A Assumptions of the Bell theorem

[Demystifier]

A closed system is an idealization. There's no such thing in the real world, let alone one containg a cat (or a virus).

By "closed" we mean approximately closed, so that the effects of environment are small. Such things exist in the real world. Not yet for a virus, but experimentalists succeeded to do it for large molecules containing a thousand atoms.

 

[PeterDonis]

What about $\phi^4$ theory, or gravity, or Yang-Mills theory? Aren't those self-interacting theories of scalar field, metric-tensor field and gauge field, respectively?

Take a lonely hydrogen atom within non-relativistic QT. It consists of a proton and an electron interacting with each other via the Coulomb interaction. That's an example for what you usually call an interacting closed system.

These are closed systems that we divide up into interacting subsystems (multiple scalar particles or gravitons or Yang-Mills bosons, or a proton and electron). The subsystems interact with each other. The system as a whole doesn't interact with itself.

 

[Demystifier]

These are closed systems that we divide up into interacting subsystems (multiple scalar particles or gravitons or Yang-Mills bosons, or a proton and electron). The subsystems interact with each other. The system as a whole doesn't interact with itself.

I think it's semantics. OK, perhaps we can say that a closed system does not interact. But we can still say that constituents of the closed system interact, or that there are interactions in the closed system. And I don't see how is that relevant to the solution of the measurement problem.

 

[PeterDonis]

I don't see how is that relevant to the solution of the measurement problem.

I think I am more or less at the same place on that that you ended up with in your earlier exchange with @vanhees71. See post #507.

 

[Demystifier]

I think I am more or less at the same place on that that you ended up with in your earlier exchange with @vanhees71. See post #507.

So do you agree with me that looking at the open (instead of closed) system does not help to solve the measurement problem? Or do you agree with @vanhees71 that it helps?

 

[PeterDonis]

do you agree with me that looking at the open (instead of closed) system does not help to solve the measurement problem?

I don't think we have any solution to the measurement problem. To me that means that all of our current quantum theories are incomplete. Which in turn means that claims about using our current quantum theories as exact descriptions of macroscopic objects like people are premature; we should not be blithely assuming that we can extend our current quantum theories into that domain.

 

[Lord Jestocost]

I think a state $|\text{alive} \rangle + |\text{alive} \rangle$ is simply a nonsensical expression, because $|\text{alive}/\text{dead} \rangle$ simply don't exist.

QM allows such an expression! Where do you know that such a state $|\text{alive}/\text{dead} \rangle$ doesn't exist.

With all due respect, maybe an error crept in your reasoning: The absence of evidence is not evidence of absence!

 

[Lord Jestocost]

I don't think we have any solution to the measurement problem. To me that means that all of our current quantum theories are incomplete.

To my mind, quantum theory is complete; but thinking about quantum phenomena with classical ideas might lead to these "problems".

 

[PeterDonis]

QM allows such an expression!

Yes, but as I noted in post #546, QM as we know it now might well be an incomplete theory. Nobody has done an actual experiment that shows a macroscopic object being in a state like $| \text{alive} \rangle + | \text{dead} \rangle$; the only reasons for thinking such a state exists are theoretical, based on assuming that we can apply QM the same way to cats as we apply it to qubits. But that assumption is only valid if QM is a complete theory. What if it isn't?

 

[Fra]

QM allows such an expression! Where do you know that such a state $|\text{alive}/\text{dead} \rangle$ doesn't exist.

With all due respect, maybe an error crept in your reasoning: The absence of evidence is not evidence of absence!

Conceptually I see this this way

From an agent perspective, as i see it, the "alive+dead" superposition might be fine in principle as it does not actually mean that something is dead and alive at the same time, it just means that this is the agents best inference, and the uncertainy is something the agent msut respect when forming it's own actions. So nothing is "strange" here (in principle).

But there is a big problem: if the agents capacity to store and process information will be saturated attempting to take on the whole environment + a subsystem, then this best inference is actually impossible. I think the scale where it makes sense likely informally relates to the relation of "information processing capacity" of the agent in question (thus likely scales with it's mass etc) and the size of the total datastreeam from the environment. Of course, if we are talking an almost infinite environment, then even for the most massive agent this would be impossible). I figure therer is even a race condition here relating to how fast information decoheres into the environment (beeing influences by spacetiem dimensionality as well) and the "inference speed" of the agent.

