
#73
Dec1012, 01:40 PM

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I think there are astrophysical observations that provide evidence that radiating EM radiation cause as body to lose gravitational mass. That's probably the closest you can come to observational support. 



#74
Dec1012, 01:51 PM

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#75
Dec1012, 01:55 PM

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As far as the numbers go, unfortunately your question is too vague to answer with a concrete number. What photon energy are you considering, what is the geometry you are interested in, what measurement technique to you plan on using to generate the number of interest, etc.? Until you completely specify the problem then all that can be done is to provide you a link to the relevant concepts and solutions. 



#76
Dec1012, 02:03 PM

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Thank you everyone, I'll leave it here and move to classical physics forum to discuss photon electromagnetic field components and Maxwell's Equations. 



#77
Dec1012, 02:47 PM

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Carlip also briefly discusses the "box of light". Carlip shows that in weak field gravity, the total system (box + light) must gravitate according to the total energy. There is a similar result for strong fields , but it requires that the metric be stationary (i.e. not a function of time). The argument is different in detail from Carlip's. While I'm not aware of any paper that specifically does the strong field calculation for a box of light, the calculations aren't hard to perform. The nontechnical summary of the strong field argument is that in some sense the interior of the box, the light, does "weigh" twice as much, but that the stress in the box walls compensates for this giving a negative contribution to the weight, due to the tension in the container walls. As an aside, recall that tension and pressure are part of the stressenergy tensor  so here we see an example of stresses contributing to gravity. The more technically accurate way removes the words "in some sense" by saying that it is the Komar mass of the interior of the box that doubles for the "box of light". This makes the argument more precise, at the cost of introducing a new term that seems to scare people away from understanding the point to be made. On the other hand, some "scariness" is perhaps warranted, at least if the fear induces some caution, for reasons which will be explained below. As previously mentioned, even though the contents of the box weight twice as much, the stresses in the walls subtract from this "extra" mass, and you recover the value E/c^2 for the mass of contents + walls. It's worth mentioning at this point, at the risk of confusion, that there are several definitions of "mass" in general relativity, and NONE of them is completely general (including the Komar mass). ALL of them require certain preconditions to be applied. Understanding the conditions where they are applicable may take some work, this is where the "scariness" factor comes in. The "big three" sorts of mass in GR are Komar mass, ADM mass, and Bondi mass  you'll see a brief discussion of them in the wiki at http://en.wikipedia.org/w/index.php?...ldid=514908524 



#78
Dec1012, 03:20 PM

P: 68

Perhaps I should be more specific. I think what PeterDonis said answers the question as "yes, photons obey 1/r^2 gravity law". Because, I think what that equation describes is analogous to gravity potential which is 1/r, so that if we somehow worked out the force or acceleration we would get 1/r^2 relation.
In other words, if instead of two beams of light there were two beams of electrons or two streams of dust, where one is passing at double the distance from the planet than the other, then further away beam of electrons or stream of dust would too be "influenced" two times 



#79
Dec1012, 03:41 PM

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A better way to phrase the question asked in the OP would be: does light respond to gravity? Or, is the path of a light ray affected by gravity? The answer to that is clearly "yes". But trying to salvage an interpretation of the bending of light as responding to a 1/r^2 force law may not work, because that force law is a nonrelativistic approximation only, and light is relativistic. 



#80
Dec1012, 04:05 PM

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Carlip's paper http://arxiv.org/abs/grqc/9909014 has an expression for the defliction of a particle moving at velocity v, and a caution about the "force" interpretation.
The defleciton angle is: [tex]\theta = \frac{2GM}{bv^2}\left(1+\frac{v^2}{c^2}\right) [/tex] where b is the impact parameter (it can be thought of as the distance of closests approach IIRC). and G,M, and v are the usual. The caution is "Not to ignore the curvature of space" when calculating light deflections. This spatial curvature produces effects in GR that can not really be well described as a force  though thinking of it as a force proportional to velocity^2 comes at least very close to working. (I don't think the resulting "force" transforms properly even so, you wind up with coordinate dependencies this way.) Hopefully it's obvious why dependence on coordinates is bad in this context, and if it's not obvious, I'm afraid I don't have the heart at the moment for another long discussion of why it is bad. 



