A Effective Dynamics of Open Quantum Systems: Stochastic vs Unitary Models

[A. Neumaier]

Why do classical objects such as cats or pointers have approximately definite positions (and approximately definite momenta, etc.)?

This is answered by the law of large numbers and statistical mechanics. It is very well-known that the standard deviations of all macroscopic variables of interest in physics scale like $O(N^{-1/2})$, where $N$ is the conserved number of particles involved, and the mean number if there is no conservation. Metastability answers why in the case of a binary measurement one of these actually comes out.

All of this is completely unrelated to MWI.

 

[stevendaryl]

This is answered by the law of large numbers and statistical mechanics. It is very well-known that the standard deviations of all macroscopic variables of interest in physics scale like $O(N^{-1/2})$, where $N$ is the conserved number of particles involved, and the mean number if there is no conservation. Metastability answers why in the case of a binary measurement one of these actually comes out.

All of this is completely unrelated to MWI.

No, I think you're completely wrong about both paragraphs above. Metastability has nothing to do with it. [edit] I shouldn't say nothing, but it doesn't explain definite outcomes. I think you're completely wrong about this.

 

[stevendaryl]

No, I think you're completely wrong about both paragraphs above. Metastability has nothing to do with it. [edit] I shouldn't say nothing, but it doesn't explain definite outcomes. I think you're completely wrong about this.

An example of a metastable system might be a lattice of 1000 magnetic dipoles. They tend to line up; the state with all dipoles pointing in the same direction is lower energy than the state with them pointing in different directions. So if you start with an unmagnetized state (the dipoles pointing in all sorts of different directions), then a small perturbation will likely result in most dipoles pointing in the same direction. But that does not mean that you can't have a superposition of one state with all dipoles pointing up, and another state with all dipoles pointing down. If you started in such a superposition, it would not ever evolve into a state with all pointing one way, or all pointing the other way. If the initial state is symmetric under parity, then the final state will be.

I know what you're going to say: Couple it to an environment--a thermal bath of some sort. But I think that that would not make any difference. The same argument holds: If the thermal bath + lattice is initially symmetric under parity, then it will never evolve into a state that is not symmetric. It will never evolve into a state with a nonzero magnetic moment. Metastability just does not explain definite outcomes.

 

[A. Neumaier]

I think you're completely wrong about this.

I cannot argue about your subjective beliefs.

But what I stated is the reason why practitioners of QM don't feel a need to investigate the foundations of quantum mechanics, except in as far as there are challenging experiments to perform. It is very clear to them that statistical mechanics explains the gradual emergence of classicality, due to the law of large numbers to an ever increasing accuracy as the object size grows, and that the quantum dynamics morphs as gradually to classical dynamics. There are even all sorts of intermediate stages modeled by quantum-classical dynamics, used a lot in situations where the quantum regime is important for some degrees of freedom but not for others. Thus there is a continuum from the fully quantum to the fully classical, and the only role of observers is to select from this spectrum the model that is most tractable computationally given a desired resolution.

A measurement problem arises only if one ignores all this and insists on the rigid, far too idealized framework in which quantum mechanics was introduced historically and is typically introduced in textbooks.

 

[Mentz114]

An example of a metastable system might be a lattice of 1000 magnetic dipoles. They tend to line up; the state with all dipoles pointing in the same direction is lower energy than the state with them pointing in different directions. So if you start with an unmagnetized state (the dipoles pointing in all sorts of different directions), then a small perturbation will likely result in most dipoles pointing in the same direction. But that does not mean that you can't have a superposition of one state with all dipoles pointing up, and another state with all dipoles pointing down. If you started in such a superposition, it would not ever evolve into a state with all pointing one way, or all pointing the other way. If the initial state is symmetric under parity, then the final state will be.

I know what you're going to say: Couple it to an environment--a thermal bath of some sort. But I think that that would not make any difference. The same argument holds: If the thermal bath + lattice is initially symmetric under parity, then it will never evolve into a state that is not symmetric. It will never evolve into a state with a nonzero magnetic moment. Metastability just does not explain definite outcomes.

