Helgoland by Rovelli, Erica (ebook reader below 3000 .txt) 📗

not mean that we cannot measure the position of a particle with great precision and then its speed very precisely as well. We can. But after the second measurement, the position will no longer be the same: measuring the speed loses information on the position, so that if we measure it again, we will find it changed.

This follows from the second postulate, which says that even when we have gathered maximum information about an object, it is still possible to learn something unexpected about it. The future is not determined by the past: the world is probabilistic.

Since measuring P alters X, measuring X first and then P gives different results than measuring P and then X. Hence in mathematics “first X and then P” is necessarily different from “first P and then X.”75 This is precisely the property that characterizes matrices: order counts.76 Remember the single new equation introduced by quantum theory?

X P – P X = i ħ

This tells us precisely about the importance of order: “first X and then P” is different from “first P and then X.” How different? By an amount that depends on Planck’s constant: the scale of quantum phenomena. This is why Heisenberg’s matrices work: because they allow the order in which information is acquired to be taken into account.

Heisenberg’s principle—that is, the equation on this page—follows with a few steps from this last equation, which therefore summarizes everything. This equation translates into mathematical terms both the postulates of quantum theory. Vice versa, the two postulates express its physical significance.

In Dirac’s version of quantum theory there is not even a need for matrices: everything may be obtained by simply using “noncommutative” variables, which is to say, the equation on this page. Dirac is a poet when he writes physics: he simplifies everything in the extreme. “Noncommutative” means: such that their order cannot be changed freely. Dirac calls the noncommuting variables “q-numbers”: quantities defined by this equation. Their pretentious mathematical name is “noncommutative algebra.”

Remember Zeilinger’s photons, with which I began to describe quantum phenomena? They could pass on the right or the left and end up either up or down. Their behavior may be described by two variables: a variable X that can have the value “right” or “left,” and a variable P that can have the value “up” or “down.” These two variables are like the position and speed of a particle: they do not commute. Hence they cannot be determined together. This is the reason why, if we close one of the paths determining the first variable (“right” or “left”), the second is undetermined: the photons go randomly “up” or “down.” Vice versa, in order for the second variable to be determined, for the photons to all go “down,” it is necessary that the first variable should not be determined; that is, that the photons must pass via both paths “right” and “left.” The entire phenomenon follows from the equation which says that these two variables “do not commute” (are noncommutative), and hence cannot be determined together.

A single equation codes quantum theory. It implies that the world is not continuous but granular. There is no infinite in going toward the small: things cannot get infinitely smaller. It tells us that the future is not determined by the present. It tells us that physical things have properties only in relation to other physical things, and that these properties make sense only when things interact. It tells us that sometimes perspectives cannot be juxtaposed.

In our everyday life we are not aware of any of this. Quantum interference gets lost in the buzz of the macroscopic world. We can reveal it only through delicate observations, isolating objects as much as possible.77

If we do not observe interference, we can ignore superposition and reinterpret it as ignorance: we just don’t know if the cat is asleep or awake. We have no need to think that there is a quantum superposition because quantum superposition—I emphasize it as there is often confusion on the issue—means only that we see interference. The delicate phenomena of interference between the cat awake and the cat sleeping are lost in the noise of the world that surrounds us. When interference is lost, we can take facts as stable, that is, we can forget that they are only true relative to something else.78

Furthermore, when we observe the world at our scale, we do not see its granularity. We cannot see single molecules: we see the whole cat. With many variables, fluctuations become irrelevant, and probability nears certainty.79 Billions of discontinuous events of the agitated and fluctuating quantum world are reduced by us to the few continuous and well-defined variables of our everyday experience. At our scale, the world is like the wave-agitated surface of the ocean seen from the moon: the smooth surface of a blue marble.

Our everyday experience is thus compatible with the quantum world: quantum theory incorporates classical mechanics and our usual vision of the world—as approximations. We understand it as a man with good sight can understand the experience of a myopic person. But at the molecular scale, the cutting edge of a sharp knife is as fluctuating and imprecise as the edge of an ocean in a storm, fraying upon the white sand of its shore.

The solidity of the classical vision of the world is nothing other than our own myopia. The certainties of classical physics are just probabilities. The well-defined and solid picture of the world given by the old physics is an illusion.

On April 18, 1947, on the sacred island of Helgoland, the Royal Navy blows up three thousand nine hundred ninety-seven tons of dynamite—what was left of munitions abandoned there by the German army. It is probably the biggest explosion ever made using conventional explosives. Helgoland is devastated. It is almost as if humanity was seeking to cancel out the rip in reality opened on the island by a young physicist.

But the rip remains. The conceptual explosion unleashed by him is