So light responds to gravitational pulls (Tests of general relativity - Wikipedia
Who knew that light gets less energetic as it leaves the sun?! “Gravitational Redshift.”)
My question is really: Does light warp space? It has no rest mass, but does its momentum correlate to a moving mass that CREATES a gravitational pull on other things/itself. Read the following if needed:
To illustrate my question, say that we have universe consisting of only a beam of light going by a massive planet. The light bends because of the planet’s gravitational pull, right? As I see it, one of the 2 following options is true, with the following implications.
Light warps space. If this is true, then so is the following: The planet feels the small warping of space from the light and moves toward it. This makes sense because the beam of light changes directions as it bends, and so it has a change in momentum. So the planet must move (ever so slightly) toward the beam of light in order for momentum to be conserved. This would be because the light warps space as well. The result is that the planet moves toward the light.
Light does not warp space. My GUESS is that the explanation is: The whole notion of a universe with a 3D grid with nice, “straight” x, y, and z coordinates must be thrown out. Gravity bends space! Thus, as the light bends it actually IS following the newly-formed “straight” line of space, which has been warped by the planet’s gravity. Thus the light isn’t changing momentum because, as it “bends,” it’s not deviating from its course, it’s that the very fabric of the course has just been altered. If it were to follow any OTHER course, THAT would be a change in momentum. (I.e. if it went “straight” as we think about it, THAT would be a change in momentum.) If this is true: In the situation above, the planet would not move.
So which is true?
In addition, if #1 is true, then couldn’t you take two parallel laser beams and put them near and each other and find that they attract each other, intersect, separate… and possible attract again, repeat ad infinitum and create one beam?
But if 2 is true, doesn’t that mean that if you had an (normally thought of) “parallel” beam #2 on the other side of the planet that beam #2 could “bend” the opposite direction and intersect the 1st beam? (The planet acting like an optical lens.) Here’s my point. Let’s say that both beams start out parallel, with only x momentum. As they follow the warped space and “bend” they actually keep having only x-momentum (or else they changed momentum, which means the planet has to move too… which means that light warps space too, which was the opposite of our supposition). But now we have 2 beams with only x-momentum that CROSS! Say the first beam is the x=0 line, the other is the x=2 line. How do those cross? Perhaps it’s just that we have to throw every notion that the universe has even somewhat of a Euclidean-type geometry. But then we have to throw out the idea of conserving momentum in each x,y,z direction, don’t we?
Well, I don’t know the answer, and I don’t think I can even guess (I would like for #2 to be true, though.) — I just came in to say, really awesome question. Can’t wait to find out what our resident physicists say.
Any kind of stress-energy – i.e. anything that contributes to this quantity, the Stress-Energy tensor – gravitates, and so does light. In General Relativity, it’s not really just mass that causes gravity, but rather energy, momentum, and pressure. And light’s got all of those.
Forgot to mention an interesting, counter-intuitive effect: two beams of light, travelling parallel, will actually not attract each other; however, if their propagation direction is opposite – if they’re anti-parallel --, they do!
Because they are at rest with respect to each other in the first case, hence massless, and have velocity c, plus relativistic mass, in the second? Is that how that works?
Almost, but ditch the idea of “relativistic mass”; it’s not really useful, and just makes things needlessly complicated. The only concept of mass that’s useful is what’s usually called “rest mass”.
Now, then, the key is that, even though a single photon has no mass, a system of more than one photon, as long as they’re not moving in exactly the same direction, does have mass. Mass can be considered as the portion of the energy of a system that doesn’t go away when you go to the zero-momentum reference frame. A single photon doesn’t have a zero-momentum reference frame, but a system of multiple photons does.
Thanks Astro. The first article makes it sound like #2 is true, or at least more the truth. (It also makes it sound like we’ve actually witnessed a black hole forming. I seem to have heard there’s a bit of controversy about whether they even exist, so I have a hard time believing the ho-hum tone of “Yeah, it happens all the time and we watch it happen.”) I couldn’t open the second article.