A small enough collection of dipoles ( eg quantum magnetic dot) may be in a superposition, but if the object was large enough then at some point it becomes fixed and irreversibly in one outcome. What else could possibly happen ? Your argument is based on Platonic ideals. "Every quantum state has fluctuations" - Ballentine ( says it twice actually)

 

[atyy]

I cannot argue about your subjective beliefs.

But what I stated is the reason why practitioners of QM don't feel a need to investigate the foundations of quantum mechanics, except in as far there are challenging experiments to perform. It is very clear to them that statistical mechanics explains the gradual emergence of classicality, due to the law of large numbers to an ever increasing accuracy as the object size grows, and that the quantum dynamics morphs as gradually to classical dynamics. There are even all sorts of intermediate stages modeled by quantum-classical dynamics, used a lot in situations where the quantum regime is important for some degrees of freedom but not for others. Thus there is a continuum from the fully quantum to the fully classical, and the only role of observers is to select from this spectrum the model that is most tractable computationally given a desired resolution.

A measurement problem arises only if one ignores all this and insists on the rigid, far too idealized framework in which quantum mechanics was introduced historically and is typically introduced in textbooks.

Landau, Dirac, Bell, Adler, Weinberg, Haroche, Raimond, Laloe, Susskind, Zurek, Zeilinger, Hartle, Gell-Mann - are these not practioners of quantum mechanics?

 

[A. Neumaier]

Landau, Dirac, Bell, Adler, Weinberg, Haroche, Raimond, Laloe, Susskind, Zurek, Zeilinger, Hartle, Gell-Mann - are these not practitioners of quantum mechanics?

Who of these thinks that there is an unsolved measurement problem? The unsolved problems Landau, Dirac, and Weinberg are concerned about are the problematic mathematical basis of relativistic quantum field theory, not the measurement problem.

 

[stevendaryl]

If the initial state is symmetric under parity, then the final state will be.

A small enough collection of dipoles ( eg quantum magnetic dot) may be in a mixed starte, but if the object was large enough then at some point it becomes fixed and irreversibly in one outcome. What else could possibly happen ? Your argument is based on Platonic ideals. "Every quantum state has fluctuations" - Ballentine ( says it twice actually)

I think you're completely wrong about that. The evolution of the wave function is linear. So if initial state I_1 leads to final state F_1, and initial state I_2 leads to final state F_2, then the superposition of I_1 and I_2 will lead to a superposition of F_1 and F_2. It will not lead to a random pick between F_1 and F_2. The same thing is true if you want to do density matrices.

Metastability cannot explain definite outcomes.

I have no idea what you mean by my argument being based on "Platonic ideals". It's based on quantum mechanics.

 

[stevendaryl]

I cannot argue about your subjective beliefs.

Then let me put it more strongly: You are wrong about this.

 

[A. Neumaier]

The evolution of the wave function is linear.

The evolution of the Fokker-Planck equation is also linear. Nevertheless it describes classical nonlinear stochastic processes.

 

[Mentz114]

I think you're completely wrong about that. The evolution of the wave function is linear. So if initial state I_1 leads to final state F_1, and initial state I_2 leads to final state F_2, then the superposition of I_1 and I_2 will lead to a superposition of F_1 and F_2. It will not lead to a random pick between F_1 and F_2. The same thing is true if you want to do density matrices.

Metastability cannot explain definite outcomes.

Linear evolution is your Platonic ideal. It can only exist in very small highly-isolated systems. It only takes energy to leak out to make the sub-system non-conservative and lose normalization. This will drive a stochastic process to a definate result.

We must agree to disagree about this.

 

[A. Neumaier]

Then let me put it more strongly: You are wrong about this.

I cannot argue about your subjective beliefs. Repeating variations on them doesn't improve the situation.

 

[atyy]

Who of these thinks that there is an unsolved measurement problem? The unsolved problems Landau, Dirac, and Weinberg are concerned about are the problematic mathematical basis of relativistic quantum field theory, not the measurement problem.

