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Lorentz violation of the Standard Model
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Gerard 't Hooft



Joined: 26 Mar 2007
Posts: 10

PostPosted: Mon Mar 26, 2007 2:05 pm    Post subject: RE: Lorentz violation of the Standard Model Reply with quote

2007-03-25 (Sun) AM 2:39

More importantly, parity violation is consistent with lorentz invariance.
Your statement that the observed parity violation cannot be reconciled with
lorentz invariance is wrong.
You say "If these matrix elements are Lorentz invariant, then the asymmetry
should have been zero." I now see where you are short-circuiting.
G. 't H
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jcyoon



Joined: 08 Aug 2006
Posts: 213

PostPosted: Mon Mar 26, 2007 2:07 pm    Post subject: RE: Lorentz violation of the Standard Model Reply with quote

2007-03-25 (Sun) AM 8:47

Dear Professor G. 't Hooft,

I am grateful for your clarification on your opinion.

In my opinion, the part 2 explicitly shows that the non-zero asymmetry is a consequence of Lorentz violation. If the matrix element of right-handed helicity electron is Lorentz invariant, then they should be the same in a frame. We can perform Lorentz transformations to a frame where only one of them is observed as left-handed helicity and thus the matrix elements should be the same and the asymmetry is zero if they are Lorentz invariant.

Could you point out where in this argument you think I am short-circuiting?

[quote]You say "If these matrix elements are Lorentz invariant, then the asymmetry should have been zero." I now see where you are short-circuiting.[/quote]

Parity violation of massive fermion is equivalent to Lorentz violation.

1. The matrix elements of left- and right-handed helicity electrons (e_L, e_R) are observed to be different as the parity violation in SLAC E158.

e_L --> <-- e_R

2. Under Lorentz transformation, those both electrons can be observed as right-handed helicity

e_R' <-- <-- e_R

so that the difference of matrix elements between left- and right-handed helicity electron is now observed as a difference in matrix elements between the right-handed helicity electrons, which violates Lorentz invariance of matrix element.

3. Therefore, the parity violation of massive fermions in the SLAC E158 is consistent with the Lorentz violation.

Sincerely yours,
J.C. Yoon
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Gerard 't Hooft



Joined: 26 Mar 2007
Posts: 10

PostPosted: Mon Mar 26, 2007 2:08 pm    Post subject: RE: Lorentz violation of the Standard Model Reply with quote

2007-03-26 (M) AM 3:53

I don't think I can point out where you are short-circuiting, because I have
already tried to do that a dozen times. Let's try once more (but at some
point I will no longer anwer your mails). The helicity states are defined in
a frame dependent way, so they are not Lorentz invariant; more precisely,
their Lorentz transformation properties are delicate. Therefore also the
amplitudes will only be Lorentz invariant if these helicity states are
transformed in the appropriate manner. Keeping the helicity of the in- and
outgoing particles fixed will lead to an apparent Lorentz invariance
violation. The real theory however continues to be fully Lorentz covariant.
G. 't H
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jcyoon



Joined: 08 Aug 2006
Posts: 213

PostPosted: Mon Mar 26, 2007 2:09 pm    Post subject: RE: Lorentz violation of the Standard Model Reply with quote

2007-03-26 (M) AM 4:53

Dear Professor G. 't Hooft,

I am glad that our perspectives are quite close now, though our discussion seems stuck at this point. Maybe it is something that I have been missing stubbornly insisting my perspective. I sincerely appreciate your earnest effort and I wish we can work this out together with little more patience.

Our discrepancy hinges on how exactly the real theory of Standard Model describes massive fermions. The Standard Model is based on left- and right-handed chirality fermions, but in real system of the Dirac equations of massive fermions, there are no such left- and right-handed chirality massive fermions, and inevitably we have to rely on the approximation from measured helicity to theoretical chirality. In other words, the theory of Standard Model is self-inconsistent, since the left- and right-handed chirality massive fermions treated as independent field fail to accurately obey the massive Dirac equations, which are fundamental equations for massive fermions.

Sincerely yours,
J.C. Yoon
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Gerard 't Hooft



Joined: 26 Mar 2007
Posts: 10

PostPosted: Mon Mar 26, 2007 2:10 pm    Post subject: RE: Lorentz violation of the Standard Model Reply with quote

2007-03-26 (M) AM 5:16

I give up.
G. 't H
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