5.1 Quantum mechanics and chance

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By 1925 it was clear that atoms consisted of positively charged cores, called nuclei, around which swarmed negatively charged electrons. It was also clear that conventional classical mechanics was incapable of correctly describing the behaviour of those electrons, and the search was on for a new mechanics that could be applied to particles in the atomic domain. The (limited) success of Bohr's model of the atom indicated that the new mechanics would involve Planck's constant, so Max Born, a leading atomic researcher at the University of Göttingen in Germany, named the new mechanics quantum mechanics, even though he had no real idea of its basic rules at the time. It was supposed that quantum mechanics would be more fundamental than classical mechanics, so that once the rules of quantum mechanics were uncovered it would be possible to deduce the laws of classical mechanics from them.

Those basic rules of quantum mechanics were actually brought to light over a period of about a year, starting in the summer of 1925. The first breakthrough was made by Werner Heisenberg, a 24-year-old researcher at Göttingen, who had been working closely with Born. Heisenberg's first paper on the subject sketched out his basic ideas, but it was far from being a systematic formulation of quantum mechanics; neither the mathematical basis of quantum mechanics (its formalism) nor its physical meaning (its interpretation) was at all clear. Intensive work by Heisenberg, Born and others over the next six months did much to clarify the formalism (which turned out to involve mathematical objects called matrices), and to show that quantum mechanics was at least as successful as Bohr's rather unsatisfactory atomic theory, but it did not clarify the interpretation. At that stage, early in 1926, Erwin Schrödinger (1887-1961), an Austrian working at the University of Zurich, published a different and somewhat simpler formulation of quantum mechanics. Schrödinger's approach was based on de Broglie's idea that matter has a wave-like aspect. Schrödinger himself soon showed that his approach was mathematically equivalent to that of Heisenberg, but he too had difficulty working out what it all meant.

The key step in the interpretation of quantum mechanics was first put into print by Born in June 1926. Imagine that you could arrange a collision between a particle and a target and that, after the collision, the particle was deflected to the left. If you could repeat the collision under exactly the same conditions, you would naturally expect to see the particle deflected to the left again. If the particle were unexpectedly deflected to the right you would probably assume that the second collision had been set up in a slightly different way to the first, in spite of your best efforts to make the conditions identical. Born used the new formalism of quantum mechanics to study collisions and realized that, in utter contrast to classical expectations, quantum mechanics allows identical experiments to have different outcomes. Two collisions could be set up in exactly the same way (the discreteness of quantum mechanics helps to enable this). Yet, in spite of starting out in the same way, a particle may be deflected to the left in one collision and to the right in the other. In any single collision it is impossible to predict which way the particle will go.

You might wonder whether science is possible at all if Nature behaves so capriciously. Fortunately, quantum mechanics does allow us to make predictions, but with some uncertainty. In any experiment, the formalism of quantum mechanics can, in principle, predict:

the possible outcomes;

the probability (i.e. the relative likelihood or chance) of each of those possible outcomes.

However, what quantum mechanics cannot do, and what Born was convinced it would never do, was to go beyond probabilities and predict a definite outcome for a particular experiment that might have more than one outcome. Returning to the example of collisions, quantum mechanics can predict that particles colliding in a certain way might be deflected to the left or to the right; it can also predict the probability of deflection to the left or the right and hence the relative numbers deflected left or right in a large number of identical collisions; but it cannot predict whether a particular particle in a particular collision will be deflected right or left. Dealing with probabilities is an intrinsic part of quantum physics that cannot be avoided.
Continue on to Quantum mechanics and chance, part 2 of 3