All believed there was an unsolved measurement problem (eg. Dirac, Weinberg) or that a classical/quantum cut is needed (eg. Landau).

 

[A. Neumaier]

that a classical/quantum cut is needed

The cut is just the decision at which description level the quantum corrections (that decay like $O(N^{-1/2})$) can be neglected. It is not a bigger problem than the problem of whether or not to include into the classical description of a pendulum the surrounding air and the way it is suspended, or whether taking it into account with a damping term is enough.

 

[atyy]

The cut is just the decision at which description level the quantum corrections (that decay like $O(N^{-1/2})$) can be neglected. It is not a bigger problem than the problem of whether or not to include into the classical description of a pendulum the surrounding air and the way it is suspended, or whether taking it into account with a damping term is enough.

Not in Landau's view.

 

[georgir]

Linear evolution is your Platonic ideal. It can only exist in very small highly-isolated systems. It only takes energy to leak out to make the sub-system non-conservative and lose normalization. This will drive a stochastic process to a definate result.

We must agree to disagree about this.

What if you look at the whole universe? Where does energy leak out to?

 

[A. Neumaier]

Not in Landau's view.

In Volume IX (Statistical physics, Part 2) of their treatise on theoretical physics, Landau and Lifshits derive the hydrodynamic equations without needing any cut. The cut is mentioned only in the introduction to quantum mechanics and nowhere used - thus recognizable as a purely pedagogical device.

 

[georgir]

The cut is just the decision at which description level the quantum corrections (that decay like $O(N^{-1/2})$) can be neglected. It is not a bigger problem than the problem of whether or not to include into the classical description of a pendulum the surrounding air and the way it is suspended, or whether taking it into account with a damping term is enough.

The air surrounding the pendulum works to disrupt the macroscopic behavior I expect to observe, not to actually explain it. So I'm not finding this comparison fair or convincing.

 

[Mentz114]

What if you look at the whole universe? Where does energy leak out to?

The whole universe only has one possible outcome

I assume you're joking.

 

[georgir]

The whole universe only has one possible outcome

I assume you're joking.

I'm not sure if you are now. The whole point of MWI etc is many possible outcomes. Or you could call it one, but it could still be a superposition of steven both in Seattle and in New York.

 

[atyy]

In Volume IX (Statistical physics, Part 2) of their treatise on theoretical physics, Landau and Lifshits derive the hydrodynamic equations without needing any cut. The cut is mentioned only in the introduction to quantum mechanics and nowhere used - thus recognizable as a purely pedagogical device.

Sorry, I cannot agree. You, vanhees71, Ballentine, and Peres are wrong.

 

[A. Neumaier]

The air surrounding the pendulum works to disrupt the macroscopic behavior I expect to observe, not to actually explain it. So I'm not finding this comparison fair or convincing.

In both cases, the explanation is in the derivation of the approximations. One needs the surrounding to explain why the pendulum is damped (as observed) rather than ideal (as the ideal Hamiltonian dynamics would suggest). Notice the complete similarity with the collapse (observed in a continuous measurement) rather than the unitary evolution (as the ideal Hamiltonian dynamics would suggest).

 

[A. Neumaier]

Sorry, I cannot agree. You, vanhees71, Ballentine, and Peres are wrong.

I cannot argue about your subjective beliefs. As stevendaryl, you simply call wrong what differs from your preferences.

 

[atyy]

I cannot argue about your subjective beliefs. As stevendaryl, you simply call wrong what differs from your preferences.

You are wrong because your thermal interpretation contradicts Bell's theorem.

 

[Mentz114]

I'm not sure if you are now. The whole point of MWI etc is many possible outcomes. Or you could call it one, but it could still be a superposition of steven both in Seattle and in New York.

Why invoke MWI when a much simpler explanation is available ?

There is no measurement problem. People make measurements and get results. The only quibble is from those who insist that something weird an inexplicable is happening. Maybe they have a need for spookiness.

(I am not being disparaging. I respect other people's freedom to hold any views they wish to)

 

[A. Neumaier]

your thermal interpretation contradicts Bell's theorem.

