Tuesday, April 23, 2013

History of Science -- Part Thirteen: Erwin Schrödinger

By the early 1920s physicists had accepted the fact that, depending on the experimental setup, matter as well as light could be displayed either as compact lumps or as widely spread-out waves. Few pretended to understand this seeming contradiction. The significance of this came a few years later with the Schrödinger equation. But Erwin Schrödinger wasn’t looking for significance. He saw de Broglie’s matter waves as a way to get rid of Bohr’s “damn quantum jumps.” Out of disbelief comes truth!

Erwin Schrödinger, the only child of a prosperous Viennese family, was an outstanding student. As an adolescent he became intensely interested in the theater and in art. Both were areas of rebellion against the bourgeois society of late nineteenth-century Vienna. Schrödinger himself rejected the Victorian morality of his upbringing. Throughout his life he channeled much energy into intense romances, his lifelong marriage notwithstanding.

After serving in the First World War as a lieutenant in the Austrian army on the Italian front, Schrödinger started teaching at the University of Vienna. About this time he embraced the Indian mystical teaching Vedanta, but always kept his philosophical leaning apart from his physics.

In 1927, just after his spectacular work in quantum mechanics, he was invited to Berlin University as Planck’s successor. With Hitler’s coming to power in 1933, Schrödinger, though not Jewish, left Germany. After visits to England and the United States, he incautiously returned to his native Austria. He was in trouble. His leaving Germany established his opposition to the Nazis. He escaped to Italy and spent the rest of his career at the School of Theoretical Physics in Dublin, Ireland.

Despite the successes of the early quantum theory, often based on Bohr’s quantum rule, Schrödinger rejected a physics where electrons moved only in “allowed orbits” and then, without cause, abruptly jumped from one orbit to another. He was outspoken:

You surely must understand, Bohr, that the whole idea of quantum jumps necessarily leads to nonsense. It is claimed that the electron in a stationary state of an atom first revolves periodically in some sort of an orbit without radiating. There is no explanation of why it should not radiate; according to Maxwell’s theory, it must radiate. Then the electron jumps from this orbit to another one and thereby radiates. Does the transition occur gradually or suddenly? … And what laws determine its motion in a jump? Well, the whole idea of quantum jumps must simply be nonsense.

Schrödinger credits Einstein’s “brief but infinitely far-seeing remarks” for calling his attention to de Broglie’s speculation that material objects could display a wave nature. The idea appealed to Schrödinger. Waves might evolve smoothly from one state to another. Electrons would not need to orbit without radiating. He might get rid of Bohr’s “damn quantum jumps.”

Willing to amend Newton’s laws to account for the quantum behavior of small objects, Schrödinger nevertheless wanted a description of the world that had electrons and atoms behaving reasonably. He would seek an equation governing waves of matter. It would be new physics, a guess that would have to be tested. Schrödinger would seek the new universal equation of motion. The old classical physics would be merely the good approximation for large objects.

From the position and motion of a tossed stone at one moment, Newton’s law predicts its future position and motion. Similarly, from a wave’s initial shape, a wave equation predicts its shape at any later time. It describes how the ripples spread from the spot where a tossed pebble hits the water, or how waves propagate on a taut rope.

However, the single-wave equation that works for waves of water, light, and sound doesn’t work for matter waves. Water, light, and sound waves move at the single speed determined by the medium in which the wave propagates. Sound, for example, moves at 330 meters per second in air. The wave equation Schrödinger sought had to allow matter waves to move at any speed because electrons, atoms — and baseballs — move at any speed (at least up to the limit of the speed of light).

Now the story gets good, this could be on daytime television: The breakthrough came during a mountain vacation with a girlfriend in 1925. His wife stayed home. To aid his concentration, Schrödinger brought with him two pearls to keep noise out of his ears. Exactly what noise he wished to avoid is not clear. Nor do we know the identity of the girlfriend, nor whether she was inspiration or distraction. Schrödinger kept discreetly coded diaries, but the one for just this period is missing.

In four papers published within the next six months, Schrödinger laid down the basis of modern quantum mechanics with an equation describing waves of matter. Almost all the puzzles of the early quantum theory seemed resolved. The work was immediately recognized as a triumph. Einstein said it sprang from “true genius.” Planck called it “epoch making.” Schrödinger himself was delighted to think that he had gotten rid of quantum jumping. He wrote:

It is hardly necessary to point out how much more gratifying it would be to conceive a quantum transition as an energy change from one vibrational mode to another than to regard it as a jumping of electrons. The variation of vibrational modes may be treated as a process continuous in space and time and enduring as long as the emission process persists.

(The Schrödinger equation is actually a non-relativistic approximation. That is, it holds only when speeds are not close to that of light. The conceptual issues are still with us in the more general case. It is simpler, clearer, and also customary to deal with the quantum situation in terms of the Schrödinger equation. And even though photons move at the speed of light, essentially everything applies equally to photons for purposes of understanding and visualizing.)

History is more complicated than the story I just told, and more acrimonious. Almost simultaneously with Schrödinger’s discovery, Bohr’s young postdoc, Werner Heisenberg, presented his own version of quantum mechanics. It was an abstract mathematical method for obtaining numerical results. It denied any pictorial description of what was going on. Schrödinger criticized Heisenberg’s approach. “I was discouraged, if not repelled, by what appeared to me a rather difficult method of transcendental algebra, defying any visualization.” Heisenberg was equally unimpressed by Schrödinger’s wave picture. In a letter to a colleague he stated, “The more I ponder the physical part of Schrödinger’s theory the more disgusting it appears to me.”

For a while it seemed that two intrinsically different theories explained the same physical phenomena, a disturbing possibility that philosophers had long speculated about. But within a few months, Schrödinger proved that Heisenberg’s theory was logically identical to his own, just a different mathematical representation.

The more mathematically tractable Schrödinger version is generally used today, although the matrices from Heisenberg are often applied to today’s latest quantum problems. Heisenberg’s concept of “Commutators” is essential in current science and a focus on Conservation and Symmetry. You never know what will spark a new discovery. Plus, today’s physicists are well schooled in the matrix and group algebras used by these predecessors.

In the following essays, I’ll focus on Schrödinger’s equations and their interpretation. If Erwin thought he had brought sense to the nonsense of “quanta,” well … we’ll see how much sense this does make. Wave-particle duality is hard to understand, but there’s even more to come. Prepare to be truly astonished!

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