Schrodinger's Cat
That’s some out-of-the-box thinking! 😉
Submitted 5 hours ago by other_cat@piefed.zip to [deleted]
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Comments
homes@piefed.world 5 hours ago
AnarchoEngineer@lemmy.dbzer0.com 3 hours ago
Not to be the 🤓 but just so we’re clear, the point of Schrödinger’s cat was to illustrate that you can’t know a quantum state until you measure it. Basically just saying “probability exists.”
The reason it’s a big deal is that this probability is a real property. One that is supposed to be only one of two states. But instead it isn’t really in a state at all until you measure it, and that’s weird.
The point is that instead of assuming it is in one state or the other, you can and often should think of both possibilities at once. This is what makes quantum computing useful. Specifically the fact that, instead of working with values, you can work with probabilities, and until you measure the outcome, you can manipulate the probabilities all you want.
So you simply apply operations that increase or decrease the chances of certain outcomes and repeat until the answer you want has an incredibly high probability and the rest are nearly zero. Then you measure your qubit, collapsing the wave function, with a high probability that collapse will give you the answer you wanted.
If you had measured the particle before hand and run it through the system, it wouldn’t work because its state was already decided.
It’s less like “the cat is both alive and dead” and more that “the terms ‘alive’ and ‘dead’ do not apply to the cat till you open the box”
bunchberry@lemmy.world 2 hours ago
Not to be the 🤓 but just so we’re clear, the point of Schrödinger’s cat was to illustrate that you can’t know a quantum state until you measure it. Basically just saying “probability exists.”
That wasn’t Schrödinger’s point at all.
Schrödinger was responding to people in Bohr and von Neumann’s camp who claim that particles described mathematically by a superposition of states literally have no real observables in the real world at all. It is not just that they are random or probabilistic, but people in the “anti-realist” camp argue that they effectively no longer even exist anymore when they are described mathematically by a superposition of states. This position is sometimes called value indefiniteness.
Schrödinger was criticizing this position by pointing out that you cannot separate your beliefs about the microworld from the macroworld, because macroscopic objects like cats are also made up of particles and should follow the same rules. Hence, he puts forward a thought experiment whereby a cat would also be described mathematically in a superposition of states.
If you think superposition of states means it no longer has real definite properties in the real world, then the cat wouldn’t have real define properties in the real world until you open the box. Schrödinger’s point was that this is such an obvious absurdity that we should reject value indefiniteness for individual particles as well.
You say:
The reason it’s a big deal is that this probability is a real property. One that is supposed to be only one of two states. But instead it isn’t really in a state at all until you measure it, and that’s weird.
But that is exactly the point Schrödinger was criticizing, not supporting.
Value indefiniteness / anti-realism ultimately amounts to solipsism because if particles lack real, definite, observable properties in the real world when you are not looking at them, other people are also made up of particles, so other people wouldn’t have real, definite, observable properties in the real world when you are not looking at them.
He was trying to illustrate that this position reduces to an absurdity and so we should not believe in that position.
The point is that instead of assuming it is in one state or the other, you can and often should think of both possibilities at once. This is what makes quantum computing useful.
No. If you perform a polar decomposition on the quantum state, you are left with a probability vector and a phase vector. The probability vector is the same kind of probability vector you use in classical probabilistic computing. The update rule for it in quantum computing literally only differs by an additional term which is a non-linear term that depends upon the phase vector.
The "advantage’ comes from the phase vector. For N qubits, there are 2^N phases. A system of 300 qubits would have 2^300 phases, which is far greater than the number of atoms in the observable universe. A single logic gate thus can manipulate far more states of the system at once because it can manipulate these phases, which the stochastic dynamics of the bits have a dependence upon the phases, and thus you can not only manipulate the phases to do calculations but, if you are clever, you can write the algorithm in such a way that the effect it has on the probability distribution allows you to read off the results from the probability distribution.
The phase vector does not contain anything probabilistic, so it contains nothing that looks like the qubit being in two places at once. That is contained in the probability vector, but there is no good reason to interpret a probability distribution as the system being in two places at once in quantum mechanics than there is in classical mechanics. The advantage comes from the phases, and the state of the phases just can influence the stochastic influence of the bits, and thus can influence the probability distribution.
So you simply apply operations that increase or decrease the chances of certain outcomes and repeat until the answer you want has an incredibly high probability and the rest are nearly zero. Then you measure your qubit, collapsing the wave function, with a high probability that collapse will give you the answer you wanted.
Again, perform a polar decomposition on the quantum state, break it apart into the probability vector and a phase vector. Then, apply a Bayesian knowledge update using Bayes’ theorem to the probability vector, exactly the way you’d do it in classical probabilistic computing. Then, simply undo the polar decomposition, i.e. recompose it back into a single complex-valued vector in Cartesian form.
What you find is that this is mathematically equivalent to the collapse of the wavefunction. The so-called “collapse of the wavefunction” is literally just a Bayesian knowledge update on the degree of freedom of the quantum state associated with the probability distribution of the bits.
It’s less like “the cat is both alive and dead” and more that “the terms ‘alive’ and ‘dead’ do not apply to the cat till you open the box”
Sure, but that position reduces to solipsism, because then you don’t exist until I look at you, either.
AnarchoEngineer@lemmy.dbzer0.com 1 hour ago
The reason I commented was mostly to clarify that Schrödinger’s cat is not like the meme implies. It’s meant to illustrate how weird it is that the cat would be neither alive nor dead until you open the box, not “the cat is in fact both at the same time.”
But that is exactly the point Schrödinger was criticizing, not supporting.
I was under the impression this was more a question than a criticism. He’s asking where the line is between this indeterminacy and determinacy. At what scale to things move from quantum to “real” and why?
Also Bell experiments have proven this indeterminacy you say is absurd. No theory of local hidden variables can describe quantum mechanics. The state is not a local property of the particle/system until it is “measured.” I’ll admit it’s an uncomfortable truth that sounds absurd, but it’s a truth nonetheless.
Anyway, thank you for the more in depth explanations of both the thought experiment and quantum computing.
jaybone@lemmy.zip 1 hour ago
This is not what the cat would have wanted.
Or is it?
edgemaster72@lemmy.world 59 minutes ago
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