AnarchoEngineer@lemmy.dbzer0.com 5 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 4 hours ago
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:
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.
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.
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.
Sure, but that position reduces to solipsism, because then you don’t exist until I look at you, either.
AnarchoEngineer@lemmy.dbzer0.com 3 hours 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.”
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.
bunchberry@lemmy.world 1 hour ago
You say Bell’s theorem disproves realism, but then you immediately follow it up with saying it disproved local realism…
It never even crossed Bell’s mind to deny reality. He believed that the conclusion to his own theorem is just that it is not local.
Also, again, this is not about indeterminacy and indeterminacy, but about indefiniteness and definiteness. These are not the same things. To say something is indeterminate is merely to imply it is random. To say something is indefinite is to say it doesn’t even have a value at all.
You could in principle make this non-realism make sense if you imposed some sort of well-defined physical conditions as to when particles take on real values, but it turns out that you cannot do this without contradicting the mathematics of quantum mechanics.
These are called physical collapse models, like GRW theory, but these transitions are non-reversible even though all evolution operators in quantum mechanics are reversible, and so in principle if you rigorously define what conditions would cause this transition, you could conduct an experiment where you set up those conditions, and then try to reverse it. Orthodox quantum theory and the physical collapse model would make different predictions at that point.
These models never end up being local, anyways.
The reason I say value indefiniteness is absurd as a way to interpret quantum mechanics is because it is not necessitated by the mathematics at all, and if you believe it:
So, either it devolves into solipsism, or it is a different theory to begin with.
Bell was fine with #2 as long as people were honest about that being what they were doing. He wrote an article “Against ‘Measurement’” where he criticized the vagueness of people who claim there is a transition “at measurement” but then do not even rigorously define what qualifies as a “measurement.” He wrote positively of GRW theory in his paper “Are there Quantum Jumps?” precisely because they do give a rigorous mathematical definition of how this process takes place.
But Bell also didn’t particularly believe there was any reason to believe in value indefiniteness to begin with. You can just interpret quantum mechanics as a kind of stochastic mechanics, just one with non-local features, where it is random but particles still have definite values at all times. The same year he published his famous theorem in 1964 in the paper “On the Einstein Podolsky Rosen Paradox” he also published the paper “On the Problem of Hidden Variables” debunking von Neumann’s proof that supposedly you cannot interpret quantum mechanics in value definite terms. He also wrote a paper “Beables in Quantum Field Theory” where he shows QFT can be represented as a stochastic theory. He also wrote a paper “On the Impossible Pilot Wave” where he promoted pilot wave theory, not necessarily because he believed it, but because he saw it as a counterexample to all the supposed “proofs” that quantum mechanics cannot be interpreted as a value definite theory.
My point isn’t about randomness/indeterminacy. It is about “indefiniteness,” the claim that things have no values until you look. This either devolves into solipsism, or into a theory which is not quantum mechanics.
AnarchoEngineer@lemmy.dbzer0.com 38 minutes ago
First, I would like to note that I’m not here to assert any “quantum woo” about measurement and the soul or anything. I don’t think conscious observation has anything to do with the collapse; more likely it’s our method of measurement that affects the outcome. In fact I’d assume these phenomena would exist even in a universe without sentient beings. I’m not advocating for solipsism.
My intuition would be that certain kinds of common interactions “cause the collapse” and then: more particles -> more interaction -> more collapse, which would explain the fact we don’t see macro scale indeterminacy but do notice it at a quantum level.
Second, I’ll admit this really isn’t my field. You sound like you know what you’re talking about and have pointed me towards interesting theories and people to look into, so thanks for that, and I’ll defer to your judgement until I have a better grasp on this topic