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- Thread starter Nickyv2423
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atyy

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Yes, the wave function can be real in Copenhagen. Copenhagen is ambivalent about the reality of psi.

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martinbn

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What does it mean for the wave function to be real?

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I think the von Neumann collapse interpretation can be considered as an ontic version of Copenhagen.

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It means ontic. If you ask what ontic means in mathematical terms, then I have two answers.What does it mean for the wave function to be real?

One is the PBR criterion: https://arxiv.org/abs/1111.3328v3

The other is "real" roughly in the sense in which numbers are real according to mathematical Platonists. For instance, is continuum hypothesis true in reality? The question makes sense for Platonists, despite the fact that it is undecidable by ZF axioms.

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One is the PBR criterion

I'm not sure I understand how this criterion is supposed to work. Their criterion basically seems to be that something is a "physical property" if for any collection of probability distributions ##L## corresponding to that property, the distributions corresponding to different labels ##L##, ##L'## are disjoint (Fig. 1 in the paper and accompanying discussion). But, using their example of a classical point particle in one dimension, position would seem to be a physical property but there are certainly collections of probability distributions corresponding to position that are not disjoint (for example, any collection of Gaussians centered on different points). Does that mean position of a classical particle is not a physical property?

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The PBR criterion is not concerned with the question whether any of the observables (position, momentum, spin, ...) is ontic. They only consider the question whether the wave function (which is not an observable) is ontic. And their conclusion is that it is. But note that conclusion is based on the assumption thatI'm not sure I understand how this criterion is supposed to work. Their criterion basically seems to be that something is a "physical property" if for any collection of probability distributions ##L## corresponding to that property, the distributions corresponding to different labels ##L##, ##L'## are disjoint (Fig. 1 in the paper and accompanying discussion). But, using their example of a classical point particle in one dimension, position would seem to be a physical property but there are certainly collections of probability distributions corresponding to position that are not disjoint (for example, any collection of Gaussians centered on different points). Does that mean position of a classical particle is not a physical property?

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The PBR criterion is not concerned with the question whether any of the observables (position, momentum, spin, ...) is ontic.

The paper uses the term "physical property", and I'm trying to understand what it means by that. In the classical case, it certainly seems to me that position should be a physical property--indeed, in the usual formulation of classical mechanics, position is part of the "underlying state" that the paper labels ##\lambda##, which is assumed to be ontic. Yet position does not seem to meet the paper's criterion for something ontic; so I'm confused about what the criterion is supposed to mean. If it doesn't mean that position in classical mechanics is ontic, then I don't see why I should care about their criterion since it doesn't match anything that seems useful to me. But if it is supposed to mean that position in classical mechanics is ontic, then their actual formulation doesn't seem to match that.

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atyy

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I'm not sure I understand how this criterion is supposed to work. Their criterion basically seems to be that something is a "physical property" if for any collection of probability distributions ##L## corresponding to that property, the distributions corresponding to different labels ##L##, ##L'## are disjoint (Fig. 1 in the paper and accompanying discussion). But, using their example of a classical point particle in one dimension, position would seem to be a physical property but there are certainly collections of probability distributions corresponding to position that are not disjoint (for example, any collection of Gaussians centered on different points). Does that mean position of a classical particle is not a physical property?

I think it is something like this:

For a single particle, the state is (x,p). If you know x=a with certainty, then the probability distribution u(x=a,p) is disjoint from the distribution u(x=b,p) if you know x=b with certainty. [Sorry for the terrible notation.]

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Position is ontic in classical mechanics, and the authors of the paper take it for granted. But that's not what they are concerned about. They want to determine whether something likeYet position does not seem to meet the paper's criterion for something ontic

$$\psi(x)=\sqrt{\delta(x-X)}$$

If you wander what is the square root of the ##\delta##-function, see

https://www.physicsforums.com/threa...luding-dirac-delta.873711/page-2#post-5487662

https://www.physicsforums.com/threa...luding-dirac-delta.873711/page-2#post-5488516

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f you know x=a with certainty

But what if you don't? That's the case the paper appears to be discussing.

They want to determine whether something likeprobability amplitudecan be ontic. So they devise a criterion which can be applied to probability amplitudes. A particle position is not a probability amplitude

But uncertain knowledge of a particle position should be--more precisely, it should be a probability distribution, and the paper's reasoning should apply to it.

- #12

atyy

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But what if you don't? That's the case the paper appears to be discussing.

In their example with energy, one knows the energy exactly.

Actually, I think the original paper introducing this definition gave a clearer motivation, might be worth looking at it: https://arxiv.org/abs/0706.2661 (Fig 2, not Fig 1).

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I think the original paper introducing this definition gave a clearer motivation

I'll take a look.

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