Helgoland

The weird behavior of electrons in atoms was not the only strange and incomprehensible phenomenon at the beginning of the twentieth century. Others had also been observed. They had one thing in common: they highlighted a curious granularity of energy and other physical quantities. Before the quanta, nobody suspected that energy could be granular. The energy of a thrown stone depends on the velocity of the stone: the velocity can be anything, hence the energy can be anything as well. But peculiar energy behaviors had been appearing in experiments.

To Heisenberg’s obscure idea that the theory only describes observations, and not what happens between one observation and another, we must add the idea that the theory predicts only the probability of observing one thing or another. The mystery deepens.

The ψ wave is something unclear, which determines the probability that the electron will be observed in one place rather than in another. It evolves in time according to the equation written by Schrödinger, as long as we do not look at it. When we look at it, pffft!, it disappears, concentrated into a point, and we see the particle there.

As if the mere fact of observing it was enough to modify reality.

Einstein relished figurative language and had a predilection for using “God” in his metaphors despite his declared atheism. But in this case his phrase can be taken literally: he loved Spinoza, for whom “God” was synonymous with “Nature.” Hence: “Does God play dice?” means literally: “Are the laws of nature really not deterministic?” As we shall see, a hundred years after Heisenberg and Schrödinger’s bickering, this question is still open.

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

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.

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

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.”

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

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