?
Bell's theorem is a theorem about classical local hidden variable theories.
How can it possibly contradict an interpretation of quantum mechanics?

 

[georgir]

Why invoke MWI when a much simpler explanation is available ?

Because I sort of understand the idealized model but do not yet understand your "much simpler" explanation?
[Though I prefer you to be right instead of MW or other models that allow macroscopic superposition]

 

[Mentz114]

Because I sort of understand the idealized model but do not yet understand your "much simpler" explanation?
[Though I prefer you to be right instead of MW or other models that allow macroscopic superposition]

Fair enough, that is rational.

It is not my explanation, and I don't understand all the details myself but I'm studying the issue at present via Lindblad and classical/quantum dynamics.

 

[georgir]

Ok, I know this is somewhat offtopic, but not entirely - it will help me understand why this whole discussion is not purely philosophical but actually matters.
Can you point me to a simple experiment (or quantum gate circuit or something similar) that distinguishes a superposition state from a "normal" state. Or is there no such thing possible for a single instance of a quantum state and only multiple repetitions with the same preparations can reveal it?

 

[A. Neumaier]

Ok, I know this is somewhat offtopic, but not entirely - it will help me understand why this whole discussion is not purely philosophical but actually matters.
Can you point me to a simple experiment (or quantum gate circuit or something similar) that distinguishes a superposition state from a "normal" state. Or is there no such thing possible for a single instance of a quantum state and only multiple repetitions with the same preparations can reveal it?

Ordinary light is unpolarized, in a mixed state with $2\times 2$ density matrix $1/2$ times the identity matrix. After passing it trough a linear polarizer, it will be in a pure state, described by a superposition of an up and a down state whose relative coefficients are real and depend on the orientation of the polarizer. With up and down defined by the most natural basis of vertical and horizontal polarization, one particular orientation will produce vertically polarized light, which is a ''normal'' up state, and with the orthogonal orientation it will produce horizontally polarized light, which is a ''normal'' down state. But what is ''normal'' depends on the basis assumed. Note that any state can be made ''normal'' by looking at an appropriate basis. Things get more interesting (and more confusing) when looking at tensor products of states...

 

[stevendaryl]

I have a comment about this thread. The claim that metastable systems explains apparent selection of one alternative out of a set of possibilities is not, as far as I know, part of mainstream physics. As Demystifier said, in an EPR-type experiment, when Alice measures the spin of her particle, the claim that her result is actually determined by microscopic facts about the environment is not mainstream, and I would think that it is actually contradicted by Bell's inequality.

In any case, to me it seems like a new physics result, and so it should really be in a refereed paper before it's appropriate to discuss it here, according to the rules of Physics Forums. Just my two cents.

 

[georgir]

As Demystifier said, in an EPR-type experiment, when Alice measures the spin of her particle, the claim that her result is actually determined by microscopic facts about the environment is not mainstream, and I would think that it is actually contradicted by Bell's inequality.

As opposed to the Bohmian claim that her result is actually determined by microscopic facts about her particle itself (namely its exact position)?
I'm not defending either theory here - as I have clearly demonstrated I understand none of them :p Just thinking out loud here...

 

[A. Neumaier]

in an EPR-type experiment, when Alice measures the spin of her particle, the claim that her result is actually determined by microscopic facts about the environment is not mainstream, and I would think that it is actually contradicted by Bell's inequality.

the Bohmian claim that her result is actually determined by microscopic facts about her particle itself (namely its exact position)?

The Bohmian claim is that Alice's result is actually determined by its exact position which in turn is determined by the wave function of the universe and the initial position of all particles, hence by microscopic facts about the entire universe! This may not be known to stevendaryl, but it shows that there is nothing mysterious in itself about full determination by the microscopic details of the environment.

Nonlocality is a known and proved fact of quantum mechanics, and operates independent of any interpretation. That quantum mechanics contradicts Bell's inequality is also well-known. Hence violation of Bell's inequality is a very poor argument to label a statement as not mainstream.

