I Determinism, realism, hidden variables

[stevendaryl]

There has been some confusion about what, exactly, "realism" means. To me, a theory is realistic if it describes the evolution of the state of the world or the relevant part of it (that at least works nonrelativistically--I'll have to think about what a realistic relativistic theory is like). That's independent of the question of whether the laws are deterministic or not. A theory might describe the world as a nondeterministic automaton, and I would consider that a realistic theory. But a probabilistic theory usually is not realistic in my sense. A probability distribution is not a fact about the world, but is a fact about our imperfect knowledge about the world.

I would say that QM as it is usually presented is not a realistic theory. The wave function does not give the state of the world, but gives probabilities for future measurements. So it captures our uncertainty about the world, but in a different way than classical probability distributions do.

 

[Derek Potter]

There has been some confusion about what, exactly, "realism" means. To me, a theory is realistic if it describes the evolution of the state of the world or the relevant part of it (that at least works nonrelativistically--I'll have to think about what a realistic relativistic theory is like). That's independent of the question of whether the laws are deterministic or not. A theory might describe the world as a nondeterministic automaton, and I would consider that a realistic theory. But a probabilistic theory usually is not realistic in my sense. A probability distribution is not a fact about the world, but is a fact about our imperfect knowledge about the world.

I would say that QM as it is usually presented is not a realistic theory. The wave function does not give the state of the world, but gives probabilities for future measurements. So it captures our uncertainty about the world, but in a different way than classical probability distributions do.

If the WF does not give the state of the world, how come QM makes successful predictions at all?

 

[Paul Colby]

Sorry, a realist explanation Z, QM is definitely not. I'm sorry if I imply it. I'm very much in the non-realist camp because all the experimental evidence fails to support it. Realism actually appears not-logical from such a world view.

 

[DrChinese]

So anti-realism is to say that there is no explanation possible whether quantum or not. ... (Yes I know each term here needs to be defined carefully but I think we've settled on the meanings by now.)

Non-realism can be explained as follows (in one version): Reality is observer dependent (dependent on the "process of measurement") if QM is complete (and locality holds). This was the EPR result (which they rejected because they thought that QM was not complete). Their early definition of non-realism stated (in bold with related context):

"One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the system in any way. No reasonable definition of reality could be expected to permit this."

 

[stevendaryl]

If the WF does not give the state of the world, how come QM makes successful predictions at all?

My definition of "realistic" doesn't imply that a non-realistic theory cannot make successful predictions. That's why I gave the example of classical probability theory. That can give successful predictions (if probabilistic) even though the probability distribution is not taken as a state of the world.

The question of how you can have a non-realistic theory that doesn't have an underlying realistic theory is one that I don't have an answer to.

 

[morrobay]

The question of how you can have a non-realistic theory that doesn't have an underlying realistic theory is one that I don't have an answer to.

That would be a description of non realism only in terms of physics. An explanation of the physical
mechanisms that produce the predicted outcomes. So QM is incomplete then.

 

[naima]

There are different kinds of locality, and people should distinguish them. The two most important kinds are signal locality and Bell locality. QFT obeys signal locality, but not Bell locality. In other words, you are both right and both wrong. Or more correctly, you are both vague unless you specify what kind of locality you have in mind.

This may be an answer to a question i asked without any answer.
I recall it.
Bell writes that $P(a,b,\lambda) = P(a,\lambda) P(b,\lambda)$
is the locality condition.
A forumer wrote that the locality condition was about the past light cones of the detection devices. He only said that the two points of view were equivalent. I had doubts because C is not in the formula.

 

[Derek Potter]

Non-realism can be explained as follows (in one version): Reality is observer dependent (dependent on the "process of measurement") if QM is complete (and locality holds). This was the EPR result (which they rejected because they thought that QM was not complete). Their early definition of non-realism stated (in bold with related context):

"One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the system in any way. No reasonable definition of reality could be expected to permit this."

Well, that's not a definition of reality, it's a rejection of the predictability criterion because it implies observer-dependent reality, which E P and R regard as absurd. I've spent a few hours chopping logic with myself but I'm still not sure where you wanted to go with this.

 

[stevendaryl]

This may be an answer to a question i asked without any answer.
I recall it.
Bell writes that $P(a,b,\lambda) = P(a,\lambda) P(b,\lambda)$
is the locality condition.
A forumer wrote that the locality condition was about the past light cones of the detection devices. He only said that the two points of view were equivalent. I had doubts because C is not in the formula.

