Assumptions of the Bell theorem

[stevendaryl]

I looked up environmentally induced superselection, and definitely in the past when people talked about superselection, they meant the rapid decaying of the off-diagonal elements of the density matrix due to decoherence. That isn't truly superselection. It's an "for all practical purposes" superselection.

The specific paper by Allahverdyan that you mention that talks about another type of superselection doesn't seem to be available for free download. Or is it?

There is a paper that discusses the application of superselection rules to resolve the measurement problem:
http://jamesowenweatherall.com/SCPPRG/EarmanJohn2008Man_SuperselectionforPhilosophers.pdf
(Chapter 11)

 

[PeterDonis]

Quantum jumps and/or collapse are just FAPP descriptions for pretty fast transition processes due to the interaction of the investigated system with the environment/measurement device leading to decoherence and irreversible defined measurement results.

This is interpretation dependent; in some interpretations collapse is not just a FAPP description.

 

[Demystifier]

No, I'm saying that you can't solve the "measurement problem" by considering only closed quantum systems. This is the one thing where Bohr was right: Measuring a quantum system means to use a macroscopic apparatus to gain information about this quantum system, and a measurement implies an irreversible process letting me read off a pointer at that instrument. This you cannot describe by a closed system (neither in classical mechanics or field theory nor in quantum (field) theory).

In classical as well as quantum physics you derive the behavior of macroscopic systems by a plethora of methods leading to an effective description leading to irreversibility, dissipation and particularly, in the quantum case, decoherence.

What is empty philosophy is to claim you can describe macroscopic systems in all microscopic detail as closed quantum systems. It's also empty philosophy to claim that there's a measurement problem only because of this impossibility.

For me, it's impossible to discuss quantum foundations with you because you use double standards. You use one set of reasoning standards in the argument above, but a totally different set of reasoning standards when you claim that there is no collapse of the wave function. With the standards of reasoning as above one could just as well claim that collapse happens in open systems, that we cannot understand it in detail because the measuring apparatus has too many degrees of freedom, and that there are plethora of methods leading to an effective description leading to collapse. But when it comes to collapse, you just shift to another, more fundamental, way of thinking which easily dismisses the argument for collapse above. And yet, when one wants to talk about the measurement problem with you, you again retreat to the effective non-fundamental mode of thinking.

You are like a laywer who argues that those under age 18 are not guilty for their actions because their actions are determined by the fundamental laws of physics, while those who are older than 18 are guilty because the guilt is an emergent phenomenon and we cannot understand all the details of physical determinations of their actions.

 

[Kolmo]

The nonlocality is another issue. If something happening at Alice's detector (the electron making contact with a superselected quantity) makes it impossible for Bob to detect an electron, when it was possible the moment before, that seems to be a nonlocal effect

This is a paper that goes through a model where infrared effects of light drive quantities into the centre of the centralizer of the algebra making the state over them be simply ignorance:
https://arxiv.org/abs/2101.01044
See Section 6. It's probably the most explicit model that's still reasonably short. Allahverdyan's paper is over 100 pages long. "ETH approach" just means using the infrared properties of QED to derive removal of interference.

As for the nonlocality I don't see it. Following the evolution of the state it would predict either Alice's detector clicked or Bob's detector clicked, i.e. the possible histories are click here or click there. Just because the possible events are far apart doesn't to me indicate nonlocality.

I looked up environmentally induced superselection, and definitely in the past when people talked about superselection, they meant the rapid decaying of the off-diagonal elements of the density matrix due to decoherence. That isn't truly superselection. It's an "for all practical purposes" superselection

Decoherence is a subdominant effect in classicality, but even in this case if one wanted to measure the off-diagonal terms say for a macroscopic body of $10^{27}$ particles for which there is decoherence of macroscopic quantities into the internal and external environment with the latter say involving scattered light, what quantity would you measure to detect interference? That is give me a measurable quantity that does not commute with macroscopic collective coordinates. Detailed calculations usually show such a quantity cannot be given an operational meaning.

 

[vanhees71]

Does that mean that you can’t have measurements in a closed system?

