Re: Noether theorem vs. Runge_Lenz (cont'd)
Posted by Pasti on Jun 02, 2003 at 01:47
(64.10.124.6)Re: Noether theorem vs. Runge_Lenz (cont'd) (Uncle Al)
Ok, you have now independent confirmation that somehow, I know what I am talking about,at least when it comes to these matters :)
"OK, so how does one rationalize voluminous journal acreage about strong force conservation of parity and weak force parity non-conservation?"
Yes, it is a big deal,but C,P,T come out of the experimentally as symmetries.So they must be considered, regardless of the fact that they cannot be fitted within some "puny" theoretical framework like the Noether's theorem.
Suppose, just for the sake of the argument that the Noether's theorem had not been invented.You would still find that in certain cases, the lagrangean(better the action) remains invariant under say rotations, or translations, etc.They would be symmetries of the action nevertheless.Same thing with C,P,T.They are symmetries regardles of the fact they cannot be fit within the Noether framework.
"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!"Sorry to disappoint you but no, it isn't the Noether theorem.It is experimental data.Elementary particle interactions are the only basis for conservation/noncnservation of these properties.
And to my knowledge, there isn't any physical property associated with parity, or charge conjugation, or time reversal(at least directly).But I guess it is obvious if in a particle reaction the electron say, comes into reaction and a positron emerges(conjugated charge, right?), or in other words, if charge would become conjugated in the process."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."
No, we are not missing anything, and there is no secret.I knew about that,remember how this discussion started?But I guess that unless you do quantum field theory,C,P,T are not exactly very common symmetries to be mentioned,especially in books of classical field theory.
"Is parity conservation an empirical observation without traceable mathematical basis?"
Yep.It is an experimental observation,in particle physics.But you can easily understand where it comes from in atomic and molecular physics.Think of the say, H2 molecule.This molecule is so symmetric that geometrically it has an inversion center, and under this inversion, you get the same molecule,which meands that the hamiltonian of the molecule should be invariant under inversion.In this particular case, you don't need experimental confirmation for the invariance under inversion of the physics of the H2 molecule.
Remember,a theory is as good as its experimental confirmation, and is useless without it.The fact that certain symmetries cannot be incorporated in a certain framework is irrelevant as long as these symmetries exist (it becomes mostly an elegance aspect of the theory, and not a fundamental issue)."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.)"First of all, GR is a metric theory, as developed by Einstein.Secondly,it can be recasted in affine form, without any problem (the Palatini action vs. the Einstein-Hilbert action for example).So the existence of geodesics is pretty much irrelevant, since I can recover the metric theory easily from an affine one.
Thirdly, I would be more careful in using the term null when talking about GR, because it usually has a dedicated meaning (like in null-geodesic, null-survace, null-4vector, etc)."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,"In case you didn't notice, #1 means that you would infirm the Strong Equivalence Principle (SEP).And I would like to see the proof for this infirmation,i.e. a proof that for a non-trivial result of your parity experiment,you can find an interaction which in a local Minkowski frame cannot have its laws cast in the special relativistic form(this is one form of the negation of the SEP).
"2) There is no unique value for local spacetime curvature for parity pair test masses,"This statement makes no sense in the form above.Would you care to elaborate in more detail?
3) There is a non-zero gravitational stress-energy tensor for parity pair test masses,That is obvious, for any pair of test masses.What is your point?
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.)Once you infirmed the SEP, I wouldn't worry about the WEP.
"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."
This is a bold statement, even if it isn't quite true.QCD in curved spacetimes gives the correct results, and it is a metric theory.QFT in flat spacetime(Minkowski)fits the experimental data, including parity, charge conjugation and time reversal.
Again, unless you want to elaborate on the above statement, it does not make a lot of sense.However, in the light of a hypothetical non-trivial result of your experiment,how can you account for the previous results on teh equivalenvce principle?
"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)"
That's not the point,you can take whoever you want as reference.The point is that based on their measurements GR is accurate to a quite high level of precision.And you will have to give an explanation why those experimental results show that GR holds, and yours infirm GR.
"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."
I don't assume anything.This is how the equivalence principle is stated.And any departures from the principle must be and are accounted in the experimental testing.And up to now, the internal structure has proven to be quite irrelevant.This is for the moment the harsh reality, irrespective of your theory, and you must face it one way or the other.
"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)."
This is again a statement that needs clarification.What exactly has the Planck volume to do with this?What do you understand by a Planck volume?In QG, the Planck length is about 10^(-35)m, and I cannot see what quantum gravity has to do with your parity experiment?
"I propose a novel case that has never been examined. Somebody has to look - or you don't know."
We agree on this issue, that someone should look.But we don't agree with the "you don't know" case.Believe it or not, one can make "educated guesses", as they are generally called.And such a guess would tell me that you are looking at a "secondary" effect.Nevertheless,one should look.
"Your WEP argument is only valid if metric theories of gravitation are valid."
And up to this moment, only metric theories have been tested experimentally.And quite successfully I might add.
"The Equivalence Principle has never been tested against calculated parity pair test masses of identical composition and maximally opposite geometric parity. The equipment exists."
That has already been established.Let's move on.
"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."
Somehow I don't think I was suggesting that.As I said, I think the experiment should be done, just for the sake of it, to cross every t and dot every i.
What I am saying is that I don't expect any fabulous results to come out from such experiment, and thsi among other things for the teh following reason:the WEP has been tested during the 400+ years you mentioned on a variety of substances,and in the case structure played such an important role, the precision of the validity of the WEP shouldn't have increased with time(and technology) as it did.Structure effects should have produced a much larger scattering in the data than observed.
On the other hand, the tests for the local Lorentz invariance (LLI)which deal exactly with mass anisotropy and "non-metric" theories (very much like what you attempt to do, in principle at least)have shown LLI is valid up to a precision of 10^(-20)(Prestage, Lamoreaux - use SPIRES for the complete refs), which is much better than the precision for the fine structure constant measured from QED.So you must realize, and I hope you do, that you are up against some very strong experimental evidence for the validity of the EP, and even if your experiment proves to yield non-trivial results, in order to infirm the EP you must explain why each and every one of these experiments are wrong.And by "explain" I mean prove, with pen and paper (or computer, or whatever else).
"The parity issue, linking mathematical symmetry and physical property, has got to be pinned down."
If you want to take my advice, don't waste your time on it, because it is not essential.There are more important things you have to think about than a "generalized Noether theorem for discrete symmetries", so to speak.
"This is a lot of fun, isnt' it?"
Yep, it is.