Gerald E Marsh - Quantum Particle Illusion, The - Conceptual Quantum Mechanics

Gerald E Marsh

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THE QUANTUM PARTICLE ILLUSION

Conceptual Quantum Mechanics

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This book is dedicated to my wife Evelyn without whom I would not and could not be who I am today. We married very early and had the privilege of traveling together through the harmony of life.

The topic of the foundations of quantum mechanics has a vast and very interesting literature and a great many papers and books have been written about the difficulties of interpreting quantum mechanics, in general, and the wavefunction, in particular. I will not make any attempt to review this literature since it stands on its own. One of the relatively most active modern periods was in the 1960s and 1970s and especially from 1973 to around 1979.

Quantum mechanics can only present the probability of a particle being found in any given region of spacetime. This raises the question of whether the position of a discrete particle can in principle only be predicted statistically by quantum mechanics or, whether the formalism of quantum mechanics applies not to a single particle, but rather to an ensemble of identical systems. The various approaches to interpreting the mathematics of quantum mechanics are motivated by somehow attempting to maintain our ideas about a classical particle in the context of the quantum world as found in nature.

This has led to great confusion not only among those approaching quantum mechanics for the first time, but also for those who have used the formalism to perform highly successful calculations for many years. In the end, it is the historical approach to the teaching of quantum mechanics that could be the root of the problem. Those brave enough to try and understand the conceptual foundations of quantum mechanics when being taught from this perspective, and often discouraged from doing so by the apocryphal advice given by many physicists to ignore the issue and just calculate, are generally left in a state of cognitive dissidence well expressed by the adaptation of a cartoon drawn by an anonymous artist that appeared, in a completely different context, in a government sponsored report from the mid-1980s, shown below.

A poor soul who tries to understand the foundations of quantum mechanics after being taught the subject using an historical approach.

It is hoped that this book can relieve some of the dismay, frustration, and confusion so well expressed by this cartoon.

Gerald E. Marsh

The statistical interpretation of the wavefunction, , is due to Max Born who, in his 1954 Nobel prize acceptance speech, ascribed his inspiration for the statistical interpretation to an idea of Einsteins. Here is the relevant quote from Borns speech: He had tried to make the duality of particles light quanta or photons and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons. This concept could at once be carried over to the -function: ||2 ought to represent the probability density for electrons (or other particles).

Einstein, in a December 1926 letter to Max Born, speaking of the secret of the Old One, said that he was convinced that He does not throw dice. And when Philipp Franck pointed out to Einstein, around 1932, that he was responsible for the idea because of papers he published during his annus mirabilis in 1905, Einstein responded that Yes, I may have started it, but I regarded these ideas as temporary. I never thought that others would take them so much more seriously than I did. Later, Einstein put it this way to James Franck: I can, if the worse comes to the worst, still realize that the Good Lord may have created a world in which there are no natural laws. In short, a chaos. But that there should be statistical laws with definite solutions, i.e. laws which compel the Good Lord to throw the dice in each individual case, I find highly disagreeable.

Einstein was not alone in being uncomfortable with the statistical nature of quantum mechanics and since then the vast literature that has appeared on the foundations of quantum mechanics was driven at least in part by an attempt to come to terms with the unusual and counterintuitive features inherent in the subject.

There were many attempts in the past to find hidden variables to avoid the statistical interpretation of the wavefunction, and there was even an informal monthly set of briefs called the Epistemological Letters put out by the Association F. Gonset or Institut de la Methode, which was distributed to, and contained theoretical correspondence from, some 100 prominent people in the field. In particular there was much discussion of Bells theorem,