“it can’t be hidden variables because they’re not as even as this math says they should be!” really just seems to be the whole QM field agreeing to stop arguing about spooky action at a distance.
The distinction between wave-functions as real things that collapse at superluminal speed and the same as mere mathematical placeholders for deterministic local effects which occur without subjective time seems to be a semantic and philosophical one, similar to the “multiple realities” explanation of quantum uncertainty or the “11 dimensions” explanation for why gravity is weaker.
As a practical matter, the only thing that students and non-physicts should remember is that wavefunction collapse allows superluminal coordination but not superluminal communication.
okay so if i understand this right, if i take half of schroedingers box and open it up, by observing the half of the cat i have i will instantly know if the half of the box the other guy’s got has got half of an alive cat in it? and i’ll be able to tell if his half of an alive cat is purring and void or garfield and shit is my stupid analogy right?
but i cannot pet my half of a cat and make it purr and thus make their half of a cat purr. because cats do not work that way.
You want to cut Schrödinger’s box in half? This kills the cat, unless the box is big enough for the cat to avoid the blade, in which case you’ve opened the box and the cat is probably going to need some convincing to get out from under whatever furniture it can find.
Quantum mechanics is more weird than that. It’s not accurate to say things can be in two states at once, like a cat that is both dead and alive at the same time, or a qubit that is both 0 and 1 at the same time. If that were true, then the qubit’s mathematical description when in a superposition of states would be |0>+|1>, but it is not, it is a|0>+b|1> where the coefficients (a and b) are neither 0 or 1, and the coefficients cannot just be ignored if one were to give a physical interpretation as they are necessary for the system’s dynamics.
You talk about it being “half” a cat, so you might think the coefficients should be interpreted as proportions, but proportions are such that 0≤x≤1 and ∑x=1. But in quantum mechanics, the coefficients can be negative and even imaginary, and do not have to sum to 1. You can have 1/√2|0>-i/√2|1> as a valid superposition of states for a qubit. It does not make sense to interpret -i/√2 as a “half,” so you cannot meaningfully interpret the coefficients as a proportion.
Trying to actually interpret these quantum states ontologically is a nightmare and personally I recommend against even trying, as you will just confuse yourself, and any time you think you come up with something that makes sense, you will later find that it is wrong.
schroedinger’s cat is an intentionally absurd metaphor from when QM dorks were still arguing about spooky action at a distance.
Both the cat, the box, the vial of poison, and the cesium atom itself are all observers as far as a real QM wavefunction would care. But as i understand it, getting any utility out of the idea of real collapsing wave-functions requires treating at least the atom as if it wasn’t, and once we start including atomic scale things we might as well just include everything up to and including the cat.
The point that Bell tried to point out in his “Against ‘Measurement’” article is that when you say “we start including atomic scale things we might as well just include everything up to and including the cat,” you have to place the line somewhere, sometimes called the “Heisenberg cut,” and where you place the line has empirically different implications, so wherever you choose to draw the line must necessarily constitute a different theory.
Deutsch also published a paper “Quantum theory as a universal physical theory” where he proves that drawing a line at all must constitute a different theory from quantum mechanics because it will necessarily make different empirical predictions than orthodox quantum theory.
A simple analogy is, let’s say, I claim the vial counts as an observer. The file is simple enough that I might be able to fully model it in quantum mechanics. A complete quantum mechanical model would consist of a quantum state in Hilbert space that can only evolve through physical interactions that are all described by unitary operators, and all unitary operators are reversible. So there is no possible interaction between the atom and the vial that could possibly lead to a non-reversible “collapse.”
Hence, if I genuinely had a complete model of the vial and could isolate it, I could subject it to an interaction with the cesium atom, and orthodox quantum mechanics would describe this using reversible unitary operators. If you claim it is an observer that causes a collapse, then the interaction would not be reversible. So I could then follow it up with an interaction corresponding to the Hermitian transpose of the operator describing the first interaction, which is should reverse it.
Orthodox quantum theory would predict that the reversal should succeed while your theory with observer-vials would not, and so it would ultimately predict a different statistical distribution if I tried to measure it after that interaction. Where you choose to draw the Heisenberg must necessarily make different predictions around that cut.
This is why there is so much debate over interpretation of quantum mechanics, because drawing a line feels necessary, but drawing one at all breaks the symmetry of the theory. So, either the theory is wrong, or how we think about nature is wrong.
Something something Bell’s Theorem. I don’t really understand it but that one was supposed to be counterevidence to hidden variables.
“it can’t be hidden variables because they’re not as even as this math says they should be!” really just seems to be the whole QM field agreeing to stop arguing about spooky action at a distance.
