Graduate Is the wavefunction subjective? How?

[DarMM]

I made that point earlier. If I believe that the wave function is $\psi$, then that implies an objective fact. I can come with an observable $\Pi_\psi$ that is guaranteed to give the result +1 if the measurement is performed on a system in state $\psi$. If the result is anything other than +1, that objectively proves that I was wrong to say that the wave function was $\psi$. So to me, that shows that there is something objective about the wave function, if you can be proved wrong about it.

Just to be clear, what's the difference between this and a Bayesian prior $\rho$ with support on a set $A \subset \Omega$ with $\Omega$ the sample space? I could test the random variable $\chi_{A}$, the characteristic function of $A$, and $\rho$ is guaranteed to give $1$ as the response.

i.e. is this anything but Subjective vs Objective Bayesianism without any additional quantum nuances?

 

[bhobba]

The quantum state has a DeFinetti's theorem and other associated subjective Bayesian results, so it's perfectly fine to think of it as subjective.

Exactly - either view - objective or subjective is valid. Have a look at Gleason's Theorem:
http://kiko.fysik.su.se/en/thesis/helena-master.pdf

It shows it exits (providing non-contextuality is assumed) but says nothing about if its just subjective or real.

Thanks
Bill

 

[DarMM]

Exactly - either view - objective or subjective is valid. Have a look at Gleason's Theorem:
http://kiko.fysik.su.se/en/thesis/helena-master.pdf

It shows it exits (providing non-contextuality is assumed) but says nothing about if its just subjective or real.

Thanks
Bill

I think you might like Cabello's work. It's a sort of weakening of the assumptions of Gleason's theorem. Although be warned heavy duty graph theory is involved.

 

[DarMM]

I should say, if you want the "Bird's eye view" of the theorem, a quick run down is as follows.

Gleason assumes two things. That observable quantities are related to each other in a specific form, i.e. the algebra of observables is a C*-algebra and also that the world is such that your probability assignments need not take note of the context within which you make measurements. As you known $P\left(\Pi\right)$, where $\Pi$ is a projector, is the same regardless what observable $A$ you measure to examine $\Pi$.

Cabello however only assumes that the algebra of observables has the weaker property that joint measurability of $A$ and $B$ implies there exists an experiment to measure $A$ that doesn't disturb $B$. This isn't quite as strong as assuming the whole C*-algebra structure, but can be shown to imply it if you want a noncontextual probability assignment.

 

[stevendaryl]

Just to be clear, what's the difference between this and a Bayesian prior $\rho$ with support on a set $A \subset \Omega$ with $\Omega$ the sample space? I could test the random variable $\chi_{A}$, the characteristic function of $A$, and $\rho$ is guaranteed to give $1$ as the response.

i.e. is this anything but Subjective vs Objective Bayesianism without any additional quantum nuances?

Yes, in Bayesian probability, you can be proved objectively wrong if you give an assignment of 0 or 1 to some possibility. So in that sense, Bayesian probability has an objective element to it, which is what is possible and what is not. The exact numbers are subjective.

 

[DarMM]

Yes, in Bayesian probability, you can be proved objectively wrong if you give an assignment of 0 or 1 to some possibility. So in that sense, Bayesian probability has an objective element to it, which is what is possible and what is not. The exact numbers are subjective.

I think the analogy is fairly direct as the pure states of classical probability theory, the point masses, have exactly the property you mentioned, i.e. always having some observable that can determine if they are wrong. Even a large class of mixed states, i.e. mixed states whose support is not the entire sample space, have this property

 

[stevendaryl]

I think the analogy is fairly direct as the pure states of classical probability theory, the point masses, have exactly the property you mentioned, i.e. always having some observable that can determine if they are wrong. Even a large class of mixed states, i.e. mixed states whose support is not the entire sample space, have this property

That's the reason I would say that quantum amplitudes are actually objective. They can always be proved wrong by a single measurement. (In contrast, other than 0 or 1 probabilities, no single observation can prove a Bayesian probability assignment wrong.)

 

[DarMM]

It shows it exits (providing non-contextuality is assumed) but says nothing about if its just subjective or real.

Do you think non-contextuality can be justified via no-signalling? If we made probability assignments that revealed the context and verified them we could know the settings of distant experiments.

 

[DarMM]

That's the reason I would say that quantum amplitudes are actually objective. They can always be proved wrong by a single measurement. (In contrast, other than 0 or 1 probabilities, no single observation can prove a Bayesian probability assignment wrong.)

In Bayesian probability all pure states and a large class of mixed states (those with support on a strict subset) can be proven wrong with a single observation.

 

[stevendaryl]

In Bayesian probability all pure states and a large class of mixed states (those with support on a strict subset) can be proven wrong with a single observation.

