effects.


If you can explain why s- d transitions don't occur, or why p-p
transitions don't occur, or why d-d transitions for high spin Fe 3+
occur with such a small probability, I'm all ears.


The atom is an electronic structure in equilibrium. Some states are
unstable and others impossible.


A sodium atoms is electronically excited by heating it. Sodium emits
light at two very specific wavelengths. These correspond to
transitions from 2P 3/2 - 1S0, or 2P 1/2 - 1S0. In the proces, the
atom "loses" 1 unit of orbital angular momentum. Where did it go? This
is a simple question...


It goes to all other electrons via interaction with the source
electrons, directly, at c. Because of the quantum states of recieving
atoms, they absorb energy by the same amount, and that you assume that
this absorbed energy all derived from the same single point source is
for you to prove, not me. That theory goes against all the known laws
of em. Statistically your version works "because" of global momentum
conservation.




The 1 unit of orbital angular momentum is carried away by the photon,
which has a spin angular momentum of 1. We never see electronic
transitions involving changes of anything OTHER than 1 unit of angular
momentum.

If you can tell us how you can derive all the selection rules (for
both 1 electron and multi-electron atoms) WITHOUT a photon, all of
chemistry and physics would be glad to hear it. Not the least, that
you would also have to explain the photoelectric effect, and how TV's
work.


See above. It's more or less a holographic process.


Please explain why my computer cannot
emit a 5terahertz signal.


When you turn it on, it almost surely does emit in the Terahertz range
(since this is the range of IR)



From the relativistic (Minkowskian) viewpoint, there doesn't even


exist em radiation period, not even in the form of classical em waves;
charges interact directly with one another, and the delay that we see
is a result of our mistaken Galilean observational perspective.


But EM interactons never propogate faster than c.


"In our theory c play the role of infinity".


"plays the role of infinity" and EQUALS infinity are NOT the same
thing. The fact that the speed of light was NOT infinity was already
known by the 18th century.

Please distinguish between "directly" and "instantaneous".


Time
is other than what Newton said it was, that is, it is not the same
time here as it is there. The em field of a charged particle subtends
space and time, rather than space alone.
There exists a coordinate system in which the field of a charged
particle remains perfectly rigid, but in that system the field extends
through time as well as space, which is contrary to our "assumed"
perspective of things existing only from moment to moment.


I've heard the photon-mass debate a million times in this NG, to the
point that it really is boring, boring, boring, but not the subject,
just argument itself. It's the SOS. The QM approach, empirically valid
as it may be, is not an explanation of things, it is only a
statistical quantification. QM physicists


ALL physicists are QM physicists :-)


should refrain from offering
up philosophical interpretations as fact, and especailly as
counterargument to arguments against their philosophical
interpretations.


Often they don't, agreeing with Dirac "Just shut up and calculate."


So it was Dirac who said that? In a previous thread it seemed that
nobody could come up with a direct reference.


It is one of those aporcryphal stories, but the sentiments are
consistent with those of Dirac.


That's what I thought



at QM is the most tested and most accurate model of
the universe ever created, we are fond of using it to poke holes in
other's philosophical musings.


Well and good. I don't argue against its empirical merit.


The curious person could have asked:


"Are you therefore asserting that the speed of light varies in a
gravitational field in accordance with Einstein's 1911 equation
c'=c(1+V/c^2) which, in the absence of a gravitational field, becomes
c'=c+v, where v is the relative speed of the light source and the
observer?"


This is simple algebra, and I've never seen a worse example of
deriving a solution. If V=0, then the equation reduces to c' = c. That
you blindly quote this stupidity over and over is good reason to
suggest that you're nothing other than a troll in this group.


John Baez would have replied:


"You can see that I did not assert anything about the variable speed
of light. I know how the speed of light varies in a gravitational
field, but I never talk about it around here because the endless
discussion of the variability of the speed of light is boring, boring,
boring."


Pentcho Valev- Hide quoted text -


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  #12  
Old May 19th 07 posted to sci.physics.relativity,sci.physics,sci.physics.cond-matter,sci.philosophy.tech,sci.astro
The_Man
external usenet poster
 
Posts: 1,304
Default RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS

On May 19, 1:11 pm, RP wrote:
On May 19, 11:43 am, The_Man wrote:





On May 19, 12:25 pm, RP wrote:


On May 19, 10:00 am, The_Man wrote:


On May 19, 9:31 am, RP wrote:


On May 18, 1:58 am, Pentcho Valev wrote:


http://groups.google.com/group/sci.p...hread/d28e668a...


