"Ohad" wrote in message
...
Hello,

About the General Theory of Relativity. Newton said that gravitation is
according to the mass of the two bodies, and according to the distance
between them. Einstein said that a proof of his theory, about changing the
space, is seeing that even light is bent according to gravitation.
My question is: the mass of the photon is zero, so the light beam cannot
be
bent according to Newton, only according to Einstein. But notice that only
the rest mass of the photon is zero! The photon is moving in the speed of
light, and its mass in velocity isn't zero, is a positive number! So even
to
Newton the beam of light should be bent.

According to Newton, the mass of the photon is zero. With no mass, there
can be no Newtonian gravity.

If you are looking at the relativistic mass-equivalent of the photon's
energy you have already left Newton behind.


Tom Davidson
Richmond, VA

In article , "tadchem" writes:

"Ohad" wrote in message
...
Hello,

About the General Theory of Relativity. Newton said that gravitation is
according to the mass of the two bodies, and according to the distance
between them. Einstein said that a proof of his theory, about changing the
space, is seeing that even light is bent according to gravitation.
My question is: the mass of the photon is zero, so the light beam cannot
be
bent according to Newton, only according to Einstein. But notice that only
the rest mass of the photon is zero! The photon is moving in the speed of
light, and its mass in velocity isn't zero, is a positive number! So even
to
Newton the beam of light should be bent.

According to Newton, the mass of the photon is zero.

Really. Where in Newtonian mechanics you find such statement?

With no mass, there can be no Newtonian gravity.

Well, in Newtonian gravity the trajectory of a test mass with given
initial conditions is *independent* of the mass (here you already can
perceive a hint to the geometric interpretation of gravity). So,
while strictly speaking the trajectory of zero mass is undefined, you
can start with a finite but arbitrarily small mass and take the limit
of m - 0. The result is independent of whatever initial mass you
assumed and of the way it approaches zero.

Mati Meron | "When you argue with a fool,
| chances are he is doing just the same"

"tadchem" wrote in message ...
"Ohad" wrote in message
...
Hello,

About the General Theory of Relativity. Newton said that gravitation is
according to the mass of the two bodies, and according to the distance
between them. Einstein said that a proof of his theory, about changing the
space, is seeing that even light is bent according to gravitation.
My question is: the mass of the photon is zero, so the light beam cannot
be
bent according to Newton, only according to Einstein. But notice that only
the rest mass of the photon is zero! The photon is moving in the speed of
light, and its mass in velocity isn't zero, is a positive number! So even
to
Newton the beam of light should be bent.


COMMENT:

As you've been told, a beam of light in Newtonian physics should be
bent in the limit of zero mass, but not if the mass were exactly zero.

However, I find it helpful to consider what Newton would say about
something that had a tiny mass and was traveling at 99.999% of the
speed of light. An electron or a neutrino, perhaps. Newton would
simply predict that the path of an electron or neutrino traveling at
"nearly c" would be bent by a certain amount, proportional to the
inverse of the velocity.

But this is wrong. Einstein made this mistake himself, but was later
able to correct himself, and show that the bending of light (or for
that matter a fast neutrino or electron) in a low gravity field would
be not the Newtonian amount, but TWICE the Newtonian amount. The
reason for this is that there's an effect of the warping of space
which is ordinarily insignificant compared with the slowing of time by
gravity, for slow objects. The slowing of time effectively gives
Newtonian gravity. But when things start to go really fast, the two
effects in weak fields get to be close to equal (this is not obvious).
However, the relative magnitude of the effects draws nearer basically
because at very fast speeds the object is traveling so fast that it
spends relatively little time (as measured by the non-moving observer
in the same frame as the source of the gravity) being subject to the
field. So the tiny warping of space gets to have as much effect as the
tiny amont of time-slowing, which (as we said) provides the Newtonian
component of bending.

Einstein never talked about fast electrons or neutrinos, which have
some rest mass. But his theory predicts that their bending in weak G
fields is also twice what Newton would have predicted for them. People
just get all hung up talking about light.

SBH