This problem would go away however, if you imagine a superobserver that has enough information processing power to easilty represent and handle all the information in the whole environment. But then we have a "non-physical" agent IMO.

I haven't digested Komo's arguments yet. I do not doubt the mathematical proofs, but the real question is to what extent the abstractions and axioms chose are really the ones best quited for physics and reality. Unfortunately this is not a question of mathematics or probability theory, this is why the somewhat obsessive reflections seems required.

My intuitive issue with classical agents and continuum probability, is that in a sense it seems possible to encode infinite amounts of information in a real number. This is why this redundancy needs to be tamed by OTHER information measures, but it yields what I see as a mess of normalisation issues where one needs to make sure that one infinitty is larger than the first one to get what you want. That is not helpful and part why I want a reconstruction, without ever lossing the track of order.

/Fredrik

 

[vanhees71]

QM allows such an expression! Where do you know that such a state $|\text{alive}/\text{dead} \rangle$ doesn't exist.

With all due respect, maybe an error crept in your reasoning: The absence of evidence is not evidence of absence!

The states "dead" and "alive" of a cat is for sure a very much coarse-grained state of a cat. It's pretty obvious that these are not pure states of cat.

 

[physika]

If it is (and I'm not saying it isn't), then so are the words "kinematics" and "dynamics". They add nothing to the actual physics; they're just labels that some people like to put on certain parts of the physics.

.

as Spekkens says

https://arxiv.org/pdf/1209.0023.pdf

"The distinction between a theory’s kinematics and its dynamics, that is, between the space of physical states it posits and its law of evolution, is central to the conceptual framework of many physicists. A change to the kinematics of a theory, however, can be compensated by a change to its dynamics without empirical consequence, which strongly suggests that these features of the theory, considered separately, cannot have physical significance.."

"it follows that the distinction must be purely conventional."

"The mistake, I believe, was to take seriously the distinction between kinematics and dynamics."

"the view that the distinction between kinematics and dynamics — a distinction that is often central to the way that physicists characterize their best theories and to the way they constrain their theory-building — is purely conventional and should be abandoned."

"The paradigm of kinematics and dynamics has served us well. So well, in fact, that it is woven deeply into the fabric of our thinking about physical theories and will not be easily supplanted. I have nonetheless argued that we must abandon it."

.

 

[vanhees71]

These are closed systems that we divide up into interacting subsystems (multiple scalar particles or gravitons or Yang-Mills bosons, or a proton and electron). The subsystems interact with each other. The system as a whole doesn't interact with itself.

Well, I'm not responsible for the usual jargon among physicists. If you are very pedantic you are of course right: In the hydrogen example it's the proton interacting with the electron (a very natural way to divide the hydrogen atom in subsystems, but there are other possible subsystems, e.g., the center of mass and the relative motion, the center-of-mass subsystem is not interacting with the relative-motion system).

In QFT it's also usual to talk about "interacting" and "non-interacting" QFTs. The latter are those for which the Lagrangian is only quadratic in the fields and its derivatives. Yang-Mills bosons are describing interacting vector fields.

But that's really again unnecessary semantics.

 

[PeterDonis]

it just means that this is the agents best inference, and the uncertainy is something the agent msut respect when forming it's own actions.

No, it doesn't; it's more than that, at least if one is going to treat QM as an exact theory that can be applied as-is to macroscopic objects. Consider the analogous case with qubits: we have states we can call, say, $| \text{up} \rangle$ and $| \text{down} \rangle$, which are eigenstates of the spin observable along the up-down axis, and then we have superpositions that we can call, say, $| \text{up} \rangle + | \text{down} \rangle$ and $| \text{up} \rangle - | \text{down} \rangle$. But the latter two states are also eigenstates of a different observable, the spin observable about an axis we could call the left-right axis, so we would have $| \text{up} \rangle + | \text{down} \rangle = | \text{left} \rangle$ and $| \text{up} \rangle - | \text{down} \rangle = | \text{right} \rangle$. (I'm ignoring normalization here, because it does not affect this discussion.) And this new observable does not commute with the spin up-down observable. These facts have implications that go well beyond just "uncertainty about the agent's best inference", and for qubits, those implications have been tested and verified by many, many experiments.