#81
Dec1012, 04:36 PM

P: 68

Which leads me to another question. If we were to measure "influence" or deflection of two beams of particles passing near some planet at the same distance away from it and with the same speed, but one beam is made of electrons and the other of particles with greater mass, say neutrons, would we be able to measure any difference? The planet would have so much more mass compared to that of those particles that it would be kind of like "hammer and feather" thing, but then again, even a small difference in the change of angle when they pass next to the planet would grow larger with the distance, and so at the end we could actually measure even the smallest differences in mass of those particles in such beams. And if all this was true and possible, then I guess that would give us a way to measure photon gravity field (mass) too, or at least put it in some perspective compared to that of an electron. 



#82
Dec1012, 05:54 PM

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#83
Dec1012, 11:10 PM

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On the other hand that perhaps makes for even more conclusive comparison regarding this topic. It seems it would mean that any beam of anything would be exactly deflected as much as any other beam of anything else, regardless of the strength of gravity field (mass) of the particles constituting any such beam. Which than means, I suppose, if everything else follows inverse square gravity law, and if beam of light bends exactly the same as a beam of anything else would, then photons too obey the same law. Does that follow? 



#84
Dec1012, 11:40 PM

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#85
Dec1012, 11:57 PM

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#86
Dec1112, 12:22 AM

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#87
Dec1112, 02:51 AM

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We are talking about electrodynamics. Quantum electrodynamics specifically, but that distinction is only necessary to establish second quantization since we are not looking at interactions. In electrodynamics, unlike electrostatics, you do not need a charge to have an electric field. Maxwell's laws allow electric field to arise as response to charge or as response to a changing magnetic field. Hence the electromagnetic wave, quantization of which is the photon. The exact electric field of a photon is given by [itex]E = E_0 e^{ik_{\mu}x^{\mu}}[/itex]. Magnetic field is given by similar expression with B=E/c. E_{0} is normalized so that total energy is [itex]\hbar \omega[/itex]. That normalization goes to zero for an exact value of k. If you take a photon in superposition of values of k, it behaves as a wave packet, having finite amplitude in a finite region of space. Gravity being fundamentally nonlinear, the exact effect this has on gravity depends on the exact wave packet. But for any distribution in k, you can write down the exact equation for E and B fields and that will give you an equation to solve for spacetime curvature. But there are a few special cases. There is plane wave solution. There is the Vaidya Metric which ignores some specifics of EM radiation, but otherwise models a radiating star. The later belongs to a class of null dust solutions which assume a uniform flux of massless particles. Let me stress that. Entire class of solutions that deal with gravity due to massless particles. You seem to be very confused on what mass is. It is not something that is required to generate gravity or people wouldn't be wasting time on such things. 



#88
Dec1112, 04:32 AM

P: 68

I made a new thread in Classical Physics forums to move this discussion away from here, I'll respond to the rest of what you said about it there. The title of the thread is: "Photon is electromagnetic field, right?" 



#89
Dec1112, 05:29 AM

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k is the wave vector. Specifically, look under the SR section that describes wave 4vector. The only serious known limitation of modern physics is incompatibility between QM and GR. There are people working on it. I have acknowledged these limitations in this thread, and have outlined the conditions under which they are irrelevant to this or that discussion. When I was in middle school, I did have roughly your understanding of physics. I did want to verify all these things for myself. So I read books and I studied physics. Things I'm telling you are verifiable, and I've tested many of them myself. I make mistakes, certainly, but I can actually recognize them and look for problems, because I have certain amount of background on the subjects. I can completely understand your desire of wanting to understand these things better and being able to see where these things come from. You are several years of rigorous education short of being able to actually follow most of these derivations. When I give you links confirming results, you do not understand them. When I try to explain, you do not understand explanation. There is not a whole lot that I can do. I have been at your state many years ago. The only way you are going to understand these things is if you start learning the underlying theory. And you have to start with basics. You have no concepts of relativity or quantum, and your understanding of electrodynamics is rudimentary. I suspect your mechanics isn't much better. That's where you have to start. Not asking questions about advanced topics in General Relativity. I mean, it's fine if you are just curious and want to know the answer, and I'm happy to give you answers as I have been for several pages, but you need to accept that neither me nor anybody else can explain these things to you on the level you will understand without learning a whole lot more physics than you know now. 



#90
Dec1112, 06:05 AM

P: 68

Trajectories, that's all that matters, to me at least. What I wanted is something concrete I can relate to classical mechanics so I can compare it with upper limits given for estimation of photon mass. I was hoping someone would spill some numbers related to photon gravity field, but I'm just as happy with those equations given by PeterDonis and pervect related to light bending. All that so I can keep my understanding that photons actually do have intrinsic mass.



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