No, because you have to irreversibly store the measurement result in order to read it off. That argument is already due to Bohr. Unfortunately it came with all this confusing philosophy characteristic for him and, even worse, Heisenberg.

 

[vanhees71]

I don't know if that counts. But anyway, let's take a typical experimental result: You pass an electron through a Stern-Gerlach device, and the electron either goes left, and makes a spot on the left side of a photographic plate, or goes right, and makes a spot on the right side. Are you saying that there can't be a superposition of those two possibilities? There is a rigorous superselection rule preventing it?

I certainly believe that you can't in practice observe interference effects between the two possibilities.

Of course there can be superpositions. E.g., if you measure the spin component in another direction. What the SGE realizes is (almost perfect) entanglement between spin and momentum (or position) in the sense you described. This is well understood with (unitary!) time evolution for the electron in the Stern-Gerlach magnet.

This has nothing to do with a superselection rule. Superselection rules result from some symmetry principle. E.g., the impossibility within non-relativistic QT of superpositions of states with different mass (due to the fact that mass in non-relativistic QT is a central charge of the Galilei group's Lie algebra) or the superselection rule forbidding superpositions of states with half-integer and inter spin etc.

 

[Demystifier]

No, because you have to irreversibly store the measurement result in order to read it off.

So there are no measurements in the Universe, because Universe is a closed system by definition.

 

[vanhees71]

For me, it's impossible to discuss quantum foundations with you because you use double standards. You use one set of reasoning standards in the argument above, but a totally different set of reasoning standards when you claim that there is no collapse of the wave function. With the standards of reasoning as above one could just as well claim that collapse happens in open systems, that we cannot understand it in detail because the measuring apparatus has too many degrees of freedom, and that there are plethora of methods leading to an effective description leading to collapse. But when it comes to collapse, you just shift to another, more fundamental, way of thinking which easily dismisses the argument for collapse above. And yet, when one wants to talk about the measurement problem with you, you again retreat to the effective non-fundamental mode of thinking.

You are like a laywer who argues that those under age 18 are not guilty for their actions because their actions are determined by the fundamental laws of physics, while those who are older than 18 are guilty because the guilt is an emergent phenomenon and we cannot understand all the details of physical determinations of their actions.

There is no collapse and I think my argument is consistent. It is just a wrong attitude to say that the QT of macroscopic open quantum systems by statistical means is less fundamental than the treatment of closed systems. To the contrary, it's very fundamental to understand the "classicality" of the behavior of macroscopic systems, and thus also measurement devices, as an emergent phenomenon. It's not enough to know the Standard Model of elementary particles or some future "better theory beyond the Standard Model". You also have to understand the phenomena of all kinds of "condensed matter" (from the QGP at the high-energy end to the matter surrounding us at the low-energy end).

It's obvious that you cannot even write down the state of a macroscopic system consisting of $\sim 10^{24}$ "molecules/atoms/particles" in all detail, let alone solve the full unitary time evolution of its dynamics as a closed system. This is not even possible in classical physics.

 

[Kolmo]

Of course there can be superpositions

He's talking about superpositions of the macroscopic collective coordinates of the device, i.e. a superposition of the location of marks on the photographic plates in a Stern-Gerlach device, not whether one can later go on to see superposition of the spin of the particle.

This has nothing to do with a superselection rule. Superselection rules result from some symmetry principle.

The absence of interference for the macroscopic collective coordinates is equivalent to and often called a superselection principle. Only some superselected quantities result from symmetry principles, i.e. the typical easiest ones to derive like mass in NRQM. Dynamical ones are usually much harder and require solving detailed models.

 

[vanhees71]

I prefer the expression of "environment induced selection (eins).

It's also true that there is no limit in the size of a system to show "quantum behavior" like interference/superposition and even entanglement. It's just a matter of being able to isolate the system enough from "the environment" to prevent decoherence, and this is a very challenging task for macroscopic systems.

I think Feynman would have been very pleased about the newest example using with drums (at a size in the micrometer region):

https://www.nature.com/articles/d41586-021-01223-4

 

[Kolmo]

I prefer the expression of "environment induced selection (eins).

