Our universe within a larger universe? So suggests wormhole research (2010)(newsinfo.iu.edu)
newsinfo.iu.edu
Our universe within a larger universe? So suggests wormhole research (2010)
http://newsinfo.iu.edu/news/page/normal/13995.html
45 comments
The paper (at http://arxiv.org/abs/0902.1994) does offer some justification for the identification of B and C, or rather points at the work of someone else who allegedly does so.
"The completeness of the particle's geodesic in the spacetime of the Einstein-Rosen bridge in the Kruskal coordinates can be explained if we note that both coordinate pairs (-U,-V) and (U,V) mathematically correspond to the same coordinates r,t. Rindler suggested that both coordinate pairs (-U,-V) and (U,V) physically represented the same coordinates r,t, i.e. region III is identical with region I, and (interior) region IV is identical with region II; the Kruskal spacetime is elliptic. In order to represent the Einstein-Rosen bridge in the Kruskal coordinates, we need to impose Rindler's elliptic identification of event antipodes only on the line V=U, i.e. only the two antipodal future event horizons are identical. After the particle reaches the event horizon of an Einstein-Rosen black hole at point B, it moves from point C, which is identical with point B, to point D, which is related to point A via the transformation (2) of the isotropic radial coordinate r. As the particle moves from point C to D, the proper time tau increases, while the coordinate time t decreases (runs in the reverse direction with respect to observers in region I). This reversion does not cause any problems, because it occurs after t -> infinity, so observers in region I never see it."
I know approximately nothing about general relativity so shan't attempt to comment on the physics of this, but I have to say that there are a bunch of stylistic features that to me strongly suggest an author who isn't thinking very clearly.
A bit of googling for the Rindler reference brings up a snippet from "300 years of gravitation" by Hawking and Israel:
"Since it is, indeed, 'hard to believe that every mass point should have the effect of splitting the universe in two, thus necessitating a second copy of ours' (Rindler, 1965), the elliptic interpretation was resurrected six years later, with varying degrees of reservation, independently by a number of authors (...), but was soon abandoned. Quite apart from the conical singularity there were obvious problems with causality which proved to be insurmountable."
With, again, the caveat that I know scarcely anything about general relativity, my understanding of this is that the bit about not splitting the universe in two is a reason in favour of this "elliptic interpretation" (saying that certain pairs of points in a particular model are actually the same physical point) but that for other reasons -- that singularity, and the "obvious problems with causality" -- the interpretation was abandoned. In the particular context of Popławski's paper, it seems like that singularity might correspond to something with some physical significance, and the causality problems -- IIUC, the point is that if you identify (u,v) with (-u,-v) everywhere then it's easy to make closed timelike loops, so that you could keep going "forward" in time and end up back where you started -- might not matter because the black hole is "in the way" of all the loops you could make. It all seems a bit dodgy, though -- but, I repeat, I don't know anything and you probably shouldn't take much notice of anything I say.
"The completeness of the particle's geodesic in the spacetime of the Einstein-Rosen bridge in the Kruskal coordinates can be explained if we note that both coordinate pairs (-U,-V) and (U,V) mathematically correspond to the same coordinates r,t. Rindler suggested that both coordinate pairs (-U,-V) and (U,V) physically represented the same coordinates r,t, i.e. region III is identical with region I, and (interior) region IV is identical with region II; the Kruskal spacetime is elliptic. In order to represent the Einstein-Rosen bridge in the Kruskal coordinates, we need to impose Rindler's elliptic identification of event antipodes only on the line V=U, i.e. only the two antipodal future event horizons are identical. After the particle reaches the event horizon of an Einstein-Rosen black hole at point B, it moves from point C, which is identical with point B, to point D, which is related to point A via the transformation (2) of the isotropic radial coordinate r. As the particle moves from point C to D, the proper time tau increases, while the coordinate time t decreases (runs in the reverse direction with respect to observers in region I). This reversion does not cause any problems, because it occurs after t -> infinity, so observers in region I never see it."
I know approximately nothing about general relativity so shan't attempt to comment on the physics of this, but I have to say that there are a bunch of stylistic features that to me strongly suggest an author who isn't thinking very clearly.
A bit of googling for the Rindler reference brings up a snippet from "300 years of gravitation" by Hawking and Israel:
"Since it is, indeed, 'hard to believe that every mass point should have the effect of splitting the universe in two, thus necessitating a second copy of ours' (Rindler, 1965), the elliptic interpretation was resurrected six years later, with varying degrees of reservation, independently by a number of authors (...), but was soon abandoned. Quite apart from the conical singularity there were obvious problems with causality which proved to be insurmountable."
With, again, the caveat that I know scarcely anything about general relativity, my understanding of this is that the bit about not splitting the universe in two is a reason in favour of this "elliptic interpretation" (saying that certain pairs of points in a particular model are actually the same physical point) but that for other reasons -- that singularity, and the "obvious problems with causality" -- the interpretation was abandoned. In the particular context of Popławski's paper, it seems like that singularity might correspond to something with some physical significance, and the causality problems -- IIUC, the point is that if you identify (u,v) with (-u,-v) everywhere then it's easy to make closed timelike loops, so that you could keep going "forward" in time and end up back where you started -- might not matter because the black hole is "in the way" of all the loops you could make. It all seems a bit dodgy, though -- but, I repeat, I don't know anything and you probably shouldn't take much notice of anything I say.
