Reality Is Not What It Seems: The Journey to Quantum Gravity

by Carlo Rovelli

It is not just its position that is undefined, as Heisenberg had recognized: no variable of the object is defined between one interaction and the next. The relational aspect of the theory becomes universal.

Dirac provides the general recipe to compute the set of values that a physical variable can take.* These values are analogous to the spectra of the light emitted by atoms. Today we call the set of the particular values that a variable may assume—the “spectrum” of that variable, by analogy with the “spectra” into which the light of elements decomposes—the first manifestation of this phenomenon.

For example, the radius of the orbitals of an electron around a nucleus can only acquire specific values, those that Bohr had hypothesized, that form the “spectrum of the radius.”

We do not know with certainty where the electron will appear, but we can compute the probability that it will appear here or there. This is a radical change from Newton’s theory, where it is possible, in principle, to predict the future with certainty.

While Newton’s physics allows for the prediction of the future with exactitude, if we have sufficient information about the initial data and if we can make the calculations, quantum mechanics allows us to calculate only the probability of an event.

The apparent determinism of the macroscopic world is due only to the fact that the microscopic randomness cancels out on average, leaving only fluctuations too minute for us to perceive in everyday life.

Dirac’s quantum mechanics thus allows us to do two things. First, to calculate which values a physical variable may assume. This is called “calculation of the spectrum of a variable”; it captures the granular nature of things.

The second thing that Dirac’s quantum mechanics allows us to do is to compute the probability that this or that value of a variable appears at next interaction. This is called “calculation of an amplitude of transition.”

What happens between one interaction and the next is not mentioned in the theory. It does not exist.

The probability of finding an electron or any other particle at one point or another can be imagined as a diffuse cloud, denser where the probability of seeing the particle is stronger.

The efficacy of the theory soon proves extraordinary. If today we build computers, have advanced molecular chemistry and biology, lasers and semiconductors, it is thanks to quantum mechanics.

The matter surrounding us is made up of a thousand different substances. During the nineteenth and twentieth centuries, chemists understood that all these different substances are just combinations of a relatively small number (less than a hundred) of simple elements: hydrogen, helium, oxygen, and so on—to uranium.

take the equation of quantum mechanics that determines the form of the orbitals of an electron. This equation has a certain number of solutions, and these solutions correspond exactly to: hydrogen, helium, oxygen . . . and the other elements!

Quantum mechanics deciphers perfectly the secret of the structure of the periodic table of elements. Pythagoras and Plato’s ancient dream is realized: to describe all of the world’s substances with a single formula.