Re: The time it takes to emit one photon

> 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?

The SFED is a separate node not shown on your diagram. Its
various approximations correspond to the 4 nodes on the
diagram. The Carleman linearization represents the arrows
from SFED to MPQM and QED/QFT. In Barut's work, the arrow
SFED to MPQM (which I call Barut's ansatz, cf. [1], eq. (11)
pp 8) is a special case, a fixed-N truncated form, of the
Carleman's linearizing ansatz (cf. [6], eq. (2), pp 100,
which also covers the unlimited N for Fock space).

More precisely, the Barut's ansatz (in SFED) for fixed
N particles, plus dropping of the self-interaction integrals
in the resulting Maxwell-Dirac action (cf. [1] eq. (10)-(12)
pp 8, more details in [2] pp 353-356) result in the N particle
direct product Hilbert space formalism of MPQM (Dirac or
Schrodinger QM particles with Coulomb & Lorentz interactions
and in any external fields). Without dropping of the
self-interaction terms, but with the linearizing Barut's ansatz
(of infinite order) Barut obtains SFED approximation
corresponding to QED with all radiative corrections.

The expansions in powers of alpha are not identical between
the linearized SFED and QED since Barut uses an iterative
method (which expands in alpha) only on parts of the action
(the fermion self-interaction terms), while using the exact
closed form for other terms (e.g. for EM vacuum fluctuations).
Also, unlike the QED recipe for subtractions of infinities
(and at best the asymptotic expansion), Barut uses only the
legitimate mathematics (finite quantities, convergent series).
The first theoretical differences between the linearized SFED
and QED show up at the alpha^5 order corrections, although
both formalisms fall within the experimental figure ranges
for all high precision QED measurements (as of late 1980s).

A detailed review of experimental & theoretical comparisons
is in the monograph [2], which also includes separate chapters
from Barut's students & coworkers. Much of that material
is available online in scanned ICTP preprints, ref [1],[3].
For a brief intro into the relation of SFED to QM entanglement,
measurement theory and to Carleman linearization (CL) see my
Physics Forum posts [4]. The main reference for CL is
Kowalski & Steeb monograph [6], with a brief sketches given
in Kowalski's arXiv preprints [7] and a tutorial [9] with
Mathematica code (for engineering applications of CL).
Kowalski has also utilized the relation of CL to QFT in
reverse direction, by porting the QFT phase space methods
(Wigner & Glauber pseudo-distributions, coherent states)
to solve CL problems arising in nonlinear dynamics and
general nonlinear ODE/PDE (cf. [7],[8]).


> 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 non-linear effects of SFED are visible -- they manifest as
radiative corrections (in higher orders) and the absence of
QM nonlocality, such as Bell's inequality violations or various
QO non-classicalities (in the first order). Note that the
regular multiparticle QM is experimentally wrong on both of
these tests (and QO/QED on nonlocality only, assuming the
orthodox QM interpretation transplanted to QED; QED itself
doesn't make such nonlocal predictions from dynamics but
only via the QM composite system projection postulate, its
strong form interpretation as proposed by von Neumann &
Dirac). In SFED the entangled states are non-physical
artifacts of the particular (Carleman) linearization
scheme -- they correspond to solutions of variation of
action obtained by using a weakened variational principle
(a subset of the full variation, constrained via Barut's
ansatz) i.e. they are not true stationary/extremal solutions.

Although Barut has mostly tried to stay away from the tar-pit of
QM nonlocality debates and experiments, he did analyze classical
fields Stern-Gerlach (e.g. see [1]-b,c; [3]-i). For this case,
which is a low order phenomenon, he didn't even need the full
SFED to replicate what the Stern-Gerlach experiments show. There
were no claims of experimental violations of classicality (Bell
inequalities) in Stern-Gerlach experiments.

