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revised What is the role of the vacuum expectation value in symmetry breaking and the generation of mass?
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revised What is the justification for continuing to model space-time as a manifold in string theory?
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revised What is the justification for continuing to model space-time as a manifold in string theory?
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Mar
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comment What is the justification for continuing to model space-time as a manifold in string theory?
@RobinEkman Yup. Agreed.
Mar
6
comment What is the justification for continuing to model space-time as a manifold in string theory?
@RobinEkman Well, I suppose I am being sloppy here. If by "observer" we mean a world-line in space-time (the idea being that our observer is traveling along this world-line), then what I really meant is "observer together with a choice of smooth orthonormal frame along the world-line, with the single time-like vector in each basis being the tangent to the world-line".
Mar
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comment What is the justification for continuing to model space-time as a manifold in string theory?
@ACuriousMind Well I suppose it doesn't need a priori justification, but in this case the "only [reason] that matters" (a posteriori justification via experiment) doesn't exist, and so I think a priori justification is more important here than it might otherwise be.
Mar
6
comment What is the justification for continuing to model space-time as a manifold in string theory?
@RobinEkman I don't disagree with what what you say (regarding coordinate-independent theories), but I also don't understand how this is in contradiction with that I previously stated. The laws of physics must be coordinate-independent, but in order for an experimentalist to verify the laws, they must first pick coordinates. The statement that the laws are coordinate-independent then means that it doesn't matter what choice of coordinates the experimentalist happens to make: his physical conclusions should be the same regardless.
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asked What is the justification for continuing to model space-time as a manifold in string theory?
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comment Density matrix: error with diagonalization claim and fixing it
@NorbertSchuch Thanks again. I've updated the answer with the slicker proof.
Feb
21
revised Density matrix: error with diagonalization claim and fixing it
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21
revised Density matrix: error with diagonalization claim and fixing it
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Feb
21
comment Density matrix: error with diagonalization claim and fixing it
Actually, this conversation you guys have had made me realize I made quite a serious error. When I wrote down the example I alluded to in which $\sum _k\lambda _k\neq 1$, I forgot to normalize the original $\left| \psi ^{(k)}\right>$. If you do this, it seems that indeed you will have $\sum _k\lambda _k=\operatorname{tr}(\rho )=1$. I will update the answer accordingly. Thanks!
Feb
20
revised Density matrix: error with diagonalization claim and fixing it
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revised Density matrix: error with diagonalization claim and fixing it
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