5.1 Quantum mechanics and chance

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The use of probability in physics was not new. But the suggestion that probability was intrinsic and unavoidable was shocking. In classical physics, probability was used when something which could be known in principle (such as the exact path of a particle) was not known; probability filled the gap left by ignorance. Statistical mechanics, for example, used probabilities to estimate likely pressures and entropies, compensating for ignorance about detailed molecular motions. It was not doubted however, that such details existed, and could be determined in principle. In quantum mechanics the situation was completely different; a probabilistic statement along the lines of 'this has a 30% chance of happening' might well be the most that could be said in a certain situation, even in principle.

Figure 1.30 A quantum mechanical model of a hydrogen atom, which has one electron, in its state of lowest energy. The varying density of the spots indicates the relative likelihood of finding the electron in any particular region. Click here for larger image (11.88kb)

Niels Bohr, whose atomic theory was overthrown by quantum mechanics, was a keen supporter of the new mechanics. He had partly inspired Heisenberg to undertake its development in the first place, and in May 1926 he welcomed Heisenberg to his institute in Copenhagen where a great deal of effort went into formulating a complete interpretation of quantum mechanics that included the idea of intrinsic probabilities. The Copenhagen interpretation that emerged from this work is now regarded as the conventional interpretation of quantum mechanics, though there have always been those who have questioned its correctness. Some of the features of this interpretation are:

The measurable properties of objects (position, velocity, etc.) do not generally have values except just after a measurement.

Measurement causes potentiality to become actuality.

The measured values occur at frequencies determined by probabilistic rules. The probabilities are intrinsic and fundamental, and can be predicted by quantum mechanics.

The last of these points represents a substantial shift from classical determinism. In classical mechanics the past uniquely determines the present and hence the future. In quantum mechanics this is not so. Even the most complete possible knowledge of the past would only permit the calculation of the probability of future events. Some, perhaps a little naively, saw in this a scientific basis for free will: there was an element of freedom, or at least of chance, in the Universe.

The Copenhagen interpretation calls simple realism into question. If the most that you can say about a position measurement you are about to perform is that various values may be obtained, with various probabilities, then it may well mean that the object has no position until it is measured. Note that this is quite different from saying that the object has a position which you don't happen to know - it is as if the object had not made up its mind where to appear until the position measurement has been made. Clearly if you say that the object has no position, you call into question its independent reality, and hence the philosophy of realism, at least in its simplest form. This emphasizes the enormous importance of measurement in quantum physics and the motivation for making statements such as '...they form a world of potentialities or possibilities rather than one of things or facts' and 'there is no quantum world'.

An alternative stance is to assume that there is a real world out there, but to admit that it cannot be adequately described in terms of classical concepts such as position or velocity. This is plausible. We have no right to expect microscopic physics to be just a scaled-down version of everyday experience. Given that quantum mechanics deals with a microscopic world well beyond the immediate reach of our senses and intuitions, perhaps the most surprising thing is that we can make predictions at all. From this perspective, the price that must be paid for the mismatch between our classical concepts and the quantum world is astonishingly small, and is reflected mainly in the appearance of probabilities. In philosophical terms, the concept of a real world can be preserved by admitting that certain aspects of it are inaccessible to us, clumsy giants that we are. But in practical, or scientific, terms this makes no difference. It is hard to see how we could ever develop an understanding that was not based on classical concepts, so probabilities seem destined to remain intrinsic and unavoidable, offering the only gateway through which we can glimpse the microscopic world.

Question 1.6 Answer In Section 1 it was said that the notion of scientific law was based on the fact that identical situations produced identical outcomes. To what extent does this remain true in quantum physics where identical experiments may produce different outcomes?
Continue on to 5.2 Quantum fields and unification