Fiction

Waves are certainly visualizable, but the world we live in, the world of laboratory experiments, does not present itself as made of waves. It presents itself, if anything, as made of particles. How do we get from waves to recognizable everyday stuff?

This, in a nutshell, is the central conundrum of quantum mechanics: how does the mathematical formalism used to represent a quantum system make contact with the world as given in experience? This is commonly called the measurement problem, although the name is misleading. It might better be called the where-in-the-theory-is-the-world-we-live-in problem.

For Bohr and Heisenberg, the measurement problem is how the unvisualizable can influence the observable (and hence visualizable). For Schrödinger it is how waves can constitute solid objects such as cats. In wave mechanics, the little planetary electron of the old quantum theory gets smeared out into a cloud surrounding the nucleus. If quantum mechanics provides a complete description of the electron—as Bohr insisted—this diffuseness is not merely a reflection of our ignorance about where the electron is, it is a characteristic of the electron itself. As Schrödinger memorably wrote to Albert Einstein, “There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.” This unexpected (but perfectly visualizable) mistiness of the electron was fine by Schrödinger: after all, we have no direct experience of electrons to contradict it. But the dynamics of the theory could not confine the smeariness to microscopic scale. In certain experimental situations, the haziness of the electron would get amplified up to everyday scales. The electron that is nowhere-in-particular gives birth to a cat that is no-state-of-health-in-particular. Schrödinger found this result manifestly absurd: something must have gone wrong somewhere in the physics.

For his part, Bohr insisted—as he had to—that the description of an experimental procedure and its outcome be classical, which is to say visualizable. Otherwise, you could not tell what experiment was done and how it came out. But at some point, if we are probing the microscopic realm, we must reach the unvisualizable. And the interaction between the two must itself be unvisualizable, since one part is. So all one can ask for is a mathematical rule: if an interaction occurs, what are the probabilities of the various possible classical outcomes? There is no more to be sought from quantum theory than these numbers. And matrix mechanics typically does not provide a precise prediction but a set of probabilities for different outcomes. The deterministic world of classical physics has been lost.