That's a fine term. Working in this area we often wouldn't use it as not all of these effects are actually driven by the environment or decoherence. If you read Allahverdyan et al's long paper they discuss how decoherence is actually a subdominant source of classicality in the Curie-Weiss model of measurement. For that reason I prefer to use a more generic term.

 

[Demystifier]

it's very fundamental ... as an emergent phenomenon.

By definition, emergent means not fundamental.

 

[vanhees71]

Emergent means to explain a phenomenon from an underlying fundamental theory using some appropriate approximation to find the adequate description in terms of an "effective theory".

 

[Demystifier]

Emergent means to explain a phenomenon from an underlying fundamental theory.

Is the Born rule fundamental or emergent?

 

[vanhees71]

The Born rule is fundamental. Ho often do you want to hear this answer?

 

[Demystifier]

The Born rule is fundamental. Ho often do you want to hear this answer?

Until you make it consistent with your other claims.

But measurement is emergent, am I right? Hence the Born rule must be valid even without measurement, is that correct? Then, in the absence of measurement, what determines the basis in the Born rule?

 

[Kolmo]

It's also true that there is no limit in the size of a system to show "quantum behavior" like interference/superposition and even entanglement

I always liked the last few sections of Daneri et al's classical 1962 paper "Quantum theory of measurement and ergodicity conditions" in this regard:
https://doi.org/10.1016/0029-5582(62)90528-X

They basically show that an experimental situation where one could display the relevant interference terms for coarse-grained observables of a macroscopic measuring device¹ necessarily breaks the molecular bonds allowing it to function as a macroscopic body, effectively reducing it to a heated soup of atoms.

It always seemed an easier to understand version of Bohr's talk about the dual nature of the apparatus as a measuring device or a quantum system, i.e. an experiment where you can see the interference terms in such a body explicitly means it doesn't induce irreversible processes.

¹By measuring some operator that doesn't commute with them. Gottfried's old text shows of course how difficult this is regardless since such operators are often "highly nonlocal" in his terminology. "Nonlocal" here meaning requiring simultaneous measurement of nearly each atom individually across the device, not "Nonlocal" as in faster than light.

 

[stevendaryl]

As for the nonlocality I don't see it. Following the evolution of the state it would predict either Alice's detector clicked or Bob's detector clicked, i.e. the possible histories are click here or click there. Just because the possible events are far apart doesn't to me indicate nonlocality.

If what is possible for Bob in the next second depends on what happens at Alice's detector 1 billion miles away, then that seems nonlocal to me.

 

[Demystifier]

If what is possible for Bob in the next second depends on what happens at Alice's detector 1000 miles away, then that seems nonlocal to me.

Then internet communication is nonlocal too.

 

[stevendaryl]

Then internet communication is nonlocal too.

Okay change 1000 miles to 1 billion miles.

 

[Kolmo]

If what is possible for Bob in the next second depends on what happens at Alice's detector 1 billion miles away, then that seems nonlocal to me.

I don't get it I have to say. There is a possibility for one of two events to happen, you wait and then you find out which happens. The fact that the two possible events are separated by billions of miles doesn't seem important to me. It's just that the particle might be detected here or there, it just seems probabilistic.

 

[stevendaryl]

I don't get it I have to say. There is a possibility for one of two events to happen, you wait and then you find out which happens. The fact that the two possible events are separated by billions of miles doesn't seem important to me. It's just that the particle might be detected here or there, it just seems probabilistic.

If a random event affects something far away, then that random has nonlocal effects. Sort of by definition.

The random event of Alice detecting a particle affects Bob's chance of detecting a particle.

 

[Kolmo]

If a random event affects something far away, then that random has nonlocal effects. Sort of by definition.

The random event of Alice detecting a particle affects Bob's chance of detecting a particle.

I would say given how you prepared the system there is a chance $p$ of Alice detecting a particle and a chance $1 - p$ of Bob detecting a particle. So the theory just predicts two mutually exclusive events with different probabilities.
If Alice detects a particle, then since the events are mutually exclusive we know Bob did not, i.e. the click only occurs in one place.

