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Re: [Phys-l] starlight deflection



Hi all-
This thread is traversing the boundary of a very sticky problem in general relativity, about which I know very little. - namely, the two-body problem. About all I know are the words; the general problem was solved in the '60's, I think that Fre Ernst (then at IIT) was prominently involved in the solution, and the inverse scattering method played a crucial role in Ernst's solution. Roughly everything I know about this I learned from Fred when several of us theorists were enjoying meals in some of Chicago's Japanese restaurants. I doubt that anything was reduced to writing on those occasions.
Regards,
Jack



On Sun, 14 Oct 2007, LaMontagne, Bob wrote:

How do we accomodate the wavelenth and frequency changes of the photon as it traverses the varying gravitational field (warpage?) as it skims by the sun?

Bob at PC

________________________________

From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of Fayngold, Moses
Sent: Sun 10/14/2007 11:58 AM
To: Forum for Physics Educators; phys-l@carnot.physics.buffalo.edu
Subject: Re: [Phys-l] starlight deflection



David Ward wrote:

"Starlight deflects as it grazes the sun, as the sun's mass warps space...so the vector momentum of a photon is altered by its encounter with the sun. But an altered momentum means that a force was exerted. So, does the starlight tug ever-so-slightly on the sun? Photons lack mass, so I suspect they don't warp spacetime..."

The last sentence in this question illustrates disadvantages of the current fashion to consider ONLY invariant characteristics of an object as something worth considering. Such view applied straightforwardly to the described situation might indeed tempt one to think that a photon does not warp spacetime since its rest mass is zero. Such conclusion would be wrong for two reasons. First, in case of a photon, its rest mass does not store any information about this photon whatsoever (except for the trivial notion that it moves with the invariant speed.) It is its RELATIVISTIC MASS (its energy) that is relevant characteristic. Second, the spacetime is warped by RELATIVISTIC MASS (more accurately, by energy-momentum) of an object rather than by its rest mass alone. Neglecting this distinction is OK in case of a massive stationary object, but not OK for a moving object, especially such as a photon. A photon does warp spacetime, and the resulting spacetime curvature is entirely d!
et
ermined by its relativistic mass.

"In any event, this boils down to "if the sun exerts a force (momentum alteration) on a photon does the photon do the same to the sun?" My general relativity is so very poor- I suspect the answer may lie there."

The answer to this question is yes, although its details may be rather subtle. If you have two electric charges - one stationary and the other passing by, they exert forces on one another, but these forces do not generally satisfy the requirement of Newton's third law (equal in magnitude and opposite in direction); this may appear to contradict conservation of the net momentum, but it does not, because the net momentum includes also the momentum of the EM field of the system, which was left out when we considered the charges only.
The same reasoning applies to masses and gravitational field of a system.


Moses Fayngold,
NJIT




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