I'm still digesting the arxiv preprint, and I've also posted it to Physics Forums, which I frequent, and which has a number of relativity experts who have commented on other papers by Poplawski. Hopefully they will be able to shed further light.
The PhysicsForums thread is here:
http://www.physicsforums.com/showthread.php?t=672252
The PhysicsForums thread is here:
http://www.physicsforums.com/showthread.php?t=672252
I see comments like this all the time - where people with a strong background find faults in scientific articles and such written online. Why do these articles get things wrong so often? In this case I think you're saying the paper itself should not have been using isotropic coordinates. Is this because of different schools of thought in this higher realm of physics? Or... what?
Why do these articles get things wrong so often?
Different journals have different standards of rigor. I believe Physics Letters B, where this paper was published, is one of the less rigorous ones. They might also be more inclined to publish speculative papers, figuring that it's better to publish it and let someone else publish a refutation if it's wrong, as opposed to refusing to publish it in the first place.
In this case I think you're saying the paper itself should not have been using isotropic coordinates.
I suspect that the use of isotropic coordinates misled the paper's author, yes. I can't know for sure since I can't read the paper itself (it's behind a paywall). [Edit: someone downthread posted a link to an arxiv preprint; I'll take a look and respond further there.]
Is this because of different schools of thought in this higher realm of physics?
This could be a factor--it certainly is in some cases--but I'm inclined to think that in this case it's more a matter of a less rigorous journal being willing to publish a speculative paper, as above.
Different journals have different standards of rigor. I believe Physics Letters B, where this paper was published, is one of the less rigorous ones. They might also be more inclined to publish speculative papers, figuring that it's better to publish it and let someone else publish a refutation if it's wrong, as opposed to refusing to publish it in the first place.
In this case I think you're saying the paper itself should not have been using isotropic coordinates.
I suspect that the use of isotropic coordinates misled the paper's author, yes. I can't know for sure since I can't read the paper itself (it's behind a paywall). [Edit: someone downthread posted a link to an arxiv preprint; I'll take a look and respond further there.]
Is this because of different schools of thought in this higher realm of physics?
This could be a factor--it certainly is in some cases--but I'm inclined to think that in this case it's more a matter of a less rigorous journal being willing to publish a speculative paper, as above.
Isotropic coordinates have a discontinuity at the event horizon. It is therefore invalid to make any assumptions about worldlines inside the event horizon. However it is possible to use coordinates that do not have discontinuities. If the papers intent was to consider what happens to world lines as they cross the event horizon the paper should not have used isotropic coordinates.
Isotropic coordinates have a discontinuity at the event horizon.
No, they don't; I think you're thinking of Schwarzschild coordinates. Isotropic coordinates are continuous at the horizon, which is at R = M/2 (where R is the isotropic radial coordinate and M is the mass of the hole); but the region R < M/2 corresponds to the exterior of the horizon, not the interior.
The standard interpretation of this is that isotropic coordinates double cover the same exterior region (which is labeled region I on a Kruskal diagram like the one in Figure 2 on the ScienceDirect page); in other words, for every value of R < M/2, there is a corresponding value of R > M/2 that labels the same point in the same exterior region.
Poplawski's paper appears to claim that there is a valid alternate interpretation in which the region R < M/2 is a second, separate exterior region (labeled region III on a Kruskal diagram). That interpretation appears to me to violate the Einstein Field Equation, but I'm still digesting the paper (see my other posts in this thread).
No, they don't; I think you're thinking of Schwarzschild coordinates. Isotropic coordinates are continuous at the horizon, which is at R = M/2 (where R is the isotropic radial coordinate and M is the mass of the hole); but the region R < M/2 corresponds to the exterior of the horizon, not the interior.
The standard interpretation of this is that isotropic coordinates double cover the same exterior region (which is labeled region I on a Kruskal diagram like the one in Figure 2 on the ScienceDirect page); in other words, for every value of R < M/2, there is a corresponding value of R > M/2 that labels the same point in the same exterior region.
Poplawski's paper appears to claim that there is a valid alternate interpretation in which the region R < M/2 is a second, separate exterior region (labeled region III on a Kruskal diagram). That interpretation appears to me to violate the Einstein Field Equation, but I'm still digesting the paper (see my other posts in this thread).
you have to show that it's physically valid. I strongly doubt that the paper can do that, for reasons which are too long to fit in the margin of this post.
I'd love to hear about it if you have some time.
I'd love to hear about it if you have some time.
I'll try to give the short version. Look at the Figure 2 diagram on the ScienceDirect page. That is a diagram of a solution to the Einstein Field Equation, which is the central equation of General Relativity. In that diagram, B and C are not the same event; the curve A-B-C-D is disconnected. That's not physically valid as it stands.
