Timeline for Do we actually need negative probabilities in quantum mechanics?
Current License: CC BY-SA 4.0
19 events
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| Mar 28, 2023 at 17:45 | comment | added | ZeroTheHero | WF (even in the discrete case) are always densities. | |
| Mar 28, 2023 at 13:38 | comment | added | Dast | @ZeroTheHero. I think the "density" component is orthogonal. If we are in phase space (x, p) then we use QP density. However, in the Feynman notes you link and the related papers of eg. Bill Wooters QP distributions are used to study discrete quantum variables (eg. spin) and in this case it is proper QP, not a QP density. (It sums to 1, not integrates to 1). However, I certainly agree that no experiment has (or even really can) prove the existence of negative probabilities, any more than it could prove the existence of a wavefunction. Both exist in the realm of quantum interpretations. | |
| Mar 28, 2023 at 13:30 | comment | added | ZeroTheHero | @Dast the confusion I feel is at your end, as you appear unwilling to make a clear distinction between probability densities and probabilities. We can agree that regions with negative probability densities are theoretically and even experimentally established (see this famous paper ) but can we also agree this does not imply negative probabilities? | |
| Mar 28, 2023 at 12:54 | comment | added | Dast | @ZeroTheHero. I feel like we are talking past one another. The exact equivalence of phase space approaches and wavefunctions is the entire point. Some people say that wavefunctions "exist". (For example all many worlds interpretations, and some kinds of Copenhagen interpretations). But wavefunctions are mathematically equivalent to quasiprobability distributions, so either one has as much experimental evidence of "real existence" as the other. There are people who go a bit far-out "interpreting" the wavefunction (many worlds). I think similar thinking on QProb is not guaranteed to be useless. | |
| Mar 28, 2023 at 12:42 | comment | added | Dast | @tparker. Discrete quantum systems can be described using discrete quasi-probability distributions, (journals.aps.org/pra/abstract/10.1103/PhysRevA.70.062101 or the Feynman link shared above). The negatives still arise. So, while I agree that probability density is very much not equal to probability that difference is orthogonal to the distinction between probability vs. quasiprobability. A classical system can very well have a probability density above 1, but it cannot have a probability density below 1. | |
| Mar 28, 2023 at 3:42 | comment | added | A rural reader | Seriously, if you want to exploit mathematical probability, the secret amongst others is the 'negative probabilities' are right up there with 'probabilities greater than one.' Maybe they balance out in the next-gen physics? | |
| Mar 27, 2023 at 23:49 | comment | added | tparker | So if you say that the existence of quasiprobability distributions should be interpreted as a negative probability, then you would also have to say the existence of a regular PDF should be interpreted as saying that probabilities can be greater than 1. But I don't think this perspective is useful. | |
| Mar 27, 2023 at 23:47 | comment | added | tparker | I agree with @ZeroTheHero that the distinction between probabilities and probability densities is important here. The fact that a quasiprobability distribution takes on negative values at certain points isn't so different from the fact that a regular PDF can be greater than 1 at certain points. In neither situation should any probability be thought of as either greater than 1 or less than 0, because those values aren't probabilities. In both cases, in order to get the actual probability, you need to integrate the (q-)PDF over a region such that the integral always lies in $[0,1]$. | |
| Mar 27, 2023 at 14:25 | comment | added | ZeroTheHero | Additionally, you're making a point of distinction between the wavefunction approach and the phase space approach. Both are completely equivalent so the distinction is no more essential than claiming the Heisenberg picture is different from the Schrodinger picture. | |
| Mar 27, 2023 at 14:22 | comment | added | ZeroTheHero | sorry but even when the quasiprobability distribution has negative regions you never get negative probabilities. There is no physically meaning process that allows you to restrict the integration of the quasiprobability distribution to the negative regions only. To be clear: yes there are distributions with negative pieces, but these are not probabilities, they are just distributions. Nobody has issues with negative regions in the WF, but those still produce non-negative probabilities. | |
| Mar 27, 2023 at 14:07 | history | edited | Dast | CC BY-SA 4.0 |
Took out the meanness.
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| Mar 27, 2023 at 14:02 | comment | added | Dast | Yes, no one (that I know of) is saying that you will ever be able to see an event happen a negative number of times, and therefore all click frequencies will yield positive probabilities. They are claiming more interpretational things (like Feynman's) about there really existing something strange localised in those specific regions of the phase space, that may as well be termed negative probability. In a world where some people believe that complex valued probability amplitudes "exist", I don't think its that surprising that some other people think that negative probabilities "exist". | |
| Mar 27, 2023 at 13:43 | comment | added | ZeroTheHero | we have Feynman to blame for this, although he did like to be provocative and in that link he's really discussing negative probability regions in the quasi-probability distribution... I have myself never seen serious mainstream work where there are true negative probabilities. | |
| Mar 27, 2023 at 13:37 | comment | added | Dast | @ZeroTheHero I have met a couple of them at conferences actually. Maybe I just go to weird conferences (quantum foundations people are strange). Although you are probably correct that provocative clickbaits are more common. | |
| Mar 27, 2023 at 13:35 | comment | added | ZeroTheHero | Your edit doesn't cut it. I'd rather not downvote your answer but your first paragraph is simply uninformed. Any suggestion of "negative probability" in a title would be carefully qualified as the fact remains there are no negative probabilities in physics. | |
| Mar 27, 2023 at 13:28 | history | edited | Dast | CC BY-SA 4.0 |
deleted 7 characters in body
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| Mar 27, 2023 at 13:02 | comment | added | ZeroTheHero | You also want to be precise when you state that Wigner functions are real. It is true if you clarify that the Wigner function is the Wigner symbol of a (hermitian) density operator for the state but the core quantity in the phase space formulation is the Wigner symbol, and you can have Wigner symbols of non-hermitian operators - - for instance a raising operator - that are complex or at least not necessarily real. | |
| Mar 27, 2023 at 13:01 | comment | added | ZeroTheHero | Actually, nobody in a physics conference would seriously claim there are negative probabilities: statements of "negative probabilities" are provocative clickbaits. Some might talk of negativity of WF (which leads to cwey interesting consequences), and everyone agrees WF can have regions of negativity but the WF is a (quasi-)probability density so regions of negativity do not imply negative probabilities and is no more strange than regions where a PDF is larger than since what matters is their integral. | |
| Mar 27, 2023 at 10:45 | history | answered | Dast | CC BY-SA 4.0 |