Science > Physics > Solitons vs Leptons vs Bosons vs Gravity 5: Leptons
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Science > Physics |
| User: |
"OsherD" |
| Date: |
17 Jul 2005 07:31:07 AM |
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Solitons vs Leptons vs Bosons vs Gravity 5: Leptons |
From Osher Doctorow
This will be concerned mostly with electrons.
Markw... has given an interesting clue that electrons are most simply
obtained from GR, although the paper that he cited has a rather
specific picture that won't be considered here.
What singles out electrons from "everything else" is largely another
sort of clue. Remember the experiments in the double slit using
one-at-a-time photons and electrons, and the resulting quantum
strangeness/entanglement?
Photons satisfy the Riccati Differential equation almost "trivially" in
terms of their constant velocity in the usual conditions, and light
itself is key to the Lorentz transformations via c, but in being so
fundamental it turns out to border on an unobserved phase involving
complex variables (the superluminal phase, which at least applies to
group velocities).
Electrons appear to come from the Dirac equation and in particular from
spinors which via Dirac spinors involve Dirac matrices of which 2 out
of 16 are complex-valued and the others involve a constraint related to
those two.
But the Dirac equation generalizes the Schrodinger equation (which is
fundamentally a Riccati Differential equation), and yet spinors
specialize tensors via the tensor construction of spinors. Whereas
tensors are mostly studied with all real valued entries of their matrix
or "hyper-matrix" representations, spinors specialize to complex and
indeed imaginary-valued components in the manner indicated.
Imaginary components in all the contexts cited above play the role of
generating additional or separate dimensions, just as the real and
complex fields in algebra are fundamentally different fields. Yet this
is not always the case in other contexts. Hermitian operators and
related matrices in QM tend to obscure rather than reveal the real vs
complex differences. It is differential equations with their Birkhoff
causation which play the central role, and we see more consequences in
creation and annihilation operators in the Dirac picture.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Solitons vs Leptons vs Bosons vs Gravity 5: Leptons |
17 Jul 2005 07:45:04 AM |
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From Osher Doctorow
There is another thing that helps to cross-validate the picture of the
previous posting, namely the infinitesimal Lie algebra nature of
spinors. Infinitesimals are the basis of Lie algebra, and
infinitesimals are fundamentally of Rare Event type and Local.
An infinitesimal here is the limiting form of small transformations,
and spinors involve Lorentz transformations infinitesimally close to
the identity, which is to say that L(a, b) = delta(a, b) + w(a, b) with
/w(a, b)/ << 1 where a is a superscript and b is a subscript (indented)
in the usual covariant-contravariant senses. Delta(a, b) is the
Kronecker symbol tensor. See Steven Weinberg (1972) p. 58.
Osher Doctorow
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