Does an object's gravitational pull increase when its relativistic mass increases? Or is it dependant only on rest mess?
The source of gravitational field, within the framework of GR, is not the mass, but the so called energy-momentum tensor. At low energies, its principal component is the mass.
Was that a yes or a no? Think about it intuitively. You have an infinite number of distinct relativistic rest masses, relative to an infinite number of objects moving at various speeds relative to you. If gravitational pull increased when relativistic mass increased, some of your relativistic rest masses would warrant you being a black hole, which I’m assuming you’re not. So the answers are no to the first question, and yes to the second. Speed is relative. No relative thing is going to affect an object intrinsically; if it did then observers would disagree on what that object is (e.g. is it a black hole or not). A relative thing can affect only other relative things, like comparisons of distance measurements and comparisons of time elapsed.
What about photons, which have only relativistic mass? Would a photon produce a gravitational field equivalent to an object with a mass of hv/c^2?
Imagine I have a thermodynamically impossible perfectly insulated and incredibly strong box. Inside that box is a ball, bouncing around very very fast. All collisions between the ball and the box wall are perfectly elastic. The ball and the box both have rest mass m. Relative to the box, the ball has a speed of 0.866 c, giving it a relativistic mass of 2m. Does the box + ball system have rest mass of 3m? Is it possible to differentiate this box from a box containing two stationary balls (or substance of equivalent mass distributed evenly through the box) without opening the box?
So the box with the moving ball would produce a stronger gravitational field than a similar ball/box system were the ball was stationary? I'm mainly curious about whether or not photons produce their own gravitational fields because of their relativistic mass. If two photons were sent out on parallel courses, would they attract each other and gradually move closer together?
No photons cannot attract each other. The only way that apparently they would is if they were following geodesics in curved space (i.e. non-inertial frame of reference) thus producing the illusion that they are attracting each other.
yup yes, photons produce their own gravitational fields. anything with a nonzero stress tensor does. so they will attract each other.
yeah. if the velocity of the photon were less than c, the stress tensor would be zero, so the nonzero-ness of the stress tensor constrains the velocity of the EM radiation to be c. this is a sort of backwards way to approach it, but i suppose it is valid.
Lethe, Posted by Ryans: No photons cannot attract each other. The only way that apparently they would is if they were following geodesics in curved space (i.e. non-inertial frame of reference) thus producing the illusion that they are attracting each other. Posted by Lethe: yes, photons produce their own gravitational fields. anything with a nonzero stress tensor does. so they will attract each other. So you are in disagreement with Ryans?
Lethe knows more than me about GR. However that is not to say that I accept what he says, as I will only accept this when I do the calculation myself, as any good physicist should. Thus pending a calculation, my position is still the same, which is intuitive, but most probably incorrect.(I love it when I complete a proof or some derivation whereby the result is kicks my intuition in the arse). Lethe, are you specifically talking about the 00 component of the stress tensor, or its determinant or something similiar(I work with a metric with signature + - - -, 0 obviously being the time component. How is this generalised for curved spaces, and what Lagrangian are you using?) Cheers Ryans
so it would seem. electromagnetism has a nonzero stress tensor. nonzero stress tensor means nonzero coupling to gravity, since Einstein's equation is G=T. what else is there to consider?
Gravitationally free metrics, i.e. euclidean space. They do not interact it would seem, in euclidean (i.e. flat space), as any free field theory I know (i.e. V(phi)=0) Means that field modes do not couple. For example quantisation of the field in terms an infinite lattice of harmonic oscillators is inherently linear and homogenous, thus no photon, photon interaction. Is this correct or not?
i am not sure why you are talking about theories with no gravity. in the universe i live in, there is a nonzero gravitational field. sure, if you restrict yourself to a theory with zero gravitational field, then photons won't interact. of course, there cannot be photons at all, or else you cannot satisfy Einstein's equation. but instead of theories with no gravity, let's consider theories with nonzero gravitational fields, like the universe we live in. right, but like i said, we don't live in flat space QED is not a free field, even in flat space. sure, a free field doesn't interact. by definition. but what does this have to do with our universe?
Well I am assuming that in regions of space where the local curvature is zero, the coupling between photons would tend to zero.
gravity is a very weak force, and photons have very little mass-energy. so, yes, the gravitational coupling will be very weak. you have to have as much energy as a planet or star for the gravitational coupling to be noticeable. but that doesn't mean the coupling is zero.
Lethe, The above statement appears to me to be a very narrowily crafted statement as an attempt to undo an otherwise completely false statement. It seems more a play on words than physics and reality. It basically says "When something is zero then it is zero" but fails to acknowledge that theoretically if gravity is 1/r^2 per Newton across the universe then there is no "zero" point and the statement merely suggests a hypothetical which doesn't exist.
yeah, if you want me to admit that i think that ryans was mistaken in his statement, then here it is: i think ryans was mistaken. be careful here. the Newtonian 1/r<sup>2</sup> force only holds for slow moving massive bodies. photons are ultrarelativistic, so you cannot use that approximation with them. furthermore, photons are massless, so Newton's Law thinks that the gravitational force is zero. but, like i said, you have to take into account relativistic effects when dealing with photons. Newton's law is just wrong here.
