Re: gravitational bending of light, surprising?

On 19 mai, 18:19, carlip-nos...@xxxxxxxxxxxxxxxxxxx wrote:
mluttg...@xxxxxxxxx wrote:
On 18 mai, 18:37, carlip-nos...@xxxxxxxxxxxxxxxxxxx wrote:
mluttg...@xxxxxxxxx wrote:

[...]

Do you agree that a photon can behave as a corpuscule
having a kinetic energy E = mc^2 = hNu, where Nu is
its frequency?
Depends what you mean by "m."
Do you agree that m represents hNu/c^2?

Sorry, but this still depends on what you mean by "m."

Do you agree that, if the author of the paper had
used in his calculation E=mc^2 instead of E=mc^2/2
for the photon energy, he would have obtained exactly
the GR result?
No, of course not!  A basic feature of Newtonian gravity is
that the acceleration of an object in a gravitational field
is independent of its mass.  You can use a mass of mc^2,
or 1/2 mc^2, or you can say the photon has the mass of your
pet cat.  As the article you cite points out,  "As expected,
the light particle mass m cancels out."
(You can, of course, cheat and use different values of m in
different steps of the calculation.  But then you're no longer
talking about anything resembling Newtonian gravity.)

[...]

There is one remark I can't agree with:
"You can use a mass of mc^2, or 1/2 mc^2, or you can say the
photon has the mass of your pet cat.  As the article you cite
points out,  "As expected, the light particle mass m cancels out.""
Indeed, m cancels out in the derivation, but *not* the coefficient,
which is 1/2 when strangely assuming, like the author, that the
photon energy is (1/2) mc^2.
But when assuming that the photon energy is mc^2, which seems
to be much more justified, the coefficient is 1. And with that
coefficient, *which doesn't cancel out*, one gets the same
deflection as GR.

If you are finding an answer that depends on the mass you attribute
to the photon, you are doing something wrong.  This is completely
elementary.  All you need to know is Newton's second law, F=ma,
and Newton's law of gravity, F=GMm/r^2.  If you set these equal,
m drops out -- the acceleration of a body in a gravitational field
is independent of its mass.  This is the principle of equivalence, and
it goes back at least to Galileo.  It's the reason Cavendish and von
Soldner were able to do the cpmutation 200 years ago; they didn't
need to know anything about the mass of light, because the mass
is irrelevant to the answer.

You claim that you are getting a different answer depending on
what mass you attribute to a photon.  This means one of two things:
you're not using Newtonian gravity (or anything even vaguely like
it), or you've made a mistake in your calculation.  My guess is the
latter -- I suspect you're coming in in the middle of a computation
that already used one value of m, and switching to another half way
through, effectively treating a photon as an object that has two
different masses in two different parts of the calculation.  This is
just a guess, though; I have enough homework to correct without
adding this to my list.

Again, the issue is really very simple.  Honest.  In Newtonian gravity,
acceleration is independent of the mass of the object undergoing
acceleration.  You can attribute whatever mass you like to light;
if your answer depends on that choice, you've made a mistake.

My answer doesn't depend on the mass of the photon, but
on its kinetic energy.

You said that the paper

Newtonian gravitational deflection of light revisited
arXiv: physics/0508030v4 [physics. gen- ph] 17 Apr 2009
(http://xxx.if.usp.br/abs/physics/0508030)

looks right.

Or it based on the following formula

E = (1/2) mv^2 - GmMs/Rs,
where Ms and Rs are the Sun's mass and radius, v being the
speed of a particle.

Immediately afterwards, the author makes v = c, the speed of
light in vacuum, meaning that he considers that E = (1/2) mc^2
represents the kinetic energy of a photon.

As you, in your eyes, the paper looks right, you agree with the
author that a photon has such a kinetic energy, which is awfully
incorrect. Using that kinetic energy, he concludes that his
"result is precisely the same as obtained with modern space-time
curvature calculations except for a factor of two."

If the author had used the correct formula for the photon's kinetic
energy, i.e. E = mc^2, he would have obtained the same result as GR.
This is easy to verify. No need to be a brilliant mathematician for
that.

Alas, you prefer to repeat again and again the GRists' mantra

OM
EXCEPT FOR A FACTOR OF TWO

OM OM
EXCEPT FOR A FACTOR OF TWO
EXCEPT FOR A FACTOR OF TWO

OM OM OM
EXCEPT FOR A FACTOR OF TWO
EXCEPT FOR A FACTOR OF TWO
EXCEPT FOR A FACTOR OF TWO

etc. etc. etc... AD NAUSEAM

Marcel Luttgens



Steve Carlip

.

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