Isn't that what I said? (Except I said it in the language of probability 0 and probability 1)

 

[DarMM]

Isn't that what I said? (Except I said it in the language of probability 0 and probability 1)

It's this part:

In contrast, other than 0 or 1 probabilities, no single observation can prove a Bayesian probability assignment wrong

I don't see how that is different from the quantum case or why it is a contrast.

 

[stevendaryl]

I don't see how that is different from the quantum case or why it is a contrast.

Every quantum case corresponds to the perfect knowledge case of Bayesian probability, and the perfect knowledge case of Bayesian probability is objective.

 

[DarMM]

I get that, are you saying there is a difference in the quantum case or not?

All I mean is that there doesn't seem to be anything additional that quantum mechanics adds to the subjective/objective probability debate.

 

[stevendaryl]

I get that, are you saying there is a difference in the quantum case or not?

All I mean is that there doesn't seem to be anything additional that quantum mechanics adds to the subjective/objective probability debate.

I really don't understand what's the difficulty. Bayesian probability becomes objective in the case where all probabilities are either 0 or 1. Quantum mechanics corresponds to this case. So it's objective.

 

[DarMM]

I really don't understand what's the difficulty. Bayesian probability becomes objective in the case where all probabilities are either 0 or 1. Quantum mechanics corresponds to this case. So it's objective.

There's no difficulty. I'm saying that I don't think QM adds anything to the subjective/objective probability debate, i.e. it doesn't have anything new to say about that issue compared to classical probability theory.

 

[stevendaryl]

There's no difficulty. I'm saying that I don't think QM adds anything to the subjective/objective probability debate, i.e. it doesn't have anything new to say about that issue compared to classical probability theory.

And I'm saying that you're wrong. If in classical probability, you only allowed 0 or 1 values for the probability, then probability wouldn't be considered subjective, since disagreements could be objectively resolved. Quantum mechanics is in this situation: Disagreements about the value of the wave function can be objectively resolved.

 

[DarMM]

And I'm saying that you're wrong.

QM does add something to the debate then. What is it?

 

[DarMM]

And I'm saying that you're wrong. If in classical probability, you only allowed 0 or 1 values for the probability, then probability wouldn't be considered subjective

That's not classical probability theory though, that's Boolean logic.

Quantum mechanics is in this situation: Disagreements about the value of the wave function can be objectively resolved.

I don't get it, what is the feature QM has, mathematically, that classical probability lacks that adds something to the subjective/objective probability debate?

 

[stevendaryl]

I don't get it, what is the feature QM has, mathematically, that classical probability lacks that adds something to the subjective/objective probability debate?

I really don't get what it is that you don't get. I've answered the question many times, and I guess to no avail. Quantum wavefunctions are objective, not subjective.

 

[DarMM]

Um. I answered that question several times. I believe that the quantum wave function is objective. If I'm right, then doesn't that resolve the subjective/objective question?

Well obviously if the wave function is objective then it resolves the question.

I'm asking what features are you using that indicate quantum states are objective and classical probability states are not.

Let's look at equivalent states:

1. Pure states. In both cases there are questions that definitively show you are correct or not
2. Somewhat Mixed states. These are states with strict subset support in the classical case and states like $\omega = \frac{1}{2}\left(\omega_1 + \omega_2\right)$ (with $d \geq 3$ of course) in the quantum case. It can be possible to establish one's mixed state is wrong in a single observation.
3. Highly mixed states. Probability measures with support on the whole sample space in the classical case, states like $\mathbb{I}$ in the quantum case. It is not possible to establish you are wrong in one measurement.

To me they seem the same.

 

[DarMM]

In contrast, other than 0 or 1 probabilities, no single observation can prove a Bayesian probability assignment wrong

Basically I think you are comparing quantum pure states with high entropy classical states with some assignment to all outcomes and concluding objectivity. Rather you should compare like with like. All quantum states with all classical states. Then you will see there is no difference.

Bayesian probability assignments which cover the whole sample space are analogous to mixed states in quantum mechanics, thus there is no difference. You shouldn't compare these to pure states.

 

[DarMM]

And I'm saying that you're wrong. If in classical probability, you only allowed 0 or 1 values for the probability, then probability wouldn't be considered subjective, since disagreements could be objectively resolved. Quantum mechanics is in this situation: Disagreements about the value of the wave function can be objectively resolved.

This might be the post to focus on, disagreements about mixed quantum states can't be resolved in one measurement in general, just as classical probability distributions can't be discarded in one measurement in general.

However in both cases, quantum and classical, there is a subset of mixed states (of which pure states are a special case) which can.

Every quantum case corresponds to the perfect knowledge case of Bayesian probability, and the perfect knowledge case of Bayesian probability is objective.

