4 ms·

Schrödinger's Cat and Heisenberg's Cut

25 points by lawrenceyan 2y ago

GoblinSlayer 2y ago
>In truth, we don’t know what the state of the electron really is, or how to describe its real physical situation. But if we represent this state as a superposition, we know we will get predictions consistent with experiment. If electron behaves according to superposition, maybe superposition describes the real physical situation, why not? Antipods, length contraction and homeopathic infections were thought as absurd too because they didn't match traditional memes, now we have yet another presumably absurd concept. Everything new is just forgotten old.
- tsimionescu 2y ago
  Because the superposition model tells you that you should detect "some amount" of the electron in one place (with some speed), and "some other amount" in another (with some other speed). And yet, if you have detectors in both places, only one of the detectors will ever fire, even when the "amount" is perfectly equal. Actually, even this is much more definite than what the model actually gives you: for any two position vectors x, y that are a solution for where the electron would be, ax+by for any a, b are also solutions. So in fact every QM system has an infinity of solutions. And you, as the person making a measurement, get to decide which "family" of solutions you want to test for. And yet, not only will you never find the electron in two places at once, but once you do find it in one place, you will never see effects from the electron being in the other location. So superposition can't be the real physical situation, as it doesn't agree at all with observations. That's why the Born rule is necessary to make any use whatsoever of QM to describe measurable reality.
  - GoblinSlayer 2y ago
    According to quantum physics it's possible to measure the electron in several places at once, you just need to measure in a basis, where mixed coordinate states are eigenstates, e.g. energy basis. Imagine you have an atom with the electron on 2s orbital, then it emits a photon and goes to 1s orbital, you catch a photon and check it has the right energy, thus you know the electron is on 1s orbital, but it's smeared over that entire orbital in the coordinate basis, which is easy to check by measuring its coordinate later.
    - tsimionescu 2y ago
      Sure, this is what I was alluding to with choosing "the family of solutions". This choice of basis is a major problem for the MWI, in fact, in that without a preferred basis there is no way for classical reality to emerge, with its fixed measurables. But even if you are just measuring position, the fact remains that the electron's wavefunction can have the same value at multiple positions, yet if you install detectors at all of those positions, only one will fire, and that it is impossible to predict which one with probability 1, no matter how much information you are given about the system.
      - GoblinSlayer 2y ago
        The basis of measurement is provided by method of measurement: if you measure coordinate, you measure in coordinate basis, if you measure energy, you measure in energy basis. It's not specific to MWI.
        tsimionescu 2y ago
        That's OK for things like the Copenhagen Interpretation, which don't consider the wave function to be anything more than a method for computing probabilities of measurement. However, the MWI is claiming that the real world is described by the Universe wave function, and that classical properties we're used to seeing are merely a consequence of the decoherence of pure quantum states as they get entangled with the general environment. However, this process doesn't set any preferred basis. So this doesn't explain why all of the classical world appears to have definite properties in the same basis. That is, decoherence explains why we don't see phenomena like self-interference when throwing a basketball at a double slit experiment. But it doesn't explain why we can observe an electron in multiple places at once if we measure it in an energy basis, but we can never observe a basketball in multiple places at once if we measure it in an energy basis. How does the classical world's preferred basis emerge out of the wave function where any basis is just as