[General] Quantisation of classical electromagnetism

Tue May 5 00:54:15 PDT 2015

Good morning everyone,
None of us gets the whole picture- yet. We, however, may each understand some aspects of science, which need to be resolved within the group (and the rest of the science community for that matter) as a whole. I think that, if we want to make progress, as a group, to making a collective effort to eventually solve Hilbert’s sixth problem and understand how everything works, we need a proper theoretical basis with which to calculate and with which to model. Maxwell theory is good to a point, but is not quantized and does not have a mechanism to confine light to go round and round in circles in our models. We need a better theory.
By a theory here I do not mean some loose idea with some nice consequences and able to calculate a number or two (like the WvdM model for example!). To properly understand how things work it is not good enough to just flag-up the problems of this or that model – all models have problems (the standard model more than most!)- we need to put-up and develop a real theories and then try to knock them down with experiment. If they fail- just make up a new theory. That is the scientific method.
First problem in creating any new theory is where to start? On which basis?
Some of you may not have yet come across Hilbert’s sixth. It is one of the famous set of problems he posed at the turn of the century before last which remains unsolved. Briefly it is finding an axiomatic, logical and complete mathematical system that precisely parallels reality – just and no more.  In other words finding a mathematics which precisely describes all of physics.
Coming back to the task in hand. Physics is now so vast that there are many possible starting bases. All may give some insight into the truth, but none yet solves Hilbert’s sixth. I will not bother with theories set up, by design, to be outwith the boundaries of that which is measureable experimentally as I see no point in starting from somewhere where one is already lost. Others may play that game if they wish.
Lets just list a few of the possible starting candidate frameworks (some within the umbrella of the “standard model”):

1.     Shroedinger quantum mechanics

2.     Dirac relativistic quantum mechanics

3.     Quantum electrodynamics

4.     General relativity

5.     Special relativity

6.     Maxwell electromagnetism
These all stand on their own – of course. Any final theory should also be manifestly consistent- at some level of simplification – with all of the above.
Now comes my personal view of each as a candidate starting frameworks on which to make further progress. The conclusions at the end of each are not definitive – just my personal opinion at present. Each sentence starting “Conclusion” contains a pun, which is intended.
The first, while it has many practical applications, is too simple as it is is non-relativistic. Conclusion-too uncertain.
The second is a good possibility, however I think it is too complicated in one respect and too simple in another. Too complicated in that it contains BOTH a non-commutative (Dirac) algebra AND yet uses the far simpler complex algebra in solutions. I think its starting point has already passed the proper basis point and has implicitly added something which is just not there in reality. I think it contains a great deal of truth but that the added complexity (pun) makes for confusion. It confused Dirac himself (as stated in his famous textbook by himself). If he was confused then what chance have any of the rest of us got. This stand-point is backed up by the fact that, despite being a corner-stone of the “Standard Model”, it has not yet been used in any practical engineering application at all (delighted if anyone can pose a counter-example by the way). Conclusion-too complex.
Now the third, quantum electrodynamics, looks good. It is not (yet) in conflict with any known experiment within its realm of validity.  Indeed this is the starting point for many. Personally, having worked with it back in the eighties in develping (parts of) big monte-carlo programmes (incorporating both QED and QCD) - I do not think this is the right answer. The problem is that it has neither a detailed, microscopic dynamics of the charges which are its sources, nor of the photon which is, for it the exchange particle responsible for electromagnetism. For it, the photon is that thing that carries the electromagnetic interaction more than a particle in its own right. I do not see how to make it work starting from its starting points. Lots of other folk (much smarter than me) have been trying just that for many years without success. Good luck folk! Conclusion-I think folk just do not get the point.
On to the fourth. This is also good, also consistent with all of experiment (within its realm of validity). Could be made to work. Again, many have tried. Wheeler made a good attempt with Geometro-dynamics. Any new theory had better be consistent with it in the weak limit. I think it is still missing its heart and foundation though. Conclusion- it is just too weak.
Now to the fifth. All good. Not much in it though – per se. Conclusion: not special enough.
Now to the sixth. This is often neglected as being old-hat, but (as Chandra has said) it is also consistent with all of experiment within its realm of validity. It is, and always was fully (special) relativistic. This is at least more special then than the preceding candidate. There is just more in it. The main deficiency –up till now – is that it has been missing a proper means of quantizing it and a proper wave-function for the photon. Conclusion: the area seems a good field from which to start - just need to properly investigate its boundaries and find a proper means to quantize it.
On this theme, I have attached a paper, containing a few speculations of my own, to set myself up to be knocked down on anything which is too speculative, ill-informed or downright wrong! It explains and expands on the theory presented at FFP14 last year and outlined in the paper I circulated earlier. The paper as it stands can be shortened as it contains some repetition and a quite a lot of background analogy (such as pretty much all of the discussion on page 7, for example). I’ve decided to leave this in for the moment as it may help understanding. There are also other things that should probably go in if I have the time – such as a wavefunction separating the polarization and rotation-horizon parts of the wave function. Am still working on that.
This was intended as a draft paper for the upcoming conference in San Diego, even though it is more about the photon itself than the electron or its inter-actions, so I was thinking of withdrawing it and replacing it with one on the problems of causality in absorber interaction theory (to address the problems raised by, amongst others, Chip). I’m re-considering this, as I think it provides some of the background theory for the other paper on the electron nature. An alternative may be to place it elsewhere within the conference as it is more relevant to the photon itself than to the electron. What do you think, Chandra and Andrew?
I think it is correct that it has limited value to try to understand one thing (the electron) in terms of another thing which is, perhaps, even more poorly understood (the photon). I agree as well that we need to address the underlying root-cause of quantisation if we are really to understand what is going on. Understanding the photon is what the paper aims to do
I’m a bit shy, in the present company, of jumping in with both feet here. This is not really my field. I know more about (and have published widely in) elementary particle physics and solid state physics (and I think this helps in some respects) but am by no means an optics or a photonics guy. I am relying on you all (especially people such as Chandra, Robert and Tim) to put me straight on this. I do not want to step on everyones toes! The paper attached contains a development of the Maxwell equations to include dynamical mass, dual mass and angular momentum terms. The development here looks pretty simple to me. Has it been done before? Please, all of you, fill me in here. It would be very embarrassing to miss an important reference to this.
There is also an argument in the paper as to why classical electromagnetism must be quantized in its travelling-wave solutions. I think this must be new as I’m sure I should have heard of it otherwise. Am I wrong? There is also a fully relativistic, quantized, Schroedinger-like, first-order electromagnetic wave-function. Again- have such things ever been studied elsewhere?
The paper, as it stands, does not yet contain a calculation of  hbar from first principles – though I am working on this as well as with a more advanced 4D wave-function and in conjunction with the polarization discussion and have what I think may be an answer – though that lies also within the realms of physical chemistry where I am even less at home. If I cannot sort it out before August it could, possibly, become a topic for discussion.
I will circulate the draft paper to other people in other groups as well (some on the mailing above). Another thing I would be grateful for is suggestions as to which peer-reviewed journal would be an appropriate place to submit this work for a more general circulation.
Regards, John W.
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