Posted by Pasti on May 14, 2003 at 15:20
(64.10.124.93)
Re: Parity Eotvos Experiment-Discrete Noether (Uncle Al)
"You are wrong. You would do better if you read the proposal, below, rather than shooting from your hip."
Let me try to give you an answer to the above.
First of all, I am not attacking your work, and yes, it is true, I haven't read thoroughly what is on your website.This does not mean I am not interested in what you are doing,it just means that I would prefer to read a more organized material, a draft or pdf file or something similar.That is the reason why I asked you that if you upload your work on arxiv, to let me know because I would like to read it.
Second of all, if you really want to go through with your work, to make something out of it,you will have to make it public some way or the other.And I am not doing anything different from what people listening to you at a conference won't do.With the only difference in your favor that that you have time to think about the question.You mentioned Noether theorem in conjunction with discrete symmetries,which raises a big red flag, whether you like it or not.And again,wheter you like it or not I have seen at conferences people that could not continue their talk because off some elementary mistaken statement they made,which didn't have too much bearing on their presentation.And this seems to be your case.
Third of all,I have not even drawn the guns yet.Moreover,I don't have any intention to do it, since I don't want to "start a war".If you want to have a discussion about your work (or your statements at least),fine,if you don't want to discuss what you are doing, fine again.It is your choice.
Let's get back to the Noether theorem, which was the subject under discussion.
"Noether's theorem couples the mathematical discrete symmetry of parity to the physical property of parity. If you deny that, then you also have to deny charge conjugation (also discrete). Do you deny charge conjugation? If so, you are at odds with all of physics: tests of cosrvaiton laws."
Your statement is wrong.Noether thorem deals only with continuous symmetry transformations, i.e. with symmetries that can be parametrized continuously (this does not imply only infinitesimal symmetries,but also finite continuous symmetries).Let me give you an example.Suppose that you rotate a vectorr in a plane.The rotated x component of the vector will have the expression
x1=x0sin(a)+y0sin(a)
where a is the rotation angle.This is a finite transformation parametrized by a continuous parameter a.Of course,this transformation has also an infinitesimal form (around a=0):
dx1=x0da
The parity transformation is
x1=-x0
and you might be tempted to interpret this transformation as a rotation by 180 deg. It is not, because the parity transformation "flips" the sign,and does not exactly sweep the 180deg range.Or, equivalently,parity changes the right-handedness of the system to left-handedness,and viceversa,which is something rotations cannot do.
Or, in point group language(Schoenflies notation-you do the conversion to your notation),the C2 rotation group is different from the inversion group S2.
Of course, you are actually dealing with space groups, but it is easier to understand the concept on point groups.
So these being said,parity is not a consequence of the Nother theorem,very much as the Runge-Lenz vector conservation is not.
Let me put it another way:Parity is a symmetruy of the hamiltonian, and the hamiltonian of a system (if conserved)is a consequence of the time translation symmetry.
the same is valod for charge conjugation, and time reversal,you cannot obtain them from the Noether theorem.You cannot construct the associated conserved charges from Noether theorem.
This does not mean this symmetries do not exist, of course they do.They just cannot be obtained from the Noether formalism(if you don't believe me, prove me wrong by constructing the Noether current associated with parity, and calculate the conserved charge).They only impose restrictions on the analytical form of the lagrangean.If you are lucky, you can find some quantity that is conserved and embodies the C,P,T conservation(or violation for that matter).
This is the reason why I told you that I hope you didn't implement in your work parity as a continuous transformation using the numerical methods in Marsden paper.
Moreover,I still have no clue why you mentioned that reference,since it refers to a discrete system of particles, and not to systems with discrete symmetries,at least as much as the proof given for the Noether theorem is concerned.
"We expect to explicitly calculate (much of) an entire centimeter ball test mass of 1.5x10^22 atoms."
This sounds good.But I cannot keep wondering about the fact that the ball won't be exacly spherical, in the sense that by trying to get a spherical ball by machining (processing)a single Te crystal you will get a lot of defects in the first few surface layers, with the possibility of these defects to propagate and develop further in the bulk.Did you account for that, and in case you did, how did you do it?
Re: Parity Eotvos Experiment-Discrete Noether Uncle aAl 14/5 17:41
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