Connection between Einstein-Cartan and "Baby Universes"

[stevendaryl]

The Einstein-Cartan theory is, to my mind, a completely straightforward generalization of General Relativity, and indeed seems like a necessary generalization if we are to accommodate particles with intrinsic spin. (The mathematics for this claim is beyond me, but the layman's summary is this: General Relativity assumes a symmetric stress-energy tensor, while a nonzero spin density would lead to an asymmetric stress-energy tensor. Einstein-Cartan is the (unique?) generalization of General Relativity that allows a nonsymmetric stress-energy tensor.) But according to this Wikipedia article, Einstein-Cartan avoids singularities in black holes and solves the black hole information paradox through proposing that the lost information is found in a "baby universe" spawned by the black hole. https://en.wikipedia.org/wiki/Black_hole_information_paradox

The connection between Einstein-Cartan and "baby universes" is completely mysterious to me. Is there a relatively non-technical explanation for that connection?

 

[bcrowell]

Are we talking about classical gravity here, or quantum gravity? Can you point us to a more detailed statement of the claim that GR can't handle particles with intrinsic spin? Is this a claim about classical gravity, or quantum gravity?

 

[stevendaryl]

Are we talking about classical gravity here, or quantum gravity? Can you point us to a more detailed statement of the claim that GR can't handle particles with intrinsic spin? Is this a claim about classical gravity, or quantum gravity?

Well, I'm out of my depth in talking about this, but it was my understanding, as I said that

1. Intrinsic spin leads to an asymmetric stress-energy tensor.
2. General Relativity assumes a symmetric stress-energy tensor.

I don't think there is anything quantum about it.

For example: "Intrinsic spin requires gravity with torsion and curvature" http://arxiv.org/abs/1304.0047

and from http://arxiv.org/ftp/arxiv/papers/1301/1301.1588.pdf

As the master theory of classical physics, general relativity (GR) has an outstanding flaw: it cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. The simplest manifestation of this problem is that the Einstein tensor in Riemannian geometry is symmetric, hence the momentum tensor must be symmetric. However, classical continuum mechanics shows that the momentum tensor is non-symmetric during exchange of intrinsic and orbital angular momentum.

 

[strangerep]

This all sounded a bit strange to me initially, since MTW deals with both intrinsic and orbital angular momentum well enough (or so I thought). But...

[...] momentum tensor is non-symmetric during exchange of intrinsic and orbital angular momentum.

... sounds like they're talking about a system with an interaction involving spin-orbit coupling. (?)

 

[bcrowell]

As the master theory of classical physics, general relativity (GR) has an outstanding flaw: it cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. The simplest manifestation of this problem is that the Einstein tensor in Riemannian geometry is symmetric, hence the momentum tensor must be symmetric. However, classical continuum mechanics shows that the momentum tensor is non-symmetric during exchange of intrinsic and orbital angular momentum.

I haven't looked at the two papers, but based on this quote, I'm wondering what is meant by "classical intrinsic angular momentum." In classical physics there is no such thing as intrinsic angular momentum AFAIK.

 

[pervect]

The suggestions of this nature I've seen are based on papers by Nikodem Poplawski and ECKS gravity, which is much as stevendaryl describes it. I don't fully understand the details, but the ECKS theories have torsion (unlike general relativity) which is described as causing gravitational repulsion under the right circumstances. The amount of torsion is tiny, so it doesn't become a factor unless you have extreme densities such as in a black hole, making the theory rather difficult to test. A specific paper I've seen with these ideas is http://arxiv.org/abs/1007.0587, there are lot of popularizations that talk about "baby universes". There may be better papers out there, but this should be a start. The author in question also has a website with a listing of his papers.

 

[ShayanJ]

I haven't looked at the two papers, but based on this quote, I'm wondering what is meant by "classical intrinsic angular momentum." In classical physics there is no such thing as intrinsic angular momentum AFAIK.

Section 10.7 of "Special Relativity in General Frames" treats particles with spin. The following quote is from that section:

The concept of a particle with spin is fundamentally a quantum notion (Le Bellac 2006; Penrose 2007). We have defined the spin S of an isolated system as the angular momentum with respect to its centre of inertia [cf. Eq. (10.46)]. However, if the system is reduced to a single particle, the comparison of Eq. (10.1) with M = G and Eq. (10.48) leads to S=0. Another argument against the concept of “classical” (i.e. non-quantum) spin relies on the existence of a minimal size for any system with nonvanishing spin, as we have seen in Sect. 10.5.5: one can therefore not reduce the size of the system to zero to take the “particle limit”. Nevertheless, one can extend the concept of particle beyond the simple particle model introduced in Chap. 9 to include the spin. We define formally a particle with spin as the following data:

1. A worldline $L \subset E$, either timelike or null
2. A field of linear forms p defined along L such that the vector p(M) to L at any point $M \in L$
3. A field of antisymmetric bilinear forms (2-forms) S defined along L such that $S(p,.)=0$

The 2-form S is called spin of the particle. Items 1 and 2 are those already considered in the definition of a simple particle in Sect. 9.2.1. The extension is thus constituted by item 3. The relation $S(p,.)=0$ is motivated by the result (10.49) obtained for a system of particles.

 

[strangerep]

[...] I'm wondering what is meant by "classical intrinsic angular momentum." In classical physics there is no such thing as intrinsic angular momentum AFAIK.