Indeed, everything I said is mainstream (though possibly unfamiliar to stevendaryl):

1. There is essentially a continuum of approximations leading from full quantum models over lots of different intermediate quantum-classical models to models with a full classical dynamics.
2. The accuracy of the classical part becomes better and better the larger the classically modeled system is.
3. The accuracy becomes excellent when the latter is macroscopic.
4. Classical systems exhibit random choices when perturbed arbitrarily little from a metastable state in a bistable context.
5. A bistable quantum-classical system obtained as a reduced description from a larger unitary system behaves the same.
6. One can find plenty of literature about each point, some of which I linked to in this thread.

Thus one expects a few-particle quantum system coupled to a macroscopic metastable detector to behave the same. This conclusion is trivial, a matter of simple logic. So simple that it would be difficult to publish such a triviality in a high level research journal. Otherwise I would have written the paper, you can be sure! (I know what I am talking about; I wrote quite a number of research papers on quantum mechanics and other areas of physics.)

 

[Mentz114]

I have a comment about this thread. The claim that metastable systems explains apparent selection of one alternative out of a set of possibilities is not, as far as I know, part of mainstream physics. As Demystifier said, in an EPR-type experiment, when Alice measures the spin of her particle, the claim that her result is actually determined by microscopic facts about the environment is not mainstream, and I would think that it is actually contradicted by Bell's inequality.

In any case, to me it seems like a new physics result, and so it should really be in a refereed paper before it's appropriate to discuss it here, according to the rules of Physics Forums. Just my two cents.

Steven, this is the nearest I can get right now. I don't know if this paper has appeared in a refereed journal.

Bohmian Mechanics, Collapse Models and the emergence of Classicality
Marko Toroš, Sandro Donadi, and Angelo Bassi

We discuss the emergence of classical trajectories in Bohmian Mechanics (BM), when a macroscopic object
interacts with an external environment. We show that in such a case the conditional wave function of the
system follows a dynamics which, under reasonable assumptions, corresponds to that of the Ghirardi-Rimini-
Weber (GRW) collapse model. As a consequence, Bohmian trajectories evolve classically. Our analysis also
shows how the GRW (istantaneous) collapse process can be derived by an underlying continuous interaction
of a quantum system with an external agent,...

arXiv:1603.02541v1 [quant-ph] 8 Mar 2016

 

[atyy]

Landay and Lifshitz were perfectly aware that one can get classical behaviour in certain limits from quantum behaviour. They explicitly comment that that does not negate the need for a classical/quantum cut. Again this is all wrt to the orthodox or Copenhagen or minimal interpretation.

There are of course well respected approaches like Many-Worlds, Bohmian Mechanics or Consistent Histories which attempt to solve the measurement problem of Copenhagen. All of these have to add in assumptions (eg. multple outcomes, hidden variables, weaker reality) for the ones they remove (classical/quantum cut and/or observer-dependent collapse). The minimal interpretation without the cut and collapse that seem to be advocated by Ballentine and Peres are not consistent with the vast majority of physics textbooks from Landau and Lifshitz through Cohen-Tannoudji, Diu and Laloe through Nielsen and Chuang through Weinberg. Of course correctness is not based on mainstream physics, so the reader will have to decide for himself whether the opponents of mainstream physics like Ballentine and Peres are correct.

 

[A. Neumaier]

The minimal interpretation without the cut and collapse that seem to be advocated by Ballentine and Peres are not consistent with the vast majority of physics textbooks

To be valid, only consistency with experiment is needed, not consistency with textbooks presenting in their introductions to quantum mechanics highly idealized settings that are known to apply without approximation only to toy situations.

Landay and Lifshitz were perfectly aware that one can get classical behaviour in certain limits from quantum behaviour. They explicitly comment that that does not negate the need for a classical/quantum cut.

Please provide a concise reference for further discussion.

 

[A. Neumaier]

whether the opponents of mainstream physics like Ballentine and Peres are correct.

In contrast to your personal choice of terminology, Ballentine and Peres are mainstream according to the definition relevant for the present Forum:

We wish to discuss mainstream science. That means only topics that can be found in textbooks or that have been published in reputable journals.

