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> Wave functions are just a mathematical representation of a physical property that are (only?) ever operated on using quantum operators which result in a stati

by stared 2y ago

> Wave functions are just a mathematical representation of a physical property that are (only?) ever operated on using quantum operators which result in a statistical distribution. It is not correct— at least not unless you subscribe to the Copenhagen interpretation. Yet, while this interpretation is a simple heuristic for interaction with big systems (e.g., a photon hits a CCD array), none of the quantum physicists I know treat it seriously (for that matter, I have a PhD in quantum optics theory). I mean, at some certain level, everything is "just a mathematical representation" - in the spirit of "all models are wrong but some are useful". But the wavefunction is more fundamental than measurement. The other can be thought of as a particle entangling with a system so large that, for statistical reasons, it becomes irreversible - because of chaos, not fundamental rules. For some materials, I recommend materials on decoherence by WH Zurek, e.g. https://arxiv.org/pdf/quant-ph/0105127 https://arxiv.org/pdf/quant-ph/0105127. Some other references (here a shameless self ad) in https://www.spiedigitallibrary.org/journals/optical-engineering/volume-61/issue-08/081808/Visualizing-quantum-mechanics-in-an-interactive-simulation--Virtual-Lab/10.1117/1.OE.61.8.081808.full https://www.spiedigitallibrary.org/journals/optical-engineer... - mostly in the introduction and, speaking about interpretations, section 3.7. EDIT: or actually even simpler toy model of measurement, look at the Schrodinger cat in this one: https://arxiv.org/abs/2312.07840 https://arxiv.org/abs/2312.07840

bop24 2y ago
Thank you, I will look into these resources
tsimionescu 2y ago
The measurement, i.e. the Born rule, is just as fundamental as the wavefunction. The wavefunction doesn't mean anything on its own, it's not a measurable quantity that can be used to make any observable prediction whatsoever. If I claim that the wavefunction amplitude for some electron being at some location at some point in time is 1/2(1+i), how would you verify this prediction without invoking the Born rule?
- 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.

by stared 2y ago

bop24 2y ago

Thank you, I will look into these resources

tsimionescu 2y ago

The measurement, i.e. the Born rule, is just as fundamental as the wavefunction. The wavefunction doesn't mean anything on its own, it's not a measurable quantity that can be used to make any observable prediction whatsoever. If I claim that the wavefunction amplitude for some electron being at some location at some point in time is 1/2(1+i), how would you verify this prediction without invoking the Born rule?

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.