The main non-classical effects were claimed in Quantum Optics,
both for Bell tests and for non-local state collapse (e.g.
sub-Poissonian photocounts; cf [5]). Although Barut hasn't
bothered with QO experiments and non-classicality "predictions",
the SFED replicates the vacuum fluctuations effects of QED
via the the self-field component of EM (cf [1]-a, [3]) which
turn out to have an effective field approximation identical
to Zero Point Field (ZPF) of Stochastic Electrodynamics
(SED). The SED proponents (such T. Marshall and E. Santos)
have been battling the QO non-locality magic (experimental
and theoretical claims) since Aspect's 1980 claim. They
have refuted the non-locality claim of every QO experiment
by replicating it via purely local EM model which includes
ZPF initial & boundary conditions. Note that in QO-speak
"classical" means EM model with zero fields boundary
conditions, so QO-non-classical is very limited. If you
allow ZPF boundary conditions, all the QO-non-classical
phenomena are classical (see [5] for discussion & ref's).

> 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?

Barut, like regular QED/QFT, postulates quantization of
charge, even though he does recognize (cf. [3]-h) that unlike
QED where it has to be postulated, the charge quantization
should folow from the SFED first principles. All other
observed quantization effects then follow. Although
it is not essential for SFED approach, Barut uses
source form ED (analogous to Schwinger's source QED),
where the EM field is eliminated from the SFED action
via currents integrals, so there are no photons in SFED.
Of course, there are no non-local (non-classical) effects
in SFED which the presently dominating QM interpretation
suggest to exist (but which no experiment has demonstrated
as yet).


> You also mentioned your doubts about the results
> of Bell's inequality tests.

Neither I, nor the experimenters, nor anyone who has studied
the experiments in sufficient detail, have any doubts about
the results of the Bell tests -- no test has as yet violated
the inequalities. That is the plain factual situation (as
opposed to the pedagogical & popular accounts).

The only differences are in the expectations about future
experiments -- I doubt (along with other "heretics", from
Einstein & Schrodinger, through Barut, Jaynes, Marshall,
Santos...) that the inequalies will ever be violated,
while the believers claim it is only a matter of technology
until they obtain violations (the hope euphemistically
referred to as the "loophole free" violations, which is
trying to say 'violations which do violate' as opposed,
I guess, to the present "violations" which don't violate).


> 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?

As suggested above, the SFED via its effective field form
suitable for Quantum Optics, the SED, replicates all
QO-non-classical effects (Bell inequalities "violations",
the photon "anticorrelations" etc; see ref's in [5]).
The only difference is in how the two sides label the
absence of violations -- in SFED/SED the absence of
violations is fundamental since the theory is local.
In QM/QO the absence of experimental violations is
introduced as a correction to the "ideal detector"
case (expected to be feasable in the future).

Considering that:

(a) SFED reproduces the high order effects of QED (to at
least alpha^5),

(b) SFED can deduce the multiparticle QM (MPQM) formalism,
the formal basis of entaglement and Bell's violations
predictions & von Neumann's QM measurement theory,
as a linearization approximation of SFED,

(c) MPQM is itself is a low order approximation to QED,
failing to match experiments of (a),

it seems hopless to expect with MPQM that future detector
technology will somehow make SFED fail in the low order
QED phenomena (make it fail in the leading digit of
the experimental data), while matching the remaining 8+
digits known already (which it does match).



References
----------

1. A.O. Barut "Quantum Electrodynamics based on self-energy"
IC1987248: http://library.ictp.trieste.it/DOCS/P/87/248.pdf

2. A.O. Barut "Foundations of self-field electrodynamics"
"New Frontiers in QED and Quantum Optics" pp 345-371
NATO ASI Series B, Vol. 232, Plenum 1990

a) See also in the same volume, pp 371-389
J.P. Downling "QED Based on Self-Fields: Cavity Effects"

b) A.O. Barut "QED - The Unfinished Business" pp 493-503
in "IIIrd Reg. Conf. on Mathematica Physics" 1989
World Scientific 1990

c) A.O. Barut "Fundamental Problems in Quantum Physics"
http://redshift.vif.com/JournalFiles/Pre2001/V02NO4PDF/V02N4FUN.PDF

