PUERTO RICO--One of my favorite talks at the recently concluded FQXi conference was Sean Carroll's takedown of the concept of quantum fluctuations in inflationary cosmology. Regardless of the fate of his overall argument--which my fellow FQXI bloggers Zeeya Merali and Ian Durham have already discussed--I think Carroll's essential point about fluctuations is extremely important and not widely appreciated.
Whenever physicists talk about quantum mechanics, they conjure up a world gone mad. "The universe is a teeming, chaotic, frezied arena on microscopic scales," wrote Brian Greene in The Elegant Universe. Particles squirm like kindergartners after too much circle time. Fields jitter uncontrollably. Spacetime itself tosses like a stormy sea. These are not merely images that physicists offer when simplifying their arguments for the general public. They appear in academic papers, too.
But what, exactly, is fluctuating? The usual accounts imply there is some definite reality that wavers from moment to moment. Yet most physicists eschew such a definite reality. In the orthodox interpretation of quantum theory, a particle doesn't exist at a specific position (except in special cases). It doesn't exist at multiple positions. It simply doesn't have a position. As philosopher David Albert has put it, position has as much meaning for the particle as political affiliation has for a tuna sandwich. So, the particle can no sooner fluctuate in position than the sandwich could quit Occupy Wall Street and join the Tea Party.
The Schrödinger equation of quantum mechanics describes a particle or other physical system using a wavefunction. A wavefunction does not fluctuate. It evolves deterministically. The idea of a fluctuation enters when the system is measured. If the wavefunction spans multiple positions, then the particle will appear in one of those positions at random. If you prepare a series of particles in exactly the same way and then measure them one by one, they will show up in different positions. This is what physicists mean by quantum fluctuation: not the quivering of a single particle, but the spread that arises for an ensemble of identical particles. Single particles do quiver--for instance, in Brownian motion--but this is a thermal rather than a quantum effect.
You commonly hear that the vacuum is ceaselessly burbling with particles fluctuating in and out of existence. This, too, is a misconception. Rather, what happens is that a vacuum--a state of a field with zero particles--does not have a well-defined energy, but is a superposition of multiple possible energies. Every time a detector measures the energy of the field, it obtains a different value. It's not that the field's energy is fluctuating. It's that the energy isn't even properly defined.
Cosmologists invoke fluctuations all the time to explain, for example, why the process of inflation can never end. "There is a conventional wisdom," Carroll told the FQXi meeting. "I know this because I have promulgated this conventional wisdom for years now." And he now thinks it's wrong. I can't wait to see the paper he is now writing to elaborate on the implications.