The paper, as far as I can tell, is claiming that it is somehow physically possible for the curve A-B-C-D to be connected, so that it can be a physically valid worldline for an observer. For that to be the case, we would have to be able to obtain another solution to the Einstein Field Equation by cutting the Figure 2 diagram along the "southwest-northeast" diagonal (the one on which B and C lie), and sliding one half of the diagram along that diagonal until B and C coincide. I strongly doubt that the spacetime described by the resulting diagram is a solution of the Einstein Field Equation; and if it isn't, then the paper's claim is incorrect.
[Edit: someone downthread posted a link to an arxiv preprint of the paper; I'll take a look and respond further there.]
The paper, as far as I can tell, is claiming that it is somehow physically possible for the curve A-B-C-D to be connected, so that it can be a physically valid worldline for an observer. For that to be the case, we would have to be able to obtain another solution to the Einstein Field Equation by cutting the Figure 2 diagram along the "southwest-northeast" diagonal (the one on which B and C lie), and sliding one half of the diagram along that diagonal until B and C coincide. I strongly doubt that the spacetime described by the resulting diagram is a solution of the Einstein Field Equation; and if it isn't, then the paper's claim is incorrect.
[Edit: someone downthread posted a link to an arxiv preprint of the paper; I'll take a look and respond further there.]
cutting the Figure 2 diagram along the "southwest-northeast" diagonal (the one on which B and C lie), and sliding one half of the diagram along that diagonal until B and C coincide.
After reading through the paper, that I think the transformation the author intends is somewhat different than what I described: what he is doing is cutting the Figure 2 diagram along the diagonal containing B and C, then flipping the top half over so that C coincides with B.
This is not a valid solution of the vacuum Einstein Field Equation (neither is the transformed spacetime I originally described, where the top half is "slid" along the diagonal), which the original spacetime diagrammed in Figure 2 (before any transformations to move C around) is. But the author is claiming that it is a solution if we put an infinitely dense sheet of lightlike radiation on the diagonal. This may be true mathematically speaking (I haven't verified it), but that doesn't make it physically reasonable. So I still think the paper's claims are not physically valid; they may describe a mathematically consistent solution, but it's not something that would ever happen in the real universe.
After reading through the paper, that I think the transformation the author intends is somewhat different than what I described: what he is doing is cutting the Figure 2 diagram along the diagonal containing B and C, then flipping the top half over so that C coincides with B.
This is not a valid solution of the vacuum Einstein Field Equation (neither is the transformed spacetime I originally described, where the top half is "slid" along the diagonal), which the original spacetime diagrammed in Figure 2 (before any transformations to move C around) is. But the author is claiming that it is a solution if we put an infinitely dense sheet of lightlike radiation on the diagonal. This may be true mathematically speaking (I haven't verified it), but that doesn't make it physically reasonable. So I still think the paper's claims are not physically valid; they may describe a mathematically consistent solution, but it's not something that would ever happen in the real universe.
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Worse, wormholes contradict general relativity's own postulate, the equivalence principle, as shown by rock-solid logic here: http://finbot.wordpress.com/2008/03/05/no-black-holes/
Wormholes provide an endless stream of grant money, careers and tenure. That's why we still read about them. Einstein spent a decade trying to refute his own theory about them and black holes. (It's a throwaway account so I won't see the unscientific replies.)
Wormholes provide an endless stream of grant money, careers and tenure. That's why we still read about them. Einstein spent a decade trying to refute his own theory about them and black holes. (It's a throwaway account so I won't see the unscientific replies.)
Because of course a blog titled "Solutions to 5 Major Problems in Physics" wouldn't be talking out of its own ass. Among other things claimed to be solved on there are problems related to dark energy and quantum gravity.
Perhaps the sarcastic tone is too much, but "peer review" (flawed though it may be) exists for a reason. If there's a paper, you should link that instead, and if there isn't a paper then maybe that tells you something. There's too much crap on the Internet and it makes it far too easy for a layman to be led astray by almost-but-not-quite logic. I don't know if your link is an example of that or not, but I've seen far too many blogs that claim to have solved some big mystery that's alluded great minds for the last several decades, but yet somehow their work remains unpublished.
Perhaps the sarcastic tone is too much, but "peer review" (flawed though it may be) exists for a reason. If there's a paper, you should link that instead, and if there isn't a paper then maybe that tells you something. There's too much crap on the Internet and it makes it far too easy for a layman to be led astray by almost-but-not-quite logic. I don't know if your link is an example of that or not, but I've seen far too many blogs that claim to have solved some big mystery that's alluded great minds for the last several decades, but yet somehow their work remains unpublished.
So you didn't even read the content of his link, but somehow you felt entitled to dismiss it on the basis that... on what basis, exactly? That no information that wasn't pre-approved by a certified, "well-respected" expert is worth considering? Science doesn't work like that. Academia does.
It's an admirable attitude to have but sadly only in theory. In practice there's sadly far too much crackpottery on the Internet. That's absolutely fine if the only people reading it are experts who can judge it for themselves, but often that isn't the case. If you are an expert then I agree; don't dismiss something out of hand because it isn't peer reviewed! but if you're one of those people, you don't need to be told that.