In fact, their textbooks are excellent and recommended reading for everyone interested in the foundations of quantum mechanics:

Leslie E Ballentine, Quantum Mechanics. A Modern Development. World Scientific 1998.
''Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.''
(http://www-dft.ts.infn.it/~resta/fismat/ballentine.pdf)

Asher Peres, Quantum Theory: Concepts and Methods. Springer 1995.
''There are many excellent books on quantum theory from which one can learn to compute energy levels, transition rates, cross sections, etc. The theoretical rules given in these books are routinely used by physicists to compute observable quantities. Their predictions can then be compared with experimental data. There is no fundamental disagreement among physicists on how to use the theory for these practical purposes. However, there are profound differences in their opinions on the ontological meaning of quantum theory. The purpose of this book is to clarify the conceptual meaning of quantum theory, and to explain some of the mathematical methods which it utilizes. This text is not concerned with specialized topics such as atomic structure, or strong or weak interactions, but with the very foundations of the theory. This is not, however, a book on the philosophy of science. The approach is pragmatic and strictly instrumentalist. This attitude will undoubtedly antagonize some readers, but it has its own logic: quantum phenomena do not occur in a Hilbert space, they occur in a laboratory.''
(http://www.fisica.net/quantica/Peres%20-%20Quantum%20Theory%20Concepts%20and%20Methods.pdf)

 

[atyy]

I do not agree with everything in this article, but here Peres articulates that his interpretation includes a classical/quantum cut (which is not clear from his textbook). This article is much closer to the orthodox Copenhagen interpretation. My main reservation is in statements such as "Collapse is something that happens in our description of the system, not to the system itself." The textbook by Cohen-Tannoudji, Diu and Laloe is more cautious, agreeing that collapse is something that happens in our description of the system, but agnostic as to whether it also represents something that happens to the system itself.

Quantum Theory Needs No ‘Interpretation’
Christopher A. Fuchs and Asher Peres
http://www.phy.pku.edu.cn/~qhcao/resources/class/QM/PTO000070.pdf

 

[vanhees71]

You are wrong because your thermal interpretation contradicts Bell's theorem.

Of course, QT violates Bell's theorem. That's the very point of it!

 

[atyy]

Of course, QT violates Bell's theorem. That's the very point of it!

QT does not violate Bell's theorem. QT violates Bell's inequality. Consequently, Bell's theorem asserts that reality is nonlocal (or retrocausal etc).

 

[vanhees71]

Bell's theorem is about local "realistic" deterministic theories and shows, in form of an inequality, that QT cannot be equivalent to such a theory, and that's its very point. It made the philosophical mumblings of Einstein and Bohr a scientifically testable statement, and it has now been tested to overwhelming precision in favor of QT.

 

[A. Neumaier]

Bell's theorem asserts that reality is nonlocal

Bell's theorem asserts a mathematical fact about local hidden variable theories, nothing about reality.

The experiments that prove that Bell inequalities are violated imply, together with Bell's theorem, only that reality modeled by classical variables is intrinsically nonlocal.

It implies nothing about reality modeled by quantum mechanics, hence nothing about any interpretation consistent with quantum mechanics. In particular, my thermal interpretation explicitly acknowledges that the positions of all objects are uncertain, hence nonlocal. Thus it violates the assumptions of Bell's theorem, hence cannot be in conflict with it.

 

[A. Neumaier]

the need for a classical/quantum cut.

What about treating the observer's consciousness as the classical system and the whole universe minus the observer's consciousness as the quantum system? This makes it obvious that the collapse (of the universe) is a subjective process, since we can remove from the universe the consciousness of any single observer without changing the physics.

 

[N88]

Bell's theorem asserts a mathematical fact about local hidden variable theories, nothing about reality.

The experiments that prove that Bell inequalities are violated imply, together with Bell's theorem, only that reality modeled by classical variables is intrinsically nonlocal.

It implies nothing about reality modeled by quantum mechanics, hence nothing about any interpretation consistent with quantum mechanics. In particular, my thermal interpretation explicitly acknowledges that the positions of all objects are uncertain, hence nonlocal. Thus it violates the assumptions of Bell's theorem, hence cannot be in conflict with it.

