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

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in density matrices”; we know that the older interaction picture for wave functions “does not exist” (e.g. our yet unpublished, unposted paper on MEWT,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...)

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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... 

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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!)...