To illustrate my point, consider the hoards of climate change deniers, or young earthers out there. To someone who doesn't study the climate or geology, their arguments might sound valid but are actually dangerously misleading. Physics crackpottery is a slightly more intellectual version of that, in that the subject matter isn't accessible to most, but it's no less dangerous. And there's so much of it. So, so much. Some physics bloggers have all but given up the will having battled these people for so long. They're like the conspiracy theorists of the science world. So I feel like it's not unreasonable for a layman to dismiss things out of hand until it's been properly peer reviewed.
We should all be wary of argument to authority, but perhaps less so to argument to experience and mutual respect.
To illustrate my point, consider the hoards of climate change deniers, or young earthers out there. To someone who doesn't study the climate or geology, their arguments might sound valid but are actually dangerously misleading. Physics crackpottery is a slightly more intellectual version of that, in that the subject matter isn't accessible to most, but it's no less dangerous. And there's so much of it. So, so much. Some physics bloggers have all but given up the will having battled these people for so long. They're like the conspiracy theorists of the science world. So I feel like it's not unreasonable for a layman to dismiss things out of hand until it's been properly peer reviewed.
We should all be wary of argument to authority, but perhaps less so to argument to experience and mutual respect.
Have you read the content of his link? I have; its reasoning is invalid.
Peer review may exist for a reason but there's no evidence it helps to advance science. There is evidence however that peer review has blocked valid works. It may be throwing the babies out with the bath water.
Your "rock-solid logic" makes at least one incorrect assumption about local inertial frames in curved spacetime.
Care to elaborate? I saw no such issue.
In the diagram of Frame X, which purports to be an inertial frame "centered" on the horizon, the horizon is shown as a vertical line. If this diagram is supposed to be a spacetime diagram, this is incorrect; the horizon is an outgoing lightlike surface, so it should appear in a spacetime diagram of Frame X as a 45-degree line going up and to the right, just like a light ray.
However, if the diagram is just supposed to be a diagram of "space" at the horizon (not spacetime), then it is not correct because the direction to the left of the diagram, towards the singularity, is not a spacelike direction; that direction is supposed to be the inward radial direction, but that direction is a timelike direction, not a spacelike direction.
In short, the diagram of Frame X can't be correct, so no valid logical argument can be based on it.
[Edit: The argument given in words has the same problems, but it's easier to illustrate them in the diagram.]
However, if the diagram is just supposed to be a diagram of "space" at the horizon (not spacetime), then it is not correct because the direction to the left of the diagram, towards the singularity, is not a spacelike direction; that direction is supposed to be the inward radial direction, but that direction is a timelike direction, not a spacelike direction.
In short, the diagram of Frame X can't be correct, so no valid logical argument can be based on it.
[Edit: The argument given in words has the same problems, but it's easier to illustrate them in the diagram.]
As I interpreted it, it's a diagram of a lab falling through a horizon, as viewed by someone at rest with respect to the lab. The horizon would be a plane traversing the lab; thus the horizon is drawn correctly. The singularity would be in one direction perpendicular to the horizon, whereas the escaping particle would be heading toward infinity in the opposite direction; thus those are drawn correctly.
> that direction is supposed to be the inward radial direction, but that direction is a timelike direction, not a spacelike direction.
It's an inward radial direction according to the diagram. The "but" part of your sentence doesn't offer evidence to invalidate that or otherwise show a problem. There's a coffee mug in front of me now. Regardless whether it's a spacelike or timelike direction, the mug is in that direction. Likewise to someone in that frame X the singularity is definitely in a particular direction. I'm not seeing a problem with the diagram.
> that direction is supposed to be the inward radial direction, but that direction is a timelike direction, not a spacelike direction.
It's an inward radial direction according to the diagram. The "but" part of your sentence doesn't offer evidence to invalidate that or otherwise show a problem. There's a coffee mug in front of me now. Regardless whether it's a spacelike or timelike direction, the mug is in that direction. Likewise to someone in that frame X the singularity is definitely in a particular direction. I'm not seeing a problem with the diagram.
The horizon would be a plane traversing the lab
No, it wouldn't. That's the point. The horizon is an outgoing lightlike surface; with respect to Frame X (or to any inertial frame that straddles the horizon), it's moving radially outward at the speed of light. It's not a plane stationary in space.
The singularity would be in one direction perpendicular to the horizon
No, it wouldn't. The singularity is to the future of the horizon; the direction from the horizon to the singularity is timelike, not spacelike.
There's a coffee mug in front of me now. Regardless whether it's a spacelike or timelike direction, the mug is in that direction.
This is not correct; timelike directions are fundamentally different from spacelike directions. What direction is next Tuesday from you now? That's a timelike direction, and it's not the same direction as the direction of a coffee mug, or any object that is in the space around you now. It's not even the same kind of direction. But that kind of direction--the kind that next Tuesday is in from you now--is the direction the singularity is in from the horizon.
I'm not seeing a problem with the diagram.
That's because you evidently don't understand what the curved spacetime around a black hole is like. It's a perfectly self-consistent model; but it doesn't work the way the web page author, and evidently you, think it works.
