The Science of Discworld IV

Schrödinger’s cat according to quantum physicists, though not according to Schrödinger, who used a cat because cats aren’t like that. But electrons are, so quantum physicists view a cat as a sort of super-electron. There is, however, a different view: that HHTTTHH
was
what happened, and that the other possibilities, like the other people whose sperms didn’t make it to an egg, or the other histories that didn’t result in Morris being a great naturalist, didn’t actually happen. Anywhere.
    Now, there is a sense in which the classical universe is the superposition of all conceivable quantum states, and that’s what the quantum physicists are so keen to explain. But only
one
classical universe arises from of all those quantum alternatives – and that’s why a cat is not a super-electron. Feynman explained this in
QED
using light rays as an example. The classical (that is, non-quantum) law of reflection tells us that when a light ray hits a mirror, ‘the angle of incidence equals the angle of reflection’. That is, the ray bounces off at the same angle as it hit. In a classical world, there is only one outcome, determined by this simple geometric law. In a quantum world, there is no such thing as a light ray; instead, there is a quantum superposition of wavelike photons, going in all directions.
    If you model the incoming ray in such terms, these photons concentrate
around
the classical ray in a particular manner. Each photon follows its own path; even the places where they hit the mirror can be different, and where they go afterwards need not obey the classical equal-angles law. Wonderfully, if you add up all of the waves corresponding to all of the photons – all of the potential quantum states of the system – with the right probabilities, the answer concentrates very tightly around the classical reflected ray. Feynman manages to convince his readers of this technical point (the principle of stationary phase)
without
doing any sums. Brilliant!
    Notice how here the entire quantum superposition, of all possible states – including crazy ones where the photon follows wiggly paths, hits the mirror many times, and so on – leads to a
single
classical result: the one we observe. It does not lead to a superposition of many different classical worlds, like the traditional story of a world in which Adolf Hitler won the Second World War coexisting alongside one in which he didn’t, together with endless variants in which all possible choices occurred at all possible times.
    Yes, but … Can we somehow pull that quantum superposition apart into many different
classical
scenarios, so that their superposition is the same as the quantum one? Each classical scenario would be a superposition of some of the quantum ones, and we must be careful not to use any of them twice, but is it possible? If so, our objection to the many-Hitlers universe would be irrelevant.
    The most reasonable classical variations on the equal-angles scenario involve classical choices about where the incident light ray hits (which determines the angle of incidence) and what angle it comes off at (the angle of reflection). That is, we draw lots of straight lines that start at the light source, hit the mirror and bounce off – possibly with
unequal
angles.
    Now, there are indeed photon-paths, submerged in the ocean of all possible quantum states, which mimic all of those classical paths. But if we change the point at which the ray hits the mirror, and try to synthesise that ray as a sum of nearby quantum states, it doesn’t work. To make the original set of photon-paths represent the original incident ray correctly, these paths must be assigned probabilities that are concentrated near that ray. The paths near a different ray then have the wrong probabilities to represent that alternative ray. In short, we can’t change the point at which the classical ray hits the mirror. But then, paths that reflect at a different angle aren’t classical at all; in classical physics they are impossible, because classical paths obey the law of reflection.
    This thought-experiment with a mini-universe containing a mirror and a light ray seems to indicate that the quantum superposition concerned determines a unique classical state,
and
that it can’t be pulled apart into several different classical states. Perhaps there’s a clever way to do that, but not in the world of incident and reflected rays. In short, although this mini-universe has infinitely many