On Oct 25, 1995, John Baez wrote in sci.physics:


"Nonetheless, it's a fact that a photon has a nonzero momentum."


A curious person asked:


"Are you therefore asserting that it has nonzero mass? If not, why
not?"


John Baez replied:


"You can see that I did not assert anything about the photon's mass. I
know what the photon's mass is, but I never talk about it around here
because the endless discussion of the photon's mass is boring, boring,
boring."


While I don't agree that the topic is boring, I do agree that it isn't
easy to understand, so I'll try to explain it. Photons don't exist.
Nothing that doesn't exist has mass.


You state as a fact what seems more like an opinion.


If special relativity is opinion, then I retract my statement


Photons have (spin) angular mometum. If photons "don't exist", the law
of conservation of angular momentum falls apart. Along with it, the
understanding of which electronic transitons occur, and how often they
occur (what we call "selection rules")


Photons don't have anything, because they don't exist. Momentum is
globally conserved, not locally conserved. The solution to the
radiation reaction problem is that there isn't a reaction, just an
action. Electrons are foward acting particles. The past light cone
contains events that influence the electron, the foward light cone
those events that it influences. There is no experimental evidence of
electron recoil under the influence of its own emitted radiation.
Before replying please note a distinction between a single electron
and an array of electrons, the latter of which produces feedback
effects.


If you can explain why s- d transitions don't occur, or why p-p
transitions don't occur, or why d-d transitions for high spin Fe 3+
occur with such a small probability, I'm all ears.


The atom is an electronic structure in equilibrium. Some states are
unstable and others impossible.


A sodium atoms is electronically excited by heating it. Sodium emits
light at two very specific wavelengths. These correspond to
transitions from 2P 3/2 - 1S0, or 2P 1/2 - 1S0. In the proces, the
atom "loses" 1 unit of orbital angular momentum. Where did it go? This
is a simple question...


It goes to all other electrons via interaction with the source
electrons, directly, at c.


So the angular momentum of the other electrons change? Yet, if that
happened, you would violate the law of conservation of energy. There
is an even easier refutation - suppose we talking about the spectrum
of hydrogen, which has NO other electrons.

Now the ball is in your court, to explain the selection rules for
hydrogen: Delta l = +/1 1, delta s =0; delta m sub l = 0, +/-1.

Because of the quantum states of recieving
atoms, they absorb energy by the same amount, and that you assume that
this absorbed energy all derived from the same single point source is
for you to prove, not me.


Proven LONG ago. Lasers do single photo absorption experiments all the
time. This is the so-called "resonance condition" - It is the basis of
all spectroscopy.

That theory goes against all the known laws
of em. Statistically your version works "because" of global momentum
conservation.



The 1 unit of orbital angular momentum is carried away by the photon,
which has a spin angular momentum of 1. We never see electronic
transitions involving changes of anything OTHER than 1 unit of angular
momentum.


If you can tell us how you can derive all the selection rules (for
both 1 electron and multi-electron atoms) WITHOUT a photon, all of
chemistry and physics would be glad to hear it. Not the least, that
you would also have to explain the photoelectric effect, and how TV's
work.


See above. It's more or less a holographic process.


No. There is a one-to-one correspondence between the number of photns
absorbed and the number of electrons emitted during the photoelectric
effect.








Please explain why my computer cannot
emit a 5terahertz signal.


When you turn it on, it almost surely does emit in the Terahertz range
(since this is the range of IR)


From the relativistic (Minkowskian) viewpoint, there doesn't even


exist em radiation period, not even in the form of classical em waves;
charges interact directly with one another, and the delay that we see
is a result of our mistaken Galilean observational perspective.


But EM interactons never propogate faster than c.


"In our theory c play the role of infinity".


"plays the role of infinity" and EQUALS infinity are NOT the same
thing. The fact that the speed of light was NOT infinity was already
known by the 18th century.


Please distinguish between "directly" and "instantaneous".


Time
is other than what Newton said it was, that is, it is not the same
time here as it is there. The em field of a charged particle subtends
space and time, rather than space alone.
There exists a coordinate system in which the field of a charged
particle remains perfectly rigid, but in that system the field extends
through time as well as space, which is contrary to our "assumed"
perspective of things existing only from moment to moment.