No, it wouldn't. That's the point. The horizon is an outgoing lightlike surface; with respect to Frame X (or to any inertial frame that straddles the horizon), it's moving radially outward at the speed of light. It's not a plane stationary in space.
The singularity would be in one direction perpendicular to the horizon
No, it wouldn't. The singularity is to the future of the horizon; the direction from the horizon to the singularity is timelike, not spacelike.
There's a coffee mug in front of me now. Regardless whether it's a spacelike or timelike direction, the mug is in that direction.
This is not correct; timelike directions are fundamentally different from spacelike directions. What direction is next Tuesday from you now? That's a timelike direction, and it's not the same direction as the direction of a coffee mug, or any object that is in the space around you now. It's not even the same kind of direction. But that kind of direction--the kind that next Tuesday is in from you now--is the direction the singularity is in from the horizon.
I'm not seeing a problem with the diagram.
That's because you evidently don't understand what the curved spacetime around a black hole is like. It's a perfectly self-consistent model; but it doesn't work the way the web page author, and evidently you, think it works.
> The horizon is an outgoing lightlike surface; with respect to Frame X (or to any inertial frame that straddles the horizon), it's moving radially outward at the speed of light. It's not a plane stationary in space.
"Lightlike surface" and plane are not incompatible ideas. Surface = plane in this case. The diagram or its caption doesn't say the horizon is stationary, it says the frame is falling through the horizon. Presumably the horizon is indeed moving in that frame at the speed of light (an outgoing lightlike surface).
> What direction is next Tuesday from you now?
The singularity is not a date; it's an object, like my coffee mug is. It's not invalid to show a direction to an object just because you'll reach the object next Tuesday.
> That's because you evidently don't understand what the curved spacetime around a black hole is like.
I've take a couple years of classes on this stuff. You're using the terminology inappropriately. The terms spacelike and timelike are not limited to black holes. By saying the diagram incorrectly shows the direction to the singularity you're implying that neither can I point to my coffee mug and say it's in that direction. But I can point to my coffee mug as validly as someone in frame X could point to the singularity.
I can even point to a real purported singularity by walking outside and pointing to the direction of the center of the Milky Way. It's no more complex than that. Can I validly point to the center of the Milky Way? If yes, then there's no problem with the diagram in that regard.
> It's a perfectly self-consistent model
An assumption that should be set aside when considering an objection to it.
"Lightlike surface" and plane are not incompatible ideas. Surface = plane in this case. The diagram or its caption doesn't say the horizon is stationary, it says the frame is falling through the horizon. Presumably the horizon is indeed moving in that frame at the speed of light (an outgoing lightlike surface).
> What direction is next Tuesday from you now?
The singularity is not a date; it's an object, like my coffee mug is. It's not invalid to show a direction to an object just because you'll reach the object next Tuesday.
> That's because you evidently don't understand what the curved spacetime around a black hole is like.
I've take a couple years of classes on this stuff. You're using the terminology inappropriately. The terms spacelike and timelike are not limited to black holes. By saying the diagram incorrectly shows the direction to the singularity you're implying that neither can I point to my coffee mug and say it's in that direction. But I can point to my coffee mug as validly as someone in frame X could point to the singularity.
I can even point to a real purported singularity by walking outside and pointing to the direction of the center of the Milky Way. It's no more complex than that. Can I validly point to the center of the Milky Way? If yes, then there's no problem with the diagram in that regard.
> It's a perfectly self-consistent model
An assumption that should be set aside when considering an objection to it.
Presumably the horizon is indeed moving in that frame at the speed of light
If that's true, the the diagram that's shown cannot portray a steady state of Frame X, as it claims to do. At most it can show how things look in Frame X at a single instant of time. The horizon plane is moving to the right in the diagram at the speed of light, and none of the cloud particles can move at the speed of light, so the horizon plane will quickly overtake them and be to the right of the entire cloud. The argument in the text is not consistent with this.
The singularity is not a date; it's an object, like my coffee mug is.
No, the singularity is not an object like your coffee mug. That's the point. The singularity is a moment in time, not a place in space. If you don't know this then you need to do some review; it's a basic fact about the black hole solution in General Relativity.
I've take a couple years of classes on this stuff.
What material have you covered? Have you specifically covered the Schwarzschild solution to the Einstein Field Equation, and the description of it in the Kruskal coordinate chart? (Or the Painleve chart, or the Eddington-Finkelstein chart, or any other chart which is not singular at the horizon?) If not, I suggest you wait until those things are covered, or read ahead in your course material.
You're using the terminology incorrectly. The terms spacelike and timelike are not limited to black holes.
I didn't say they were. You're correct, they are general terms describing different kinds of directions in spacetime. ("Lightlike" or "null" is the third kind of direction.) A black hole is a spacetime, therefore the terms apply in it, and I was using them correctly.
Can I validly point to the center of the Milky Way?
Sure, but you won't be pointing to the singularity in the center of the black hole there. Once again, that would be like pointing to next Tuesday--or, since the center of the galaxy is some thirty thousand light years from us, it would be like pointing to a moment thirty thousand years or more into your future.