Schrodinger's point with the "cat" thought experiment was that those implications are extremely weird when applied to a macroscopic object, and even more so to one like a cat that is supposed to be sentient and to have experiences, and therefore we should not just blithely assume that the QM models that work so well for qubits will just scale up to cats without any modification. For example, one implication is that, for a cat, there should be an observable whose eigenstates are $| \text{alive} \rangle + | \text{dead} \rangle$ and $| \text{alive} \rangle - | \text{dead} \rangle$. But we have no experimental evidence that there is such an observable; it certainly isn't anything as simple as rotating the axis about which we are measuring spin from up-down to left-right as we can with qubits.

 

[PeterDonis]

the states "dead" and "alive" of a cat is for sure a very much coarse-grained state of a cat. It's pretty obvious that these are not pure states of cat.

This is true, but it doesn't help to resolve the issue of whether states like $| \text{alive} \rangle + | \text{dead} \rangle$ are possible. Even if $| \text{alive} \rangle$ and $| \text{dead} \rangle$ are not single pure states but huge, disjoint subspaces of the cat Hilbert space, standard QM still says we can form superpositions of a state in the $| \text{alive} \rangle$ subspace and a state in the $| \text{dead} \rangle$ subspace. But our ordinary experience is that no such thing is possible.

 

[vanhees71]

How do you form superpositions of mixed states?

 

[PeterDonis]

How do you form superpositions of mixed states?

$| \text{alive} \rangle$ and $| \text{dead} \rangle$ in the Schrodinger's cat thought experiment, with your observation in post #551 taken into account, aren't mixed states; they're disjoint subspaces, as I said. But those subspaces contain pure states, and we can just pick one pure state from the $| \text{alive} \rangle$ subspace and one pure state from the $| \text{dead} \rangle$ subspace and form a superposition of them. Standard QM says this should be possible.

 

[physika]

This is a really strange view to me and I've never really heard views like yours...calling it just semantics doesn't match anything I've read, but I'll just leave it at that.

.

...then you have to read more

.

 

[Lord Jestocost]

Yes, but as I noted in post #546, QM as we know it now might well be an incomplete theory. Nobody has done an actual experiment that shows a macroscopic object being in a state like $| \text{alive} \rangle + | \text{dead} \rangle$; the only reasons for thinking such a state exists are theoretical, based on assuming that we can apply QM the same way to cats as we apply it to qubits. But that assumption is only valid if QM is a complete theory. What if it isn't?

Maybe, quantum theory is an incomplete theory. Maybe, however, we merely have this feeling because quantum theory forces us to “describe” something solely in a pure mathematical formalism because we are not equipped with adequate mental images.

 

[Fra]

No, it doesn't; it's more than that, at least if one is going to treat QM as an exact theory that can be applied as-is to macroscopic objects
...
But we have no experimental evidence that there is such an observable; it certainly isn't anything as simple as rotating the axis about which we are measuring spin from up-down to left-right as we can with qubits.

Not sure if I implied somewhere that superposition of macroscopic objects are ever going to be "observed" in practice. It's not what I meant.

I totally agree that QM as it stands is corroborated for small subsystems only, and relative to macroscopic "agents". This is what we know.

All else is all about possible future revisions of QM. But on here many have different reasons for such revision. Some don't see why it's neeed at all, and those that do have different reasons for it. (My reasons reasons unification of forces and intrinsic vs extrinsic inferences. Some of these motivations extend beyond traditional physics.)

I gave two reflections, one in which it makes in principle sense for the original agent, to maintain the superposition in isolation, awaiting information updates, thus is it's "best inference", eften if it turns out to be way off during future updates.

The other reflection was that, there seems to be a possiblity that not even this best inference, for principal reasons is "intrisic" and thus on those ground should be rejected as well. But I am not sure to what extent that is something that follows also from the current information theoretic approach Kolmo and others refers to, or if it requires additional ideas. I don't know how all other people think about hard problems (that are of theoretical nature and lacks continuous daily experimental feedback) but for me, a the formal axiomatic and deductive backbone needs to be challenged with a more fuzzy philosophical reflections ot make sure we don't make use of suspicous axioms, the intuition basically comes from your own accumulated and acquired intuition and understanding of the topic. This why indeed, the concept of "agent" and "inference" is about as fuzzy as "information" or measurement so it's trick to discuss because the exact mathematical definition of an agent or and inference, would be theory dependent, and as we are dicussion foundations, it i presume means perturbing the theory and thus the terms as well. The "general inference" I think about is clearly NOT like anything in QM. But one needs to find a correspondence limit somwhere, so this is why i enjoy the reflections.