By "C", do you mean the speed of light? It's there, implicitly. \lambda represents any facts about the intersection of the backwards lightcones of the two measurement events. The factorization only makes sense if the measurements are spacelike separated.

 

[stevendaryl]

If the WF does not give the state of the world, how come QM makes successful predictions at all?

Here's another issue about the wave function being realistic or not. Technically, the wave function is not a function on space, but is a function on configuration space. So to me, that means that it can't be a physical field in the sense that the electromagnetic field is classically. Of course, it could be that "the world" actually is a point in Hilbert space, and the three dimensions is an emergent property of the world, rather than being fundamental.

 

[stevendaryl]

Well, that's not a definition of reality, it's a rejection of the predictability criterion because it implies observer-dependent reality, which E P and R regard as absurd. I've spent a few hours chopping logic with myself but I'm still not sure where you wanted to go with this.

I don't know what you mean by "a rejection of the predictability criterion". E P and R were saying that being able to predict something with certainty (without disturbing it) DID imply the existence of a corresponding element of reality. What they were rejecting was the idea that what's real for Bob should be affected by what Alice decides to measure.

A little more about the last statement. Assume that we have a source of anti-correlated electron/positron pairs. Assume that in Alice's rest frame, her measurement takes place slightly before Bob's. So Alice measures spin-up in the z-direction. Afterward, she knows with certainty that Bob will measure spin-down in the z-direction. So the property of being definitely spin-down in the z-direction is for Einstein et. al. an "element of reality". Bob's particle definitely has that property. But if Alice had instead measured spin in the x-direction, she would have concluded that Bob's particle has a definite spin in x-direction. In general, no matter what direction Alice decides to measure spin, she would conclude that Bob's particle has a definite value for spin in that direction. So either Bob's particle's properties depend on Alice's choices (which is the possibility that E P and R are rejecting) or Bob's particle had those properties before Alice performed her measurement, and maybe even before she decided what measurement to perform.

 

[Derek Potter]

That would be a description of non realism only in terms of physics. An explanation of the physical
mechanisms that produce the predicted outcomes. So QM is incomplete then.

Only if you regard the formalism as the whole of the subject. It's interesting that QM hangs on so few postulates. However the postulates are not tautological, so if QM refers to anything at all, there must be something that chugs away to produce the structure. In that sense it's incomplete as we don't know how to describe this "something." But as a self-contained theory which happens not to have anything to say about why (or even whether) its own postulates are true, it is complete.

Beware - the term incomplete is dangerous. EPR use it to mean that quantum theory is actually inconsistent and needs more structure to make it work properly. They were wrong of course, but it is another meaning of incomplete and you need to be clear about which sense you are using the word in.

 

[stevendaryl]

Only if you regard the formalism as the whole of the subject. It's interesting that QM hangs on so few postulates. However the postulates are not tautological, so if QM refers to anything at all, there must be something that chugs away to produce the structure. In that sense it's incomplete as we don't know how to describe this "something." But as a self-contained theory which happens not to have anything to say about why (or even whether) its own postulates are true, it is complete.

I don't think that the standard formulation of QM is complete. The standard formulation makes a distinction between two different types of phenomena:

1. Unobserved phenomena, which is described by a wave function (or density matrix) that evolves smoothly and deterministically according to the Schrodinger equation.
2. Measurement phenomena, where a measurement nondeterministically produces an eigenvalue of the quantity being measured.

To be complete, I would think you would need to have a unified theory that describes measurement as a special case of an interaction, and the fact that it always results in an eigenvalue should be derivable. Without such a unification, QM requires an artificial split between ordinary systems and measurement devices without concrete rules for how to decide on the split.

As a rule of thumb, I use that a measurement is an amplification process resulting in a persistent macroscopic record that corresponds to the microscopic quantity being measured. But that's a fuzzy criterion, and QM doesn't at all suggest how to make it more precise.

Maybe something along the lines of Many-Worlds or Consistent Histories might succeed in describing QM as a complete theory, but I don't think that the standard formulation does.

 

[stevendaryl]

Beware - the term incomplete is dangerous. EPR use it to mean that quantum theory is actually inconsistent and needs more structure to make it work properly.

No, I don't think they were suggesting that it was inconsistent. They thought that it was an effective theory that would be explained in terms of something more fundamental, in the same way that thermodynamics can be explained in terms of the statistical properties of huge numbers of particles.

 

[Derek Potter]

I don't know what you mean by "a rejection of the predictability criterion". E P and R were saying that being able to predict something with certainty (without disturbing it) DID imply the existence of a corresponding element of reality.

