Helgoland Rovelli, Erica (cat reading book .TXT) 📖

What does Nature know or care about whether we are observing it or not?

It is Max Born—him again—who understands for the first time the significance of Schrödinger’s ψ, adding a crucial ingredient to the understanding of quantum physics.23 Born, with his air of a serious but somewhat superannuated engineer, is the least flamboyant and the least well known of the creators of quantum mechanics, but he is perhaps the real architect of the theory—in addition to being, as they say, “the only adult in the room,” in an almost literal sense. It was he who in 1925 was clear that quantum phenomena made a radically new mechanics necessary; it was he who had instilled this idea in younger physicists. It was Born, too, who recognized at once the right idea in Heisenberg’s first confusing calculation, translating it into a true theory.

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.24 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.

Schrödinger’s ψ is therefore not a representation of a real entity: it is an instrument of calculation that gives the probability that something real will occur. It is like the weather forecasts telling us what could happen tomorrow.

The same—it soon becomes clear—is true of Göttingen matrix mechanics: the mathematics gives predictions that are probabilistic, not exact. Quantum theory, just as much in Heisenberg’s version as in Schrödinger’s, predicts probability, and not certainty.

But why probability? We usually speak of probability when we do not have all the data. The 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. (In the 1980s a group of brilliant young gamblers went on a winning streak in a Las Vegas casino, using a small computer concealed in a shoe, exploiting this fact.25) When we don’t have all of the data, we do not know for certain what will happen—and we speak of probability.

Does this mean that the quantum mechanics of Heisenberg and Schrödinger fails to take all the relevant givens of the problem into account? Is this why we have probability? Or is it that Nature actually leaps about here and there by chance?

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

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.

In any case, Schrödinger’s ψ wave is definitely not sufficient to clarify the obscurity of the quanta. It is not enough to think of the electron as a wave. 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.26

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

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 GRANULARITY OF THE WORLD: QUANTA

I have told the story of how quantum theory was born between 1925 and 1926, and have introduced two ideas: the peculiar idea, found by Heisenberg, of describing only observables, and the fact that the theory predicts only probabilities, understood by Born.

There is a third idea at the core of quantum physics. In order to illustrate it, we had better go back a bit, to the two decades before Heisenberg’s fateful journey to the Sacred Island.

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.

Inside an oven, for example, electromagnetic waves behave in a curious way. The heat (that is, the energy) is not distributed among all frequencies, as we would naturally expect: it never reaches higher frequencies. In 1900, twenty-five years before Heisenberg’s journey to Helgoland, the German physicist Max Planck had discovered a formula that reproduced well the way that the energy of heat, measured in a laboratory, distributed among waves of different frequency.27 He derived this formula from general rules, but added a curious hypothesis: the energy could be transmitted to the waves only in integer multiples of elementary energies. In discrete packets.

The dimensions of these packets, in order to make Planck’s calculation work, must be different for waves of different frequency: they must be proportional to the frequency.28 High-frequency waves can only receive more energetic packets. Energy does not reach the very high frequencies because there is not enough of it to transmit big enough packets.

Using experimental observations, Planck had calculated the proportionality constant between the energy