4 ms·

> Because spacetime is curved, and the curvature limits the size of a local inertial frame straddling the horizon. True but irrelevant. The thought experiment

by genwin 14y ago

> Because spacetime is curved, and the curvature limits the size of a local inertial frame straddling the horizon. True but irrelevant. The thought experiment needs only an arbitrarily small time interval as measured in X to make its case, so the size of X doesn't matter. That said, X can be arbitrarily large in principle, even light years across, just make the black hole as massive as needed. When X is light years across the escaping particles needn't exit X for years, yet the thought experiment is concluded in as little as a nanosecond. > Because the particles that are escaping have to be moving to the right at very, very close to the speed of light, whereas the particles that are not escaping are not. This is not a contradiction. The particles below the horizon can have a higher velocity in the outward direction than the escaping particles do. The velocities of the particles below the horizon is not specified in the diagram, and there's no limit to how close any of the particles' velocities can be to c, as measured in X. When all the particles above the horizon are escaping and all the particles below the horizon are let to have a velocity closer to c in the outward direction than the escaping particles have, GR still demands that the cloud splits, unlike what would be predicted for an inertial frame with the same velocities for particles specified. In an inertial frame under those conditions the particles with higher velocities would be moving closer to the other particles, not getting further away from them. There is a contradiction. > Another way to see what's going on is to ask what a line of constant radius r looks like in Frame X. I understand your example here. Nevertheless the cloud splits under conditions where it wouldn't split in an inertial frame in special relativity, in contradiction with the principle of equivalence. Unless that can be disproved it seems the blog raises a valid issue with GR. > I haven't done any such thing. You said "you won't be pointing to the singularity in the center of the black hole there". When you say that singularities have a location in time only you can't then refer to their location in space without contradicting yourself. The "in the center of the black hole there" references a place in space. You'd have to instead be careful to say something like "you won't be pointing to the singularity that you say is in the center of the black hole there". > You say you have taken classes on this material; have you raised the issues you are raising here in class? I first saw this blog yesterday.

pdonis 14y ago
When all the particles above the horizon are escaping and all the particles below the horizon are let to have a velocity closer to c in the outward direction than the escaping particles have, GR still demands that the cloud splits, unlike what would be predicted for an inertial frame with the same velocities for particles specified. In an inertial frame under those conditions the particles with higher velocities would be moving closer to the other particles, not getting further away from them. There is a contradiction. This is actually a better statement of the argument than the one given on the web page (better because it's more concise and doesn't get bogged down in irrelevancies); in fact it makes it clearer to me just what the argument is actually supposed to be. However, it's still not a valid argument against GR. Here's why: GR agrees that, with respect to Frame X, the particle above the horizon and the particle below the horizon get closer together! But only within the confines of Frame X, and only with respect to distance relative to Frame X. Distance is frame-dependent; distance relative to Frame X is not the same thing as distance with respect to the radial coordinate r that is used in a global coordinate chart. The fact that the particles are getting closer with respect to distance relative to Frame X does not mean that they are getting closer together with respect to the coordinate r; in fact they are not. The particle inside the horizon has an r coordinate that decreases with time, while the one outside the horizon has an r coordinate that increases with time (here "time" is time with respect to Frame X). Also, the fact that the particles are getting closer together with respect to Frame X does not mean that they will be getting closer together with respect to some other local inertial frame centered on an event further along the horizon. Local inertial frames centered on different events don't "line up" in curved spacetime the way they do in flat spacetime; that's one way of expressing what it means for a spacetime to be curved. So you can't assume that, just because the particles are getting closer together with respect to Frame X, they will continue to get closer together once they've left Frame X, much less that they will continue to get closer together until they meet. That deduction would be valid in flat spacetime, but it isn't in curved spacetime. When you say that singularities have a location in time only you can't then refer to their location in space without contradicting yourself. The "in the center of the black hole there" references a place in space. You'd have to instead be careful to say something like "you won't be pointing to the singularity that you say is in the center of the black hole there". Fine, consider my statement suitably modified (it should have been obvious from context that that's what I meant anyway, but if you insist on quibbling over language, so be it). As modified, the statement is true. Instead of quibbling over language, you could have asked a relevant question: what are you pointing at when you point at the center of the galaxy? The problem with this question is that it assumes that there is a unique answer to it; that there is some unique "object" sitting "at the center of the galaxy". In an ordinary spacetime without a black hole present, that would be a valid assumption; but it isn't when there is a black hole present. In one sense, when you point at the center of the galaxy, you could be said to be pointing at the object or objects that originally collapsed to form the black hole there; in another sense, you could be said to be pointing at the hole's horizon. Once again, a spacetime with a black hole in it doesn't work like the ordinary flat spacetime you are used to, or even like an ordinary curved spacetime with a planet or star in the center instead of a black hole (so that there is no event horizon and no singularity). I first saw this blog yesterday. But haven't scenarios at least something like this come up in your classes?

