Hi Bob,

Thanks for your further comments!

I agree with you. It is just the meanings of words that differ between us. The “reality of the wavefunction” is usually understood as “the wavefunction applies to a single system” (e.g. in the PBR theorem).

As you have seen from my previous posts, my interpretation in terms of RDM of particles indeed…[Read more]

For example, in his scheme, one get many inaccurate expectation values, from which the right one can only be constructed (which is very like the standard tomography based on projective measurements). But in a PM, one directly get the right expectation value with arbitrary accuracy.

Hi Max,

Thanks for your comments! I think you will agree that Matt’s scheme is not a PM. Right?

Shan

Hi Matt L.,

I’m hope I’m not joining this conversation too late. Regarding your comment in #1094:

The issue is that the protection is repreparing the system in an independent copy of the initial state, so you effectively have an ensemble of independent copies which you are measuring.

This way of describing the protection seems specific to the…[Read more]

Dear Ruediger,

Thank you for your patience and helpful answers!

Best,
Ulrich

[Duplicate post was here]

Shan #1089,

Getting inaccurate expectation values is something that may or may not happen to Bob. Charlie just sits there doing projective measurements in a fixed basis over and over again, right?

Regards,
Matt

Dear Shan,

It seems to me that your argument is somehow getting weaker as time progresses. It is not the reality of the wavefunction that you want to argue for, but rather that the wavefunction applies to a single system, and if you buy Matt’s analogy, the wavefunction tells us something about statistical properties of the motion of the system.…[Read more]

Hi Bob and Matt,

Thanks again for your very helpful discussions! I think both of you may be sympathy with my interpretation of the wave function in terms of random discontinuous motion of particles (see http://philsci-archive.pitt.edu/10659/), as you already presented similar examples.

I will catch a bus now. Your later comments and criticisms…[Read more]

Hi Shan,

As the other Matt has already mentioned, the existence of psi-epistemic models of protective measurement makes your argument difficult to swallow. But let me focus here on two more specific questions here:

1) Why couldn’t somebody also run your argument using the tomography-of-protector then projective measurement-of-system scheme?

2)…[Read more]

Hi Bob,

Thanks for your further comments!

I think the point is that people usually believe that a wave function ONLY describes an ensemble, but if the psi-ontic view is right, a wave function also describes a SINGLE system. This is new. Certainly, a wave function can still describe an ensemble.

Shan

Matt #1094:

In my picture of random motion of particles, it seems that we may say that classical probability distributions are also properties of individual systems. The word “classical” is in the sense of an ergodic, random motion of individual particles.

Shan

I agree with most of your analyses in your ergodic motion example.

In my interpretation of the wave function in terms of random motion of particles, what PM measures is indeed a probability distribution, such as the position probability density of a particle. But this probability density describes the single particle, not an ensemble. This…[Read more]

Following up a bit on Matt Leifer’s comment in #1094. I myself find it very helpful to think of the sample space (or state space) of a Markov chain of length n, in which there are, let us say, just 6 possibilities at each time step, as the same thing as the sample space for a collection of n dice all rolled at once, except that you have to…[Read more]

Dear Matt,

Thanks for your very helpful criticisms!

I am not familiar with the equivalence between quantum mechanics and classical Liouville mechanics. But I think this equivalence will not imply the physical interpretations of these two theories must be the same; otherwise will already has a classical int. of QM. (Moreover, I think your…[Read more]

Dear Bob,

Thanks for your very helpful comments!

Yes, I agree that PMs can also measures <P_j>. My point is that these measured quantities describe a single quantum system, and not just an usual probability distribution in QM. The latter interpretation depends on what happens during a conventional measurement.

As to the second comment, I would…[Read more]

One big objection to your argument is that, if true, it would imply that classical probability distributions are also properties of individual systems. The reason is that we can do the whole protective measurement scheme for Gaussian states using only Gaussian operations. Quantum mechanics with only Gaussian states and operations is equivalent…[Read more]

Resend. I think I inserted some symbols which gave the computer indigestion; let me try again.

Dear Shan,
A couple of comments. First on your reply #1087 to Ken.
If PMs can measure expectation values of observables, they can presumably also measure the probability distribution of an observable as well as its average Avg(). Thus if observable A…[Read more]

Dear Shan,

A couple of comments. First on your reply #1087 to Ken. If PMs can measure excpectation values of observables, they can presumably also measure the probability distribution of an observable as well as its average. Thus if observable A has a spectral decomposition A = a_1 P_1 + _2 P_2 + a_3 P_3, where I = P_1 + P_2 + P_3 is the…[Read more]

I should clarify one point for my argument. My argument, if valid, only says that the wave function describes certain state or property of a single quantum system, and it does not imply that the wave function itself is real, e.g. the wave function describes a continuous field a la Albert.

What physical state or property the wave function…[Read more]