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  Prospectus for a Locally Causal Quantum Wave Model 

 
A.G.Booth     WWW original 9 May 2004     Copyright © A.G.Booth 2004 All rights reserved
Document ident: Last updated 20 June 2006 Prospectus for a Locally Causal Quantum Wave Model. A.G.Booth
Keys: quantize quantized quantization

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    Introduction

For many people there is a sense of personal mission in attempting to grasp, and in some also to clarify in public, ideas of that field of microscopic physical science called quantum mechanics. For myself as an electrical engineer this mission takes on a special significance in two ways:

Others, including chemists and biologists, have a close working relationship with matters quantum mechanical too, and are involved with issues not dissimilar to those raised here.

Unfortunately the remit of the research physicist is sufficiently different from that of a working engineer that the theories and models that suit the one turn out to be unsuitable and even intractable for the other. It is in attempting to deal with this incompatibility that this prospectus and the work to which it relates is being pursued.

There can be many approximations and rules of thumb, which help in day to day work, and these must necessarily continue to exist and develop. However, there is a "holy grail" dimly visible in the mists behind all this daily work that promises, if it were ever brought into clear view, to smooth the paths to comprehension of modern electrodynamics for many who have today to work in the presence of disjointed empirical facts, anomalies and weirdnesses. For those people working with an engineering remit there is currently no compact rationale. For them learning of disparate items by rote from another specialisation is the only available path to a working enlightenment, and it is a poor one. We must face the question of whether we believe this is really the best that is possible. Judging the signs from that dim visibility, I, for one, believe that better is very probably possible.

It is not that the existing models for quantum mechanics and electrodynamics cannot produce the right predictions. Indeed for current engineering purposes they appear to be virtually flawless in terms of their accuracy. The problem is more about the nature of the model.

 

    Features of the Model

We need to express a model that is rational whilst economical in its basic parts, so that it has these features:

Rational Continuity
The model and its analysis is "of a piece" with the other models, all of them basically causal, as are used in engineering, thereby allowing comprehension to grow spontaneously in the process of working, as it largely does in other branches of engineering.
Consistent Logic of Approximations
Approximations can be formed on a working basis that achieve convincing completeness and logical integrity through no more than the perception of the model user alone.
One might say that the current physics models are crafted too much as the aggregate through written documents of specialist endeavours. They are negligent of systematic and rational cohesion for any but the specialist workers, and in the minds of those specialists, one suspects, still lack general purview. This results in methods that lean too heavily on corporate perceptions and resources to be a safe component of societal activity. It is nearly impossible for individuals to watch over and criticise such processes.

The motivation for seeking a solution to this problem is not entirely a matter of hope in the face of adversity. Rather, there are techniques of analysis and ideas that are already at large in engineering (and fortunately in some other fields too) that hint at how such a desirable result might be achieved.

As of this date (May 2004) I myself am working through the testing of a model that uses a compact set of structural basics (see Smooth and Quantal Properties of the Complex Wave). Don't be misled if it looks complicated. That is almost all made up of the analysis. The precepts are very few, and there are, in the current QED phase, no arbitrary constants at all. I hope to reach a point after nailing down the model in terms of essential qualitative and quantitative features where it is possible to fill out its explanation and depiction in visualisable ways.

 

    Model Criteria

In order to gain a wider view of how to direct and criticise the choice of path in such efforts we might try to use a prospectus or recipe for any such model and what we require of it. Therefore in attempting to deal with the above cited problems my approach uses a certain set of criteria regarding the nature of the required model as follows. They are chosen to move as directly as possible to the field of electrodynamics. It appears, and for me it was rather unexpected, that with development they have also quite a lot to say in the more general fields of physics, even including cosmology. However, "sticking to our electrodynamical knitting", these are the criteria for adequacy of any such model:

1   Wave Model
It is built solely as a locally causal rule over a (set of) continuous variable(s) on a continuous coordinate space, all of these parts being the simplest we can get away with.
2   Compact Rational Expression
It is generally well behaved as a compromise with both human lay comprehensibility and mathematical tractability and smoothness.
3   Conformance to Observed Phenomena
Through a process that we can understand and describe as observation operating within the same model, it yields, either as an explicit precept or as emergent, evidence of at least each of the following generally accepted phenomena as we believe exist:
a)   Distinct entities with quantal properties of observation.
b)   An uncertainty principle and wave phenomena for ultimately small observations.
c)   Frequency domain spectral properties of interactions.
d)   Zeeman effect.
e)   Stark effect.
f)   Stern-Gerlach effect.
The presence of relativistic effects could usefully be added, but are really already implicit, though perhaps only subtly, in the above list. Certainly invariance of the observed speed of electromagnetic radiation is paramount.

In due course it may be necessary to add other phenomenal requirements, and indeed, some may be able to be omitted from a minimum set without altering the resulting form of possible models. However, such details might best be dealt with when a given candidate model is brought into view for evaluation. That may sound dangerously circular, but when paradigms are at stake we inherently build upon shifting sands and cannot then afford an absolute standpoint of judgement. The pursuit of honesty, clarity and rigour is about all we can rely upon.

We may also say that to achieve an emergent uncertainty principle in a causal and therefore deterministic model will require some special manoeuvre. Indeed, the only such manoeuvre possible appears to be by using the necessity that the observer, as a deterministic mechanism, is essentially part of the same model. That feature alone does appear to be sufficient to introduce the necessary form of uncertainty. Proof of that and of the emergence of quantal effects from a process that is entirely continuous in both its variables and its coordinates are parts of the necessary explanation of any such model.

 

    Comments

Clearly the Standard Model of quantum mechanics fails item 1, if only because of its reliance on the Copenhagen interpretation of wave function collapse. At that point it is non-causal. That definitely leads to conceptual problems and thereby also fails item 2 above.

Models that approach this set of criteria but seem as yet to fail in one way or another include the following:

Comment regarding philosophical stance
You will notice that my approach is one of modelling rather than a quest to understand some mystical thing called "reality" in any absolute sense. This is more an instrumentalist than a realist stance. It is concerned at root with our abilities through individual developments to talk (and sometimes agree) about these things, person to person. Absolute reality is too hypothetical for my liking. Usability and elegance of a model are good and will in any case always have to be enough for the public expressions by mere humans. What I am after are models that we like primarily in the sense of making use of them and preferably also as works of poetic art with some sort of appeal through elegance.

 

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