/Fredrik

 

[Fra]

Maybe, quantum theory is an incomplete theory. Maybe, however, we merely have this feeling because quantum theory forces us to “describe” something solely in a pure mathematical formalism because we are not equipped with adequate mental images.

This is what I love about the agent abstraction. It seems perfectly suited to describe all the weirdness of QM, in an intuitive way. Why do I say this: it's beacuse a human is a prime example of an interacting inferring agent, and we have emergen social rules. This is a rich sources of mental abstractions, that fits me perfectly. Try to think about how social rules emerge, are supported, and evolve, and how causality of these interactions works. And then try to look at QM, and there is a good chance you will see it in a new light. At least its my story.

I remember well the journey from first QM class, when i during one particular lecture realized that my whole prior worldview was deeply wrong.

(this isn't a joke)

/Fredrik

 

[RUTA]

Maybe, quantum theory is an incomplete theory. Maybe, however, we merely have this feeling because quantum theory forces us to “describe” something solely in a pure mathematical formalism because we are not equipped with adequate mental images.

Despite its ineluctably probabilistic nature, QM can be understood to be as complete as possible given that everyone has to measure the same value for Planck's constant h. Thus, there exists a principle account of QM equivalent to that for SR whereby QM must be probabilistic with all of its mysterious properties. If you are like most physicists who have long since given up on causal mechanisms for time dilation and length contraction in SR, then given this exact same principle account of QM you should also be willing to give up on causal mechanisms responsible for QM. This 3-min video "Beyond Causal Explanation" https://encyclopedia.pub/10904 in Encyclopedia gives a conceptual overview and links to one of four published papers on the idea. Its extension to GR received Honorable Mention in the GRF 2021 Essay Contest this month as well and should be published in a special issue of IJMPD for Essay Contest winners this October. I've attached a paper that is under review at a journal for physics teachers and students that is probably the clearest exposition to date.

For those who are still looking for the "luminiferous aether" or its causal counterpart in SR, you may disregard this post and continue looking for a causal mechanism behind QM as well :-)

 

[physika]

Classical mechanics is supposed to be a physical theory, not simplectic geometry.

.
Right.

abstract mathematical forms and its "applications"* to physical systems.

not otherwise.

...simplectic geometry is not the physical system.

just:
*aproximate "descriptions"

...at most.

 

[Fra]

If you are like most physicists who have long since given up on causal mechanisms for time dilation and length contraction in SR, then given this exact same principle account of QM you should also be willing to give up on causal mechanisms responsible for QM.

I think the principle account stance is great. I like the ambition of the principal account.

But I don't think it has to conflict with seeking and deeper causation, if causation is applied to the principles we can enjoy both principal accounts and causation of principles?

Why does NPRF hold? ie. what would happen if it didnt?
For example why is there an upper speed of signal propagation, and why does everyone see it the same?
Why would everyone agree on the minimum action? or in minimum information gain?

I think we can ask these things, and still enjoy the principal explanations. It's still significant progress as the explanatory value increases.

/Fredrik

 

[RUTA]

I think the principle account stance is great. I like the ambition of the principal account.

But I don't think it has to conflict with seeking and deeper causation, if causation is applied to the principles we can enjoy both principal accounts and causation of principles?

Why does NPRF hold? ie. what would happen if it didnt?
For example why is there an upper speed of signal propagation, and why does everyone see it the same?
Why would everyone agree on the minimum action? or in minimum information gain?

I think we can ask these things, and still enjoy the principal explanations. It's still significant progress as the explanatory value increases.

