Simon Carnell

What kind of relation can there be between a wave, which spreads out, and a particle that remains compact, following a fixed, defined trajectory? Think of a beam of light from a laser: it seems to follow a neat trajectory, like a beam of particles. But it is made of light, which is a wave, an oscillation of the electromagnetic field. The precise line described by the trajectory of a ray of light is an approximation, concealing its dispersion and spread.

Schrödinger is captivated by the idea that the trajectories of elementary particles are also approximations of the behavior of an underlying wave.

Schrödinger, too, is a product of that lively early-twentieth-century Viennese philosophical and intellectual milieu: a friend of the philosopher Hans Reichenbach, he is fascinated by Asian thought, in particular Vedanta Hinduism, and passionate (as Einstein was) about the philosophy of Arthur Schopenhauer, which interprets the world as “representation.” Unconstrained by conformism, having no fear of conventional opinion, of “what people will think,” he has no qualms about replacing a world of solid matter with a world of waves.

This “wave mechanics” instantly seems more convincing than Göttingen’s “matrix mechanics,” even if the two give the same predictions. Schrödinger’s calculation is simpler than Pauli’s. Physicists of the first half of the twentieth century were familiar with waves and wave equations; they were unfamiliar with matrices, the math we call today “linear algebra.”

“Schrödinger’s theory came as a relief: we no longer had to learn the peculiar mathematics of matrices.”

wave mechanics is no clearer than the matrix mechanics of Göttingen. It is another calculation tool that produces the right numbers, and is sometimes easier to use, but it does not give a clear and immediate picture of what happens, as Schrödinger had hoped it would

urtured the illusion of having eliminated the discontinuities in quantum theory. But the discontinuities eliminated from the equations of the theory reappear the moment the theory is confronted with what we observed.”

What Born understands is that the value of Schrödinger’s ψ wave at a point in space is related to the probability of observing the electron at this point. If an atom emits an electron and is surrounded by particle detectors, the value of ψ where there is a detector determines the probability of that detector, and not another, detecting the electron

he probability that the ball will land on the number five when we spin a roulette wheel is one in thirty-seven. If we knew the exact position of the ball when it was thrown, and all the forces acting on it, we would be able to predict the number on which it would land.

Einstein put the question in colorful language: Does God play dice?