Assumptions of the Bell theorem

[Demystifier]

It is beyond me how you can give meaning to empty symbolism such as |dead> + |alive>.

If it was not a cat but a virus, would it still be empty for you?

 

[Kolmo]

Now there are old arguments from Ludwig in:
G. Ludwig: “Die Grundlagen der Quantenmechanik”, Springer, Berlin 19541
that such Q in most cases probably can't be performed at all as the coupling Hamiltonians needed to enact them aren't physical at all

Addendum:
More explicit in:
G.Ludwig: “Geloeste und ungeloeste Probleme des Messprozesses in der Quantenmechanik”, in “W.Heisenberg und die Physik unserer Zeit”, ed. F.Bopp, Vieweg, Braunschweig 1961

 

[Fra]

What we would then intuitively expect — and perhaps even demand — is that when it’s all said and done, measurement-as-axiom and measurement-as-interaction should turn out to be equivalent, mutually compatible ways of getting to the same final result.

I agree this is more or less the the core problem.

Another thing I would by the same reasoning "inutitively expect and perhaps demand" is to reconstruct the hamiltonians of the standard model from the inference rules of the RIGHT inference/measurement theory, in the right context.

Anything less, and we will still be here in hundred years discussing the same thing.

/Fredrik

 

[PeterDonis]

It is interacting with itself.

No, it isn't; such a statement makes no sense. You might be able to partition the closed system into subsystems that interact with each other, but any such partitioning is basis dependent. But the system as a whole can't "interact with itself"; interaction requires at least two systems.

 

[PeterDonis]

But if the spin-1/2 particle entangled with the drop are isolated from the rest of environment

Which they can't be in practice. And the claim that they can be in principle, even if not in practice, is a claim that cannot be tested experimentally, so it should be viewed with great caution.

 

[Kolmo]

If it was not a cat but a virus, would it still be empty for you?

For a literal virus I wouldn't say it was "empty" as such, but certainly an incorrect state assignment, since an actual virus will be in thermal equilibrium with some environment, emitting EM radiation and so forth. Perhaps WernerQH means simply that. A state that is so wrong could be said to have little practical meaning.

 

[Lord Jestocost]

A state that is so wrong could be said to have little practical meaning.

Why is a superpositon state as |dead> + |alive> so "wrong". Only because we don’t know at present how to look for such a state doesn't justify statements like this, not at all from a scientific point of view.

 

[Kolmo]

Why is a superpositon state as |dead> + |alive> so "wrong". Only because we don’t know at present how to look for such a state doesn't justify statements like this, not at all from a scientific point of view.

As I said above, a virus in real life is embedded in a thermal environment, it's characterised by values for macroscopic observables and so forth. All of these things give a mixed state as the correct state, not a pure state.

 

[Demystifier]

But the system as a whole can't "interact with itself"; interaction requires at least two systems.

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?

 

[vanhees71]

But then you are no longer talking about unitary evolution of kets, but ordinary classical statistical physics.

For a closed system the states (no matter whether they are pure or mixed ones) and observable operators evolve by unitary time evolution. The choice how they do that is pretty arbitrary. That's known as the choice of the picture of time evolution. What's of course independent are all measurable quantities like probabilities for the outcome of measurements, expectation values/correlation functions, S-matrix elements in scattering theory, etc.

 

[vanhees71]

No, it isn't; such a statement makes no sense. You might be able to partition the closed system into subsystems that interact with each other, but any such partitioning is basis dependent. But the system as a whole can't "interact with itself"; interaction requires at least two systems.

Well, yes. 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.

 

[vanhees71]

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?

Of course. There's a clear meaning of what interacting closed systems are. I think this is again just some semantical discussion about words, whose meaning is clearly established in the scientific community.

 

[WernerQH]

For a closed system the states (no matter whether they are pure or mixed ones) and observable operators evolve by unitary time evolution. The choice how they do that is pretty arbitrary. That's known as the choice of the picture of time evolution. What's of course independent are all measurable quantities like probabilities for the outcome of measurements, expectation values/correlation functions, S-matrix elements in scattering theory, etc.

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

So you can detect a modicum of sense in an expression like |dead> + i × |alive> ?

 

[Lord Jestocost]

As I said above, a virus in real life is embedded in a thermal environment, it's characterised by values for macroscopic observables and so forth. All of these things give a mixed state as the correct state, not a pure state.

What do you think is the effect when a superposition state interacts with its environment? The quantum mechanical formalism is here unambiguous: You get an entangled quantum state for the composite “system-plus-environment”. Maybe, the interaction between system and environment scrambles up the phases so that it would be impossible, from a practical point of view, to unscramble them. However, the superposition state does not evolve by the Schrödinger equation into a mixed one. With all due respect, this statement is wrong.

 

[vanhees71]

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.

 

[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