5 ms·

You may say that nuclear fusion in stars does not mean anything; only what matters is that we see light. At a certain level it is true, but to simulate a system

by stared 2y ago

You may say that nuclear fusion in stars does not mean anything; only what matters is that we see light. At a certain level it is true, but to simulate a system we need to simulate its inner workings, not only - the end effect. The exact phase of a wavefunction does not matter - but it is an important phenomenon, giving raise to gauge invariance. The Born rule can be derived. In short, since we use unitary operators, length is preserved. For a derivation, see https://journals.aps.org/pra/abstract/10.1103/PhysRevA.71.052105 https://journals.aps.org/pra/abstract/10.1103/PhysRevA.71.05.... Also, to be nitpicky, we also never measure probabilities. Something (macroscopic) happened or not. It gives rise to quite fundamental and philosophical questions, including "what is (classical) probability" (I don't know an answer that fully satisfies me), many world interpretations (maybe all possible things just are), and in general what on indeterminism and free will.

tsimionescu 2y ago
I'm not a quantum physicist and so can't really comment on why, but it's clear that the paper you linked is not widely accepted, as the Born rule is still taught as a postulate of quantum mechanics, not a derived property of the wavefunction. I'd wager a guess that the paper ends up inventing some other postulate that is itself not derivable from the wavefunction, so it becomes at best a philosophical matter which postulate you actually prefer. I also don't agree with your comparison of what I said to the nuclear reactions happening inside a star. The problem with the wavefunction without the Born rule is not that it's difficult to observe, it's that it's literally meaningless: knowing the value of the wavefunction for some state of a system doesn't tell you anything at all unless you apply the Born rule to this value. And as for probabilities, certain kinds of probabilities at least have a very clear and simple definition (though they are rather narrow cases): if you repeat an experiment in exactly the same conditions N times, and an outcome O happens in p/N times and doesn't happen (1-p/N) times, then we define P(O), the probability of outcome O, as the value p/N. For systems where this applies, it is very much a measurable quantity (with some noise, of course, related to the fidelity with which you can reproduce the same experiment). I do agree that this well-defined, measurable, concept of probability is rarely what we mean by "the probability of O", since (a) it's often hard or impossible to repeat (or even perform) the experiment, and (b) we often care about what will happen the next M times we repeat this experiment, and the measure P(O) I defined above does not tell us anything about future events.
- GoblinSlayer 2y ago
  Wavefunction has the Born rule, it's just not an independent postulate, but an emergent behavior from the Schrodinger equation. Also knowing the wavefunction does tell you everything, all properties are derived from it. You say you need the Born rule to understand what's going on, for this you don't need it as a fundamental phenomenon, you only need to eventually observe the Born statistics, which is sufficient to provide understanding for you.
  - tsimionescu 2y ago
    Again, the wavefunction just tells you "the amplitude of the state in which the photon is at location (x, y) on the screen at time t is sqrt(i); the amplitude of the state in which the particle is at position (x+2,y) at time t is sqrt(1+i/2)". Given these numbers, where do you expect to find the particle at time t?
    - GoblinSlayer 2y ago
      I expect to find it where it is - in sqrt(i)|x,y>+sqrt(1+i/2)|x+2,y>
      - tsimionescu 2y ago
        How do you verify whether this expectation is correct?
        GoblinSlayer 2y ago
        This expectation is according to the model that matches reality.
        tsimionescu 2y ago
        Sure, but how specifically do you think it was checked? Actually, I'll tell you how it was checked: they ran lots of experiments, and confirmed that the probability to find the particle in one state or the other is precisely equal to the norm of the wavefunction of the respective state. Also known as the Born rule.

by stared 2y ago

tsimionescu 2y ago

I'm not a quantum physicist and so can't really comment on why, but it's clear that the paper you linked is not widely accepted, as the Born rule is still taught as a postulate of quantum mechanics, not a derived property of the wavefunction. I'd wager a guess that the paper ends up inventing some other postulate that is itself not derivable from the wavefunction, so it becomes at best a philosophical matter which postulate you actually prefer. I also don't agree with your comparison of what I said to the nuclear reactions happening inside a star. The problem with the wavefunction without the Born rule is not that it's difficult to observe, it's that it's literally meaningless: knowing the value of the wavefunction for some state of a system doesn't tell you anything at all unless you apply the Born rule to this value. And as for probabilities, certain kinds of probabilities at least have a very clear and simple definition (though they are rather narrow cases): if you repeat an experiment in exactly the same conditions N times, and an outcome O happens in p/N times and doesn't happen (1-p/N) times, then we define P(O), the probability of outcome O, as the value p/N. For systems where this applies, it is very much a measurable quantity (with some noise, of course, related to the fidelity with which you can reproduce the same experiment). I do agree that this well-defined, measurable, concept of probability is rarely what we mean by "the probability of O", since (a) it's often hard or impossible to repeat (or even perform) the experiment, and (b) we often care about what will happen the next M times we repeat this experiment, and the measure P(O) I defined above does not tell us anything about future events.

GoblinSlayer 2y ago
Wavefunction has the Born rule, it's just not an independent postulate, but an emergent behavior from the Schrodinger equation. Also knowing the wavefunction does tell you everything, all properties are derived from it. You say you need the Born rule to understand what's going on, for this you don't need it as a fundamental phenomenon, you only need to eventually observe the Born statistics, which is sufficient to provide understanding for you.
- tsimionescu 2y ago
  Again, the wavefunction just tells you "the amplitude of the state in which the photon is at location (x, y) on the screen at time t is sqrt(i); the amplitude of the state in which the particle is at position (x+2,y) at time t is sqrt(1+i/2)". Given these numbers, where do you expect to find the particle at time t?
  - GoblinSlayer 2y ago
    I expect to find it where it is - in sqrt(i)|x,y>+sqrt(1+i/2)|x+2,y>
    - tsimionescu 2y ago
      How do you verify whether this expectation is correct?
      - GoblinSlayer 2y ago
        This expectation is according to the model that matches reality.
        tsimionescu 2y ago
        Sure, but how specifically do you think it was checked? Actually, I'll tell you how it was checked: they ran lots of experiments, and confirmed that the probability to find the particle in one state or the other is precisely equal to the norm of the wavefunction of the respective state. Also known as the Born rule.