# Uncertainty About the Uncertainty Principle

## Can't anybody get Heisenberg's big idea right?

In the* Routledge Encyclopedia of Philosophy*, "Heisenberg, Werner" lies between "Heidegger, Martin" and "Hell." That is precisely where he belongs. Heisenberg, one of the inventors of quantum mechanics, was the leader of Hitler's atomic bomb project during World War II. After the war, he claimed that he had deliberately sabotaged the Nazi bomb effort. Many believed him. But last month, his protestations of innocence (indeed, valor) were revealed to have been almost certainly a lie. Letters written by the Danish physicist Niels Bohr, released to the public for the first time, make it pretty clear that Heisenberg was doing everything he could to produce a nuclear weapon for the Third Reich. His failure was due not to covert heroism but to incompetence.

Heisenberg (1901-76) was a wonderful physicist. At the age of 24, in a rapture on a rock overlooking the North Sea, he had an insight that revolutionized our understanding of the subatomic world. Two years later he announced, in what is probably the most quoted paper in the history of physics, his "uncertainty principle." Today, even the greatest physicists admit to bafflement at Heisenberg's mathematical non sequiturs and leaps of logic. "I have tried several times to read [one of his early papers]," confesses the Nobel laureate Steven Weinberg, "and although I think I understand quantum mechanics, I have never understood Heisenberg's motivations for the mathematical steps ..."

Though he may have been a magician as a theorist, Heisenberg was something of a dunce at applied physics. His doctoral exam in 1923 was a disaster. Asked about it many years later by Thomas Kuhn, he gave the following account (his examiner was the experimental physicist Wilhelm Wien): "Wein asked me ... about the Fabry-Perot interferometer's resolving power ... and I'd never studied that. ... Then he got annoyed and asked about a microscope's resolving power. I didn't know that. He asked me about a telescope's resolving power, and I didn't know that either. ... So he asked me how a lead storage battery operates and I didn't know that. ... I am not sure whether he wanted to fail me ..." When, during the war, Heisenberg tried to determine how much fissionable uranium would be necessary for a bomb, he botched the calculation and came up with the impossible figure of several tons. (The Hiroshima bomb required only 56 kilograms.) This is not the kind of scientist you want to put in charge of a weapons project.

Those who, prior to last month's revelation about Heisenberg, wished to stress the supposed murkiness of his wartime motives often reached for a metaphor from his physics: the uncertainty principle. Michael Frayn did it in *Copenhagen*, his play about a mysterious 1941 encounter between Heisenberg and Bohr. Thomas Powers did it in *Heisenberg's War*, the 1993 book that defended Heisenberg's claim to have destroyed the Nazi bomb project from within. David C. Cassidy did it in the very title of his 1991 biography of Heisenberg, *Uncertainty*. They should all have known better.

And they're hardly alone. No scientific idea from the last century is more fetishized, abused, and misunderstood—by the vulgar and the learned alike—than Heisenberg's uncertainty principle. The principle doesn't say anything about how precisely any particular thing can be known. It does say that some *pairs* of properties are linked in such a way that they cannot both be measured precisely at the same time. In physics, these pairs are called "canonically conjugate variables." One such pair is position and momentum: The more precisely you locate the position of a particle, the less you know about its momentum (and vice versa). Another is time and energy: The more precisely you know the time span in which something occurred, the less you know about the energy involved (and vice versa).

How could this principle of physics be applied to Heisenberg the man? In the postscript to *Copenhagen*, Frayn writes, "There is not one single thought or intention of any sort that can ever be precisely established." Well, maybe; but the uncertainty principle applies to pairs of properties. In Heisenberg's case, the relevant pair is motivation and competence. How willing was he to help Hitler? How competent was he to produce an atomic bomb? But notice that there is a positive relationship between our knowledge of one and of the other: The more certain we become that Heisenberg was willing to serve the Third Reich, the more certain we become that he was incompetent to produce a bomb. This is not the uncertainty principle, but its exact opposite. Evidently, knavishness and incompetence are not canonically conjugate variables.

A more banal misuse of Heisenberg's principle can be found in the social sciences. There the principle is often taken to mean that the very act of observing a phenomenon inevitably alters that phenomenon in some way; that is why, say, Margaret Mead could never know the sexual mores of the Samoans—her very presence on the island distorted what she was there to observe. Postmodern theorists (like Stanley Aronowitz) invoke the uncertainty principle as proof of the unstable hermeneutics of subject-object relations, arguing that it undermines science's claim to objectivity.

Even physicists show considerable uncertainty about what the uncertainty principle really means. Dozens of different interpretations have been proposed over the years. Some locate the uncertainty in some inherent clumsiness in the act of measurement itself. How do you learn the position of an electron with great accuracy? By bouncing a photon off of it. But since the electron is quite tiny, the photon must have a comparably tiny wavelength and thus a very great energy (since wavelength and energy are inversely related). So, the photon will impart a random "kick" to the electron that will affect its momentum in an unknowable way. Heisenberg himself opted for this kind of interpretation, which is called "epistemic," since it places the burden of uncertainty on the knower. Niels Bohr, by contrast, plumped for an "ontic" interpretation, attributing the uncertainty not to the knower and his measurement apparatus but to reality itself. Familiar concepts like "position" and "momentum" simply do not apply at the quantum level, Bohr argued. The contemporary physicist Roger Penrose has declared himself unhappy with the whole gamut of interpretations of Heisenberg's principle, while admitting he has nothing better to replace them with just now.

From a mathematical point of view, there is nothing the least bit problematic about Heisenberg's uncertainty principle. If you try to translate the sentence, "Electron *e* is exactly at position *x* with a momentum of exactly *p*," into the formal language of quantum theory, you get ungrammatical gibberish, just as you would if you tried to translate "the round square" into the language of geometry. It is only when you try to make sense of the principle philosophically that the waters begin to rise up around you. Years ago, the Princeton physicist John Wheeler began to wonder whether Heisenberg's uncertainty principle might not have some deep connection to Gödel's incompleteness theorem (probably the second most misunderstood discovery of the 20^{th} century). Both, after all, seem to place inherent limits on what it is possible to know. But such speculation can be dangerous. "Well, one day [Wheeler recounts] I was at the Institute of Advanced Study, and I went to Gödel's office, and there was Gödel. It was winter and Gödel had an electric heater and had his legs wrapped in a blanket. I said, 'Professor Gödel, what connection do you see between your incompleteness theorem and Heisenberg's uncertainty principle?' And Gödel got angry and threw me out of his office."