## quantum mechanics -- 1/19/22

**Today's selection -- from Seven Brief Lessons on Physics by Carlo Rovelli.** The development of quantum mechanics:

"The two pillars of twentieth-century physics -- general relativity, of which I spoke in the first lesson, and quantum mechanics, which I'm dealing with here -- could not be more different from each other. Both theories teach us that the fine structure of nature is more subtle than it appears. But general relativity is a compact gem: conceived by a single mind, that of Albert Einstein, it's a simple and coherent vision of gravity, space, and time. Quantum mechanics, or 'quantum theory,' on the other hand, has gained unequaled experimental success and led to applications that have transformed our everyday lives (the computer on which I write, for example), but more than a century after its birth it remains shrouded in mystery and incomprehensibility.

"It's said that quantum mechanics was born precisely in the year 1900, virtually ushering in a century of intense thought. The German physicist Max Planck calculated the electric field in equilibrium in a hot box. To do this he used a trick: he imagined that the energy of the field is distributed in 'quanta,' that is, in packets or lumps of energy. The procedure led to a result that perfectly reproduced what was measured (and therefore must be in some fashion correct) but clashed with everything that was known at the time. Energy was considered to be something that varied continuously, and there was no reason to treat it as if it were made up of small building blocks. To treat energy as if it were made up of finished packages had been, for Planck, a peculiar trick of calculation, and he did not himself fully understand the reason for its effectiveness. It was to be Einstein once again who, five years later, came to understand that the 'packets of energy' were real.

Wave functions of the electron in a hydrogen atom at different energy levels. |

"Einstein showed that light is made of packets: particles of light. Today we call these 'photons.' He wrote, in the introduction to his article:

It seems to me that the observations associated with blackbody radiation, fluorescence, the production of cathode rays by ultraviolet light, and other related phenomena connected with the emission or transformation of light are more readily understood if one assumes that the energy of light is discontinuously distributed in space. In accordance with the assumption to be considered here, the energy of a light ray spreading out from a point source is not continuously distributed over an increasing space but consists of a finite number of 'energy quanta' which are localized at points in space, which move without dividing, and which can only be produced and absorbed as complete units.

"These simple and clear lines are the real birth certificate of quantum theory. Note the wonderful initial 'It seems to me . . . ,' which recalls the 'I think . . .' with which Darwin introduces in his notebooks the great idea that species evolve, or the 'hesitation' spoken of by Faraday when introducing for the first time the revolutionary idea of magnetic fields. Genius hesitates.

"The work of Einstein is initially treated by colleagues as the nonsensical juvenilia of an exceptionally brilliant youth. Subsequently it will be for the same work that he is awarded the Nobel Prize. If Planck is the father of the theory, Einstein is the parent who nurtured it.

"But like all offspring, the theory then went its own way, unrecognized by Einstein himself In the second and third decades of the twentieth century it was the Dane Niels Bohr who pioneered its development. It was Bohr who understood that the energy of electrons in atoms can take on only certain values, like the energy of light, and crucially that electrons can only 'jump' between one atomic orbit and another with determined energies, emitting or absorbing a photon when they jump. These are the famous 'quantum leaps.' And it was in his institute in Copenhagen that the most brilliant young minds of the century gathered together to investigate and try to bring order to these baffling aspects of behavior in the atomic world, and to build from it a coherent theory. In 1925 the equations of the theory finally appeared, replacing the entire mechanics of Newton.

"It's difficult to imagine a greater achievement. At one stroke, everything makes sense, and you can calculate everything. Take one example: do you remember the periodic table of elements, devised by Dmitri Mendeleev, which lists all the possible elementary substances of which the universe is made, from hydrogen to uranium, and which was hung on so many classroom walls? Why are precisely these elements listed there, and why does the periodic table have this particular structure, with these periods, and with the elements having these specific properties? The answer is that each element corresponds to one solution of the main equation of quantum mechanics,. The whole of chemistry emerges from a single equation.

"The first to write the equations of the new theory, basing them on dizzying ideas, would be a young German of genius, Werner Heisenberg.

"Heisenberg imagined that electrons do not *always* exist. They only exist when someone or something watches them, or better, when they are interacting with something else. They materialize in a place, with a calculable probability, when colliding with something else. The 'quantum leaps.' from one orbit to another are the only means they have of being 'real': an electron is a set of jumps from one interaction to another. When nothing disturbs it, it is not in any precise place. It is not in a 'place' at all.

"It's as if God had not designed reality with a line that was heavily scored but just dotted it with a faint outline. In quantum mechanics no object has a definite position, except when colliding headlong with something else. In order to describe it in mid-flight, between one interaction and another, we use an abstract mathematical formula that has no existence in real space, only in abstract mathematical space. But there's worse to come: these interactive leaps with which each object passes from one place to another do not occur in a predictable way but largely at random. It is not possible to predict where an electron will reappear but only to calculate the *probability* that it will pop up here or there. The question of probability goes to the heart of physics, where everything had seemed to be regulated by firm laws that were universal and irrevocable.

"Does it seem absurd? It also seemed absurd to Einstein. On the one hand he proposed Heisenberg for the Nobel Prize, recognizing that he had understood something fundamental about the world, while on the other he didn't miss any occasion to grumble that this did not make much sense."

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