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waitedavid137
Posted: Sep 20 2011, 05:26 PM


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QUOTE (brucep @ Sep 20 2011, 07:36 AM)
I'm convinced there's no point inside a black hole where infinite spacetime curvature is going to be a physical solution. What I base this on is the mass of the black hole can be known and it's not infinite. If they find a physical solution they'll probably still call it a singularity based on historical precedence. Let me ask you if the 'singularity' hiding behind an event horizon is coordinate independent?

Its not the amount of mass that is singular in classical general relativity for a black hole, it is the "density" of the mass that is singular. Who knows, maybe the correct quantum gravity theory will not have an infinite density for it. My point is that both classical electromagnetism without general relativity, and general relativity treat charges as point masses. Both treat them as having finite mass, but infinite density. Both describe the density as a singularity. The only difference is that for black holes there are event horizons around the singularity. I don't think the divergent terms in the Reimann tensor corresponding to the mass density at its location can be transformed into something finite without giving rise to other divergent terms.

This post has been edited by waitedavid137 on Sep 20 2011, 05:32 PM
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brucep
Posted: Sep 20 2011, 07:02 PM


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QUOTE (waitedavid137 @ Sep 20 2011, 05:26 PM)
Its not the amount of mass that is singular in classical general relativity for a black hole, it is the "density" of the mass that is singular. Who knows, maybe the correct quantum gravity theory will not have an infinite density for it. My point is that both classical electromagnetism without general relativity, and general relativity treat charges as point masses. Both treat them as having finite mass, but infinite density. Both describe the density as a singularity. The only difference is that for black holes there are event horizons around the singularity. I don't think the divergent terms in the Riemann tensor corresponding to the mass density at its location can be transformed into something finite without giving rise to other divergent terms.

I'm aware of the point particle treatment but I never thought about treating the black hole that way. Treating a particle as a 'string' with finite extent eliminates the infinite density. String theory has it's own problem with finding a preferred vacuum from a 'huge' population of candidates. I certainly don't think GR has any problems since all this stuff is outside the GR domain of applicability. Just want to make that clear so that boundaries don't get theoretically washed over. Thank you for your comments. Have you thought about 'choosing the preferred vacuum for string theory'? The two camps of thought. One requiring empirical confirmation and the other utilizing anthropic reasoning. A bit off topic.
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waitedavid137
Posted: Sep 21 2011, 11:25 AM


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QUOTE (brucep @ Sep 20 2011, 12:02 PM)
I'm aware of the point particle treatment but I never thought about treating the black hole that way. Treating a particle as a 'string' with finite extent eliminates the infinite density. String theory has it's own problem with finding a preferred vacuum from a 'huge' population of candidates. I certainly don't think GR has any problems since all this stuff is outside the GR domain of applicability. Just want to make that clear so that boundaries don't get theoretically washed over. Thank you for your comments. Have you thought about 'choosing the preferred vacuum for string theory'? The two camps of thought. One requiring empirical confirmation and the other utilizing anthropic reasoning. A bit off topic.

I really don't put too much stock in strings yet. It seems presumptuous to me to be trying to determine which string theory, or which guage for strings really, is correct when there's no real physical evidence that strings are the correct approach to unification at all yet.
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brucep
Posted: Sep 21 2011, 03:21 PM


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QUOTE (waitedavid137 @ Sep 21 2011, 11:25 AM)
I really don't put too much stock in strings yet. It seems presumptuous to me to be trying to determine which string theory, or which guage for strings really, is correct when there's no real physical evidence that strings are the correct approach to unification at all yet.

I wouldn't say presumptous since the domain of applicability is, for the most part, untestable. I take from your comment that you might think the research on quantum gravity is doomed to failure because the domain is essentially untestable?
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waitedavid137
Posted: Sep 21 2011, 04:08 PM


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QUOTE (brucep @ Sep 21 2011, 08:21 AM)
I wouldn't say presumptous since the domain of applicability is, for the most part, untestable. I take from your comment that you might think the research on quantum gravity is doomed to failure because the domain is essentially untestable?

No, I'm sure we'll come to be able to test it someday. This is still a world of savages. There is a lot of room for growth for our descendants yet.
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brucep
Posted: Sep 21 2011, 08:07 PM


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QUOTE (waitedavid137 @ Sep 21 2011, 04:08 PM)
No, I'm sure we'll come to be able to test it someday. This is still a world of savages. There is a lot of room for growth for our descendants yet.

I like to hear that. Thanks for all the informative comments in this thread.
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yoron
Posted: May 4 2012, 12:08 PM


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QUOTE (waitedavid137 @ Sep 19 2011, 05:41 AM)
Actually its the "length" of the tensor that is invariant, its full contraction. The elements of the tensor depend on frame. This can be thought of as analogous to considering how an arrow looks when you rotate your coordinates. The mathematical description of the arrow called a vector or in this case the tensor changes its components with frame rotation, but the length stays the same, invariant to rotation. This is why Einstein and the few folk who understood relativity phrased the general principle of relativity as the laws of physics being frame covariant rather than invariant. The tensor equation representing the law of physics is indeed invariant, but the elements of the tensor which the equation ultimately relates do depend on frame, but co-vary in frame transformation in such a way that the "equation" is the same for any frame. Pseudo means something superficially looks like something that it is really not. I don't know why anyone would bother to point out how a pseudo tensor does not have the same properties as a tensor as by definition then it isn't a tensor, but I think the point is that one can define things that look like a tensor for example Christoffel symbols which actually are not tensors and that unlike a tensor, a pseudo-tensor needn't have an invariant "length". And yes if you tried to model natural laws with something other than a real tensor it would indeed defeat the point. So in GR one doesn't do that. Mass isn't the only thing that curves spacetime. Anything that you put into the stress-energy tensor will do it. If for example you have a field of massless particles such as an electromagnetic field, the length of the stress energy tensor will be zero and so will the Ricci-scalar be, but the stress-energy tensor will have nonzero components for energy pressure momentum that result in a nonzero Reimann tensor thus spacetime curvature. What is conserved in general relativity isn't Newtonian energy and momentum, but is relativistic energy and momentum parameters that correspond to isometries in the spacetime geometry.

Very nice explanation. Pleased to read you.
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