You are not mistaken about time apparently stopping at the event horizon (or SR). It's just that even a gentle mostly unaccelerated approach allows the clock at the SR to advance from the perpective of the approach. The event horizon (not the SR) seems to recede into the black hole by an amount determined by the acceleration or speed of the approach.
Tidal conditions at the SR (Schwarzschild Radius) can be very mild for a large black hole, which made me wonder about Susskind's argument that it will seem extremely hot to a gently approaching probe. He was using field and string theory, which is not naturally fully compatible with general relativity, but must be manually adjusted for compliance. No unified theory is in view yet from string theory alone in spite of the claims being made.
It seems to me that observers can agree on the location of the SR, but not that of the event horizon. And, none of this critique modifies Susskind's identification of a severe and very revealing paradox.
-- Mike Burns "Contradiction resolution is the (underlying) stuff of the (classical) universe."
Time only stands still as seen from afar. Matter close to and within the black hole continues to experience the advancement of time until it hits the singularity.
As for your notion of a shell, see Susskind's article, Sci. Am. April 1997 p. 52.
You have duplicated part of his argument. Your fog notion is incorrect; the shell, as seen from afar, moves out with more mass accumulated. Susskind then notes that the shell does not appear at all to an observer following matter into the horizon, but that the shell, when approached slowly and not in free fall, becomes apparently very hot. This is a paradox so severe that he calls it "black hole complementarity".
But, complementarity, proper, is not a paradox but a deep mathematical property of physics. Wave-particle duality is more like this problem. And, Susskind's reasoning is partially suspect because his picture does not uphold the equivalence principle (that the rules of physics are locally the same everywhere in spite of various speeds, accelerations, and gravitational fields). Using equivalence, the slowly lowered observer would see the shell sunk farther into the black hole than a farther observer would see, and the two would disagree on the corrected temperature and time of existence of the shell. The two observers would accuse each other of being subject to an illusion.
-- Mike Burns "Nothing unphysical can be a physical cause."
A steadily moving source of gravitation always attracts toward its instantaneous position. This is to fulfill the correspondence principle to Newtonian physics, and also to acknowledge that a steadily moving source can be understood as stationary in another coordinate system. Stationary sources have plenty of time to "advertise" their positions at the speed of light.
It is accelerating sources of gravitation which must "advertise" their new trajectories effective only at the speed of light. The forces between charged particles work the same way.
In introductory physics, a contradiction is created by drawing the result of a cross product as a vector, and then claiming this as a physical object or accurate representation.
I have thought of replacing introductory physics with a study of the action principle.
The use of vectors to obscure the tensor rank of physical objects is not an innocent convention, but part of a cultural neurosis, I think. The cultural studies required to support this claim are very extensive, but I think the burden of proof has shifted to the defense of the conventional use of vectors.
In Jackson's text on electromagnetism, he uses, at least once, the contravariant property of vectors explicitly, even when they represent covariant wave numbers. This forces his example of the transverse red-shift to be worked with compensating errors. And, the compensating errors needed to work electromagnetism when the E and B fields are represented by vectors completely hide the nature of the subject.
But, there is a contradiction in representing cross products as a vector. This little thought experiment is a reducio ad absurdum of the practice.
There is an occasional duality between one-forms and vectors, but this does not justify losing the distinction. It is mostly convention and not physical reality which hides this difference; the convention requires the consistent use of compensating errors and restricted conditions for its salvation, so this convention of ignoring proper tensor rank, therefore, does not contribute to real science.
Yes, you are speaking of a pure convention with no actual effect.
But cross products as vectors actually violate or obscure a principle of the universe which is not a mere convention. That is, the elements of classical physics are geometric objects, having extents, boundaries, densities, etc., that exist before a coordinate system is imposed on them.
Cross products create an actual contradiction in introductory physics. Just calculate and draw a cross product using meters as the unit of measurement, then calculate and draw the same cross product using millimeters as the unit. That is, one of the original vectors becomes 1000 mm instead of 1 m. In the drawings, the actual length of the resultants will disagree by a factor of one thousand.
Academics tiptoe around this difficulty without actually disclosing it. And, I can only see some kind of irrationality as responsible for this behavior. So, reproducibility as a method of science needs to be supplemented, I think, with other methods of skepticism.
"But, the Scientific Method is clearly not going anywhere, and reproduceability is a very strict standard."
But, a bad theory can be reproduced by following the given system of compensating errors with enough care.
