Tuesday, August 13, 2019

Still trying to kill the cat

Some discussion stemming from Erwin Schrödinger’s birthday prompts me to set out briefly why his cat is widely misunderstood and is actually of rather limited value in truly getting to grips with the conundrums of quantum mechanics.

Schrödinger formulated the thought experiment during correspondence with Einstein in which they articulated what they found objectionable in the view of QM formulated by Niels Bohr and his circle (the “Copenhagen interpretation”, which should probably always be given scare quotes since it never corresponded to a unique, clearly adduced position). In that view, one couldn’t speak about the properties of quantum objects until they were measured. Einstein and Schrödinger considered this absurd, and in 1935 Schrödinger enlisted his cat to explain why. Famously, he imagined a situation in which the property of some quantum object, placed in a superposition of states, determines the fate of a cat in a closed box, hidden from the observer until it is opened. In his original exposition he spoke of how, according to Bohr’s view, the wavefunction of the system would, before being observed, “express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.”

This is (even back then) more careful wording than the thought experiment is usually afforded today, talking specifically about the wavefunction and not about the cat. Even so, a key problem with Schrödinger’s cat if taken literally as a thought experiment is that it refers to no well defined property. In principle, Schrödinger could have talked instead about a macroscopic instrument with a pointer that could indicate one of two states. But he wanted an example that was not simply hard to intuit – a pointer in a superposition of two states, say – but was semantically absurd. “Live” and “dead” are not simply two different states of being, but are mutually exclusive. Then the absurdity is all the more apparent.

But in doing so, Schrödinger undermined his scenario as an actual experiment. There is not even a single classical measurement, let alone a quantum state one can write down, that defines “live” or “dead”. Of course, it is not hard to find out if a cat is alive or dead – but it is very hard to identify a single variable whose measurement will allow you to fix a well defined instant where the cat goes from live to dead. Certainly, no one has the slightest idea how to write down a wavefunction for a live or dead cat, and it seems unlikely that we could even imagine what they might look like or what would distinguish them.

This is then not, at any rate, an experiment devised (as is often said) to probe the issue of the quantum-classical boundary. Schrödinger gives no indication that he was thinking about that, except for the fact that he wanted a macroscopic example in order to make the absurdity apparent. It’s now clear how hard it would be to think of a way of keeping a cat sufficiently isolated from the environment to avoid (near-instantaneous) decoherence – the process by which “quantumness” generally becomes “classical” – while being able to sustain it in principle in a living state.

Ignoring all this, popular accounts typically take the thought experiment as a literal one rather than as a metaphor. As a rule, they then go on to (1) misunderstand the nature of superpositions as being “in two states at once”, and (2) misrepresent the Copenhagen interpretation as making ontological statements about a quantum system before measurement, and thereby tell us merrily that, if Bohr and colleagues are right, “the cat is both alive and dead at the same time!”

My suspicion is that, precisely because it is so evocative, Schrödinger’s thought experiment does not merely suffer from these misunderstandings but invites them. And that is why I would be very happy to see it retired.

Of course, there is more discussion of all these things in my book Beyond Weird.

25 comments:

Peter Morgan said...

It's true enough that "There is not even a single classical measurement, let alone a quantum state one can write down, that defines “live” or “dead”", or at least that to do so requires some arbitrary cutoff, but a classical Lewis Carroll would have no conceptual difficulty with the operation "If the cat is dead, resuscitate it; if the cat is alive, kill it", even if it would be acknowledged that it is also difficult to implement this operation for a cat. Even more, one could in principle ask whether a cat is in an eigenstate of the Kill-Resuscitate operator. Critically, this classically comprehensible operation does not commute with the measurements "is alive" and "is dead", and noncommutativity is a central distinction for QM/CM.
Surely the cat is a whimsical example, and so is this discussion, but the central idea of a two-dimensional Hilbert space isn't empty of lessons both for classical and quantum physics.

Jayarava said...

The cat interacts with the box and becomes entangled with it. So it's never really in a state of superposition for any appreciable length of time.

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