I've heard the photon-mass debate a million times in this NG, to the
point that it really is boring, boring, boring, but not the subject,
just argument itself. It's the SOS. The QM approach, empirically valid
as it may be, is not an explanation of things, it is only a
statistical quantification. QM physicists


ALL physicists are QM physicists :-)


should refrain from offering
up philosophical interpretations as fact, and especailly as
counterargument to arguments against their philosophical
interpretations.


Often they don't, agreeing with Dirac "Just shut up and calculate."


So it was Dirac who said that? In a previous thread it seemed that
nobody could come up with a direct reference.


It is one of those aporcryphal stories, but the sentiments are
consistent with those of Dirac.


That's what I thought

at QM is the most tested and most accurate model of



the universe ever created, we are fond of using it to poke holes in
other's philosophical musings.


Well and good. I don't argue against its empirical merit.


The curious person could have asked:


"Are you therefore asserting that the speed of light varies in a
gravitational field in accordance with Einstein's 1911 equation
c'=c(1+V/c^2) which, in the absence of a gravitational field, becomes
c'=c+v, where v is the relative speed of the light source and the
observer?"


This is simple algebra, and I've never seen a worse example of
deriving a solution. If V=0, then the equation reduces to c' = c. That
you blindly quote this stupidity over and over is good reason to
suggest that you're nothing other than a troll in this group.


John Baez would have replied:


"You can see that I did not assert anything about the variable speed
of light. I know how the speed of light varies in a gravitational
field, but I never talk about it around here because the endless
discussion of the variability of the speed of light is boring, boring,
boring."


Pentcho Valev- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -

- Show quoted text -- Hide quoted text -

- Show quoted text -



  #13  
Old May 19th 07 posted to sci.physics.relativity,sci.physics,sci.physics.cond-matter,sci.philosophy.tech,sci.astro
Y.Porat
external usenet poster
 
Posts: 7,128
Default RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS

On May 18, 9:58 am, Pentcho Valev wrote:
http://groups.google.com/group/sci.p...hread/d28e668a...

On Oct 25, 1995, John Baez wrote in sci.physics:

"Nonetheless, it's a fact that a photon has a nonzero momentum."

A curious person asked:

"Are you therefore asserting that it has nonzero mass? If not, why
not?"

John Baez replied:

"You can see that I did not assert anything about the photon's mass. I
know what the photon's mass is, but I never talk about it around here
because the endless discussion of the photon's mass is boring, boring,
boring."

The curious person could have asked:

"Are you therefore asserting that the speed of light varies in a
gravitational field in accordance with Einstein's 1911 equation
c'=c(1+V/c^2) which, in the absence of a gravitational field, becomes
c'=c+v, where v is the relative speed of the light source and the
observer?"

John Baez would have replied:

"You can see that I did not assert anything about the variable speed
of light. I know how the speed of light varies in a gravitational
field, but I never talk about it around here because the endless
discussion of the variability of the speed of light is boring, boring,
boring."

Pentcho Valev


----------------
THE ****EN jOHAN bAEZ IS bOARING!

that aprrot idiot was manyyears a moderator
of sci.physics research
and was depelling anyidea about the photon having mass
nopw
that wak\lking damage was nominated as a moderator of
sci. research can you immagine corruptin like
that in science
(not to mension pionnerind science !!

the idot crook is preparing now a
'respectable retreat' from his position
that the photon does not ahve mass
ipresented a trivial profe
that the photon has a nonzero reat mass!!
based on the formula
E=hf
only idiots lkike Baez caound not see
a long a century the mass
in the h factor while there si nothing there
tomultiply it by zero !!!

now one would say
ok it has mass but relativistic mass!!
thwat was another ****en idea
of people who could not interpret correctly
the gama factor
*and where it belongs!
it does not belong to the mass
it belongs to the energy side
or momentum side
now waht can you expact form a mathematician
that calles hiself a physicist ???!!!
(and in addition being a moderator
of a scientific ng ???!!!)
(a walking damage to science !!and a parrot mumbler )

Y.Porat
-------------------



  #14  
Old May 19th 07 posted to sci.physics.relativity,sci.physics,sci.physics.cond-matter,sci.philosophy.tech,sci.astro
Eric Gisse
external usenet poster
 
Posts: 17,705
Default RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS

On May 19, 11:05 am, "Y.Porat" wrote:

[...]

