Re: Noether theorem vs. Runge_Lenz (cont'd)
Posted by Uncle Al on May 30, 2003 at 12:19
Re: Noether theorem vs. Runge_Lenz (cont'd) (Pasti)
I got through to my savant on the East Coast. Parity is priviledged among all symmetries by
1) Being an external symmetry and therefore being couple to spacetime rotation and translation (internal symmetries, e.g., charge conjugation, by definition do not couple to spacetime rotation and translation);
2) Plus not being amenable to any infintesimal or Taylor expansion approximation.
OK, so how does one rationalize voluminous journal acreage about strong force conservation of parity and weak force parity non-conservation?
It's a big deal.
What ties the mathematical symmetry parity to the conserved physical property parity? Noether's theorem! Except nobody states the details and the details - when one gets down to the nitty gritty - appear to say it isn't so no mater how the issue is jiggled. Where is the missing boojum?
Nobel Prizes have been awarded. Fine. Given the mathematical symmetry parity, state the rigorous basis by which the physical property parity is conserved. Noether's theorem! So either both of us are missing something painfully obvious, or everybody else has a secret, one way or the other, they are not sharing.
Is parity conservation an empirical observation without traceable mathematical basis? If not, the parity Eotvos experiment is rationalized - for there is the math justifying the look. If so, the parity Eotvos experiment is rationalized - because nobody can make a call *except* by looking.
Geodesic paths are present in metric theories of gravitation. Affine theories of gravitation don't have geodesic paths (Teleparallelism has
torsion acting as a force, analogous to electrodynamics' Lorentz force equation.) A non-null parity Eotvos experiment enforces
1) There is no free fall coordinate frame in which local spacetime is Minkowski spacetime for parity pair test masses,
2) There is no unique value for local spacetime curvature for parity pair test masses,
3) There is a non-zero gravitational stress-energy tensor for parity pair test masses,
4) The Weak Equivalence Principle can be violated at will by at least one specific class of contrasted test masses - geometric parity pair crystal lattices. (The next experiment would then be to relax the constraint and examine merely chiral lattices of opposite hands.)
5) Metric theories of gravitation have the wrong mathematical symmetry toward parity transformation overall. They are falsified - but only detectably so at their singular failing where they diverge from affine (teleparallel) theories.
Braginsky and Panov, if you read their paper, are second rate. Adelberger, Newman, and Wei-Tou Ni are the standard. (Ramanath Cowsik is out of the business; the TATA Institute's Eotvos balance is arguably non-local for its large span.)
You don't know internal structure is irrelevant. You don't know all test masses default to point masses. You assume this because it empirically works. Geometric parity is an emergent phenomenon with a non-point floor (the crystal unit cell volume, ~0.1 nm3 vs. a Planck volume of ~10-78 nm3). I propose a novel case that has never been examined. Somebody has to look - or you don't know.
Your WEP argument is only valid if metric theories of gravitation are valid. Since there is a wholly unexamined case that is mathematically quantified, there is no decision until the last possiblity is examined. I've got the alpha-quartz numbers stated and graphed. Tellurium is better on several counts, but quartz is acceptable - and 100-500X cheaper.
The numbers for both
The Equivalence Principle has never been tested against calculated parity pair test masses of identical composition and maximally opposite geometric parity. The equipment exists. It is running and rerunning the same dreary composition contrasts that have failed for 400+ years. To have examined the problem for 400+ years in every conceivable way to achieve 100% null results within experimental error, then to reject one additional very different quantititative test mass variable as "too risky" vs. failure is insanity.
The parity issue, linking mathematical symmetry and physical property, has got to be pinned down.
This is a lot of fun, isnt' it?
(Do something naughty to physics)
- Re: Noether theorem vs. Runge_Lenz (cont'd) Pasti 02/6 01:47 (0)
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