/Fredrik

NPRF is a fundamental principle (an ultimate principle explanans). If you want NPRF to become an explanandum, then whatever you use to explain it becomes an ultimate explanans. The explanatory sequence stops where there is consensus on fundamentality. Building a model of objective reality is germane to physics and an objective model of reality is constructed from a collection of individual data collecting contributions (of any sort). No preferred reference frame simply says that none of the individual contributions carries more weight than any other for building the objective model. So, most physicists are happy to accept NPRF as a fundamental principle when it comes to SR without any constructive counterpart needed. A notable exception is Mermin's book on SR.

The point of the papers referenced above is that those physicists should be equally happy to use NPRF as a fundamental principle when it comes to QM. Since those physicists are no longer interested in finding a causal mechanism for time dilation and length contraction a la the luminiferous aether, they need no longer be interested in finding a causal mechanism for quantum entanglement.

 

[Fra]

Building a model of objective reality is germane to physics and an objective model of reality is constructed from a collection of individual data collecting contributions (of any sort). No preferred reference frame simply says that none of the individual contributions carries more weight than any other for building the objective model.

About NPRF, or it's generalisation, the specific "objection" I had in mind was that normally NPFR is taken to be essentially an "observer equivalence constraint" on the set of subjective views. I argue that this is a stronger condition than what you wrote on bold. The bold state is more what i call "observer democracy".

The difference in an "interacting subjects/agent" view, is that the observer democracy represents the fact that all contributions carry equal weight. The equivalence constraints rather is a stronger statement where one assumes the existence of an exact matehmatial transformation between the views, elevating it to a perfect symmetry. In my view, this somewhat subtle distinction is a key when pondering how symmetrys are emergent. ie. the observer democracy is a process that "cause" the emergence of an "effective equivalence", but it need not be perfect such as a mathematical constraint.

/Fredrik

 

[RUTA]

About NPRF, or it's generalisation, the specific "objection" I had in mind was that normally NPFR is taken to be essentially an "observer equivalence constraint" on the set of subjective views. I argue that this is a stronger condition than what you wrote on bold. The bold state is more what i call "observer democracy".

The difference in an "interacting subjects/agent" view, is that the observer democracy represents the fact that all contributions carry equal weight. The equivalence constraints rather is a stronger statement where one assumes the existence of an exact matehmatial transformation between the views, elevating it to a perfect symmetry. In my view, this somewhat subtle distinction is a key when pondering how symmetrys are emergent. ie. the observer democracy is a process that "cause" the emergence of an "effective equivalence", but it need not be perfect such as a mathematical constraint.
/Fredrik

Yes, perhaps we do think of it differently. Every perspective is unique, i.e., every observation is unique (again, these aren't necessarily human observations). We use our mathematical model of objective reality to blend these disparate data together self-consistently. That self-consistent collection of shared information possesses symmetries in accord with NPRF, e.g., Poincare and gauge invariances. NPRF is just one of two principles required to underwrite physics, the other is the boundary of a boundary principle. We published that in Entropy, here is a short overview with a link to the Entropy paper https://encyclopedia.pub/9753. You can skip the neutral monism stuff and go straight to the physics part of the paper if that's your interest. All of this is getting much deeper than is strictly required to do physics though :-)

 

[Fra]

We published that in Entropy, here is a short overview with a link to the Entropy paper https://encyclopedia.pub/9753. You can skip the neutral monism stuff and go straight to the physics part of the paper if that's your interest. All of this is getting much deeper than is strictly required to do physics though :-)

With space and time in the context of your axiom 1 and 2, are you actually talking about 4D space (from classical physics) are do you by "space" mean a more abstract space of say distinguishable events? (not necessarily making a difference between and internal("local") events and "external" events?

For me to take 3D+1 as input is not acceptable as it likely misses a lot of explanatory opportunities that has to do with how 3D+1 is constructed/selected/evolved?

I do enjoy your focus on the logic of reasoning, but as I need to reinterpret everything in terms of my view, I am not sure how to characterise what you write in the agent abstraction. I am leaning towards that the two views are philosophically incompatible. While I seek to understand the emergent objectivity from "interating agents", you seem to seek to use the "presumed emergent symmetry" as a constructing constraints - this method is what I think is the standard method in physics (even though physicists dont' use a lot of philosophical terms). But it's this method I find not satisfactory, I think one can find a similar principal account for WHY symmetry follows from demoracy, is a kind of "nash-equilibrium" between agents. This would not only explain why the symmery exists, it would also explain why some symmetries are not perfect but a bit noisy.

