4 ms·

I've been offline for a few days. I don't do PF if only because it's common there that things are rarely really answered. If there's a problem with this simple

by genwin 14y ago

I've been offline for a few days. I don't do PF if only because it's common there that things are rarely really answered. If there's a problem with this simple thought experiment then a statement from it could be quoted and shown what's wrong with it. Instead you see only obfuscation and baseless allegations of wrongness. I see no solution there as I write this. > 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. This is false. Frame X is equivalent to an inertial frame says the principle of equivalence. Nothing about an inertial frame prevents one of the higher-velocity particles from passing by one of the lower-velocity (escaping) particles, like cars passing each other on the highway, which could happen in as little as a nanosecond as measured in X. In that case the r-coordinate of the higher velocity particle would not only have gotten closer to the r-coordinate of the escaping particle, it would have now the higher r-coordinate of the two particles, have passed outward through the horizon and be escaping itself. > 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). R-coordinates aren't limited to discussion of black holes of course. Your head has an r-coordinate, as do your feet. Assuming your feet are lower initially, if the r-coordinate of your feet is decreasing while the r-coordinate of your head is increasing, you are stretching and your feet are not getting closer to your head in any inertial frame. Conversely if the r-coordinate of your feet is increasing faster than the r-coordinate of your head increases, your feet are getting closer to your head in every inertial frame that contains you. Eventually your feet will pass by and be higher than your head; you will have flipped upside down. I think we've exceeded the limits of HN discussion. If you want I'll email you; let me know.

pdonis 14y ago
If you want I'll email you; let me know. No need. What you're saying is still incorrect, but the correct answer is already in what I've posted here and what's posted in the PF thread. If that doesn't answer it for you, I don't think there's any point in further discussion.
pdonis 14y ago
I think we've exceeded the limits of HN discussion. Probably, but I do see a couple of things in your post worth a brief comment: You seem to be under the impression that the r coordinate is the space coordinate of the local inertial frame. It's not; it's a coordinate in a global coordinate chart. Two objects can be approaching each other with respect to the space coordinate of the LIF but be separating with respect to the r coordinate. You also seem to be under the impression that the predicted trajectories in the LIF, if it could be extended indefinitely (which it can't), would have the particle inside the horizon moving outside it. That's not correct; the predicted trajectories in the LIF would have the particle outside the horizon falling inside it, then falling past the one that started out inside the horizon. (This has to be true because the horizon is moving outward at the speed of light, so neither particle can outrun it from the standpoint of the LIF.) The resolution of the puzzle does not depend on explaining why the particle that starts inside the horizon doesn't escape out; it depends on explaining why the particle that starts outside the horizon doesn't fall in even though the LIF predicts that it should.
pdonis 14y ago
If there's a problem with this simple thought experiment then a statement from it could be quoted and shown what's wrong with it. Since it's Saturday and I have some time I'll respond to this as well, just for the record. This is wrong in two ways: (1) I did say what was wrong with the thought experiment. You just don't want to accept that what I said is right. Of course that's your decision to make, but the fact that you don't agree with my criticism doesn't mean I didn't make one. (2) Your view of how things work in these kinds of arguments is backasswards. Extraordinary claims demand extraordinary evidence. You are making an extraordinary claim: that the theory of General Relativity, which has been developed and refined and tested against evidence for almost a century now, and which has passed every test with flying colors, somehow has a basic error of logic in one of its fundamental principles. For a comprehensive study of how well tested GR is experimentally, see here: http://relativity.livingreviews.org/Articles/lrr-2001-4/ http://relativity.livingreviews.org/Articles/lrr-2001-4/ The burden of proof is on you to back up this extraordinary claim. You don't do that by making or referring to a quick blog post that makes elementary errors and misstatements about what GR actually says. You do that the way Galileo and Einstein did it: by having extremely detailed knowledge of the theory you are attacking--knowing it better than its proponents--and by making sure that every single thing you say about that theory is correct according to its proponents. It's up to you to dot every i and cross every t and dig into the textbooks and the literature to make sure you are representing the theory correctly. You have not even come close to doing all that, and neither has the author of the blog post. When I see elementary misstatements like the ones you and the blog post author have made, that tells me it's not even worth my time to read through the blog post in detail to try to figure out what's wrong with it, because it's not even wrong. That happens quite a bit on PF as well; the things you think are "rarely really answered" there are examples of the same kind of not even wrongness. For the specific scenario under discussion here, this is what extraordinary evidence would look like: you would be able to construct, in detail, the local inertial frame in question, centered around the event of an infalling observer just crossing the horizon. By "construct, in detail", I mean you would be able to draw a spacetime diagram of it showing all the curves of interest: the horizon itself, the worldlines of all objects, curves of constant radial coordinate r, etc. You would also be able to exhibit the mathematical transformation from the coordinates in the local inertial frame to and from a global coordinate chart, such as the Painleve chart. And you would be able to exhibit the mathematical equations that give the size of the local inertial frame, and demonstrate, mathematically, that the event of two cloud particles crossing (one that starts inside the horizon and one that starts outside) must happen within that size. (When I do this computation, I find that the crossing event cannot happen within the LIF--the distance that would be required for the two particles to meet is much, much larger than the distance the LIF can cover. If you want to prove me wrong, first you have to get to that point, and you have given me no evidence that you have done so.)