valid? This is why, even with the MWI, the wave function alone is not a satisfactory explanation for the universe - it doesn't explain, without additional postulates, how the illusion of a classical world can form. Contrast this to other counter-intuitive theories like special relativity. Special relativity says that lengths contract in the direction of motion, which we don't observe in normal experiments such as when running really fast or even when driving in our car. But we have a good account of this: the contraction is so small that it just can't be noticed. So there is no real conflict between our most immediate perceptions and the theory, because the effects of the theory are just too small for us to perceive. But the effects that the wave function description of the universe predicts are actually massive: if basket balls could be in multiple places at once just as long as they have a definite kinetic energy level, then we would notice that very clearly.
- coffeeaddict1 2y ago
  > maybe superposition describes the real physical situation It may or may not. What really needs explaining IMO is the mechanism of collapse of psi, something standard QM is pretty much silent upon.
  - Joker_vD 2y ago
    Maybe it doesn't collapse, and the world is quantum through and through?
    - coffeeaddict1 2y ago
      Then why do we observe a collapse?
      - evanb 2y ago
        Decoherence may be enough. The idea is that the starting wavefunction of us and some experiment (say, an electron) is a tensor product | us > ⊗ | electron in superposition > and unitary time evolution governed by the Schrödinger equation evolves that state to | us seeing spin up in a detector > ⊗ | spin up > + | us seeing spin down > ⊗ | spin down > (I elided the amplitudes since we're just interested in the idea and not some particular values). In each 'branch' of the wavefunction (meaning: in each addend) we're left wondering "wow, how did the wavefunction collapse to the value that I am seeing", because we're inside the wf. But that's just a question we have that we've been tricked into by our limited sight; if we could see the whole wf of the universe, with our own superposition included, we'd see there is no collapse but just unitary Schrödinger evolution forever.
        GoblinSlayer 2y ago
        Quantum physics doesn't use normalization much and these formulas work better without normalization. Normalization can be provided by the Bayes formula, so postulating it is redundant. Also I heard QFT has some problem with global normalization, because everything must be local there, so normalization is replaced by Stokes' formula: the flux of state norm through closed spacetime surface is zero, i.e. the norm only conserves locally. And the evolution formula U(t)|0,0> = |1,t> + |2,t> can be seen as local conservation of the norm.
K0balt 2y ago
Just because we intuit that something seems absurd does not mean it is. What is at odds with nature seems to me to be our intuition. Our measurements of the subject seem fairly clear. The double slit experiment works, and scales to larger and larger particles with improvements in experimental rigor. We observe Casimir pressure, and we observe changes in that pressure based on probabilistic constraints that we place or remove in the vicinity of the detector. We observe reduced certainty of observations as they become distant in spacetime. All of these point in one direction-that our intuition on observing things is much less predictive than we tend to imagine. Whether that means multiverse, simulation, unlimited reach of wave function, holographic universe, or one of the other many possible explanations has yet to be established, but there is no indication that classical physics is reconcilable with observation.
- nis0s 2y ago
  To add cognitive context to what you’re saying, which is right, I’ll add that intuition is an unconscious averaging of direct or indirect observations, which doesn’t translate well to anything which hasn’t been experienced in some manner. We cannot develop gut feelings about physical phenomena that is outside of our experience or perception, which is why some quantum level effects seem surprising to us, but both simulations and experiments can confirm these counterintuitive effects.