/Fredrik

 

[Fra]

NPRF is just one of two principles required to underwrite physics, the other is the boundary of a boundary principle. We published that in Entropy, here is a short overview with a link to the Entropy paper https://encyclopedia.pub/9753.

I think what you acually said I didn't get on first reading is that physics is constructed either from one of the two principles, and you choose NPFR? If so we agree. I wasn't sure about the terminiology, but I assume with the "boundary of boundary principle" you refers to something along the lines of strong emergence and Wheelers law without law? If so, then I'm definitely in the strong emergence camp. This is essentially how I think as well of self-organising agents.

Here is a nice paper that I clearly illustrates part of the ideas, that is probably one of the closests to my own views that i have found published. Although the notion "statistical phenomenon" should be understood as an evolutionary phenomenon, as one can not be sure fo say "universal" or global equilbrium.

Law without law: from observer states to physics viaalgorithmic information theory
"In this work, I propose a rigorous approachof this kind on the basis of algorithmic informa-tion theory. It is based on a single postulate:that universal induction determines the chances of what any observer sees next. That is, instead of a world or physical laws, it is the local state ofthe observer alone that etermines those proba-bilities. Surprisingly, despite its solipsistic foundation, I show that the resulting theory ecoversmany features of our established physical world-view: it predicts that it appears to observersas if there was an external world that evolves according to simple, computable, probabilistic laws. In contrast to the standard view, objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon. "
-- Markus P. M¨uller, https://arxiv.org/pdf/1712.01826.pdf

The association with agents is the athe algorithmic information is processed byt the agents themselves, and if you consider arbitrary agents, the agents say "mass" must constraint the processing power and thus possible inferences. So there are a dual support from both emergence and constraints. So I do not see the views are contradictory. I think one can understand the "constraint" as a truncated emergence (where truncation is a lossy retention, that can be argued to be physically motivated and proviging a "natural regulator")

That makes me curious how you say view the line of reasoning in that papers, relative to your neural monism perspective?

/Fredrik

 

[RUTA]

I think what you acually said I didn't get on first reading is that physics is constructed either from one of the two principles, and you choose NPFR? If so we agree. I wasn't sure about the terminiology, but I assume with the "boundary of boundary principle" you refers to something along the lines of strong emergence and Wheelers law without law? If so, then I'm definitely in the strong emergence camp. This is essentially how I think as well of self-organising agents.

Here is a nice paper that I clearly illustrates part of the ideas, that is probably one of the closests to my own views that i have found published. Although the notion "statistical phenomenon" should be understood as an evolutionary phenomenon, as one can not be sure fo say "universal" or global equilbrium.

Law without law: from observer states to physics viaalgorithmic information theory
"In this work, I propose a rigorous approachof this kind on the basis of algorithmic informa-tion theory. It is based on a single postulate:that universal induction determines the chances of what any observer sees next. That is, instead of a world or physical laws, it is the local state ofthe observer alone that etermines those proba-bilities. Surprisingly, despite its solipsistic foundation, I show that the resulting theory ecoversmany features of our established physical world-view: it predicts that it appears to observersas if there was an external world that evolves according to simple, computable, probabilistic laws. In contrast to the standard view, objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon. "
-- Markus P. M¨uller, https://arxiv.org/pdf/1712.01826.pdf

The association with agents is the athe algorithmic information is processed byt the agents themselves, and if you consider arbitrary agents, the agents say "mass" must constraint the processing power and thus possible inferences. So there are a dual support from both emergence and constraints. So I do not see the views are contradictory. I think one can understand the "constraint" as a truncated emergence (where truncation is a lossy retention, that can be argued to be physically motivated and proviging a "natural regulator")

That makes me curious how you say view the line of reasoning in that papers, relative to your neural monism perspective?

/Fredrik

Thnx for the reference, I'll check it out.

Both the relativity principle and boundary of a boundary principle are necessary to recover known physics, as we argue in the paper.

Classical objects (obeying classical mechanics) interact via the quantum exchange of momentum (per quantum mechanics). Neither is fundamental to the other (they are co-fundamental) and nothing "emerges" from something more fundamental in our model.