Yes, there is. See Box 5.6 in MTW. (IIRC, Rindler also covers it in one of his textbooks.)

One inconvenient subtlety is that intrinsic and orbital angular momentum get mixed together (in general) under Lorentz boosts. Hence the non-relativistic decomposition of total angular momentum into spin and orbital is perhaps less useful in the relativistic case.

IIUC, only the quantization of angular momentum is a "quantum" feature.

BTW, in Roy Kerr's covariant generalization of the Einstein-Infeld-Hoffman approximation method for determining the paths of test particles, the most general low-order solution representing the test particle has spin degrees of freedom as well as the usual mass parameter that falls out of the EIH treatment. The resulting equation of motion is more general than the usual geodesic equation. This suggests that the concept of intrinsic angular momentum is present at a reasonably fundamental level.

 

[stevendaryl]

I haven't looked at the two papers, but based on this quote, I'm wondering what is meant by "classical intrinsic angular momentum." In classical physics there is no such thing as intrinsic angular momentum AFAIK.

This discussion is drifting back toward the subject matter of a similar post in 2012, which wasn't my intention (even though I didn't think the resolution in that discussion was very clear).

But about intrinsic spin, this article in Wikipedia gives a non-quantum definition in terms of the stress-energy tensor:
https://en.wikipedia.org/wiki/Spin_tensor

The claim is made there that a nonvanishing spin tensor implies a nonsymmetric canonical stress-energy momentum tensor. That article says (without proof) that the asymmetry represents a "torque density showing the rate of conversion between the orbital angular momentum and spin".

 

[stevendaryl]

Yes, there is. See Box 5.6 in MTW. (IIRC, Rindler also covers it in one of his textbooks.)

One inconvenient subtlety is that intrinsic and orbital angular momentum get mixed together (in general) under Lorentz boosts. Hence the non-relativistic decomposition of total angular momentum into spin and orbital is perhaps less useful in the relativistic case.

IIUC, only the quantization of angular momentum is a "quantum" feature.

Certainly we can classically describe the angular momentum of an extended object such as the Earth as having two contributions:

1. The Earth has orbital angular momentum about the sun given by: \vec{L} = \vec{r} \times \vec{p}
2. The Earth has spin angular momentum about its own axis given by: \vec{S} = I \vec{\Omega}

Classically, without point-particles, the spin angular momentum can be seen, at a fine-grained level, to be due to orbital angular momentum about a different axis. The Earth as a whole has nonzero spin, but the little grains of matter that make it up do not. Those grains of matter contribute to the Earth's spin through regular orbital angular momentum about the Earth's center of mass. I don't know whether this fact is important for this discussion, or not.

 

[bcrowell]

This sounds like the kind of thing that might be detected experimentally by the kinds of experiments that would detect torsion. E.g., UW has a torsion pendulum containing a magnetized test mass, which they're using for this kind of search.

 

[stevendaryl]

Getting back to the original post, what I've heard claimed is that Einstein-Cartan (which I guess is the same thing as GR generalized to allow torsion?) is indistinguishable from GR in normal situations, but differs in that there is no singularity associated with black holes (or that it is possible to have a black hole without a singularity).

https://en.wikipedia.org/wiki/Einstein–Cartan_theory#Avoidance_of_singularities

 

[pervect]

Getting back to the original post, what I've heard claimed is that Einstein-Cartan (which I guess is the same thing as GR generalized to allow torsion?) is indistinguishable from GR in normal situations, but differs in that there is no singularity associated with black holes (or that it is possible to have a black hole without a singularity).

https://en.wikipedia.org/wiki/Einstein–Cartan_theory#Avoidance_of_singularities

Several of the referenced papers in the Wiki articles you cite are by Poplawski , and I've had pretty good luck finding full-text pdf versions of Poplawski's articles on the WWW. I also find them readable. I can't really single out a specific paper by this author I'd especially recommend (though I did post a link to one of his papers and his homepage ina previous post). You can probably use the wiki reference section as a guide, if you have the luxury of getting the paper you want rather than browsing through what articles you can find full-text for then looking through those to see if any are relevant. You might be able to find some of the original Cartan papers too, though my experience is that a lot of the older papers are still behind paywalls.

On the general topic of torsion, I found http://www.slimy.com/~steuard/teaching/tutorials/GRtorsion.pdf quite useful for a detailed treatment. As it is an extension of Wald's treatment it might be helpful to have Wald's treatment first.

There are innumerable pop-sci versions of pop-sci treatments of Poplawski you'll find scattered on the WWW , mostly involving "bouncing baby universes", though they might be oversimple for your interests.

 

[martinbn]

Getting back to the original post, what I've heard claimed is that Einstein-Cartan (which I guess is the same thing as GR generalized to allow torsion?) is indistinguishable from GR in normal situations, but differs in that there is no singularity associated with black holes (or that it is possible to have a black hole without a singularity).

https://en.wikipedia.org/wiki/Einstein–Cartan_theory#Avoidance_of_singularities

Are these just examples of non-singular space-times, where the analogs in GR would be singular, or are there general results, theorems that show that in EC under certain conditions generically there are no singularities?

Also if one follows the steps in a typical singularity theorem in GR, what would deffer in EC to prevent the singularity theorems to hold?