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They don't need to be because they describe totally different phenomena. In which way are they describing different phenomena? They both describe the evolution

They don't need to be because they describe totally different phenomena. In which way are they describing different phenomena? They both describe the evolution of the wave function, the Schrödinger equation while everyone is leaving the system alone, wave function collapse at those special moments when somebody is looking at the system, performing one of those mysterious measurements. Without explaining more precisely when I should use unitary evolution and when I should collapse the wave function, the Schrödinger equation together with wave function collapse are at the very least an incomplete and maybe even an inconsistent theory.

bowsamic 3y ago
Again, just take a look at the postulates: Schrödinger equation describes the unitary time evolution of the system under a given Hamiltonian, wavefunction collapse describes the outcome of the non-unitary measurement process. > Without explaining more precisely when I should use unitary evolution and when I should collapse the wave function, the Schrödinger equation together with wave function collapse are at the very least an incomplete and maybe even an inconsistent theory. I don't think that QM postulates are incomplete, you just take the set of things that constitute a measurement as a premise. Let's put it this way, we have never designed an experiment where this has been an issue. So long as we define which part is the measurement beforehand, QM always predicts the results we measure. Usually it will be a photodiode or something of the sort. If QM were incomplete or inconsistent, surely we would be able to find contradictory experimental results? To summarise, the 5 basic postulates of quantum mechanics, which contains unitary evolution and non-unity measurement collapse, form a microscopic theory which no experiment has ever been able to contradict.
- danbruc 3y ago
  Again, just take a look at the postulates: Schrödinger equation describes the unitary time evolution of the system under a given Hamiltonian, wavefunction collapse describes the outcome of the non-unitary measurement process. The outcome distribution of a measurement is described by the Born rule, the collapse postulate on the other hand tells us that the wave function will change to the actually measured state. Related but not the same. For the state |0> + |1> (unnormalized) the Born rule tells us that a measurement will yield |0> or |1> with 50 % probability each. The collapse postulate tells us that the state will change from |0> + |1> to either |0> or |1> depending on the measurement outcome. This change is non-unitary and therefore incompatible with the Schrödinger equation which tells us that quantum systems evolve unitarily. If you want, consider the combined quantum system of the system under investigation and the measurement device, why should that system not evolve unitarily?
  - bowsamic 3y ago
    > The outcome distribution of a measurement is described by the Born rule, the collapse postulate on the other hand tells us that the wave function will change to the actually measured state. Related but not the same. Born rule is also a postulate. > This change is non-unitary and therefore incompatible with the Schrödinger equation Yes that's why unitary evolution has a separate postulate > If you want, consider the combined quantum system of the system under investigation and the measurement device, why should that system not evolve unitarily? Well, because that's the postulate
    - danbruc 3y ago
      The postulates are roughly quantum system evolve unitarily except when they are measured, then a non-unitary wave function collapse happens. That is inconsistent. For the system under investigation this works, it evolves unitarily until measured, then the wave function collapses non-unitarily. The combined system of system under investigation and measurement device however is never measured, therefore must evolve unitarily. This is a conflict, the combined system can not evolve unitarily and also have some subsystem, the system under investigation, evolve non-unitarily, i.e. undergo a wave function collapse. This problem has been recognized for the better part of a century, that is nothing I am pulling out of thin air.
      - bowsamic 3y ago
        I mean, it's objectively not inconsistent. If you take the formal postulates you will not produce an inconsistent result.
        danbruc 3y ago
        It is objectively inconsistent, the postulates contradict each other. But for almost a century we did not make any substantial progress, neither resolving the issue theoretically or philosophically, nor experimentally demonstrating any problems. Or at least nothing reached broad consensus.

bowsamic 3y ago

Again, just take a look at the postulates: Schrödinger equation describes the unitary time evolution of the system under a given Hamiltonian, wavefunction collapse describes the outcome of the non-unitary measurement process. > Without explaining more precisely when I should use unitary evolution and when I should collapse the wave function, the Schrödinger equation together with wave function collapse are at the very least an incomplete and maybe even an inconsistent theory. I don't think that QM postulates are incomplete, you just take the set of things that constitute a measurement as a premise. Let's put it this way, we have never designed an experiment where this has been an issue. So long as we define which part is the measurement beforehand, QM always predicts the results we measure. Usually it will be a photodiode or something of the sort. If QM were incomplete or inconsistent, surely we would be able to find contradictory experimental results? To summarise, the 5 basic postulates of quantum mechanics, which contains unitary evolution and non-unity measurement collapse, form a microscopic theory which no experiment has ever been able to contradict.

danbruc 3y ago
Again, just take a look at the postulates: Schrödinger equation describes the unitary time evolution of the system under a given Hamiltonian, wavefunction collapse describes the outcome of the non-unitary measurement process. The outcome distribution of a measurement is described by the Born rule, the collapse postulate on the other hand tells us that the wave function will change to the actually measured state. Related but not the same. For the state |0> + |1> (unnormalized) the Born rule tells us that a measurement will yield |0> or |1> with 50 % probability each. The collapse postulate tells us that the state will change from |0> + |1> to either |0> or |1> depending on the measurement outcome. This change is non-unitary and therefore incompatible with the Schrödinger equation which tells us that quantum systems evolve unitarily. If you want, consider the combined quantum system of the system under investigation and the measurement device, why should that system not evolve unitarily?
- bowsamic 3y ago
  > The outcome distribution of a measurement is described by the Born rule, the collapse postulate on the other hand tells us that the wave function will change to the actually measured state. Related but not the same. Born rule is also a postulate. > This change is non-unitary and therefore incompatible with the Schrödinger equation Yes that's why unitary evolution has a separate postulate > If you want, consider the combined quantum system of the system under investigation and the measurement device, why should that system not evolve unitarily? Well, because that's the postulate
  - danbruc 3y ago
    The postulates are roughly quantum system evolve unitarily except when they are measured, then a non-unitary wave function collapse happens. That is inconsistent. For the system under investigation this works, it evolves unitarily until measured, then the wave function collapses non-unitarily. The combined system of system under investigation and measurement device however is never measured, therefore must evolve unitarily. This is a conflict, the combined system can not evolve unitarily and also have some subsystem, the system under investigation, evolve non-unitarily, i.e. undergo a wave function collapse. This problem has been recognized for the better part of a century, that is nothing I am pulling out of thin air.
    - bowsamic 3y ago
      I mean, it's objectively not inconsistent. If you take the formal postulates you will not produce an inconsistent result.
      - danbruc 3y ago
        It is objectively inconsistent, the postulates contradict each other. But for almost a century we did not make any substantial progress, neither resolving the issue theoretically or philosophically, nor experimentally demonstrating any problems. Or at least nothing reached broad consensus.