5 ms·

I do appreciate your effort. Unfortunately I only have like half an hour a day to devote to this kind of stuff. So I have to keep this short. > the size of th

I do appreciate your effort. Unfortunately I only have like half an hour a day to devote to this kind of stuff. So I have to keep this short. > the size of the LIF is much, much smaller than the predicted distance, extrapolated from within the LIF, that it will take for the horizon to catch the probe. I'm discussing the simple picture in the blog and its caption. Not a more complex puzzle, or Laws J & K. The cloud of particles is demanded by GR to be splitting in two along the horizon, when all the particles above the horizon are let to be escaping. This "splitting in two" contradicts the equivalence principle and occurs in every arbitrarily short period of time in the life of frame X. There is always an arbitrarily short duration of time available in any LIF, so frame X's size in spacetime is not an issue. When you talk about "global coordinate chart" and a "lightlike curve" you're being unnecessarily complex, I say. We're talking a simple inertial frame of special relativity here, plus one basic prediction of GR as it relates to the horizon, namely that everything below the horizon moves inexorably inward toward the singularity. This discussion can be much simpler than you're making it. After reading your explanation I shouldn't be left wondering which sentence in the blog is incorrect or doesn't follow from its premises. The cloud splits in two and that's a "bug". To prove the blog wrong you need to show that the cloud doesn't split in two, that all the cloud's particles can in fact move outward in formation. Can you do that in a way that clearly shows which sentence in the picture's caption is incorrect?

pdonis 13y ago
Since you're keeping it short, I will as well. I don't think it's worth discussing the blog post because it's too vague and it makes too many misstatements about what relativity says. That's why I tried to take out what I saw as the essential points and put them into puzzles that were properly stated. If you can't or won't discuss the puzzles as I presented them, I won't be able to give much of a response. All I can do is point out some particular items that seem to me to capture the mistakes you and the blog post author are making. The cloud of particles is demanded by GR to be splitting in two along the horizon This is wrong; GR "demands" no such thing. The blog post's author has misunderstood GR in this respect. See below. When you talk about "global coordinate chart" and a "lightlike curve" you're being unnecessarily complex, I say And I say that you are making a big mistake here, because a proper understanding of those concepts and how they relate to the LIF centered on the horizon is crucial to properly understanding and stating what GR says about this scenario. You'll see several examples of this below. one basic prediction of GR as it relates to the horizon, namely that everything below the horizon moves inexorably inward toward the singularity That means everything below the horizon must decrease its r coordinate in the global coordinate chart. It does not mean that everything below the horizon must decrease its x coordinate in the LIF. Remember: the horizon itself is the line t = x in the LIF; i.e., the horizon is moving in the positive x direction in the LIF at the speed of light, and it passes through the origin of the LIF at t = 0, x = 0. So a "cloud" particle that is at some negative x value at t = 0 in the LIF will be inside the horizon, and a "cloud" particle that is at some positive x value at t = 0 in the LIF will be outside the horizon; and it is perfectly possible for the first particle (inside the horizon) to be moving in the positive x direction in the LIF faster than the second particle. And this can be true even if the second particle (the one outside the horizon) is moving at "escape velocity". And it can also be true even though the first particle's r coordinate is decreasing and the second particle's r coordinate is increasing. My previous post gave more details on why those statements are true. Oh, and one other thing: what does "toward the singularity" mean in the LIF? Which direction is the singularity in? The answer is, it's in the positive t direction--i.e., it's in the future. So any object in the LIF is moving "toward the singularity" as far as the LIF is concerned, since all objects move towards the future. There is no way to tell, from within the LIF, which objects are going to ultimately hit the singularity and which ones are not. That's a global concept. To prove the blog wrong you need to show that the cloud doesn't split in two, that all the cloud's particles can in fact move outward in formation. My previous posts (plus all the ones in the earlier HN thread I linked to, plus what I posted on PF) have already done that, multiple times. However, I've given a quick recap above. This discussion can be much simpler than you're making it. If only that were true.
- fargolime 13y ago
  > That means everything below the horizon must decrease its r coordinate in the global coordinate chart. Agreed. > It does not mean that everything below the horizon must decrease its x coordinate in the LIF. Agreed. > ...it is perfectly possible for the first particle (inside the horizon) to be moving in the positive x direction in the LIF faster than the second particle. Agreed. > And this can be true even if the second particle (the one outside the horizon) is moving at "escape velocity". Agreed. > And it can also be true even though the first particle's r coordinate is decreasing and the second particle's r coordinate is increasing. Disagree. There is no way you could show this for an inertial frame falling in the Earth's atmosphere, like for a skydiver (ignoring air friction). The EP demands that the laws of physics in the skydiver's frame and frame X are the same, so what you say here should be the same for the skydiver. Of course in the skydiver's frame you wouldn't use terms like "global coordinate chart" and a "lightlike curve", as that would be unnecessarily complex. In the skydiver's LIF under the conditions above, the first particle (the lower particle) would always be moving in the positive x direction in the LIF slower than the second (upper) particle, regardless of the skydiver's speed relative to the Earth, and regardless of the second particle's speed relative to the Earth (i.e. it doesn't need to be escaping).
  - pdonis 13y ago
    > Disagree. Then you are disagreeing with the theory of relativity, because what I've said is what the theory of relativity says. See below. > The EP demands that the laws of physics in the skydiver's frame and frame X are the same True. > so what you say here should be the same for the skydiver False, because there is no law of physics that says the r coordinate has to behave the same in every LIF. The r coordinate is a global coordinate, not a coordinate in the LIF; so as soon as you talk about the r coordinate, you are not just talking about the LIF, you are talking about the relationship between the LIF and a global coordinate chart. And there is no law of physics that says that relationship must be the same for every LIF. In fact that relationship is very different for the skydiver LIF as compared to the LIF that is falling through the horizon of a black hole. So any reasoning you do based on the assumption that that relationship is the same for both is simply wrong. > Of course in the skydiver's frame you wouldn't use terms like "global coordinate chart" As soon as you talk about the r coordinate, you are using a global coordinate chart, whether you realize it or not. So by not using such terms, you are failing to understand a key aspect of the scenario. > as that would be unnecessarily complex. It's (somewhat) complex, yes, but it's not "unnecessarily" complex. As I've said several times, understanding the proper relationship between the LIF and the global r coordinate is crucial if you want to correctly state what relativity says about this scenario. You and the blog post author have given excellent demonstrations of the mistakes you make if you don't have that understanding.