So what is the mass of the photon, Porat?

  #15  
Old May 19th 07 posted to sci.physics.relativity,sci.physics,sci.physics.cond-matter,sci.philosophy.tech,sci.astro
Eric Gisse
external usenet poster
 
Posts: 17,705
Default RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS

On May 19, 10:11 am, RP wrote:
[...]

I love watching idiots, like you, argue with someone who has a PhD in
that subject.

  #16  
Old May 19th 07 posted to sci.physics.relativity,sci.physics,sci.physics.cond-matter,sci.philosophy.tech,sci.astro
RP
external usenet poster
 
Posts: 2,224
Default RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS

On May 19, 3:20 pm, Eric Gisse wrote:
On May 19, 10:11 am, RP wrote:
[...]

I love watching idiots, like you, argue with someone who has a PhD in
that subject.


Get yourself a second mirror then, and have twice the fun.

  #17  
Old May 19th 07 posted to sci.physics.relativity,sci.physics,sci.physics.cond-matter,sci.philosophy.tech,sci.astro
RP
external usenet poster
 
Posts: 2,224
Default RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS

On May 19, 12:30 pm, The_Man wrote:
On May 19, 1:11 pm, RP wrote:





On May 19, 11:43 am, The_Man wrote:


On May 19, 12:25 pm, RP wrote:


On May 19, 10:00 am, The_Man wrote:


On May 19, 9:31 am, RP wrote:


On May 18, 1:58 am, Pentcho Valev wrote:


http://groups.google.com/group/sci.p...hread/d28e668a...


On Oct 25, 1995, John Baez wrote in sci.physics:


"Nonetheless, it's a fact that a photon has a nonzero momentum."


A curious person asked:


"Are you therefore asserting that it has nonzero mass? If not, why
not?"


John Baez replied:


"You can see that I did not assert anything about the photon's mass. I
know what the photon's mass is, but I never talk about it around here
because the endless discussion of the photon's mass is boring, boring,
boring."


While I don't agree that the topic is boring, I do agree that it isn't
easy to understand, so I'll try to explain it. Photons don't exist.
Nothing that doesn't exist has mass.


You state as a fact what seems more like an opinion.


If special relativity is opinion, then I retract my statement


Photons have (spin) angular mometum. If photons "don't exist", the law
of conservation of angular momentum falls apart. Along with it, the
understanding of which electronic transitons occur, and how often they
occur (what we call "selection rules")


Photons don't have anything, because they don't exist. Momentum is
globally conserved, not locally conserved. The solution to the
radiation reaction problem is that there isn't a reaction, just an
action. Electrons are foward acting particles. The past light cone
contains events that influence the electron, the foward light cone
those events that it influences. There is no experimental evidence of
electron recoil under the influence of its own emitted radiation.
Before replying please note a distinction between a single electron
and an array of electrons, the latter of which produces feedback
effects.


If you can explain why s- d transitions don't occur, or why p-p
transitions don't occur, or why d-d transitions for high spin Fe 3+
occur with such a small probability, I'm all ears.


The atom is an electronic structure in equilibrium. Some states are
unstable and others impossible.


A sodium atoms is electronically excited by heating it. Sodium emits
light at two very specific wavelengths. These correspond to
transitions from 2P 3/2 - 1S0, or 2P 1/2 - 1S0. In the proces, the
atom "loses" 1 unit of orbital angular momentum. Where did it go? This
is a simple question...


It goes to all other electrons via interaction with the source
electrons, directly, at c.


So the angular momentum of the other electrons change? Yet, if that
happened, you would violate the law of conservation of energy. There
is an even easier refutation - suppose we talking about the spectrum
of hydrogen, which has NO other electrons.

Now the ball is in your court, to explain the selection rules for
hydrogen: Delta l = +/1 1, delta s =0; delta m sub l = 0, +/-1.

Because of the quantum states of recieving
atoms, they absorb energy by the same amount, and that you assume that
this absorbed energy all derived from the same single point source is
for you to prove, not me.


Proven LONG ago. Lasers do single photo absorption experiments all the
time. This is the so-called "resonance condition" - It is the basis of
all spectroscopy.





That theory goes against all the known laws
of em. Statistically your version works "because" of global momentum
conservation.