To ascribe this to nonlocality, in fact to say it is nonlocal "by definition" is very difficult to understand for me. I've never heard anybody describe mutually exclusive events being some form of nonlocality.

 

[stevendaryl]

To ascribe this to nonlocality, in fact to say it is nonlocal "by definition" is very difficult to understand for me. I've never heard anybody describe mutually exclusive events being some form of nonlocality.

I think some people work really hard at not understanding things.

Mutually exclusive events are only nonlocal if they are NONLOCAL events. If a particle nondeterministically turns left or right, that's local. If the particle nondeterministically decides to be here or a billion miles away, that's nonlocal.

I have made this example before. Suppose that there is a pair of coins, and by some strange law, the $nth$ time you flip one coin will always result in the opposite of the $nth$ time you flip the other coin. This works regardless of how far away the two coins are. But looking at one coin individually, it seems like it randomly produces heads or tails.

I think that most people would assume that there are two possibilities:

1. There is some yet-unknown internal mechanism determining the outcome. Maybe the coin is programmed so that the result is "heads" if the $n^{th}$ digit in the decimal expansion of $\pi$ is even, and the result is "tails" otherwise.
2. There is some nonlocal effect keeping the two results correlated.

I assume that you would say: There's nothing mysterious or nonlocal going on. It's just that there are two mutually exclusive events: One gets heads, or the other gets heads.

To my mind, such an attitude is deadly for physics. Once you stop noticing mysteries, you are no longer doing science.

 

[stevendaryl]

I think some people work really hard at not understanding things.

Mutually exclusive events are only nonlocal if they are NONLOCAL events. If a particle nondeterministically turns left or right, that's local. If the particle nondeterministically decides to be here or a billion miles away, that's nonlocal.

I have made this example before. Suppose that there is a pair of coins, and by some strange law, the $nth$ time you flip one coin will always result in the opposite of the $nth$ time you flip the other coin. This works regardless of how far away the two coins are. But looking at one coin individually, it seems like it randomly produces heads or tails.

I think that most people would assume that there are two possibilities:

1. There is some yet-unknown internal mechanism determining the outcome. Maybe the coin is programmed so that the result is "heads" if the $n^{th}$ digit in the decimal expansion of $\pi$ is even, and the result is "tails" otherwise.
2. There is some nonlocal effect keeping the two results correlated.

I assume that you would say: There's nothing mysterious or nonlocal going on. It's just that there are two mutually exclusive events: One gets heads, or the other gets heads.

To my mind, such an attitude is deadly for physics. Once you stop noticing mysteries, you are no longer doing science.

I would say that such a correlation is nonlocal by definition. It's a correlation between events that are far apart. What else should it be called, other than a nonlocal correlation?

 

[Kolmo]

I think some people work really hard at not understanding things.

I can assure you I'm not "working hard" here as it seems a trivial physical situation, but okay I guess I'm not one of these "deep conceptual" thinkers who notices these "mysteries". It just seems to me to be two mutually exclusive events which are spatially separated, not some sort of nonlocality and I have never really heard anybody consider such a basic "double slit"-type situation as nonlocal. The theory doesn't tell you which occurs because it is probabilistic, but I don't see that as nonlocality.

I think that most people would assume that there are two possibilities:

To my mind, such an attitude is deadly for physics. Once you stop noticing mysteries, you are no longer doing science.

That's a bit overblown I think. I do recognize the differences between quantum and classical probabilistic cases, I was the one originally arguing the theory was not Kolmogorovian after all, and that it's not a trivial one.

Your two possible choices have been investigated in several papers and are so highly constrained as to be effectively ruled out. If you consider these the only possible options and anybody who doesn't choose between them is "not doing science", fine I guess I don't do science or something.

 

[Nullstein]

I would say that such a correlation is nonlocal by definition. It's a correlation between events that are far apart. What else should it be called, other than a nonlocal correlation?

