eMPIRICISM IS A HOAX:

Physicists' theories work. They predict the arc of planets and the flutter of electrons, and they have spawned smartphones, H-bombs and--well, what more do we need? But scientists, and especially physicists, aren't just seeking practical advances. They're after Truth. They want to believe that their theories are correct--exclusively correct--representations of nature. Physicists share this craving with religious folk, who need to believe that their path to salvation is the One True Path.

But can you call a theory true if no one understands it? A century after inventing quantum mechanics, physicists still squabble over what, exactly, it tells us about reality. Consider the Schrödinger equation, which allows you to compute the "wave function" of an electron. The wave function, in turn, yields a "probability amplitude," which, when squared, yields the likelihood that you'll find the electron in a certain spot.

The wave function has embedded within it an imaginary number. That's an appropriate label, because an imaginary number consists of the square root of a negative number, which by definition does not exist. Although it gives you the answer you want, the wave function doesn't correspond to anything in the real world. It works, but no one knows why. The same can be said of the Schrödinger equation.

Maybe we should look at the Schrödinger equation not as a discovery but as an invention, an arbitrary, contingent, historical accident, as much so as the Greek and Arabic symbols with which we represent functions and numbers. After all, physicists arrived at the Schrödinger equation and other canonical quantum formulas only haltingly, after many false steps.

Imagine you are the Great Geek God, looking down on the sprawling landscape of all possible mathematical ways of representing the microrealm. Would you say, "Yup, those clever humans found it, the best possible set of solutions." Or would you exclaim, "Oh, if only they had taken a different path at this moment, they might have found these equations over here, which would work much better!"

Moreover, the Schrödinger equation is far from all-powerful. Although it does a great job modeling a hydrogen atom, the Schrödinger equation can't yield an exact description of a helium atom! Helium, which consists of a positively charged nucleus and two electrons, is an example of a three-body problem, which can be solved, if at all, only through extra mathematical sleights of hand.

And three-body problems are just a subset of the vastly larger set of N-body problems, which riddle classical as well as quantum physics. Physicists exalt the beauty and elegance of Newton's law of gravitational attraction and of the Schrödinger equation. But the formulas match experimental data only with the help of hideously complex patches and approximations.

When I contemplate quantum mechanics, with all its hedges and qualifications, I keep thinking of poor old Ptolemy. We look back at his geocentric model of the solar system, with its baroque circles within circles within circles, as hopelessly kludgy and ad hoc. But Ptolemy's geocentric model worked. It accurately predicted the motions of planets and solar and lunar eclipses.

Quantum mechanics also works, better, arguably, than any other scientific theory. But perhaps its relationship to reality--to what's really out there--is as tenuous as Ptolemy's geocentric model. Perhaps our descendants will look back on quantum mechanics a century from now and think, "Those old physicists didn't have a clue."

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