Re: The time it takes to emit one photon

On 2005-08-15, nightlight <nightlight@xxxxxxxxxxxxxx> wrote:

> Indeed, the Barut's self-fields predictions do deviate experimentally
> from the predictions of the multiparticle QM (which is obtained as a
> truncated linearization approximation of the Maxwell-Dirac coupled
> fields, hence they are certainly not equivalent). This difference,
> though, turns out to be precisely the radiative corrections, where the
> QM is wrong and the Barut's self-fields ED is right, and where QM needs
> to be superseded by QED to obain the experimentally correct results.
> Barut's self-fields ED agree with the experiments (and QED) here as far
> as he had carried out the computations (equivalent to the QED's alpha^5
> order). So, the QM "works" in the sense of getting the numbers right,
> but only to the extent that the truncated linear approximation of
> Maxwell-Dirac dynamics (which is what the multiparticle QM formalism
> is) works.

I'm curious about Barut's approach. So, perhaps you can help me
understand better the differences and similarities between it and
standard QFT.

First, let me say how I see the connection between non-linear classical
field theory, QFT, many particle quantum mechanics, and classical
particle mechanics.

Quantization
Classical Field Theory <-----------------> QFT
Classical Limit ^
|
Fock Space |
Construction | Wave Function
| Representation
Classical Quantization V
Particle Mechanics <-----------------> Many Particle QM
Classical Limit

Let me clarify the two steps that are less known than they should be.
In many particle QM (MPQM), states are represented by wave functions of
3N variables, where N represents the number of particles and may take on
different values. Before taking the classical limit, we fix N and, as
hbar -> 0, we obtain Hamiltonian mechanics of N particles. Fock space
construction relates the space of all symmetric (resp. antisymmetric)
wave functions to the modes of a number of bosonic (resp. fermionic)
quantum harmonic oscillators, one for each mode of the single particle
Hilbert space in MPQM. On the other hand, given a QFT with a Fock space
and an algebra of field operators, each N-particle state |N> can be
expressed as a wavefunction using the formula <N|psi(x)psi(y)...|0> and
other similar ones, with psi(x) being field operators and |0> the vacuum
state. Note that, in the classical limit of a QFT, a fermionic field
must reduce to a Grassmann-valued classical field.

Both Fock space construction and wave function representation are exact
equivalences, no approximation here. Not so for the other steps. The
classical limit is an approximation, hbar -> 0. And quantization is not
always unique, although it is reasonably so for important examples.

My first question is whether Self-Field ED fits into any of the above
theory categories, or does it have to be considered separately? If
applicable, which one of the arrows does "Carleman linearization"
correspond to?

I would also like to know exactly where standard QED and Self-Field ED
agree or part ways on experimental predictions. I don't want to discuss
measurement theory here. For me, a theory is a black box that takes
input parameters and spits out numbers that can be checked with existing
apparatus. If a theory does not make a prediction for a measurement that
we can't make, that doesn't bother me much. But it will if the
measurement can in fact be made.

You mentioned that, since Barut's theory is non-linear, state
superposition goes out the window. In that case, does it account for
Stern-Gerlach and interference-type experiments? If superpositions are
possible for weak fields (in the linear approximation) at what field
strength should non-linear effects become visible?

The quantization of electromagnetic excitations (photons) as well as
excitations of other fields (electrons, protons, etc.) is intimately
related to the Fock space structure of QFT and is seen all around us.
Does Barut's theory account for that as well?

QED takes the particle masses and the fine structure constant as input.
It outputs a great deal of predictions, including cross sections. Some
of which show some of the best known agreemet with experiment. Two
examples are the electron's gyromagnetic ratio and the Lamb shift. Does
Barut's theory agree with experiments to the same precision as QED? And
if written as powerseries in alpha, do the coefficients of these
calculated quantities agree between QED and Self-Field ED? Does the
agreement break at some power of alpha?

You also mentioned your doubts about the results of Bell's inequality
tests. Can Barut's theory produce a prediction for the correlations
measured in these experiments (however these correlations are defined)?
If so, how does the prediction compare to the experimental data? Better
or worse than QM?

Thanks.

Igor

.

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