3 ms·

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 anothe

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.
      - GoblinSlayer 2y ago

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.
    - GoblinSlayer 2y ago