An assumption that should be set aside when considering an objection to it.
Only if the purported criticism represents the model correctly. It doesn't.
If that's true, the the diagram that's shown cannot portray a steady state of Frame X, as it claims to do. At most it can show how things look in Frame X at a single instant of time. The horizon plane is moving to the right in the diagram at the speed of light, and none of the cloud particles can move at the speed of light, so the horizon plane will quickly overtake them and be to the right of the entire cloud. The argument in the text is not consistent with this.
The singularity is not a date; it's an object, like my coffee mug is.
No, the singularity is not an object like your coffee mug. That's the point. The singularity is a moment in time, not a place in space. If you don't know this then you need to do some review; it's a basic fact about the black hole solution in General Relativity.
I've take a couple years of classes on this stuff.
What material have you covered? Have you specifically covered the Schwarzschild solution to the Einstein Field Equation, and the description of it in the Kruskal coordinate chart? (Or the Painleve chart, or the Eddington-Finkelstein chart, or any other chart which is not singular at the horizon?) If not, I suggest you wait until those things are covered, or read ahead in your course material.
You're using the terminology incorrectly. The terms spacelike and timelike are not limited to black holes.
I didn't say they were. You're correct, they are general terms describing different kinds of directions in spacetime. ("Lightlike" or "null" is the third kind of direction.) A black hole is a spacetime, therefore the terms apply in it, and I was using them correctly.
Can I validly point to the center of the Milky Way?
Sure, but you won't be pointing to the singularity in the center of the black hole there. Once again, that would be like pointing to next Tuesday--or, since the center of the galaxy is some thirty thousand light years from us, it would be like pointing to a moment thirty thousand years or more into your future.
An assumption that should be set aside when considering an objection to it.
Only if the purported criticism represents the model correctly. It doesn't.
> What material have you covered?
The material sufficient for this discussion. I know the material well enough to point out contradictions in your thinking.
> If that's true, the the diagram that's shown cannot portray a steady state of Frame X, as it claims to do.
I don't see such claim made there. Presumably it's a snapshot of X at a single instant of time, the initial state of the thought experiment. The author should be clearer however.
> The horizon plane is moving to the right in the diagram at the speed of light, and none of the cloud particles can move at the speed of light, so the horizon plane will quickly overtake them and be to the right of the entire cloud.
GR allows particles above the horizon to be escaping to infinity (since the escape velocity there is less than c), in which case the horizon plane will never overtake them. GR allows the escaping particles to never be overtaken by the horizon even though GR also demands that those particles move slower than the horizon does. If all the particles above the horizon are escaping then the cloud is splitting along the horizon.
> Sure, but you won't be pointing to the singularity in the center of the black hole there.
That's a contradiction. You can't say it has no location in space and then refer to its location in space even in relative terms like "in the center of". The singularity has a location in both space and time (a location in spacetime, if we ignore the technicality that spacetime breaks down there), and I could validly point to it now, no matter its location in my future. I suspect you're getting your idea from a cosmic singularity, like for the big bang. In that case there would be no single location in space you could point to now; it has a specific location in time only.
The material sufficient for this discussion. I know the material well enough to point out contradictions in your thinking.
> If that's true, the the diagram that's shown cannot portray a steady state of Frame X, as it claims to do.
I don't see such claim made there. Presumably it's a snapshot of X at a single instant of time, the initial state of the thought experiment. The author should be clearer however.
> The horizon plane is moving to the right in the diagram at the speed of light, and none of the cloud particles can move at the speed of light, so the horizon plane will quickly overtake them and be to the right of the entire cloud.
GR allows particles above the horizon to be escaping to infinity (since the escape velocity there is less than c), in which case the horizon plane will never overtake them. GR allows the escaping particles to never be overtaken by the horizon even though GR also demands that those particles move slower than the horizon does. If all the particles above the horizon are escaping then the cloud is splitting along the horizon.
> Sure, but you won't be pointing to the singularity in the center of the black hole there.
That's a contradiction. You can't say it has no location in space and then refer to its location in space even in relative terms like "in the center of". The singularity has a location in both space and time (a location in spacetime, if we ignore the technicality that spacetime breaks down there), and I could validly point to it now, no matter its location in my future. I suspect you're getting your idea from a cosmic singularity, like for the big bang. In that case there would be no single location in space you could point to now; it has a specific location in time only.
Presumably it's a snapshot of X at a single instant of time, the initial state of the thought experiment. The author should be clearer however.
I agree, if this is the author's intent it should be clearer. However, I'm willing to interpret the diagram that way for this discussion.
GR allows the escaping particles to never be overtaken by the horizon even though GR also demands that those particles move slower than the horizon does.
Because spacetime is curved, and the curvature limits the size of a local inertial frame straddling the horizon.
Consider a "cloud" particle in the right half of cloud in the Frame X diagram. In order to be moving at escape velocity at its location, it must be moving to the right at just a smidgen less than c. So it will move off the right edge of the diagram, and out of the region covered by Frame X, before the horizon catches it. Once it's out of Frame X, its worldline doesn't have to look like a straight line in Frame X, so it can continue to avoid the horizon; in fact it will gradually get farther and farther away from it.
