That's not correct.jwl wrote:The entire point of the Schrödinger's cat paradox is to demonstrate the difficulty in separating quantum systems (radioactive decay) with classical ones (cats).
Following the description of setup of the thought experiment, Schrödinger wrote:
Schrödinger is not particularly concerned about "the difficulty in separating quantum systems (radioactive decay) with classical ones (cats)". Instead, his first sentence simply takes it as a given that superpositions in a quantum systems can be amplified to an macroscopic, essentially classical system. That's completely correct, as that's what ordinary measurement with a macroscopic apparatus is. The rest of the paragraph uses that fact to argue that's there's something wrong with quantum superpositions (the "blurred model"): that a quantum superposition would be acceptable "in itself" (i.e., if not for the previously-mentioned microscopic-to-macroscopic amplification), but because they can be, accepting quantum superpositions as valid is naive.It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.
He's calling the "blurred model"--superpositions--invalid, rather than underlining a problem with the measurement process. Rephrased, Schrödinger's argument might be: since superpositions of macroscopic things like cats are patently ludicrous, and microscopic superpositions can be "transformed" into macroscopic ones, you shouldn't take any quantum superpositions seriously.
There's nothing there about the problem of separating the quantum from the classical. It's not even recognized as a problem in the thought experiment--instead, that one can be "transformed" into the other at some point is simply assumed as a premise of an argument pointed at completely different conclusion. Where that quantum/classical transition point is and how it is crossed is not Schrödinger's concern. Only that it happens is important. Notably, it's also how Einstein interpreted Schrödinger:
In other words, Einstein sees the point of Schrödinger's cat as not about "how does measurement collapse the wave function", but that quantum superpositions cannot be the fundamental reality, so that the measured outcome should have been determined by reality all along, independently of us. It's not about the how of measurement the how of separating quantum from classical--rather, it's that the thought experiment is supposed to illuminate a fundamental sickness in QM. This is also completely in line with the Einstein-Podolsky-Rosen argument that quantum mechanics is incomplete.You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality--reality as something independent of what is experimentally established. ... Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.
Thus, the entire point of the Schrödinger's cat paradox is that quantum superpositions don't make any sense. At least, that's definitely the conclusion Schrödinger was driving to (he was also wrong in that, but soundness is a different issue from what the conclusion was). If someone else used the same thought-experimental setup to argue something else, naturally that would be a different matter altogether.
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By the way, the von Neumann entropy of a mixed state, S = -Tr(ρ log ρ), quantifies the amount of missing information, i.e. how much you don't know about the state of the system. (N.B. 'mixed state' is basically just an ordinary probability distribution over the possible states of a system; if a state is known with probability 1, it's 'pure'.)
In classical mechanics, superpositions are always indistinguishable from the corresponding mixtures as far as classical observables are concerned, and so one can always interpret classical indeterminacy as a failure on your part: you just didn't have enough information. But in quantum mechanics, one can have (pure) superpositions of eigenstates that behave differently from any mixture of those eigenstates, and the entropy of any pure state is 0. Thus, in QM, one can know everything that can be known about a system (no missing information), yet the system still have indeterminacy.
That's another way of saying that the quantum spookiness, and one of the essential differences between classical and quantum mechanics, lies in how they treat superpositions, while connecting it to the point of Schrödinger's cat and Einstein's older saw about incompleteness of quantum mechanics: superpositions 'should have' missing information. Classically, he'd be exactly right.