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| Tags: general, gravitons, relativity |
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Gordon D. Pusch wrote in message
... (Starblade Darksquall) writes: [snip] A beam of light only exerts "no gravitational force" on _another beam of light traveling in the same direction_. On a massive particle, it exerts =TWICE= the "gravitational force" one would naively calculate by Newton, just as it experiences =TWICE= the gravitational deflection that one would naively calculate by Newton --- and two light beams traveling in opposite directions each experience _FOUR TIMES_ the "gravitational force" and gravitational deflection one would naively calculate using Newton. Wrong. In the center-of-momentum system, total energy gravitates, nothing more nor less. Newtonian physics has nothing to say about photons or light. In the proximity of massive bodies, photons follow null-geodesics wherein, even in the limit of small mass and large distance, the Newtonian gravitational potential is everywhere "mulled-out". Unlike the Newtonian trajectories followed by massive test particles, the deflection angle of light via space-time curvature is independent of photon momentum. [Old Man] -- Gordon D. Pusch |
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"Old Man" writes:
Gordon D. Pusch wrote in message ... (Starblade Darksquall) writes: [snip] A beam of light only exerts "no gravitational force" on _another beam of light traveling in the same direction_. On a massive particle, it exerts =TWICE= the "gravitational force" one would naively calculate by Newton, just as it experiences =TWICE= the gravitational deflection that one would naively calculate by Newton --- and two light beams traveling in opposite directions each experience _FOUR TIMES_ the "gravitational force" and gravitational deflection one would naively calculate using Newton. Wrong. I'm sorry, but it is YOU who are wrong. This is a =VERY= well-established general relativistic result, first derived by Tolman, Ehrenfest, and Podolsky in 1931 [Phys. Rev. v.37, p.602; see also Tolman "Relativity, Thermodynamics and Cosmology" (Oxford 1934), and "The gravitational interaction of light: from weak to strong fields," by V. Faraoni and R.M. Dumse, http://arxiv.org/abs/gr-qc/9811052]. John Wheeler makes use of this important result in his theory of "geons" --- objects composed entirely of electromagnetic or gravitational waves that are quasi-bound by their own self-gravitation. In the center-of-momentum system, total energy gravitates, nothing more nor less. Sorry, wrong. I don't know where you are getting that from, but it isn't from general relativity. I challenge you to find =ANY= literature citation supporting your claim that "In the center-of-momentum system, total energy gravitates, nothing more nor less." (Heck, the total energy isn't even _localized_, whether in the center of momentum frame or any other frame! It is the energies of the PHOTON WAVE_PACKETS that appear in the geodesic equation, not the "center of momentum energy" of the pair !!!) In the proximity of massive bodies, photons follow null-geodesics wherein, even in the limit of small mass and large distance, the Newtonian gravitational potential is everywhere "mulled-out". Sorry, wrong. The Newtonian potential does indeed appear in the weak field geodesic equation, and it is in no way "nulled out," even for null geodesics, or else there would be NO DEFLECTION OF LIGHT AT ALL! In fact, the effective "gravitational force" analog (the terms involving the Christoffel symbol in the geodesic equation) is =DOUBLED= on photons because they feel both spacelike and timelike constributions proportional to the "potential gradient," which is why the gravitational deflection of photons is twice what one naively expects. Unlike the Newtonian trajectories followed by massive test particles, the deflection angle of light via space-time curvature is independent of photon momentum. That's because a photon's momentum per unit energy (i.e., its velocity) is independent of energy. The corresponding Newtonian analog is momentum per unit MASS, not energy, which is again velocity --- and the deflection of all Newtonian test-particles with the same initial velocity is likewise independent of their momentum. You need to compare apples with apples, not oranges! -- Gordon D. Pusch perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;' |
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In sci.physics Gordon D. Pusch wrote:
"Old Man" writes: Gordon D. Pusch wrote in message ... (Starblade Darksquall) writes: [snip] A beam of light only exerts "no gravitational force" on _another beam of light traveling in the same direction_. On a massive particle, it exerts =TWICE= the "gravitational force" one would naively calculate by Newton, just as it experiences =TWICE= the gravitational deflection that one would naively calculate by Newton --- and two light beams traveling in opposite directions each experience _FOUR TIMES_ the "gravitational force" and gravitational deflection one would naively calculate using Newton. Wrong. I'm sorry, but it is YOU who are wrong. This is a =VERY= well-established general relativistic result, first derived by Tolman, Ehrenfest, and Podolsky in 1931 [Phys. Rev. v.37, p.602; see also Tolman "Relativity, Thermodynamics and Cosmology" (Oxford 1934), and "The gravitational interaction of light: from weak to strong fields," by V. Faraoni and R.M. Dumse, http://arxiv.org/abs/gr-qc/9811052]. John Wheeler makes use of this important result in his theory of "geons" --- objects composed entirely of electromagnetic or gravitational waves that are quasi-bound by their own self-gravitation. This is a bit tricky -- you're both right (or both wrong), depending on the details of the system you're talking about. For pure disordered electromagnetic radiation, it is definitely true that the effective gravitational mass is twice the energy. On the other hand, if you look at ``light in a box of mirrors,'' and assume that the matter that makes up the mirrors is electromagnetically bound, there is some cancellation between the energy of the light and the binding energy needed to keep the walls of the box from being pushed apart. If you use the virial theorem, you'll find that the total electromagnetic contribution to the mass is now just the energy, not twice the energy. I discuss this issue in section IV of gr-qc/9909014. Steve Carlip |
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#7
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Quantum gravity and GR gravity,are about as oposite as can be. One
works well in the micro the other works in the macro. QM is the way to go. Bert |
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#9
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In article ,
Starblade Darksquall wrote: (G=EMC^2 Glazier) wrote in message ... Quantum gravity and GR gravity,are about as oposite as can be. One works well in the micro the other works in the macro. QM is the way to go. Bert I really dislike how you throw the whole relativity thing out the window in favor of Quantom Mechanics. Can't one make a sort of a compromise? People have been doing quantum mechanics on curved spacetimes for years. That's how Hawking radiation was derived. It's a semiclassical theory in that the spacetime wasn't quantized. Quantum theories of gravity tend to get extra dimensions. -- "Is that plutonium on your gums?" "Shut up and kiss me!" -- Marge and Homer Simpson |
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#10
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In sci.physics, Starblade Darksquall
wrote on 11 Jul 2003 21:30:13 -0700 : (G=EMC^2 Glazier) wrote in message ... Quantum gravity and GR gravity,are about as oposite as can be. One works well in the micro the other works in the macro. QM is the way to go. Bert I really dislike how you throw the whole relativity thing out the window in favor of Quantom Mechanics. Can't one make a sort of a compromise? I have seen a relativistic form of the Schrödinger equation. :-) (...Starblade Riven Darksquall...) -- #191, It's still legal to go .sigless. |
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