Not in the passage that Dr Chinese quoted, they weren't. They were refuting the suggestion that whatever criterion they were using was not restrictive enough. So they made a more restrictive one and demolished it by reductio ad absurdum. Note that they say "only if". That makes it a necessary condition. The difference may very well be that their lax criterion was simply sufficient, but what they are rejecting was the idea that predictability is necessary. Predictability indicating an element of reality (a sufficient condition) is perfectly sensible and I am sure that EPR use exactly that criterion. But as sufficient, not as necessary.

What they were rejecting was the idea that what's real for Bob should be affected by what Alice decides to measure.

A little more about the last statement. Assume that we have a source of anti-correlated electron/positron pairs. Assume that in Alice's rest frame, her measurement takes place slightly before Bob's. So Alice measures spin-up in the z-direction. Afterward, she knows with certainty that Bob will measure spin-down in the z-direction. So the property of being definitely spin-down in the z-direction is for Einstein et. al. an "element of reality". Bob's particle definitely has that property. But if Alice had instead measured spin in the x-direction, she would have concluded that Bob's particle has a definite spin in x-direction. In general, no matter what direction Alice decides to measure spin, she would conclude that Bob's particle has a definite value for spin in that direction. So either Bob's particle's properties depend on Alice's choices (which is the possibility that E P and R are rejecting) or Bob's particle had those properties before Alice performed her measurement, and maybe even before she decided what measurement to perform.

Yes, absolutely. That's my argument too.

 

[Derek Potter]

I don't think that the standard formulation of QM is complete. The standard formulation makes a distinction between two different types of phenomena:

1. Unobserved phenomena, which is described by a wave function (or density matrix) that evolves smoothly and deterministically according to the Schrodinger equation.
2. Measurement phenomena, where a measurement nondeterministically produces an eigenvalue of the quantity being measured.

To be complete, I would think you would need to have a unified theory that describes measurement as a special case of an interaction, and the fact that it always results in an eigenvalue should be derivable. Without such a unification, QM requires an artificial split between ordinary systems and measurement devices without concrete rules for how to decide on the split.

As a rule of thumb, I use that a measurement is an amplification process resulting in a persistent macroscopic record that corresponds to the microscopic quantity being measured. But that's a fuzzy criterion, and QM doesn't at all suggest how to make it more precise.

Maybe something along the lines of Many-Worlds or Consistent Histories might succeed in describing QM as a complete theory, but I don't think that the standard formulation does.

I understood that MW does exactly that on every count (well it claims to) and that it doesn't add anything to QM except to revise the second case:

1. Unobserved phenomena, which is described by a wave function (or density matrix) that evolves smoothly and deterministically according to the Schrodinger equation.
2. none

But in view of the prevailing view it may be necessary to explain - not to postulate - that:

2. Measurement phenomena deterministically produce entanglements, in each component of which the state of the system is an eigenstate of the observation (because we choose to decompose the state in this basis) and the state of the observer is consistent with the state of the system (because it has just interacted with it) and therefore with the eigenvalue (which is presumably basic QM theory - ?)

So MW is not standard QM. It is standard QM without asserting a unique eigenvalue (and by implication a collapse of the state).

 

[Derek Potter]

No, I don't think they were suggesting that it was inconsistent. They thought that it was an effective theory that would be explained in terms of something more fundamental, in the same way that thermodynamics can be explained in terms of the statistical properties of huge numbers of particles.

Oh well I've always heard they concocted the EPR scenario explicitly to show that QM contradicted itself. It allows simultaneous measurement of position and momentum which is contrary to HUP.

 

[stevendaryl]

Oh well I've always heard they concocted the EPR scenario explicitly to show that QM contradicted itself. It allows simultaneous measurement of position and momentum which is contrary to HUP.

I don't think of the uncertainty principle as a fundamental axiom of QM. It's a rule of thumb. For precise predictions from QM, you don't use the uncertainty principle, you use Schrodinger's equation.

 

[DrChinese]

Well, that's not a definition of reality, it's a rejection of the predictability criterion because it implies observer-dependent reality, which E P and R regard as absurd. I've spent a few hours chopping logic with myself but I'm still not sure where you wanted to go with this.

EPR also thought the idea of FTL action was absurd. But they do define the non-realistic view, then reject it. Their rejection, of course, is simply on aesthetic grounds - and is not otherwise sound.

So where I am going is simple: A non-realistic interpretation essentially is one in which the uncertainty principle (and observer dependence) is more literal and fundamental. In MWI, the worlds split according to an observer's choice of measurements, for example. In other interpretations, the observer is part of the complete system (context) as well. So reality is not objective (observer independent).