pdonis 13y ago

Since you're keeping it short, I will as well. I don't think it's worth discussing the blog post because it's too vague and it makes too many misstatements about what relativity says. That's why I tried to take out what I saw as the essential points and put them into puzzles that were properly stated. If you can't or won't discuss the puzzles as I presented them, I won't be able to give much of a response. All I can do is point out some particular items that seem to me to capture the mistakes you and the blog post author are making. The cloud of particles is demanded by GR to be splitting in two along the horizon This is wrong; GR "demands" no such thing. The blog post's author has misunderstood GR in this respect. See below. When you talk about "global coordinate chart" and a "lightlike curve" you're being unnecessarily complex, I say And I say that you are making a big mistake here, because a proper understanding of those concepts and how they relate to the LIF centered on the horizon is crucial to properly understanding and stating what GR says about this scenario. You'll see several examples of this below. one basic prediction of GR as it relates to the horizon, namely that everything below the horizon moves inexorably inward toward the singularity That means everything below the horizon must decrease its r coordinate in the global coordinate chart. It does not mean that everything below the horizon must decrease its x coordinate in the LIF. Remember: the horizon itself is the line t = x in the LIF; i.e., the horizon is moving in the positive x direction in the LIF at the speed of light, and it passes through the origin of the LIF at t = 0, x = 0. So a "cloud" particle that is at some negative x value at t = 0 in the LIF will be inside the horizon, and a "cloud" particle that is at some positive x value at t = 0 in the LIF will be outside the horizon; and it is perfectly possible for the first particle (inside the horizon) to be moving in the positive x direction in the LIF faster than the second particle. And this can be true even if the second particle (the one outside the horizon) is moving at "escape velocity". And it can also be true even though the first particle's r coordinate is decreasing and the second particle's r coordinate is increasing. My previous post gave more details on why those statements are true. Oh, and one other thing: what does "toward the singularity" mean in the LIF? Which direction is the singularity in? The answer is, it's in the positive t direction--i.e., it's in the future. So any object in the LIF is moving "toward the singularity" as far as the LIF is concerned, since all objects move towards the future. There is no way to tell, from within the LIF, which objects are going to ultimately hit the singularity and which ones are not. That's a global concept. To prove the blog wrong you need to show that the cloud doesn't split in two, that all the cloud's particles can in fact move outward in formation. My previous posts (plus all the ones in the earlier HN thread I linked to, plus what I posted on PF) have already done that, multiple times. However, I've given a quick recap above. This discussion can be much simpler than you're making it. If only that were true.

fargolime 13y ago
> That means everything below the horizon must decrease its r coordinate in the global coordinate chart. Agreed. > It does not mean that everything below the horizon must decrease its x coordinate in the LIF. Agreed. > ...it is perfectly possible for the first particle (inside the horizon) to be moving in the positive x direction in the LIF faster than the second particle. Agreed. > And this can be true even if the second particle (the one outside the horizon) is moving at "escape velocity". Agreed. > And it can also be true even though the first particle's r coordinate is decreasing and the second particle's r coordinate is increasing. Disagree. There is no way you could show this for an inertial frame falling in the Earth's atmosphere, like for a skydiver (ignoring air friction). The EP demands that the laws of physics in the skydiver's frame and frame X are the same, so what you say here should be the same for the skydiver. Of course in the skydiver's frame you wouldn't use terms like "global coordinate chart" and a "lightlike curve", as that would be unnecessarily complex. In the skydiver's LIF under the conditions above, the first particle (the lower particle) would always be moving in the positive x direction in the LIF slower than the second (upper) particle, regardless of the skydiver's speed relative to the Earth, and regardless of the second particle's speed relative to the Earth (i.e. it doesn't need to be escaping).
- pdonis 13y ago
  > Disagree. Then you are disagreeing with the theory of relativity, because what I've said is what the theory of relativity says. See below. > The EP demands that the laws of physics in the skydiver's frame and frame X are the same True. > so what you say here should be the same for the skydiver False, because there is no law of physics that says the r coordinate has to behave the same in every LIF. The r coordinate is a global coordinate, not a coordinate in the LIF; so as soon as you talk about the r coordinate, you are not just talking about the LIF, you are talking about the relationship between the LIF and a global coordinate chart. And there is no law of physics that says that relationship must be the same for every LIF. In fact that relationship is very different for the skydiver LIF as compared to the LIF that is falling through the horizon of a black hole. So any reasoning you do based on the assumption that that relationship is the same for both is simply wrong. > Of course in the skydiver's frame you wouldn't use terms like "global coordinate chart" As soon as you talk about the r coordinate, you are using a global coordinate chart, whether you realize it or not. So by not using such terms, you are failing to understand a key aspect of the scenario. > as that would be unnecessarily complex. It's (somewhat) complex, yes, but it's not "unnecessarily" complex. As I've said several times, understanding the proper relationship between the LIF and the global r coordinate is crucial if you want to correctly state what relativity says about this scenario. You and the blog post author have given excellent demonstrations of the mistakes you make if you don't have that understanding.