Re: Parity Eotvos Experiment update

Posted by Pasti on Jun 15, 2003 at 08:26
(64.10.121.50)

Re: Parity Eotvos Experiment update (Uncle Al)

OK, let's get back to the problem we were discussing.

"The Equivalence Principle postulates that all local test masses fall identically in vacuum regardless of composition or internal structure. General Relativity immediately follows. Test mass opposite geometric parity has never been evaluated."

First of all, to be pedantic, what you state above is not the "Equivalence principle", but the "Weak Equivalence Principle"(WEP).There is an esential difference between the WEP and the SEP(Strong Equivalence Principle) in the sense that for the WEP you need a quasi non-local Minkowsky frame, while for the SEP you only need a local Minkowski frame.

"The existence of a symmetry operator implies the existence of a conserved observable. Given G is the Hermitian generator of nontrivial unitary operator U (e.g., parity), then if U commutes with Hamiltonian H so does G: [H,G]=0. If U commutes with H it is a symmetry and a conserved quantity. Any system that is initially in an eigenstate of U evolves over time to other eigenstates having the same eigenvalue."

Not necessarily the above.Consider a free particle.For a free particle, the momentum commutes with the Hamiltonian, and therefore, the momentum is a conserved quantity, since

dp/dt={H,P}=0

and let's keep {,} for the Poisson brackets and [,] for the quantum commutator.
p is not a symmetry, but a conserved charge.So don't confuse a symmetry with a conserved charge.There is a fundamental difference between the two.

"*All* gravitation theories are either symmetric (metric, General Relativity) or anti-symmetric (affine, teleparallel) to parity transformation. "

I think you should define more carefully what you mean that all gravitational theories are symmetric/antisymmetric with respect to parity.
Let's consider the metric

g(i,j)=g(xi,xj)

(I won't bother for the moment with covariant/contravariant indices).Assuming that g is a real bilinear operator,under parity, x goes into -x, and under this transformation, the spatial part of the metric remains invariant(is symmetric), while g(0,i)changes sign(is antisymmetric).

So what is exactly the theory that is symmetric/antisymmetric with respect to parity?What are the actions for these theories?Do you refer to the parity of "objects" embeded in the spacetime or to the parity of the spacetime itself.Because it doesn't seem to me that you make a difference between parity transformation of the spacetime and parity transformation of "objects" into the spacetime.

However, a good starting point for continuing this discussion would be if you could write down the actions of the theories you consider.This way at least we hhave a common reference background for our discussions.

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