by genwin 14y ago

pdonis 14y ago

If you want I'll email you; let me know. No need. What you're saying is still incorrect, but the correct answer is already in what I've posted here and what's posted in the PF thread. If that doesn't answer it for you, I don't think there's any point in further discussion.

pdonis 14y ago

I think we've exceeded the limits of HN discussion. Probably, but I do see a couple of things in your post worth a brief comment: You seem to be under the impression that the r coordinate is the space coordinate of the local inertial frame. It's not; it's a coordinate in a global coordinate chart. Two objects can be approaching each other with respect to the space coordinate of the LIF but be separating with respect to the r coordinate. You also seem to be under the impression that the predicted trajectories in the LIF, if it could be extended indefinitely (which it can't), would have the particle inside the horizon moving outside it. That's not correct; the predicted trajectories in the LIF would have the particle outside the horizon falling inside it, then falling past the one that started out inside the horizon. (This has to be true because the horizon is moving outward at the speed of light, so neither particle can outrun it from the standpoint of the LIF.) The resolution of the puzzle does not depend on explaining why the particle that starts inside the horizon doesn't escape out; it depends on explaining why the particle that starts outside the horizon doesn't fall in even though the LIF predicts that it should.

pdonis 14y ago

If there's a problem with this simple thought experiment then a statement from it could be quoted and shown what's wrong with it. Since it's Saturday and I have some time I'll respond to this as well, just for the record. This is wrong in two ways: (1) I did say what was wrong with the thought experiment. You just don't want to accept that what I said is right. Of course that's your decision to make, but the fact that you don't agree with my criticism doesn't mean I didn't make one. (2) Your view of how things work in these kinds of arguments is backasswards. Extraordinary claims demand extraordinary evidence. You are making an extraordinary claim: that the theory of General Relativity, which has been developed and refined and tested against evidence for almost a century now, and which has passed every test with flying colors, somehow has a basic error of logic in one of its fundamental principles. For a comprehensive study of how well tested GR is experimentally, see here: http://relativity.livingreviews.org/Articles/lrr-2001-4/ http://relativity.livingreviews.org/Articles/lrr-2001-4/ The burden of proof is on you to back up this extraordinary claim. You don't do that by making or referring to a quick blog post that makes elementary errors and misstatements about what GR actually says. You do that the way Galileo and Einstein did it: by having extremely detailed knowledge of the theory you are attacking--knowing it better than its proponents--and by making sure that every single thing you say about that theory is correct according to its proponents. It's up to you to dot every i and cross every t and dig into the textbooks and the literature to make sure you are representing the theory correctly. You have not even come close to doing all that, and neither has the author of the blog post. When I see elementary misstatements like the ones you and the blog post author have made, that tells me it's not even worth my time to read through the blog post in detail to try to figure out what's wrong with it, because it's not even wrong. That happens quite a bit on PF as well; the things you think are "rarely really answered" there are examples of the same kind of not even wrongness. For the specific scenario under discussion here, this is what extraordinary evidence would look like: you would be able to construct, in detail, the local inertial frame in question, centered around the event of an infalling observer just crossing the horizon. By "construct, in detail", I mean you would be able to draw a spacetime diagram of it showing all the curves of interest: the horizon itself, the worldlines of all objects, curves of constant radial coordinate r, etc. You would also be able to exhibit the mathematical transformation from the coordinates in the local inertial frame to and from a global coordinate chart, such as the Painleve chart. And you would be able to exhibit the mathematical equations that give the size of the local inertial frame, and demonstrate, mathematically, that the event of two cloud particles crossing (one that starts inside the horizon and one that starts outside) must happen within that size. (When I do this computation, I find that the crossing event cannot happen within the LIF--the distance that would be required for the two particles to meet is much, much larger than the distance the LIF can cover. If you want to prove me wrong, first you have to get to that point, and you have given me no evidence that you have done so.)