The EM field acts as a source of gravitational field
Hi, Alistair,
Alistair said:
Ok I'm under the impression that gravity only effects matter. therefore, because light is effected by black 'holes' it must have some form of matter that it is formed from. Einstein theorized that as an object gets closser to the speed of light, it will take on 'infinite mass'. and going by this it woudl take an infinite amount of energy to get an object to the speed of light. thus light contains an infinite amount of energy. (please explain this to me because i am having trouble with the whole thing.)
You've gotten some good information from HallsofIvy, but I'd add two pedantic quibbles:
1. When you referred to "it would take an infinite amount of energy to get an object to the speed of light", I think you were referring to trying to accelerate some particle with positive rest mass such as a neutron to the speed of light, and then your understanding of that point is correct--- but as HallsofIvy said, photons have zero rest mass, so at this point in your post, you suddently started talking about something different.
2. In the gtr literature, usually photons --- or more properly, since gtr is a classical field theory, "electromagnetic radiation"--- is not called "matter". Usually this term is reserved for something like a dust (pressure-free perfect fluid) or general fluid or elastic solid, e.g. in an idealized model of a stellar interior.
In addition, one should point out that in gtr, the electromagnetic field carries field energy (because it does according to Maxwell's theory of EM, which carries over with minimal changes to gtr), and this field energy gravitates. Specifically, it contributes to the stress-energy tensor T^{ab} which serves as the source of the gravitational field in gtr. If the only nongravitational mass-energy present is a "null" EM field (an EM wave), with respect to an "adapted frame field", this contribution looks like this:
T^{\hat{a}\hat{b}} = \epsilon \; \left[ \begin{matrix}1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 &0 & 0 \end{matrix} \right]
If the only nongravitational mass-energy present is a "non-null" EM field (e.g. outside a charged object), this contribution looks like this:
T^{\hat{a}\hat{b}} = \epsilon \; \left[ \begin{matrix}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 &0 & 1 \end{matrix} \right]
"Null dust", which you can think of as something like a "pressureless fluid composed of massless particles", hence the name, and which is used to model "incoherent massless radiation" generally, contributes the same way as a null EM field, except that in this case we do not insist upon providing an explict solution of Maxwell's equations (on our curved spacetime).
What this means is that an EM field does contribute to the curvature of spacetime and therefore it can indirectly affect the motion of test particles (if you prefer, the gravitational attraction of the EM field energy can alter their motion) and indeed of "light rays".
See
http://en.wikipedia.org/w/index.php?title=Exact_solutions_in_general_relativity&oldid=45119659 and
http://en.wikipedia.org/w/index.php?title=Electrovacuum_solution&oldid=43582933 with the usual cautions about the instability of Wikipedia. (I have linked here to specific versions of two WP articles which I myself edited and therefore have confidence in; the "canonical forms" given above differ inessentially from those given in the preferred version of the second article.)
Regarding light rays, interestingly enough, it turns out that according to gtr, two parallel light rays traveling in the same direction do not attract one another. But two parallel light rays traveling in opposite directions will attract one another. In practice this effect is too small to be measureable in the laboratory, however.
kesh said:
it is rather. from it's own frame of reference, it doesn't even exist lol.
I take it that kesh wasn't being entirely serious, but someone should point out that even in str, the notion of "an observer traveling at the speed of light" doesn't make much sense, and in particular, is NOT associated with any "Lorentz frame". This is related to a phenomenon noted above: in str (and thus also in gtr), it is impossible to accelerated matter with positive mass to the speed of light.
korican said:
Also since photons do not have rest mass they are not affected by gravity.
Well, I don't think korican should have put it that way, since this isn't true as stated, as korican admits in the next sentence. (After substituting "light ray" or "laser pulse" or "EM radiation" or "massless radiation" or "lightlike signal" for "photon", see "light bending" in any gtr textbook.). In addition to the fact that the gravitational field of a neutral object affecting the propagation of light, as I mentioned above, the EM field itself possesses field energy and momentum and therefore acts as a source of the gravitational field, so its gravitational effects will indirectly affect the motion even of uncharged matter.
Chris Hillman