Anti-parallel attracts, but parallel doesn’t. Hmm. Interesting. I assume the anti-parallel are going PAST each other, right? 2 Lasers put butt to butt, 180 degrees, wouldn’t attract, right? Anyway, oh please do go on!
Yes a system of photons can have active gravitational ‘mass’.
One way to think of it is this:
For a (local) system of parallel photons is that for any given frame of reference you can always find another frame of reference where the energy of the system is smaller, infact the energy of the system considered in all frames of reference has a lower bound of zero.
For a (local) system of photons that aren’t parallel though you can always find a frame of reference where the energy of the system is non-zero and minimized. This will be the centre of mass frame for that system.
Chronos, I’m a bit lost by the zero-momentum reference frame for the system of photons. Is there such a frame for a single beam of light? The only one would be a frame traveling at c in the direction of the beam… but then the photons would be “still,” which isn’t good–they have to go c, right? So do you need 2 directions of photons? I’m guessing that if you had 2 directions you could pick a reference frame at an angle to the 2 that sums all the momentum to zero… but I think I’m going too far down a wrong idea.
So can we say that #2 is true? The planet doesn’t move? And then what of my idea of 2 beams with only x momentum crossing? (Bottom of 1st post) Do we have to throw out the the idea momentum being conserved in each of the x,y,z directions?
There isn’t a frame for a single beam of light (see my post above), but you’ve got the right idea. Local frames cannot travel at c relative to each other due to the hyperbolic geometry of spacetime.
Good intuition! Of course, photons being ‘at rest’ is a bit of a troublesome concept… It’s perhaps best to think in terms of (relativistic) Doppler shift: a wave front chasing you gets shifted towards longer wavelengths (i.e. red, in the case of light), one you’re approaching towards shorter (blue) ones (think about the classic example of a police car siren passing you – it sounds high pitched at first, then significantly lower after it passed you).
Now, for one photon in a vacuum, this means that you can find a frame of reference in which it is arbitrarily much red shifted, and hence, has arbitrarily small energy. The same game, of course, you can play for two (or more) photons, as long as they all travel in parallel. As soon as they don’t, this isn’t possible any more: if you get one to red shift, the other one will be blue shifted. Thus, there is some energy in the system you can’t ‘transform away’; you can at best hope to minimize it, by choosing the frame of reference in which both photons zoom away in exactly opposite directions (i.e. you imagine yourself moving in some direction in between those of the photons in such a way that relative to you, one photon goes of to the left, the other to the right). The energy each photon has in this frame (divided by c[sup]2[/sup]) is equal to its invariant mass.
Oh, to get back to the original question: The planet’s trajectory will be altered. The conservation of momentum argument is perfectly valid, even in GR: The photon’s momentum changes, so the momentum of something else must change in the opposite direction to balance it, and the planet’s the only other thing available.
I don’t quite understand this argument. Is the photon’s momentum changing? Locally definitely not, it’s worldline is still a geodesic.
You’d need a global definition of momentum and I don’t see that will always be conserved, especially in the case of a single photon under the influence of gravity which is well outside of the Newtonian limit.
I don’t claim to be an expert though, maybe there is some definition of momentum for some spacetimes for which this works?It just doesn’t seem trivial to me.
A note on the system of parallel photons: such a system has a temperature of absolute zero and is thus as impossible to create as any other zero-temperature system. So in practice, any system of photons you find will have finite mass.
Personally, I’d prefer to just say that it’s impossible because it requires infinite precision (this is probably also true of all other zero-temperature systems). But look at it however you like.
You don’t actually need a global definition of momentum; a local definition will work fine, so long as your locality is large enough.
I’m pretty sure this is wrong. I believe the event horizon is the boundary of the region from which no light cannot escape to infinity regardless of its initial direction.