I think the word "non-local" should be reserved for causal relationships between spacelike separated regions. Causality is a stronger requirement than correlation. In the case of entanglement, I don't think we can infer such a causal connection quite yet, because we don't fundamentally understand quantum mechanics and the changes it might bring to our understanding of causality. In modern causality research, people generally acknowledge that our current, classical notion of causality might not be applicable to quantum entanglement.

 

[stevendaryl]

I think the word "non-local" should be reserved for causal relationships between spacelike separated regions.

But science never really tells about causes. It only tells us about correlations.

The closest that we come to giving a causal story is if we assume that certain variables are "freely chosen". Then we can say that the choice of those variables has a causal influence on anything that is correlated with them.

For example, in Newtonian physics, the initial positions and momenta are freely chosen.

Causality is a stronger requirement than correlation.

But correlations are what we directly observe. Of course, nonlocal correlations can often be explained in terms of local correlations, in the sense that we can deduce the nonlocal correlation from a sequence of local correlations. For example, we observe that Alice and Bob always wear the same color hat every day, no matter how far away they are. That's a nonlocal correlation, in my terminology. However, it can be explained using local correlations: Maybe in the past, Alice and Bob got together to decide what color hat they would wear each day for the rest of their lives.

In the case of entanglement, I don't think we can infer such a causal connection quite yet, because we don't fundamentally understand quantum mechanics and the changes it might bring to our understanding of causality. In modern causality research, people generally acknowledge that our current, classical notion of causality might not be applicable to quantum entanglement.

I guess it depends on what the default position is. I would say that a connection between two events is nonlocal unless it can be "implemented" using local correlations. The other default is that the connection is local unless it can be proved to involve nonlocal influences.

 

[PeterDonis]

There is no collapse

This claim is interpretation dependent, and the rules for this forum clearly state that you should not state claims made by particular interpretations as being established facts. Please take note.

 

[PeterDonis]

The Born rule is fundamental.

This claim is also interpretation dependent. See my previous post.

 

[RUTA]

I think the word "non-local" should be reserved for causal relationships between spacelike separated regions. Causality is a stronger requirement than correlation. In the case of entanglement, I don't think we can infer such a causal connection quite yet, because we don't fundamentally understand quantum mechanics and the changes it might bring to our understanding of causality. In modern causality research, people generally acknowledge that our current, classical notion of causality might not be applicable to quantum entanglement.

That's consistent with our position in this paper https://www.mdpi.com/1099-4300/23/1/114/htm

 

[Nullstein]

But science never really tells about causes. It only tells us about correlations.

I don't think that's true. There has been quite a revolution in causality research in the last few decades. People are able to algorithmically derive causal relationships from statistical data. The definite reference is "Causality" by Pearl. These algorithms work very well, but if applied to quantum theory, they break down.

But correlations are what we directly observe.

Right, but we need to be careful about terminology in order not to accidentally draw wrong conclusions. Correlations over spacelike intervals aren't necessarily mysterious. As you say, one could e.g. look for a common cause in the past, or more generally, one could look for chains of causally related events (as formalized in the causal Markov condition today). And another serious possibility is that our current understanding of causal explanations might require revision. At least, this attitude seems to be taken serious in the modern causality research community.

I guess it depends on what the default position is. I would say that a connection between two events is nonlocal unless it can be "implemented" using local correlations. The other default is that the connection is local unless it can be proved to involve nonlocal influences.

I don't think there should be a default position at all. If we can't decide it one way or the other, we should just admit that we don't know and keep researching it further.

 

[Nullstein]

That's consistent with our position in this paper https://www.mdpi.com/1099-4300/23/1/114/htm

That's very interesting, I will have a look at it!

 

[Kolmo]

"Causality" by Pearl

That's certainly the standard reference. I also liked "Causation, prediction, and search" 2nd Edition by Spirtes, Glymour and Scheines.

 

[vanhees71]

This claim is interpretation dependent, and the rules for this forum clearly state that you should not state claims made by particular interpretations as being established facts. Please take note.

I thought we have decided on the scientific part of the theory, according to which there is no collapse.

https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/