The 1 unit of orbital angular momentum is carried away by the photon,
which has a spin angular momentum of 1. We never see electronic
transitions involving changes of anything OTHER than 1 unit of angular
momentum.


If you can tell us how you can derive all the selection rules (for
both 1 electron and multi-electron atoms) WITHOUT a photon, all of
chemistry and physics would be glad to hear it. Not the least, that
you would also have to explain the photoelectric effect, and how TV's
work.


See above. It's more or less a holographic process.


No. There is a one-to-one correspondence between the number of photns
absorbed and the number of electrons emitted during the photoelectric
effect.


Incorrect. You can't count the photons, only the photoelectrons. At
any given moment a surface is being impinged upon by radiation from
very many sources. If I'm allowed to speak, for arguments sake, of
this radiation in terms of photons, then the number of photons
striking the target is far greater than the photoelectrons. You simply
disgard the fact that the surface is pumped, because it suits your
argument. Again, it is still for you to prove the one-to-one
correspondence that you assume.

  #18  
Old May 20th 07 posted to sci.physics.relativity,sci.physics,sci.physics.cond-matter,sci.philosophy.tech,sci.astro
The_Man
external usenet poster
 
Posts: 1,304
Default RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS

On May 19, 8:17 pm, Eric Gisse wrote:
On May 19, 4:50 pm, The_Man wrote:

[...]

You're the contrary one. Just show which lines of ANY atom result from
a change in other than 1 unit of angular momentum. If you understood L-
S or j-j coupling, I would put it in the requisite clarifications, but
I am sure that it is over your head. Just as the normal or anomalous
Zeeman effect would further prove my point.


Do you really expect him to understand spin-spin or spin-orbit
coupling? pfft.


No, not at all :-(
I try to throw some chemistry in, because if I have to wade through
any more IRT "equations" my head will explode. I am not expert on GR,
but I know a little quantum chemistry.

We still haven't had any of "the usual suspects" who will even bite on
spin-orbit coupling :-)



[...]



  #19  
Old May 20th 07 posted to sci.physics.relativity,sci.physics,sci.physics.cond-matter,sci.philosophy.tech,sci.astro
Eric Gisse
external usenet poster
 
Posts: 17,705
Default RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS

On May 19, 5:58 pm, The_Man wrote:

[...]

We still haven't had any of "the usual suspects" who will even bite on
spin-orbit coupling :-)


That always amused me.

The fruitloops here focus almost entirely, without deviation, from
relativity. What makes relativity so goddamn special?

Folks like Ken Seto and Ralph "Henri Wilson" Rabbidge, et al. have
been arguing about relativity for longer than a decade. Yet none of
them even think about quantum field theory.

I don't hear about the Shroedinger fraud, or any **** like that.

Is it Einstein that attracts the fruitloops, or is it relativity? On
one hand, how many "quantum field theory for dummies" coffee table
books have *you* seen floating around? Folks read _A Brief History Of
Time_ and think they can argue cosmology...

  #20  
Old May 20th 07 posted to sci.physics.relativity,sci.physics,sci.physics.cond-matter,sci.philosophy.tech,sci.astro
Pentcho Valev
external usenet poster
 
Posts: 4,902
Default RELATIVITY HYPNOTISTS ABOUT THE PHOTON MASS


Eric Gisse wrote:
On May 19, 11:05 am, "Y.Porat" wrote:

[...]

So what is the mass of the photon, Porat?


Such that the speed of the photon varies with the gravitational
potential in accordance with Einstein's 1911 equation c'=c(1+V/c^2),
thereby determining the gravitational redshift factor:

http://www.blazelabs.com/f-g-gcont.asp "The first confirmation of a
long range variation in the speed of light travelling in space came in
1964. Irwin Shapiro, it seems, was the first to make use of a
previously forgotten facet of general relativity theory -- that the
speed of light is reduced when it passes through a gravitational
field....Faced with this evidence, Einstein stated:"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."......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."

In the absence of a gravitational field you can apply Einstein's
equivalence principle and show that Einstein's 1911 equation c'=c(1+V/
c^2) becomes c'=c+v, where v is the relative speed of the light source
and the observer. The moment you become Master Tom Roberts' PhD
student he will explain to you how exactly c'=c(1+V/c^2) becomes c'=c
+v.

Pentcho Valev

 




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