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

of the packets and the frequency. He had called this constant h—without understanding its significance. Today we often use the symbol ħ, which stands for h divided by 2π. Dirac developed the habit of placing a small line through the h, because in calculations h is frequently divided by 2π, and he got tired of writing “h/2π” every time. The symbol ħ is called “h bar.” It has come to be called “Planck’s constant,” just like h without the bar, generating a certain amount of confusion. Today it has become the symbol most characteristic of quantum theory. (I have a T-shirt with a small ħ embroidered on it, of which I am very fond.)

Five years later, Einstein suggests that light and all the other electromagnetic waves are actually made up of elementary grains.29 These are the first “quanta.” Today we call them “photons,” the quanta of light. Planck’s constant h measures their size: every photon has an energy h times the frequency of the light of which it is part.

Assuming that these “elementary grains of energy” actually exist, Einstein manages to explain a phenomenon that is not yet understood, called the “photoelectric effect,”30 and predicts its characteristics before they are measured.

Einstein has provided the inspiration for quantum mechanics in numerous ways. He begins to realize, already in 1905, that the issues raised by these phenomena were serious enough to require a complete revision of mechanics. Born learns from him the idea that mechanics needs to be revised in depth. Einstein’s idea that light is a wave but also a cloud of photons inspires de Broglie to think that all the elementary particles could be waves, and that leads Schrödinger to introduce the ψ wave. Heisenberg is inspired by Einstein to restrict his attention to quantities that are measurable. There is more: Einstein is also the first to study atomic phenomena using probability, opening the path that leads Born to understand that the meaning of the ψ wave is to be found in probability. Quantum physics owes much to Einstein.

Planck’s constant reappears in 1913: in Bohr’s rules.31 Here, too, the same logic: the orbit of the electron in the atom can only have certain energies, as if energy was in packets, granular. When an electron leaps from one of Bohr’s orbits to another, it frees a packet of energy that becomes a photon, a quantum of light. Then again, in 1922, an experiment conceived by Otto Stern and carried out by Walter Gerlach in Frankfurt shows that even the rotation speed of atoms is not continuous but takes only certain discrete values.

These phenomena—photons, the photoelectric effect, the distribution of energy among electromagnetic waves, Bohr’s orbits, the discreteness of rotation—are all regulated by the Planck constant ħ.

When the quantum theory of Heisenberg and his friends finally appears in 1925, it allows for all of these phenomena to be accounted for at a stroke: to predict them, to calculate their characteristics.

The name “quantum theory” comes, indeed, from “quanta,” which is to say “grains.” “Quantum” phenomena reveal the granular aspect of the world, at a very small scale.

My field of study, quantum gravity, shows that the very physical space in which we live can be granular at a very small scale. The Planck constant determines the (extremely small) scale of the elementary “quanta of space.”

Granularity is the third idea of quantum theory, next to probability and observations. The rows and columns of Heisenberg’s matrices correspond directly to the individual discrete values that the energy can take.

We are nearing the end of the first part of the book, the story of the birth of the theory and the confusion it has generated. In the second part, I describe ways out of this confusion.

Before concluding, here are a few words about the single equation that quantum theory adds to classical physics. It is a strange equation. It states that multiplying the position by the velocity is different from multiplying the velocity by the position. If position and velocity were numbers, there could be no difference, because 7 × 9 is the same as 9 × 7. But position and velocity are now tables of numbers, and when you multiply two tables, the order counts. The new equation gives us the difference between multiplying two quantities in an order and in the reverse order.

It is beautifully compact, very simple. Incomprehensible.

Do not try to decipher it: scientists and philosophers are still wrestling with its meaning—and among themselves. Later on, I will return to it to discuss its content a little better. I’ll write it now, anyway, because it is the heart of quantum theory. Here it is:

X P – P X = i ħ

That’s it. The letter X indicates the position of a particle, the letter P indicates its speed multiplied by its mass (what we call “momentum”). The letter i is the mathematical symbol of the square root of –1 and, as we have seen, ħ is Planck’s constant divided by 2π.

In a sense, Heisenberg and company have added to physics only this simple equation: everything else follows from it—from the quantum computer to the atomic bomb.

The price of this formal simplicity is the obscurity of its meaning. Quantum theory predicts granularity, quantum leaps, photons and all the rest, on the basis of adding a single equation of eight characters to classical physics. An equation which says that to multiply position by speed is different from multiplying speed by position. The opaqueness is complete. Perhaps it is no coincidence that F. W. Murnau is said to have shot some scenes of his classic silent Gothic movie Nosferatu on Helgoland.

In 1927, Niels Bohr gives a lecture at Lake Como, in Italy, in which he summarizes everything that was understood (or not) about the new quantum theory and explains how to use it.32 In 1930, Dirac writes a book in which the formal structure of the new theory is beautifully elucidated.33 It is still today the