3. Scanned ICTP preprints (enable Javascript & enter "Barut")
http://library.ictp.it/pages/psearch/prep.php?PAGE=0
Self-fields start (Barut's preprints 61-148)

http://library.ictp.it/pages/psearch/prep.php?PAGE=7&NEXT=/ARCHIVE/preprint/SDW?W%3DAUTHOR+PH+WORDS+%27barut%27+ORDER+BY+EVERY+ICNUM/Ascend%26M%3D61%26R%3DY

a. COMBINING RELATIVITY AND QUANTUM MECHANICS: SCHRODINGER'S
INTERPRETATION OF PSI
IC1987157: http://library.ictp.trieste.it/DOCS/P/87/157.pdf

b. ON THE COVARIANCE OF TWO-FERMION EQUATION FOR QUANTUM
ELECTRODYNAMICS
IC1986162: http://library.ictp.trieste.it/DOCS/P/86/162.pdf

c. NON-PERTURBATIVE QUANTUM ELECTRODYNAMICS WITHOUT INFINITIES
IC1986228: http://library.ictp.trieste.it/DOCS/P/86/228.pdf

d. QUANTUM ELECTRODYNAMICS BASED ON SELF-ENERGY: SPONTANEOUS
EMISSION IN CAVITIES
IC1986330: http://library.ictp.trieste.it/DOCS/P/86/330.pdf

e. RELATIVISTIC THEORY OF THE LAMB SHIFT BASED ON SELF ENERGY
IC1987210: http://library.ictp.trieste.it/DOCS/P/87/210.pdf

f. QUANTUM ELECTRODYNAMICS BASED ON SELF-ENERGY WITHOUT
SECOND QUANTIZATION: THE LAMB SHIFT AND LONG-RANGE CASIMIR-POLDER
VAN DER WAALS FORCES NEAR BOUNDARIES
IC1986341: http://library.ictp.trieste.it/DOCS/P/86/341.pdf

g. SELFFIELD QUANTUM ELECTRODYNAMICS WITHOUT INFINITIES. A NEW
CALCULATION OF VACUUM POLARIZATION
IC1993105: http://library.ictp.trieste.it/DOCS/P/93/105.pdf

h. CAN WE CALCULATE THE FUNDAMENTAL DIMENSIONLESS
CONSTANTS OF PHYSICS?
IC1987187: http://library.ictp.trieste.it/DOCS/P/87/187.pdf

i. EXPLICIT CALCULATIONS WITH A HIDDEN VARIABLE SPIN MODEL
IC1986367: http://library.ictp.trieste.it/DOCS/P/86/367.pdf

j. QUANTUM THEORY OF SINGLE EVENTS: LOCALIZED DE BROGLIE-WAVELETS,
SCHRODINGER WAVES AND CLASSICAL TRAJECTORIES
IC1990099: http://library.ictp.trieste.it/DOCS/P/90/099.pdf

4. Physics Forum posts on Barut's self-field & QM entanglement
http://www.physicsforums.com/showpost.php?p=540794&postcount=100
http://www.physicsforums.com/showpost.php?p=541484&postcount=114
http://www.physicsforums.com/showpost.php?p=541708&postcount=118

5. PhysicsForum: Photon "Wave Collapse" Experiment...
http://www.physicsforums.com/showthread.php?t=71297

References:
http://www.physicsforums.com/showpost.php?p=544829&postcount=122

On SED analysis of the QO experiments:
http://arxiv.org/find/quant-ph/1/au:+Santos_E/0/1/0/all/0/

6. K. Kowalski, W. Steeb
"Nonlinear Dynamical Systems and Carleman Linearization"
World Scientific, 1991.
http://www.worldscibooks.com/mathematics/1347.html

7. K. Kowalski's arXiv preprints on Carleman linearization:
http://arxiv.org/find/grp_nlin/1/au:+kowalski_k/0/1/0/all/0/1
http://arxiv.org/abs/hep-th/9212031

8. K. Kowalski
"Methods of Hilbert Spaces in the Theory of Nonlinear
Dynamical Systems" World Scientific, 1994.
http://www.worldscibooks.com/chaos/2345.html

9. B.W. Gaude "Solving Nonlinear Aeronautical Problems Using the
Carleman Linearization Method"
Sandia National Labs, SAND2001-3064, OSTI ID: 787644

http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/2001/013064.pdf
http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=787644&query_id=0

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