 

[Derek Potter]

EPR also thought the idea of FTL action was absurd. But they do define the non-realistic view, then reject it. Their rejection, of course, is simply on aesthetic grounds - and is not otherwise sound.

So where I am going is simple: A non-realistic interpretation essentially is one in which the uncertainty principle (and observer dependence) is more literal and fundamental. In MWI, the worlds split according to an observer's choice of measurements, for example. In other interpretations, the observer is part of the complete system (context) as well. So reality is not objective (observer independent).

Yes, I'm learning that what people mean by MWI varies according to whom you ask. I suppose that's a sort of observer dependence... But seriously I have always thought of worlds splitting as a fanciful metaphor for relative states. And relative states exist between any two subsytems whether one of them is an observer or not. And they exist in every basis without there necessarily being an interaction to define a particular one. I believe that as an interpretation of the Born Rule/ Collapse postulate (i.e. get rid of it) relative states do the job. Actual worlds splitting - the emergence of a preferred basis etc during measurement is not interpretational, it's just relative states applied to a complicated situation. Would you agree?

However to say that the state of A only exists relative to B does not seem, to me, to mean that reality is observer-dependent. It means that reality is a superposition. I'd use a classical analogy - the outcome of tossing a coin is not usually observer-dependent because typically two observers look at the coin from the same side. But if a coin were spun and made to come to rest in a vertical plane between two observers, they would see opposite faces. Does that mean the observed outcome is observer-dependent? I'd say yes it does. But does that mean reality is observer-dependent? Surely not! To make such a claim you would have to equate reality with the observed outcome. Why would anyone do that knowing the nature of coins? So why do they do it knowing the nature of quantum superposition?

 

[DrChinese]

I'd use a classical analogy - the outcome of tossing a coin is not usually observer-dependent because typically two observers look at the coin from the same side. But if a coin were spun and made to come to rest in a vertical plane between two observers, they would see opposite faces. Does that mean the observed outcome is observer-dependent? I'd say yes it does. But does that mean reality is observer-dependent? Surely not! To make such a claim you would have to equate reality with the observed outcome. Why would anyone do that knowing the nature of coins? So why do they do it knowing the nature of quantum superposition?

Precisely because the quantum world is not the classical world. There are an infinite number of choices of how the observers measure the quantum coins. By Bell, we know that the observations cannot be locally predetermined as in the classical case (and as EPR expected). So there is plenty of reason to reject classical realism. Or locality if you prefer.

I do not believe in observer independence (objective realism) regardless. There is no meaning to counterfactual measurements, a view I believe most Bohmians share. That is a rejection of the EPR viewpoint regarding elements of reality.

 

[dlgoff]

I do not believe in observer independence (objective realism) regardless.

Not to be speculative, but could there be some sort of mathematical step function where this could be possible for some quantum states? Thinking of Wojciech H. Zurek's pointer states here.

 

[naima]

implicitly. \lambda represents any facts about the intersection of the backwards lightcones of the two measurement events.

You can say that it is implicit if somewhere else Bell wrote it explicitly.
Where?

 

[Derek Potter]

I do not believe in observer independence (objective realism) regardless.

Yes, well that's the point, isn't it? You do not "believe in" objective realism. But you cannot justify that non-belief from Bell. It is perfectly possible to construct a theory which asserts an observer-independent reality but predicts observer-dependent observations of the quantum kind. You don't have to look very far to find one.

 

[naima]

It is perfectly possible to construct a theory which asserts an observer-independent reality

Is it what you "believe"? how would you write this reality mathematically? equality, inequality, with another relation?

 

[stevendaryl]

You can say that it is implicit if somewhere else Bell wrote it explicitly.
Where?

In "Speakable and Unspeakable in Quantum Mechanics", Bell has an essay called "Theory of Local Beables", where he expands on the idea.

 

[Markus Hanke]

To be complete, I would think you would need to have a unified theory that describes measurement as a special case of an interaction, and the fact that it always results in an eigenvalue should be derivable.

Does the act of "measurement" not produce an entanglement relationship between aspects of the system, and the measurement apparatus ? Shouldn't this count as an "interaction" ?

 

[naima]

In "Speakable and Unspeakable in Quantum Mechanics", Bell has an essay called "Theory of Local Beables", where he expands on the idea.

And i will have to spend
45 dollars on Amazon to verify what you said.

 

[Jilang]

Here it is
http://cds.cern.ch/record/980036/files/197508125.pdf

 

[naima]

Thank you for the link