I would like to be clear about the meaning of this statement: "In particular, my thermal interpretation explicitly acknowledges that the positions of all objects are uncertain, hence nonlocal."

Is this saying that "my thermal interpretation explicitly acknowledges that the positions of all objects are uncertain, hence my thermal interpretation is nonlocal"?

If so, how does this nonlocality arise from your acknowledgment "that the positions of all objects are uncertain"?

 

[A. Neumaier]

If so, how does this nonlocality arise from your acknowledgment "that the positions of all objects are uncertain"?

Uncertain position may mean two things.
1. It may mean that the position could be certain, as in classical Newtonian physics.
2. it may mean that the position belongs to an extended object, such as a city, a chair or a tyre.
In the second case there is no way to specify the position exactly. (Classically, one could think of replacing the position of the object by the position of its center of mass - but what is the center of mass of a city? And is a tire really located at its center of mass - which is well outside the material the tyre is made of?)

The second case is the paradigm for the thermal interpretation, which regards every object as extended to the extent determined by the computable uncertainty $\sigma_q$.

In an object in the form of a 2-photon state prepared in an experiment checking Bell inequalities over long-distances, this uncertainty becomes huge. Thus the object is vastly extended - so nonlocal that the assumptions in Bell's argument are obviously violated. No wonder the conclusions can be violated, too.

 

[N88]

Uncertain position may mean two things.
1. It may mean that the position could be certain, as in classical Newtonian physics.
2. it may mean that the position belongs to an extended object, such as a city, a chair or a tyre.
In the second case there is no way to specify the position exactly. (Classically, one could think of replacing the position of the object by the position of its center of mass - but what is the center of mass of a city? And is a tire really located at its center of mass - which is well outside the material the tyre is made of?)

The second case is the paradigm for the thermal interpretation, which regards every object as extended to the extent determined by the computable uncertainty $\sigma_q$.

In an object in the form of a 2-photon state prepared in an experiment checking Bell inequalities over long-distances, this uncertainty becomes huge. Thus the object is vastly extended - so nonlocal that the assumptions in Bell's argument are obviously violated. No wonder the conclusions can be violated, too.

Which assumptions in Bell's argument are violated by this extended object? (I take it that you are referring to the 2 photons (and not the 2-photon state) as an extended object.)

 

[secur]

What about treating the observer's consciousness as the classical system and the whole universe minus the observer's consciousness as the quantum system? This makes it obvious that the collapse (of the universe) is a subjective process, since we can remove from the universe the consciousness of any single observer without changing the physics.

- No, that's not an allowable gedanken since we have no theory of consciousness proving it can be treated as a classical system.

You're probably figuring that consciousness is produced by a brain, and a brain is a "classical" system. Of course any physical system is, fundamentally, based on quantum behavior. To call it a "classical" system can only mean that, in the context of whatever's being discussed, we can ignore quantum effects. Consider for example locating a brain's position or determining its angular momentum. Although both these properties are subject to quantum uncertainty at some very tiny scale, we all agree the brain is a "classical system" regarding such measurements.

On the other hand consciousness, unlike position and angular momentum, is a property of the brain for which no explanation is available in current science. I certainly can't agree that it is "obviously" classical, i.e. has nothing to do with QM. Many prominent researchers in the field, such as Roger Penrose, have speculated that it could be quantum-based. I can give citations if necessary.

My point is only that you're assuming something which hasn't been proved or even generally accepted - not to debate cause of consciousness which would be far outside scope of this thread, and PF.

On the plus side I agree your thermal interpretation of a Bell experiment's 2-photon state, which extends the "uncertain position" so much that the 2 photons actually remain "in contact" (if I can put it that way), clearly violates Bell's assumptions. Which is not to imply that my opinion matters :-)

 

[A. Neumaier]

Which assumptions in Bell's argument are violated by this extended object? (I take it that you are referring to the 2 photons (and not the 2-photon state) as an extended object.)