Another way to see what's going on is to ask what a line of constant radius r looks like in Frame X. An observer at constant r close to the horizon has to accelerate very hard to stay at the same radius; that means a line of constant r in Frame X is going to look like a hyperbola in a spacetime diagram. If we imagine a bunch of observers at constant r passing through the cloud in the Frame X diagram as shown, they will all be accelerating very hard to the right, hard enough to keep the horizon from catching up with them; but a cloud particle moving at escape velocity just a little to the right of the horizon will be moving to the right faster than any of the constant-r observers, so he will pass them one by one as they accelerate; they won't be able to catch him. That means the escape velocity particle is increasing its radius with time, i.e., escaping.
If all the particles above the horizon are escaping then the cloud is splitting along the horizon.
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.
[Edit: I suppose the intent could be that all of the cloud particles are moving to the right at just a smidgen less than c; but if that's the case, the ones to the right of the horizon line will make it out of Frame X before the horizon catches them, as above, but the ones at or to the left of the horizon line obviously won't, because the horizon will move ahead of them.]
You can't say it has no location in space and then refer to its location in space even in relative terms like "in the center of".
I haven't done any such thing. You appear to be reading things into my posts that I am not saying. I have said, consistently, that the singularity is a moment in time. More precisely, the singularity is represented by a spacelike line. A "place in space" is represented by a timelike line, not a spacelike one. A point in space at an instant of time is just a point, not a line.
The singularity has a location in both space and time
No, it has a location in time only; it is all of space (or at least all of it inside the horizon) at that moment in time.
I suspect you're getting your idea from a cosmic singularity, like for the big bang.
The black hole singularity is indeed very similar to the big bang singularity; both of them are spacelike lines. The only real differences are that the black hole singularity is hidden behind a horizon, and that the black hole singularity is a future singularity while the big bang singularity is a past one.
You say you have taken classes on this material; have you raised the issues you are raising here in class? If so, what response did you get?
I agree, if this is the author's intent it should be clearer. However, I'm willing to interpret the diagram that way for this discussion.
GR allows the escaping particles to never be overtaken by the horizon even though GR also demands that those particles move slower than the horizon does.
Because spacetime is curved, and the curvature limits the size of a local inertial frame straddling the horizon.
Consider a "cloud" particle in the right half of cloud in the Frame X diagram. In order to be moving at escape velocity at its location, it must be moving to the right at just a smidgen less than c. So it will move off the right edge of the diagram, and out of the region covered by Frame X, before the horizon catches it. Once it's out of Frame X, its worldline doesn't have to look like a straight line in Frame X, so it can continue to avoid the horizon; in fact it will gradually get farther and farther away from it.
Another way to see what's going on is to ask what a line of constant radius r looks like in Frame X. An observer at constant r close to the horizon has to accelerate very hard to stay at the same radius; that means a line of constant r in Frame X is going to look like a hyperbola in a spacetime diagram. If we imagine a bunch of observers at constant r passing through the cloud in the Frame X diagram as shown, they will all be accelerating very hard to the right, hard enough to keep the horizon from catching up with them; but a cloud particle moving at escape velocity just a little to the right of the horizon will be moving to the right faster than any of the constant-r observers, so he will pass them one by one as they accelerate; they won't be able to catch him. That means the escape velocity particle is increasing its radius with time, i.e., escaping.
If all the particles above the horizon are escaping then the cloud is splitting along the horizon.
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.
[Edit: I suppose the intent could be that all of the cloud particles are moving to the right at just a smidgen less than c; but if that's the case, the ones to the right of the horizon line will make it out of Frame X before the horizon catches them, as above, but the ones at or to the left of the horizon line obviously won't, because the horizon will move ahead of them.]
You can't say it has no location in space and then refer to its location in space even in relative terms like "in the center of".
I haven't done any such thing. You appear to be reading things into my posts that I am not saying. I have said, consistently, that the singularity is a moment in time. More precisely, the singularity is represented by a spacelike line. A "place in space" is represented by a timelike line, not a spacelike one. A point in space at an instant of time is just a point, not a line.
The singularity has a location in both space and time
No, it has a location in time only; it is all of space (or at least all of it inside the horizon) at that moment in time.
I suspect you're getting your idea from a cosmic singularity, like for the big bang.
The black hole singularity is indeed very similar to the big bang singularity; both of them are spacelike lines. The only real differences are that the black hole singularity is hidden behind a horizon, and that the black hole singularity is a future singularity while the big bang singularity is a past one.
You say you have taken classes on this material; have you raised the issues you are raising here in class? If so, what response did you get?
> 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.
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.
Fermat, is that you?
(This is from April 2010.)
As usual, phys.org have simply reproduced someone else's press release and made a bunch of the words in it link to other phys.org pages. The original press release is at http://newsinfo.iu.edu/news/page/normal/13995.html and differs from the phys.org version only in not being blogspam.