Take the notion that the result of a cross product is a vector; this is a conventional result, enforced on introductory examinations, that is actually false. And, this convention obscures the higher level principle which it violates - the metric invariance of classical physics. (As Wheeler says, "Everything is a geometric object.")
The cross product is actually a bivector, a second-rank, antisymetric and contravariant tensor. All this means is that you draw the result using two arrows in the plane of the original two arrows. If you drew the result as one arrow pointing out of the plane, then the result would change size when the units of length are changed.
"... the lifespan of any unsupportable idea is inversely proportionate to the degree of interest in that idea..."
I think that a peculiar human irrationality has prolonged the life of this and many other conventions; this has gone on for one hundred years.
In the Susskind formulation, it was not necessary to be at the horizon, only near it, to generate the paradoxical differences in observation.
It is not differences in speed which are paradoxical here, but the effects of acceleration are. Special relativity resolves the problem of blue shift. But, you might want to say that the problem of relative acceleration is not unique near the horizon, occuring in any relative acceleration.
I am not sure of the resolution here. Susskind is worried about the loss of information to the universe, and he regards his article as resolving the issue of this loss; both probes see the information at different places. But I am worried about the problem of each probe seeing a different history of the universe, even before entering the horizon. I am not sure, but getting the coordination transformations right might help to improve on Susskind's presentation.
Michael J. Burns http://home.mindspring.com/~mburns9/
This brings up Susskind's paradox, Sci. Am., April 1997, p. 52. The Hawking radiation is seen from afar in the (Schwartzchild) frame of a distant observer. The observer lowers a probe on a tether so that the radiation is blue-shifted and becomes
singularly bright near the horizon. But another probe is cut loose and sees nothing bright except near the center, not the horizon. This is Susskind's paradox, absolutely critical for understanding the universe, I think.
But, I think that the calculation for the probe on the tether might be somewhat off - an artifact of the Schwartzchild frame. After all, (classical) "Physics is local." The frame of the probe on the tether is tilted toward the horizon so that the horizon seems deeper (as much as 30% deeper) into the black hole.
Is there anyone brilliant enough to straighten this one out?
Michael J. Burns http://home.mindspring.com/~mburns9/
No, nothing needs to state the hypothesis, since that would imply causality - which is to be explained in the first place. Have you considered the need for logical coherence to agree with coincidence in time? How could events which are (relativistically) simultaneous in time be logically inconsistent? And, how could events which are logically consistent be assigned locations and times which are not simultaneous?
Slashdot Mirror
You are not mistaken about time apparently stopping at the event horizon (or SR). It's just that even a gentle mostly unaccelerated approach allows the clock at the SR to advance from the perpective of the approach. The event horizon (not the SR) seems to recede into the black hole by an amount determined by the acceleration or speed of the approach.
Tidal conditions at the SR (Schwarzschild Radius) can be very mild for a large black hole, which made me wonder about Susskind's argument that it will seem extremely hot to a gently approaching probe. He was using field and string theory, which is not naturally fully compatible with general relativity, but must be manually adjusted for compliance. No unified theory is in view yet from string theory alone in spite of the claims being made.
It seems to me that observers can agree on the location of the SR, but not that of the event horizon. And, none of this critique modifies Susskind's identification of a severe and very revealing paradox.
--
Mike Burns "Contradiction resolution is the (underlying) stuff of the (classical) universe."
Time only stands still as seen from afar. Matter close to and within the black hole continues to experience the advancement of time until it hits the singularity.
As for your notion of a shell, see Susskind's article, Sci. Am. April 1997 p. 52.
You have duplicated part of his argument. Your fog notion is incorrect; the shell, as seen from afar, moves out with more mass accumulated. Susskind then notes that the shell does not appear at all to an observer following matter into the horizon, but that the shell, when approached slowly and not in free fall, becomes apparently very hot. This is a paradox so severe that he calls it "black hole complementarity".
But, complementarity, proper, is not a paradox but a deep mathematical property of physics. Wave-particle duality is more like this problem. And, Susskind's reasoning is partially suspect because his picture does not uphold the equivalence principle (that the rules of physics are locally the same everywhere in spite of various speeds, accelerations, and gravitational fields). Using equivalence, the slowly lowered observer would see the shell sunk farther into the black hole than a farther observer would see, and the two would disagree on the corrected temperature and time of existence of the shell. The two observers would accuse each other of being subject to an illusion.
