MQED2:
New Thoughts on the Issue of How to Reformulate QED to Fit New Experiment

I must
limit my typing today because of red eye due to trauma to left front side of
head at parking lot of Trader Joe just a few days ago.

Last
night I revisited the issue of how to
clean up the formulation of QED, as discussed in my recent posting at
vixra.org, which was essentially an extended journal entry following up on one
aspect of the new paper by Luda and myself published in Quantum Information
Processing. That posting was based on a whole lot of analysis, much of which is
robust and unavoidable. Nevertheless, we are called not only to implement the
various aspects of that paper, but also to reconsider, in parallel, “does it
have to be so complex?” “Could we do the work somehow, in a way which seems
closer to older formulations of QED?”

At
some point, a straw man equation popped into my head:

(1)

along with the thought: “I
really do not know whether this is ultimately a viable model, but analysis of
why and why not, and exploration of issues such as symmetry exploitation, AND
of the considerations which I tried to crystallize in this way, may lead to an
alternative MQED, whether equivalent of not to MQED1 (which is not the
immediate issue on this subtrack).

Most narrowly, equation 1
came from analogy to our very simple master equation model for light going
through a polaroid polarizer, in my joint paper with Luda in QIP. THAT master
equation was grossly time-asymmetric, expressing the traditional idea of
collapse of the wave function, but in this case the Hermitian character of the
interaction Hamiltonian H

_{I}results in a time-symmetric model. Equation 1 could be thought of as an “interaction picture in density matrices”; we know that the older interaction picture for wave functions “does not exist” (e.g. our yet unpublished, unposted paper on MEWT,
“upgrade”...), but we also
know that shifting from wave functions to density matrices has solved a lot of
other problems, and allows the use of extended Glauber-Sudarshan mapping to
disambiguate the system. This is a different
system from the usual Schrodinger equation in any case – closely related but
different.

With limited time, can I even
state (let alone explain) the important other considerations which fed into
this?

In the stream of thought
which asks: “Do we have to change so much from traditional Y dot = i H Y”, there is the ‘hope’:

“Can’t we just keep the old
dynamics for free space? Isn’t the complication all connected to RESERVOIRS (as
defined in quantum optics books like Walls and Milburn)?” Ah, but there is
nonlinearity here. If we ground MQED on a realistic base, the free space master
equations which result from that nonlinearity in the extended P mapping
(analyzed long ago in my earlier papers, generally at arxiv) result in a
dynamic operator H which is not Hermitian, and which implies a grossly
time-asymmetric flow of information. It is essential, in order to meet what the
new experiment shows, that even the “free space dynamics” be
time-symmetric. It may indeed be
possible to explore the idea of using that asymmetric H as part of a larger
system to compute Pr

^{+}... somehow... and somehow clean up the result... but it is important here that MQED is a statistical emergent outcome in any case, and that the cleaning up/time-symmetry (and parity symmetry, essential to the emergent fermi symmetry) which results from taking the limit as r goes to zero, allows a simpler, cleaner version at the level of MQED, the level where we do not account for the nonzero radius of the charged particles being modeled.
As a minor note... the
validity of the canonical expansion which ends up with the usual Feynmann
graphs (devoid of n-photon lines for n>1) depends on the “unitarity” of Y dot = i H Y, which is not powerful enough to describe these
situations, or give a proper interface to the inevitable reservoirs. We really do have to think about n-photon
states explicitly.

IN effect... the reservoir
imposes one very large and clear nonlinearity, but the internal nonlinear
effects also impose a nonlinear, which symmetrizes things in a way not so
different from what a reservoir does. Equation 1 expresses an idea that “an
actual elementary particle, ultimately ala De Broglie, acts as a reservoir for itself!”

This is all just a start to a
line of thought ... well, I put in the caveats at the start. It is so
incomplete right now that I type it only... to consolidate memory, and account
for worst case contingencies re my health. (Strictly speaking, I had not planned to
revisit any of this, but various things happened in the past few days...)

================================================================

============================================================

Added later:

1. Again, the paper at vixra
has priority over the previous day’s mulling above, especially over equation 1,
which may or may not lead anywhere.

2. A key point here is that
any MQED, LIKE the earlier MRF and CMRF models, must obey the basic rules of a
time-symmetric model. That means, to be consistent with the experimental
results favoring the rules of time-symmetric models as defined in our published
papers, the dynamics must be time-symmetric at all times (reservoir or no)
EXCEPT at points of injection of positive-time (or negative time) free energy
from the outside. Also, equation 1 does not factor trivially; that would be
true of the usual [H,r] model, not this one. HOWEVER:
there is no guarantee that a model as simple as equation 1 can work in the way
that MQED1 can. If we seek simplicity as in free space dynamics involving just r... well, we can deduce what may be possible...

But because that eye issue is
still there I will not elaborate right now. Will just lie quietly...

========================

============================

Still later... lying quietly, thoughts pop into the mind, even though I am not at all TRYING to develop an MQED2 alternative.

To find such an alternative... it helps to pose a very specific question, e.g. "is it possible to develop a model which qualifies as an MQED, as defined in the vixra paper, but which ALSO uses equation 1 or the usual [H,rho] dynamic equation or some other forward-time-looking dynamics in rho? Possible or not?

An obvious approach is to focus on the same key examples which led to MQED1... simple two-level atoms, like a part of the behavior of hydrogen or helium, informed in part by Carmichael's work on resonance flourescence.

But... why?

Left eye is a little better today. Luda has very sharp pictures from this morning, and a few days ago. Not all better, but improved enough (and similar enough to pictures of "red eye" on the web) that I will not urgently run to See Clearly but will stay a few days more on recovery regime... not full bed rest but no heavy lifting, no things which create too much blood flow to the head (though some of the reports on CNN do risk that)... no eye strain, no air of the kind which might risk infection (e.g. metro), no extended bending over. Blah, but not the worst thing. Still, am sad I have to postpone reading "The Money Behind Ted Cruz" in Bloomberg Business Week, and will totally repress the thoughts I feel I would say to Bernie Sanders if I had access (as I actually did in 2009!)...

========================

============================

Still later... lying quietly, thoughts pop into the mind, even though I am not at all TRYING to develop an MQED2 alternative.

To find such an alternative... it helps to pose a very specific question, e.g. "is it possible to develop a model which qualifies as an MQED, as defined in the vixra paper, but which ALSO uses equation 1 or the usual [H,rho] dynamic equation or some other forward-time-looking dynamics in rho? Possible or not?

An obvious approach is to focus on the same key examples which led to MQED1... simple two-level atoms, like a part of the behavior of hydrogen or helium, informed in part by Carmichael's work on resonance flourescence.

But... why?

Left eye is a little better today. Luda has very sharp pictures from this morning, and a few days ago. Not all better, but improved enough (and similar enough to pictures of "red eye" on the web) that I will not urgently run to See Clearly but will stay a few days more on recovery regime... not full bed rest but no heavy lifting, no things which create too much blood flow to the head (though some of the reports on CNN do risk that)... no eye strain, no air of the kind which might risk infection (e.g. metro), no extended bending over. Blah, but not the worst thing. Still, am sad I have to postpone reading "The Money Behind Ted Cruz" in Bloomberg Business Week, and will totally repress the thoughts I feel I would say to Bernie Sanders if I had access (as I actually did in 2009!)...

## No comments:

## Post a Comment