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

the thesis of a young French scientist, Louis de Broglie, which Einstein had advised him to read. De Broglie’s thesis examines the idea that particles such as electrons might actually be waves—like the waves of the sea, or electromagnetic waves. On the basis of some in fact rather vague theoretical analogies, de Broglie suggests it is possible to think of an electron as being like a small wave in motion.

What kind of relation can there be between a wave, which spreads out, and a particle that remains compact, following a fixed, defined trajectory? Think of a beam of light from a laser: it seems to follow a neat trajectory, like a beam of particles. But it is made of light, which is a wave, an oscillation of the electromagnetic field. The precise line described by the trajectory of a ray of light is an approximation, concealing its dispersion and spread.

Schrödinger is captivated by the idea that the trajectories of elementary particles are also approximations of the behavior of an underlying wave.14 He had spoken of this idea in a seminar in Zurich, and a student had asked if these waves obeyed an equation. In the mountains, with pearls in his ears, in the intervals between romantic moments shared with his Viennese friend, Schrödinger skillfully works back along the path that leads from the equation of a wave to the trajectory of a ray of light,15 and in this acrobatic way figures out the equation that the electron-wave must satisfy when it is in an atom. He studies solutions of this equation and manages to extract precisely the Bohr energies.16 Wow!

Then, having learned about the theory of Heisenberg, Born and Jordan, he succeeds in demonstrating that, from a mathematical point of view, the two theories are substantially equivalent: they predict the same values.17

The idea of a wave is so simple that it throws off balance the Göttingen group and their esoteric speculations on observable quantities. It’s like Columbus’s egg: Heisenberg, Born, Jordan and Dirac had built an intricate and obscure theory only because they had taken the long and winding road. Things are actually simpler: the electron is a wave. That’s all. “Observations” have nothing to do with it.

Schrödinger, too, is a product of that lively early-twentieth-century Viennese philosophical and intellectual milieu: a friend of the philosopher Hans Reichenbach, he is fascinated by Asian thought, in particular Vedanta Hinduism, and passionate (as Einstein was) about the philosophy of Arthur Schopenhauer, which interprets the world as “representation.” Unconstrained by conformism, having no fear of conventional opinion, of “what people will think,” he has no qualms about replacing a world of solid matter with a world of waves.

In naming his wave, Schrödinger uses the Greek letter psi: ψ. The quantity ψ is also called the “wave function.”18 His fabulous calculation seems to show clearly that the microscopic world is not made up of particles: it is made up of ψ waves. Around the nuclei of atoms there are not orbiting specks of matter but the continuous undulation of Schrödinger’s waves, like the waves that ruffle the surface of a small lake as the wind blows.

This “wave mechanics” instantly seems more convincing than Göttingen’s “matrix mechanics,” even if the two give the same predictions. Schrödinger’s calculation is simpler than Pauli’s. Physicists of the first half of the twentieth century were familiar with waves and wave equations; they were unfamiliar with matrices, the math we call today “linear algebra.” A well-known physicist remarked at the time: “Schrödinger’s theory came as a relief: we no longer had to learn the peculiar mathematics of matrices.”19

Above all, Schrödinger’s waves are easy to imagine and visualize. They show what it was about the “trajectory of the electron” that Heisenberg wanted to disappear: the electron is a wave that spreads, and that is all. This is why it has no trajectory.

Schrödinger seems to have triumphed in every way.

But it is an illusion.

Heisenberg immediately sees that the conceptual clarity of Schrödinger’s waves is a mirage. Sooner or later a wave spreads out and is spatially diffused; an electron does not: when it arrives from somewhere, it always arrives complete in a single point. If an electron is expelled from a nucleus, Schrödinger’s equation predicts that the ψ wave spreads out evenly through space. But when the electron is revealed, by a detector for instance, or by a TV screen, it arrives at one point only, not spatially spread out.

The discussion of Schrödinger’s wave mechanics quickly becomes lively, and then suddenly virulent. Heisenberg, who feels that the importance of his discovery is being called into question, is cutting: “The more I think about the physical portion of the Schrödinger theory, the more repulsive I find it. What Schrödinger writes about the visualizability of his theory, ‘is probably not right,’ in other words it’s crap.”20 Schrödinger tries to retort wittily: “I can’t imagine that an electron hops about like a flea.”21

But it is Heisenberg who is right. It becomes gradually evident that wave mechanics is no clearer than the matrix mechanics of Göttingen. It is another calculation tool that produces the right numbers, and is sometimes easier to use, but it does not give a clear and immediate picture of what happens, as Schrödinger had hoped it would. Wave mechanics is as obscure as the matrices of Heisenberg. If, every time we see an electron, we see it at a single point, how can the electron be a wave diffused in space?

Years later, Schrödinger, who will nevertheless become one of the most acute thinkers on questions about quanta, recognized his defeat. “There was a moment,” he writes, “when the creators of wave mechanics [that is, himself; who else?] nurtured the illusion of having eliminated the discontinuities in quantum theory. But the discontinuities eliminated from the equations of the theory reappear the moment the theory is confronted with what we observed.”22

Once again, we are back with what can be “observed.” And once again, this raises the question: