“Shut up and Calculate” (Galileo, Kepler and Schrödinger’s Cat)

by Leanne Ogasawara

Kepler-Mysterium-plate-3Nobel laureate Steven Weinberg had a wonderful piece in a recent edition of the New York Review of Books about "the trouble with quantum mechanics."

Trouble? You ask….?

Well according to science writer Tom Siegfried, "Quantum mechanics is science’s equivalent of political polarization." He says:

Voters either take sides and argue with each other endlessly, or stay home and accept politics as it is. Physicists either just accept quantum mechanics and do their calculations, or take sides in the never-ending debate over what quantum mechanics is actually saying about reality.

This is to draw attention to the fact that as the mathematical models become increasingly more sophisticated in representing a foundational picture of physical reality, the conclusions that can be drawn from the picture become "impossibly weird." Such weirdness is what led to Schrodinger's cat, for example. Or later on to the weirdness called "entanglement" and the multiverse; both which we can safely describe as being, "extreme weirdness."

To understand what physicists mean when they call something "weird," Weinberg pointedly contrasts the situation in quantum mechanics to the ever-reliable consolation that is classical Newtonian physics; in which one can quite accurately calculate where a ball will land if its velocity and direction are known. Not so in our new universe; for in the crazy upside-down world of quantum mechanics no one can say for sure where an electron will be if it is measured–only where the probability wave is most intense.

Even Einstein lost his nerve at this point, famously saying, "God does not throw dice." And Weinberg wonderfully describes how both Schrodinger and Einstein distanced themselves from quantum mechanics later in their careers for just this reason; as the observational results have led particle physicists into saying the damnedest things.

And interestingly this weirdness eventually led to the two different approaches to the issues, so wonderfully described by Tom Siegfried above. Before reading Weinberg's piece I wasn't actually aware that particle physicists thought in terms of "realism" versus "instrumentalism;" as this is a dichotomy that I associated with an older period in the history and philosophy of science.

This winter, I am auditing a fascinating class at Caltech taught by science historian Stefano Gattei on the "Parallel Lives of Galileo and Kepler." If you think about it, it is pretty incredible that two such brilliant minds, working on such similar topics and both very much taken over in religious matters (Catholicism and Lutheranism), lived basically at the same period of time. The two great men did, as we know, exchange a few letters– but these letters are simply not as many as one would have imagined, given how similarly overlapping their interests were.

Parallel lives indeed.

Today in class, Professor Gattei mentioned how historian Frances Yates once referred to Kepler as, "the last true Medieval occultist." Whereas Galileo was perhaps the world's first scientific positivist, relentlessly seeking to distance himself from any metaphysical point of view, Kepler believed that he was doing "God's work," in order to make known God's mind through mathematics. Believing that God could be recognized in the Book of Nature, Kepler saw himself to be a kind of "priest." And so, he approached his work with many metaphysical assumptions in precisely the way a Lutheran pastor approaches the world! (Kepler had wanted to become a priest after all). For example, because the universe is God's handiwork and represents "the mind of God," Kepler believed that mathematical models describing the universe must also be beautiful.

But, he also believed they must be "true" or “real."

In his book concerning his 1st and 2nd Planetary laws Astronomia Nova, Kepler took great pains to present his work as a testament to God's Glory. To which, Galileo cautions Kepler in a letter to say that, physical and metaphysical reasons should not concern the natural philosopher. That is because Galileo believed, as most physicists of the time believed, that mathematical models were only as good as they were accurate at predicting events and "preserving the phenomena."

And yet, Galileo, like Kepler, was a realist. In the words of Professor Gattei, "Both Galileo and Kepler were realists. They differed in their approaches: whereas Kepler preferred to work a priori, and draw conclusions about the world from a number of geometrical assumptions, Galileo chose first to observe, and then advance more general theories," leaving metaphysical claims aside.

In much the same way as Galileo, when it comes to quantum mechanics Steven Weinberg is also a realist. But he has some doubts as well, saying in the NYRB article that:

The realist approach has a very strange implication…, first worked out in the 1957 Princeton Ph.D. thesis of the late Hugh Everett. When a physicist measures the spin of an electron, say in the north direction, the wave function of the electron and the measuring apparatus and the physicist are supposed, in the realist approach, to evolve deterministically, as dictated by the Schrödinger equation; but in consequence of their interaction during the measurement, the wave function becomes a superposition of two terms, in one of which the electron spin is positive and everyone in the world who looks into it thinks it is positive, and in the other the spin is negative and everyone thinks it is negative. Since in each term of the wave function everyone shares a belief that the spin has one definite sign, the existence of the superposition is undetectable. In effect the history of the world has split into two streams, uncorrelated with each other.

Weinberg calls this "strange" and "unsettling." And before dismissing this all as a kind of parochial preference, says, "Like many other physicists I would prefer a single history."

Wouldn't we all?

Instrumentalists work under various assumptions as well, of course. It is impossible to be completely distanced from the current scientific paradigm, so that even the most detached instrumentalist will never be working in a complete ideological vacuum. But, one of the challenges with realism in science is that as a realist aiming to make truth statements one brings with them many more preconceived notions and blind assumptions. Instrumentalists, in only committing to create models that "save the phenomena" and make accurate predictions, simply do not have to worry much about what it all means. They don't have to concern themselves too much with conclusions or inferences, such as splitting worlds or issues of non-locality and entanglement.

A realist will "want" conclusions to be in harmony with other known facts and existing laws. The realist might also very seriously prefer conclusions to be commonsensical or perhaps beautiful. Even Galileo, says J.L Heibron in his biography on Galileo, was guided by his sensibility and taste.

Galileo could stick to an attractive theory in the face of overwhelming experimental refutation. During his period of greatest creativity in the science of motion, from 1602 to 1609, he probably jumped from theory to experiment and from one idea to another, circled back and forth, inventing the form of descriptive mathematical physics, guided by little more than his buon gusto.

There is a wonderful essay by the great S. Chandrasekhar, called "Beauty and the Quest for Science" that is highly recommended. After using Kepler as an example of science following aesthetic concepts, Chandrasekhar tells a wonderful story about Einstein and Bohr that I had never heard before.

"God does not throw dice," by Einstein; or even more provocatively, "When judging a physical theory, I ask myself whether I would have made the Universe in that way if I had been God," also by Einstein. In the context of these last two statements by Einstein, it may be well to remember Bohr's remonstrance, "Nor is it our business to prescribe to God how he should run the world!"

Isn't that great? What is it about human beings that we can first even assume that our minds are capable of fathoming ultimate truths? This is an assumption that scientists almost always carry into their work–that they can know objective truth and ultimate causes. But reading Chandrasekhar's delightful essay, I am reminded that these gut feelings regarding "beauty" or "weirdness," as well as the faith that we can believe–like Kepler or Einstein– that we "know what God would do" does lead to breakthroughs that are "right for all the wrong reasons." There have been so many instances of proof only much later catching up with a scientist's inspired hunch. Chandrasekhar gives examples of this sensibility leading to success. For example, he tells the story of Weyl, who once said that, "My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually choose the beautiful."

This aesthetic sensibility is what informs Weinberg, and I think he is in the company of Giants in having faith in his preferences for theories that "make sense" to him since the field he is working in is far from worked out. Faith assumptions cut both ways, of course, but somehow science that is a search for truth, a truth grounded in mathematical elegance and simplicity and in unified laws, seems an honorable, if risky quest. Perhaps the great scientists all want to be philosophers in secret, since the utilitarian value of instrumentalism seems hollow and ultimately a dead end.

Kepler was maybe the first astronomer in history to insist that he was not solely constructing mathematical models to "save the phenomenon" but was also doing physics. He was quite clear about this in his later work, in fact, insisting that his aim was to provide physical causes for those phenomena explained by the mathematical causes. And so in addition to mathematical models (remember up till then astronomy, like music, was a subset of mathematics–not physics), he was aiming to provide hypotheses of physical causes to explain the observations he had inherited from Tycho Brahe.

Indeed, to be visionary is to see what others have not yet seen, because that is how we know where to look. But most of all the great scientists have a sense of play. Human beings show great hubris trying to understand all of existence, and we must be prepared to be surprised– and to be delighted by the surprise. For if nothing else, we know that the Book of Nature loves to fool us again and again and again.

Recommended blog: Renaissance Mathematicus and Steven Weinberg's To Explain the World: The Discovery of Modern Science

O che bel stare è star in Paradiso

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