How come a massless particle is affected by gravity?

How come it is that a proton cannot escape a black hole? With no mass, why is it so seriously affected as to be unable to escape?

??? A proton has a mass of about 1.672×10^−24 grams. Do you mean a photon? (Which has no rest mass, but has mass because it is travelling at the speed of light).

Not just black holes, but just simple gravitational lensing of photons. How does that work? I am going to just guess that the answer has something with the fact that general theory of relativity states that space itself is warped by gravity, so the photons are just following the contours of the “fabric” of space. Am I close?

Yes [slaps head]. A photon.

Because Newtonian gravity is a special case of general relativity. Mass-energy distorts space-time so that all motion through space-time is affected.

To explain it visually: if there’s no external forces (note that in general relativity, gravity is not a force, but a pseudo-force due to the frame of reference) on an object, it will travel in a straight line. But, near a large mass, space-time is warped so that straight isn’t “straight”. The “curved” path that the object follows due to “gravity” is actually a (locally) straight path through space-time.
Or, to put it in terms of Newton, the force of gravity isF = G M m / r[sup]2[/sup]and the acceleration isF = m aIf we solve for acceleration, the mass of the small object cancels out:a = G M / r[sup]2[/sup]Of course, you can’t really cancel the mass if it’s zero, but it shows that the acceleration is not a function of the object’s mass. Which is in agreement with general relativity (to zeroth order, anyway).

Well, I don’t know about lensing, but that’s exactly how the attraction works.

The basics of it are that photons have momentum, despite not having mass*, and gravity isn’t a force one object exerts on another but rather is a, uh, thing that curves space-time.

Imagine you have some frictionless, flexible surface. Hell, forget that - imagine you have a hollowed-out table, so all you have is a rectangular frame, which you stretch a sheet of incredibly smooth plastic over. Put a bowling ball in the middle of the plastic sheet. The plastic is your black hole/planet/whatever. The warping of the plastic around it is the gravitation field as represented in space-time. Now, take a little tiny ball bearing, like the type in the slide mechanism of a file cabinet drawer. Roll the ball bearing across the plastic as fast as possible.

It’s still going to turn slightly towards the bowling ball, because the surface it’s traveling on warps that direction. It might not get pulled all the way over, but there will be some ‘attraction’, because of the way that space-time is curved a bit.

Also, instead of listening to me - because I have an extremely weak grasp on this and frankly am kind of stupid - read this.

*In simplified terms. I believe it’s more accurate to say that, “Well, they have momentum, so that makes us think that they should have mass, but we’ve tried quite a number of times to measure it, and if they do have mass, it’s far, far less than what we have the ability to measure.”

ETA: Or, what Pleonast said, only I said it dumber.

When you get a black hole, the warping of spacetime is so severe that space and time actually swap roles. The direction towards the center of the black hole is the future, and the direction away from the center is the past. So you can’t shine a light out of a black hole for the same reason you can’t shine a light towards last Thursday.

Note, by the way, that this has nothing to do with escape speed. If you use the Newtonian formula for escape speed, you find that the escape speed of a black hole is c, but this formula isn’t really relevant in general relativity, and it’s only a coincidence that it gives you the correct value for the size of a black hole (many similar formulas, if you try to shift them from Newton to Einstein, end up being off by a factor of 2 or so).

Light always takes the shortest path between two points – in Euclidean (‘flat’) space, the notions of ‘shortest path’ and ‘straight line’ merely happen to coincide, that’s all. The same is not true for a more general, ‘curved’ space; here, the notion of ‘shortest path’ generalizes to what’s called a geodesic – great circles on a sphere, for instance.