Basically they don't. Quantum pure states correspond to the perfect knowledge case, quantum states in general do not.

 

[bhobba]

Do you think non-contextuality can be justified via no-signalling? If we made probability assignments that revealed the context and verified them we could know the settings of distant experiments.

I think Kochen-Specker basically says that - but a deeper analysis than I am aware of may show there is an out to that one. Personally I find contextuality ugly which is one reason I do not like interpretations that have it. The way these threads often go forces me to emphasize my dislike for something means absolutely nothing - its simply an opinion. Nature could indeed be contextual.

Thanks
Bill

 

[atyy]

And I'm saying that you're wrong. If in classical probability, you only allowed 0 or 1 values for the probability, then probability wouldn't be considered subjective, since disagreements could be objectively resolved. Quantum mechanics is in this situation: Disagreements about the value of the wave function can be objectively resolved.

Only by people who agree on the same objective facts.

 

[Fra]

Only by people who agree on the same objective facts.

And for them to reach such an agreement they must coexist in the same classical background; where the "quantum inquiries" are defined. And there interactions for all practical purposes be classical.

This is clearly a scenario that does not cover general cases of inside observers, so this stance will not be viable in the QG or unification realm I would say.

/Fredrik

 

[zonde]

Only by people who agree on the same objective facts.

And for them to reach such an agreement they must coexist in the same classical background; where the "quantum inquiries" are defined. And there interactions for all practical purposes be classical.

This is clearly a scenario that does not cover general cases of inside observers, so this stance will not be viable in the QG or unification realm I would say.

/Fredrik

People agreeing on objective facts is basic requirement for doing science. You can not relax this stance and still pretend that your philosophy has something to do with science.

 

[DarMM]

People agreeing on objective facts is basic requirement for doing science. You can not relax this stance and still pretend that your philosophy has something to do with science.

I think what they mean is given a cut, or what Healey calls "the physical situation of the agent", there is a best wavefunction.

In other words given what you currently know there is a "best" wavefunction you should be using like Objective Bayesianism. However agents in two different physical situations (i.e. one will have witnessed a different set of events) won't have the exact same quantum state. Just like Classical Probability Theory.

 

[Fra]

People agreeing on objective facts is basic requirement for doing science. You can not relax this stance and still pretend that your philosophy has something to do with science.

If we are literally speaking of "people" or scientists, they all coexist on the same classical background, and can fapp communicate and compare their observations classically - this is of course not where the problem lies.

"People" here is a metaphor for a information processing agent - a generalisation of an observer - but one that is not necessarily "classical".

Quantum mechanics as it stands relies on a classical background and classical measurement device to be defined. This was i think understood by many of the founders of QM, but often misinterpreted to somehow involve humans or "minds".

We do not need to make the same mistake again. The above paradigm is IMO not making sense in QG, unification attempts or cosmological models. So we desperately NEED to reconstruct a measurement theory, in terms of a non-classical observer. Observers that moreoever is interacting with other observers. The correspondence is that we must recover regular QM and QFT in the appropriate limit of a dominant classical lab frame observer observing a small subsystem.

But we still lack the framework to describe this. But one trait of such a framework is indeed that effective truth values are not necessarily objective. But we should not interpret this as the breakdown of effective human science, i think it rather deepens our understanding to see how "objectivity" can emergent, from a chaotic starting point. That BIG difference is that in this paradigm, the objectivity are NOT hard god given mathematical constraints that need no explanation.

/Fredrik

 

[zonde]

But we should not interpret this as the breakdown of effective human science, i think it rather deepens our understanding to see how "objectivity" can emergent, from a chaotic starting point.

Absence of "objectivity" is subjectivity not chaos. But for any "objectivity" to emerge we need fapp objective communication channels to compare our subjective observations. So we have to assume at least some objectivity to start talking about emergence of "objectivity". This makes your idea about emergent "objectivity" circular.

 

[Fra]

Absence of "objectivity" is subjectivity not chaos. But for any "objectivity" to emerge we need fapp objective communication channels to compare our subjective observations. So we have to assume at least some objectivity to start talking about emergence of "objectivity". This makes your idea about emergent "objectivity" circular.

Yes the subjectivity is the unavoidable observer choice but this is really something you can not escape unless you engage in ontological fantasy. I require that ontologies are the result of a physical inference process, otherwise it is to me metaphysics.

Any comparasiom between two subjective views takes a third perspective. And comparasions are necessarily physical interactions.

This is a chicken and egg situation but circular is i think a bad an inappropriate descriptor as it sounds like a deadlock which it ia not.

I call i evolving. Evolving means progress and revision is made on each comparasion rather than contradictions. Agents that don't revise and negotiate will not be stable and thus not be abundant in nature.

/Fredrik