25 points by lawrenceyan 2y ago

>In truth, we don’t know what the state of the electron really is, or how to describe its real physical situation. But if we represent this state as a superposition, we know we will get predictions consistent with experiment. If electron behaves according to superposition, maybe superposition describes the real physical situation, why not? Antipods, length contraction and homeopathic infections were thought as absurd too because they didn't match traditional memes, now we have yet another presumably absurd concept. Everything new is just forgotten old.

tsimionescu 2y ago
Because the superposition model tells you that you should detect "some amount" of the electron in one place (with some speed), and "some other amount" in another (with some other speed). And yet, if you have detectors in both places, only one of the detectors will ever fire, even when the "amount" is perfectly equal. Actually, even this is much more definite than what the model actually gives you: for any two position vectors x, y that are a solution for where the electron would be, ax+by for any a, b are also solutions. So in fact every QM system has an infinity of solutions. And you, as the person making a measurement, get to decide which "family" of solutions you want to test for. And yet, not only will you never find the electron in two places at once, but once you do find it in one place, you will never see effects from the electron being in the other location. So superposition can't be the real physical situation, as it doesn't agree at all with observations. That's why the Born rule is necessary to make any use whatsoever of QM to describe measurable reality.
- GoblinSlayer 2y ago
  According to quantum physics it's possible to measure the electron in several places at once, you just need to measure in a basis, where mixed coordinate states are eigenstates, e.g. energy basis. Imagine you have an atom with the electron on 2s orbital, then it emits a photon and goes to 1s orbital, you catch a photon and check it has the right energy, thus you know the electron is on 1s orbital, but it's smeared over that entire orbital in the coordinate basis, which is easy to check by measuring its coordinate later.
  - tsimionescu 2y ago
    Sure, this is what I was alluding to with choosing "the family of solutions". This choice of basis is a major problem for the MWI, in fact, in that without a preferred basis there is no way for classical reality to emerge, with its fixed measurables. But even if you are just measuring position, the fact remains that the electron's wavefunction can have the same value at multiple positions, yet if you install detectors at all of those positions, only one will fire, and that it is impossible to predict which one with probability 1, no matter how much information you are given about the system.
    - GoblinSlayer 2y ago
      The basis of measurement is provided by method of measurement: if you measure coordinate, you measure in coordinate basis, if you measure energy, you measure in energy basis. It's not specific to MWI.
      - tsimionescu 2y ago
        That's OK for things like the Copenhagen Interpretation, which don't consider the wave function to be anything more than a method for computing probabilities of measurement. However, the MWI is claiming that the real world is described by the Universe wave function, and that classical properties we're used to seeing are merely a consequence of the decoherence of pure quantum states as they get entangled with the general environment. However, this process doesn't set any preferred basis. So this doesn't explain why all of the classical world appears to have definite properties in the same basis. That is, decoherence explains why we don't see phenomena like self-interference when throwing a basketball at a double slit experiment. But it doesn't explain why we can observe an electron in multiple places at once if we measure it in an energy basis, but we can never observe a basketball in multiple places at once if we measure it in an energy basis. How does the classical world's preferred basis emerge out of the wave function where any basis is just as valid? This is why, even with the MWI, the wave function alone is not a satisfactory explanation for the universe - it doesn't explain, without additional postulates, how the illusion of a classical world can form. Contrast this to other counter-intuitive theories like special relativity. Special relativity says that lengths contract in the direction of motion, which we don't observe in normal experiments such as when running really fast or even when driving in our car. But we have a good account of this: the contraction is so small that it just can't be noticed. So there is no real conflict between our most immediate perceptions and the theory, because the effects of the theory are just too small for us to perceive. But the effects that the wave function description of the universe predicts are actually massive: if basket balls could be in multiple places at once just as long as they have a definite kinetic energy level, then we would notice that very clearly.
coffeeaddict1 2y ago
> maybe superposition describes the real physical situation It may or may not. What really needs explaining IMO is the mechanism of collapse of psi, something standard QM is pretty much silent upon.
- Joker_vD 2y ago
  Maybe it doesn't collapse, and the world is quantum through and through?
  - coffeeaddict1 2y ago
    Then why do we observe a collapse?
    - evanb 2y ago
      Decoherence may be enough. The idea is that the starting wavefunction of us and some experiment (say, an electron) is a tensor product | us > ⊗ | electron in superposition > and unitary time evolution governed by the Schrödinger equation evolves that state to | us seeing spin up in a detector > ⊗ | spin up > + | us seeing spin down > ⊗ | spin down > (I elided the amplitudes since we're just interested in the idea and not some particular values). In each 'branch' of the wavefunction (meaning: in each addend) we're left wondering "wow, how did the wavefunction collapse to the value that I am seeing", because we're inside the wf. But that's just a question we have that we've been tricked into by our limited sight; if we could see the whole wf of the universe, with our own superposition included, we'd see there is no collapse but just unitary Schrödinger evolution forever.
      - GoblinSlayer 2y ago
        Quantum physics doesn't use normalization much and these formulas work better without normalization. Normalization can be provided by the Bayes formula, so postulating it is redundant. Also I heard QFT has some problem with global normalization, because everything must be local there, so normalization is replaced by Stokes' formula: the flux of state norm through closed spacetime surface is zero, i.e. the norm only conserves locally. And the evolution formula U(t)|0,0> = |1,t> + |2,t> can be seen as local conservation of the norm.

K0balt 2y ago

Just because we intuit that something seems absurd does not mean it is. What is at odds with nature seems to me to be our intuition. Our measurements of the subject seem fairly clear. The double slit experiment works, and scales to larger and larger particles with improvements in experimental rigor. We observe Casimir pressure, and we observe changes in that pressure based on probabilistic constraints that we place or remove in the vicinity of the detector. We observe reduced certainty of observations as they become distant in spacetime. All of these point in one direction-that our intuition on observing things is much less predictive than we tend to imagine. Whether that means multiverse, simulation, unlimited reach of wave function, holographic universe, or one of the other many possible explanations has yet to be established, but there is no indication that classical physics is reconcilable with observation.

nis0s 2y ago
To add cognitive context to what you’re saying, which is right, I’ll add that intuition is an unconscious averaging of direct or indirect observations, which doesn’t translate well to anything which hasn’t been experienced in some manner. We cannot develop gut feelings about physical phenomena that is outside of our experience or perception, which is why some quantum level effects seem surprising to us, but both simulations and experiments can confirm these counterintuitive effects.