by genwin 14y ago

pdonis 14y ago

When all the particles above the horizon are escaping and all the particles below the horizon are let to have a velocity closer to c in the outward direction than the escaping particles have, GR still demands that the cloud splits, unlike what would be predicted for an inertial frame with the same velocities for particles specified. In an inertial frame under those conditions the particles with higher velocities would be moving closer to the other particles, not getting further away from them. There is a contradiction. This is actually a better statement of the argument than the one given on the web page (better because it's more concise and doesn't get bogged down in irrelevancies); in fact it makes it clearer to me just what the argument is actually supposed to be. However, it's still not a valid argument against GR. Here's why: GR agrees that, with respect to Frame X, the particle above the horizon and the particle below the horizon get closer together! But only within the confines of Frame X, and only with respect to distance relative to Frame X. Distance is frame-dependent; distance relative to Frame X is not the same thing as distance with respect to the radial coordinate r that is used in a global coordinate chart. The fact that the particles are getting closer with respect to distance relative to Frame X does not mean that they are getting closer together with respect to the coordinate r; in fact they are not. The particle inside the horizon has an r coordinate that decreases with time, while the one outside the horizon has an r coordinate that increases with time (here "time" is time with respect to Frame X). Also, the fact that the particles are getting closer together with respect to Frame X does not mean that they will be getting closer together with respect to some other local inertial frame centered on an event further along the horizon. Local inertial frames centered on different events don't "line up" in curved spacetime the way they do in flat spacetime; that's one way of expressing what it means for a spacetime to be curved. So you can't assume that, just because the particles are getting closer together with respect to Frame X, they will continue to get closer together once they've left Frame X, much less that they will continue to get closer together until they meet. That deduction would be valid in flat spacetime, but it isn't in curved spacetime. When you say that singularities have a location in time only you can't then refer to their location in space without contradicting yourself. The "in the center of the black hole there" references a place in space. You'd have to instead be careful to say something like "you won't be pointing to the singularity that you say is in the center of the black hole there". Fine, consider my statement suitably modified (it should have been obvious from context that that's what I meant anyway, but if you insist on quibbling over language, so be it). As modified, the statement is true. Instead of quibbling over language, you could have asked a relevant question: what are you pointing at when you point at the center of the galaxy? The problem with this question is that it assumes that there is a unique answer to it; that there is some unique "object" sitting "at the center of the galaxy". In an ordinary spacetime without a black hole present, that would be a valid assumption; but it isn't when there is a black hole present. In one sense, when you point at the center of the galaxy, you could be said to be pointing at the object or objects that originally collapsed to form the black hole there; in another sense, you could be said to be pointing at the hole's horizon. Once again, a spacetime with a black hole in it doesn't work like the ordinary flat spacetime you are used to, or even like an ordinary curved spacetime with a planet or star in the center instead of a black hole (so that there is no event horizon and no singularity). I first saw this blog yesterday. But haven't scenarios at least something like this come up in your classes?