I chose my words carefully. There is a definite concept of ''a 2-photon state'' in quantum mechanics, but only a fuzzy one of ''two photons''.

The 2-photon state is the extended object. Whatever Alice and Bob measure depends on it - in an obviously nonlocal way, given by quantum mechanics. Note that the quantum mechanical state prepared at the source and propagating freely in opposite directions, together with the Schroedinger dynamics determined by the associated dispersion relation, makes (via Born's rule) assertions about measurements anywhere in the universe at any future time! Something more nonlocal cannot be conceived.

 

[A. Neumaier]

You're probably figuring that consciousness is produced by a brain

I don't assume this.

Consider a (for grammatical reasons male) observer observing a measurement of a tiny quantum system $A_1$ by a detector. Following von Neumann, I consider the joint system $A_2$ consisting of $A_1$ and the detector, observed by the observer. $A_2$ is again a quantum system/ Continuing this way I consider bigger and bigger portions $A_3,A_4,\ldots$ of the universe observed by the observer - all are quantum systems since there is nowhere any indication that the quantum laws become invalid. Each time the quantum system develops unitarily until the observer makes his observation of the system, causing its collapse.

I continue this until the quantum system includes everything in the universe except the observer himself. Noticing that the observer can observe part of himself I include these parts of the observer into the quantum system and remove it from the observing system. Continuing this process as long as possible I end up with a quantum system that comprises essentially the whole universe - even the brain, since it can be observed by the observer if he puts enough electrodes into his head and watches the responses on a screen. According to the Copenhagen interpretation (in von Neumann's specific form) the final quantum system develops unitarily except for the moments where the observer makes his observation of the system, causing its collapse.

Only very little remains that observes the now huge quantum system - whatever this is, this is commonly called the observer's mind or consciousness. Given the failure of intense efforts to relate it to physics proper, it may well be immaterial and not describable by physics. In this case, the final quantum system comprises the whole universe; in the other case, the final quantum system is still an excellent approximation of the universe. Thus the whole universe is a quantum system that develops unitarily until the observer (i.e., his mind) makes an observation of the system, causing its collapse.

One can repeat the procedure with any of the many (now male, female, animal, or inanimate) observers populating the universe, and finds that the collapse is a property of the corresponding (male, female, animal, or inanimate) mind, whatever the latter may be. Hence the collapse is something subjective, observer-dependent.

But the task of physics is to provide the tools that describe the objective part of what can be said about the universe, hence the unitary dynamics of the complete universe without the collapse.

However, typically observers want to consider a tiny part of the universe only, such as a physics lab, a laser source, or a microscopic system described by a 2-photon state. In this case, they must introduce a subjective element into the universe, namely a choice of subsystem. To specify this subsystem, the observers must specify the desired Heisenberg cut. This cut is arbitrary, subject only to what observers find convenient for their purposes. In order to be able to describe the subsystem by a reduced dynamics independent of the environment, the only sensible cuts are those where the subsystem is reasonably shielded from the environment and the effect of the environment can be condensed into the reduced dynamics.

This is what the first part of this thread was about. The quantum dynamics of the whole universe, suitably approximated, leads to an objective, reduced dynamics of the single small system in terms of a piecewise deterministic process (with unitary dynamics interspersed by quantum jumps at random times) when a discrete variable is observed (e.g., when particles are counted or the energy level is monitored), or in terms of a quantum diffusion process if instead a continuous quantity (such as a quadrature) is monitored. Averaged over many subsystems, these stochastic processes lead to a deterministic dynamics for the density operator, given by a Lindblad equation. The latter is the most used form of the dynamics of open quantum systems.

 

[A. Neumaier]

your thermal interpretation of a Bell experiment's 2-photon state, which extends the "uncertain position" so much that the 2 photons actually remain "in contact" (if I understand correctly), clearly violates Bell's assumptions.

Yes. They remain in contact as long as the decoherence along the transmission paths don't destroy its coherence. Once coherence is lost, they can be treated as individual photons. But to treat them as individuals while still in an approximate Bell state means making a simplification that (as any simplification) loses details - in the present case about the joint correlations.