--
Mike Burns "Nothing unphysical can be a physical cause."
A steadily moving source of gravitation always attracts toward its instantaneous position. This is to fulfill the correspondence principle to Newtonian physics, and also to acknowledge that a steadily moving source can be understood as stationary in another coordinate system. Stationary sources have plenty of time to "advertise" their positions at the speed of light.
It is accelerating sources of gravitation which must "advertise" their new trajectories effective only at the speed of light. The forces between charged particles work the same way.
In introductory physics, a contradiction is created by drawing the result of a cross product as a vector, and then claiming this as a physical object or accurate representation.
I have thought of replacing introductory physics with a study of the action principle.
The use of vectors to obscure the tensor rank of physical objects is not an innocent convention, but part of a cultural neurosis, I think. The cultural studies required to support this claim are very extensive, but I think the burden of proof has shifted to the defense of the conventional use of vectors.
In Jackson's text on electromagnetism, he uses, at least once, the contravariant property of vectors explicitly, even when they represent covariant wave numbers. This forces his example of the transverse red-shift to be worked with compensating errors. And, the compensating errors needed to work electromagnetism when the E and B fields are represented by vectors completely hide the nature of the subject.
But, there is a contradiction in representing cross products as a vector. This little thought experiment is a reducio ad absurdum of the practice.
There is an occasional duality between one-forms and vectors, but this does not justify losing the distinction. It is mostly convention and not physical reality which hides this difference; the convention requires the consistent use of compensating errors and restricted conditions for its salvation, so this convention of ignoring proper tensor rank, therefore, does not contribute to real science.
Yes, you are speaking of a pure convention with no actual effect.
But cross products as vectors actually violate or obscure a principle of the universe which is not a mere convention. That is, the elements of classical physics are geometric objects, having extents, boundaries, densities, etc., that exist before a coordinate system is imposed on them.
Cross products create an actual contradiction in introductory physics. Just calculate and draw a cross product using meters as the unit of measurement, then calculate and draw the same cross product using millimeters as the unit. That is, one of the original vectors becomes 1000 mm instead of 1 m. In the drawings, the actual length of the resultants will disagree by a factor of one thousand.
Academics tiptoe around this difficulty without actually disclosing it. And, I can only see some kind of irrationality as responsible for this behavior. So, reproducibility as a method of science needs to be supplemented, I think, with other methods of skepticism.
But, a bad theory can be reproduced by following the given system of compensating errors with enough care.
Take the notion that the result of a cross product is a vector; this is a conventional result, enforced on introductory examinations, that is actually false. And, this convention obscures the higher level principle which it violates - the metric invariance of classical physics. (As Wheeler says, "Everything is a geometric object.")
The cross product is actually a bivector, a second-rank, antisymetric and contravariant tensor. All this means is that you draw the result using two arrows in the plane of the original two arrows. If you drew the result as one arrow pointing out of the plane, then the result would change size when the units of length are changed.
I think that a peculiar human irrationality has prolonged the life of this and many other conventions; this has gone on for one hundred years.
It is not differences in speed which are paradoxical here, but the effects of acceleration are. Special relativity resolves the problem of blue shift. But, you might want to say that the problem of relative acceleration is not unique near the horizon, occuring in any relative acceleration.
I am not sure of the resolution here. Susskind is worried about the loss of information to the universe, and he regards his article as resolving the issue of this loss; both probes see the information at different places. But I am worried about the problem of each probe seeing a different history of the universe, even before entering the horizon. I am not sure, but getting the coordination transformations right might help to improve on Susskind's presentation.
Michael J. Burns http://home.mindspring.com/~mburns9/
singularly bright near the horizon. But another probe is cut loose and sees nothing bright except near the center, not the horizon. This is Susskind's paradox, absolutely critical for understanding the universe, I think.
But, I think that the calculation for the probe on the tether might be somewhat off - an artifact of the Schwartzchild frame. After all, (classical) "Physics is local." The frame of the probe on the tether is tilted toward the horizon so that the horizon seems deeper (as much as 30% deeper) into the black hole.
Is there anyone brilliant enough to straighten this one out?
Michael J. Burns http://home.mindspring.com/~mburns9/
No, nothing needs to state the hypothesis, since that would imply causality - which is to be explained in the first place. Have you considered the need for logical coherence to agree with coincidence in time? How could events which are (relativistically) simultaneous in time be logically inconsistent? And, how could events which are logically consistent be assigned locations and times which are not simultaneous?