An arXiv preprint of the paper in question is at http://arxiv.org/abs/0902.1994; I think it's actually identical to the version published in Phys. Lett. B.
There's a bit more information on Popławski's Wikipedia page: http://en.wikipedia.org/wiki/Nikodem_Pop%C5%82awski.
As usual, phys.org have simply reproduced someone else's press release and made a bunch of the words in it link to other phys.org pages. The original press release is at http://newsinfo.iu.edu/news/page/normal/13995.html and differs from the phys.org version only in not being blogspam.
An arXiv preprint of the paper in question is at http://arxiv.org/abs/0902.1994; I think it's actually identical to the version published in Phys. Lett. B.
There's a bit more information on Popławski's Wikipedia page: http://en.wikipedia.org/wiki/Nikodem_Pop%C5%82awski.
I am frequently bothered by the misuse of the word "universe". It is defined as the totality of all that exists -- that we can observe. So if there is anything out there, which we didn't think existed before, but we now suspect does exist, well... it's just part of our same old universe.
The definition is changing. There's a lot of people who use it to mean something like "all the stuff that resulted from the big bang". Which may or may not be the entirety of existence. If it's not, then the other stuff will be stuff that exists outside of the universe. Which does contradict the etymology of the word but is consistent with how it's being used today. Much like the word atom I think.
I'm not an astrophysicist, so hopefully one can chime in, but my understanding is that 'universe' == the x,y,z,t continuum. Anything outside of that is a different 'universe'.
If you can imagine a place that requires alternate dimensions in order to access (e.g. klein bottle), you would be traveling through a different 'universe' (though it is possible that a passage through other universes could lead back to our own). If, however, the other place has a different x,y,z,t continuum, even if there is a passage between the two (wormhole), it's still a different universe.
EDIT: (Appending this) Also, if you think of the word universe, it means one totality (uni=one, verse=totality). So, if you want to refer to all that can exist, you probably want to say 'omniverse'.
If you can imagine a place that requires alternate dimensions in order to access (e.g. klein bottle), you would be traveling through a different 'universe' (though it is possible that a passage through other universes could lead back to our own). If, however, the other place has a different x,y,z,t continuum, even if there is a passage between the two (wormhole), it's still a different universe.
EDIT: (Appending this) Also, if you think of the word universe, it means one totality (uni=one, verse=totality). So, if you want to refer to all that can exist, you probably want to say 'omniverse'.
I think the concept of outside the universe or inside of it are not developed in a sufficiently rigorous way to really define what a universe is. However in some theories objects appear were it is actually quite natural to speak of an universe and something else. For example there is a unique way to extend the Schwartzschild space time [1] such that all geodesics either terminate in the singularity or go to infinity. But if you do this, then a region of the spacetime appears, that is 'on the other side' of the black hole. And there is no way to communicate with this region of spacetime, since all geodesics leading to it are space like, that is they would require (local) superluminal travel. It is therefore sometimes called a parallel universe.
It is similar in certain string theories, that patches of spacetime with different physical laws appear, this is then called the landscape. Or the multiverse in some cosmological models, where a far away region may appear, which is vastly different from or 'local' universe, that is in this case everything we can possibly observe.
So I think that it is quite possible that a theory of quantum gravity will have some object which we will call a universe, but until we have such a theory the appearance of anything outside of the universe marks highly speculative physics.
[1] That is the spacetime describing a black hole.
It is similar in certain string theories, that patches of spacetime with different physical laws appear, this is then called the landscape. Or the multiverse in some cosmological models, where a far away region may appear, which is vastly different from or 'local' universe, that is in this case everything we can possibly observe.
So I think that it is quite possible that a theory of quantum gravity will have some object which we will call a universe, but until we have such a theory the appearance of anything outside of the universe marks highly speculative physics.
[1] That is the spacetime describing a black hole.
Are you a fan of Ayn Rand? (I am.) Just curious, as she insists on not calling a concept by a name (word) already taken by something else, which is what you're alleging in this case.
Tangentially, I think it may actually be appropriate to use "universe" to refer to a cosmological phenomenon (as modern physicists do), and "existence" to refer to the metaphysical phenomenon you are describing. I guess I'd have to research the etymology of "universe" before I could take a more definitive stand.
Tangentially, I think it may actually be appropriate to use "universe" to refer to a cosmological phenomenon (as modern physicists do), and "existence" to refer to the metaphysical phenomenon you are describing. I guess I'd have to research the etymology of "universe" before I could take a more definitive stand.
No, I have never read Ayn Rand.
And that larger universe is yet within another larger universe! We must go deeper.
Looking at the figures on the ScienceDirect page...
http://www.sciencedirect.com/science/article/pii/S0370269310...
...the second figure bears this out; it shows the worldline of an object going through the wormhole (A-B-C-D) as disconnected, which is physically invalid; it violates local energy conservation. So I've got to conclude that the paper's claimed result is not physically valid.
Note: The ScienceDirect page claims that "B and C are the same event", but you can't just claim that arbitrarily; you have to show that it's physically valid. I strongly doubt that the paper can do that, for reasons which are too long to fit in the margin of this post. :-)