Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [114]
Born had been working on applying matrix mechanics to atomic collisions while in America. Back in Germany with Schrödinger's wave mechanics suddenly at his disposal, he returned to the subject and produced two seminal papers bearing the same title, 'Quantum mechanics of collision phenomena'. The first, only four pages long, was published on 10 July in Zeitschrift für Physik. Ten days later the second paper, more polished and refined than the first, was finished and in the post.54 While Schrödinger renounced the existence of particles, Born in his attempt to save them put forward an interpretation of the wave function that challenged a fundamental tenet of physics – determinism.
The Newtonian universe is purely deterministic with no room for chance. In it, a particle has a definite momentum and position at any given time. The forces that act on the particle determine the way its momentum and position vary in time. The only way that physicists such as James Clerk Maxwell and Ludwig Boltzmann could account for the properties of a gas that consists of many such particles was to use probability and settle for a statistical description. The forced retreat into a statistical analysis was due to the difficulties in tracking the motion of such an enormous number of particles. Probability was a consequence of human ignorance in a deterministic universe where everything unfolded according to the laws of nature. If the present state of any system and the forces acting upon it are known, then what happens to it in the future is already determined. In classical physics, determinism is bound by an umbilical cord to causality – the notion that every effect has a cause.
Like two billiard balls colliding, when an electron slams into an atom it can be scattered in almost any direction. However, that is where the similarity ends, argued Born as he made a startling claim. When it comes to atomic collisions, physics could not answer the question 'What is the state after collision?', but only 'How probable is a given effect of the collision?'55 'Here the whole problem of determinism arises', admitted Born.56 It was impossible to determine exactly where the electron was after the collision. The best that physics could do, he said, was to calculate the probability that the electron would be scattered through a certain angle. This was Born's 'new physical content', and it all hinged on his interpretation of the wave function.
The wave function itself has no physical reality; it exists in the mysterious, ghost-like realm of the possible. It deals with abstract possibilities, like all the angles by which an electron could be scattered following a collision with an atom. There is a real world of difference between the possible and the probable. Born argued that the square of the wave function, a real rather than a complex number, inhabits the world of the probable. Squaring the wave function, for example, does not give the actual position of an electron, only the probability, the odds that it will found here rather than there.57 For example, if the value of the wave function of an electron at X is double its value at Y, then the probability of it being found at X is four times greater than the probability of finding it at Y. The electron could be found at X, Y or somewhere else.
Niels Bohr would soon argue that until an observation or measurement is made, a microphysical object like an electron does not exist anywhere. Between one measurement and the next it has no existence