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In General Relativity, the assumption is made that the stress-energy tensor Tαβ is symmetric. However, if there are particles with intrinsic spin, then this assumption is false, as described here: http://en.wikipedia.org/wiki/Spin_tensor
The spin tensor Sαβμ satisfies:
∂μ Sαβμ = Tβα - Tαβ
Here's what I don't understand about this: Surely, there should be not much observational difference between (A) a particle with intrinsic spin, and (B) a composite particle made of much smaller spinless subparticles, which have orbital angular momentum.
My intuitive feeling is that at a gross level of description, there should not be much difference between particles with spin and composite particles with orbital angular momentum. It seems like one should be some kind of limit of the other. (The article here http://en.wikipedia.org/wiki/Einstein–Cartan_theory#.CF.89-consistency describes a continuum limit of many tiny black holes.) But how can a symmetric Tαβ become non-symmetric in the limit?
The spin tensor Sαβμ satisfies:
∂μ Sαβμ = Tβα - Tαβ
Here's what I don't understand about this: Surely, there should be not much observational difference between (A) a particle with intrinsic spin, and (B) a composite particle made of much smaller spinless subparticles, which have orbital angular momentum.
My intuitive feeling is that at a gross level of description, there should not be much difference between particles with spin and composite particles with orbital angular momentum. It seems like one should be some kind of limit of the other. (The article here http://en.wikipedia.org/wiki/Einstein–Cartan_theory#.CF.89-consistency describes a continuum limit of many tiny black holes.) But how can a symmetric Tαβ become non-symmetric in the limit?