The distinction between wave-functions as real things that collapse at superluminal speed and the same as mere mathematical placeholders for deterministic local effects which occur without subjective time seems to be a semantic and philosophical one, similar to the “multiple realities” explanation of quantum uncertainty or the “11 dimensions” explanation for why gravity is weaker.
As a practical matter, the only thing that students and non-physicts should remember is that wavefunction collapse allows superluminal coordination but not superluminal communication.
okay so if i understand this right, if i take half of schroedingers box and open it up, by observing the half of the cat i have i will instantly know if the half of the box the other guy’s got has got half of an alive cat in it? and i’ll be able to tell if his half of an alive cat is purring and void or garfield and shit is my stupid analogy right?
but i cannot pet my half of a cat and make it purr and thus make their half of a cat purr. because cats do not work that way.
Sure, but if i open one of the doors and show you the goat’s not there, do you change your answer?
Aw I wanted the goat. I guess so
You want to cut Schrödinger’s box in half? This kills the cat, unless the box is big enough for the cat to avoid the blade, in which case you’ve opened the box and the cat is probably going to need some convincing to get out from under whatever furniture it can find.
no this is a quantum box and a quantum cat, you can do things like that
edit if you cannot tell i am high as quantum balls
Quantum mechanics is more weird than that. It’s not accurate to say things can be in two states at once, like a cat that is both dead and alive at the same time, or a qubit that is both 0 and 1 at the same time. If that were true, then the qubit’s mathematical description when in a superposition of states would be |0>+|1>, but it is not, it is a|0>+b|1> where the coefficients (a and b) are neither 0 or 1, and the coefficients cannot just be ignored if one were to give a physical interpretation as they are necessary for the system’s dynamics.
You talk about it being “half” a cat, so you might think the coefficients should be interpreted as proportions, but proportions are such that 0≤x≤1 and ∑x=1. But in quantum mechanics, the coefficients can be negative and even imaginary, and do not have to sum to 1. You can have 1/√2|0>-i/√2|1> as a valid superposition of states for a qubit. It does not make sense to interpret -i/√2 as a “half,” so you cannot meaningfully interpret the coefficients as a proportion.
Trying to actually interpret these quantum states ontologically is a nightmare and personally I recommend against even trying, as you will just confuse yourself, and any time you think you come up with something that makes sense, you will later find that it is wrong.
schroedinger’s cat is an intentionally absurd metaphor from when QM dorks were still arguing about spooky action at a distance.
Both the cat, the box, the vial of poison, and the cesium atom itself are all observers as far as a real QM wavefunction would care. But as i understand it, getting any utility out of the idea of real collapsing wave-functions requires treating at least the atom as if it wasn’t, and once we start including atomic scale things we might as well just include everything up to and including the cat.
The point that Bell tried to point out in his “Against ‘Measurement’” article is that when you say “we start including atomic scale things we might as well just include everything up to and including the cat,” you have to place the line somewhere, sometimes called the “Heisenberg cut,” and where you place the line has empirically different implications, so wherever you choose to draw the line must necessarily constitute a different theory.
Deutsch also published a paper “Quantum theory as a universal physical theory” where he proves that drawing a line at all must constitute a different theory from quantum mechanics because it will necessarily make different empirical predictions than orthodox quantum theory.
A simple analogy is, let’s say, I claim the vial counts as an observer. The file is simple enough that I might be able to fully model it in quantum mechanics. A complete quantum mechanical model would consist of a quantum state in Hilbert space that can only evolve through physical interactions that are all described by unitary operators, and all unitary operators are reversible. So there is no possible interaction between the atom and the vial that could possibly lead to a non-reversible “collapse.”
Hence, if I genuinely had a complete model of the vial and could isolate it, I could subject it to an interaction with the cesium atom, and orthodox quantum mechanics would describe this using reversible unitary operators. If you claim it is an observer that causes a collapse, then the interaction would not be reversible. So I could then follow it up with an interaction corresponding to the Hermitian transpose of the operator describing the first interaction, which is should reverse it.
Orthodox quantum theory would predict that the reversal should succeed while your theory with observer-vials would not, and so it would ultimately predict a different statistical distribution if I tried to measure it after that interaction. Where you choose to draw the Heisenberg must necessarily make different predictions around that cut.
This is why there is so much debate over interpretation of quantum mechanics, because drawing a line feels necessary, but drawing one at all breaks the symmetry of the theory. So, either the theory is wrong, or how we think about nature is wrong.
also schroedinger was an awful person so having him associated with a terrible metaphor is kind of great