I Determinism, realism, hidden variables

[Demystifier]

I mean something like this: A, B, C etc form a set. If x and y are members then x and y is a member. Existence is defined as the relation between any two (or more?) members.

I don't get it. How are x and y related to A, B and C?

This sounds incredibly similar to MWI. MWI was born out of explicitly considering entanglements and then you get exactly (?) what you describe apart from states taking the place of "things that exist". Why does relative existence pose any more problem than relative states?

That does sound similar to relative states, but not to MWI. Relative states is not the same as MWI. MWI is the Wheeler's reinterpretation of the Everett's relative states.

 

[Demystifier]

Very interesting point, thank you. A fascinating problem indeed. It reminds me a little of the concept of "motion" in relativity - it makes no sense to talk about the motion of A, unless one has a reference point B with respect to which the motion happens. Motion is quite simply not an intrinsic property that can be measured in isolation. But what about B ? Does it move, and if so, with respect to what ? And how about the A-B system ? And so on. One could also conceptualise an infinite regress. We get around this by choosing a specific reference coordinate system ( which is arbitrary ) with an origin, so that we can express relationships between events ( which are not intrinsic to the objects themselves ), and we formulate the laws of physics such that their form does not explicitly depend on our choice of coordinates. We all know that this works well and does not lead to pesky infinities ( so far as motion is concerned ). By analogy, perhaps there is also a way to get around the infinite regress in RQM, I don't know.

Interesting analogy, but there is one big difference. The property of being in motion is not a prerequisite for having other properties. The property of existing is. For how can something have any properties if it doesn't even exist? In other words, existence is elementary and motion is not. A non-elementary thing my be relative, but an elementary thing should be absolute.

OK, now it's definitely philosophy and not physics. But that's another reason for not taking relational QM seriously. Of course, all interpretations are somewhat philosophical, but relational interpretation seems to be much more philosophical than other interpretations.

 

[Paul Colby]

Is that a physical, objective fact about Bob's positrons, or not?

The terms "physical" and "objective" are being used here for their emotional content. It's like if one can label a fact "subjective" it is somehow less worthy of correctness. I'm of the opinion that additional terms like these are used to hide the "mind's eye" in. All experience to date shows that assigning a numerical value (rather than a QM state) to the positron is not a fruitful way of viewing the world.

 

[harrylin]

Well, by this criterion if the spin component along the z-axis is an "element of reality" for a given system then, by the same criterion, the spin component along a direction 0.0001 (or any finite number of) degrees off the z-axis is no longer "real" in the same sense. We would have to accept reality becoming discontinuous. We could also assume, as I would prefer, the EPR reality criterion is silly in a quantum mechanical context. I have little trouble rejecting "elements of reality" given the overwhelming evidence for QM being the way of the world.

A measured spin "component" is definitely the outcome of disturbing the system. It's therefore doubtful to consider that as an "element of reality" of the the undisturbed system, as intended by EPR and understood by Bell. There was only assumed to be an element of reality that corresponds to it.
Coincidentally, I read yesterday that a measured spin component is certainly not an "element of reality" of the electrons in the DBB interpretation - once more, http://arxiv.org/abs/1305.1280 "The Pilot-Wave Perspective on Spin" -Norsen

 

[Ilja]

So what happens to relativistic symmetry in MWI?

Please don't ask me anything about MWI. I'm unable to explain something about MWI using only decent language. It is simply inconsistent as an interpretation. Probabilities make sense only as a plausible expectation about what happens. If everything happens, it makes no sense at all.

I don't think the Einstein criterion actually addresses relative realities or superpositions that involve the observer, does it?

Of course, Einstein is a scientist, so ...

So I'm wondering whether MWI manages to keep relativistic symmetry by saying that the values are real in each world?

MWI rejects every argumentation once it does not like the results (that means, in particular, Bell's theorem) but on the other hand uses common sense postulates from the justification of Bayesian probability theory to justify the claim that they can somehow derive the Born rule. IMHO not more than an actual illustration how one can derive everything from a theory with contradictions.

 

[Ilja]

Well, by this criterion if the spin component along the z-axis is an "element of reality" for a given system then, by the same criterion, the spin component along a direction 0.0001 (or any finite number of) degrees off the z-axis is no longer "real" in the same sense. We would have to accept reality becoming discontinuous. We could also assume, as I would prefer, the EPR reality criterion is silly in a quantum mechanical context. I have little trouble rejecting "elements of reality" given the overwhelming evidence for QM being the way of the world.

To conclude from the EPR criterion of reality alone that some spin component is an element of reality is not possible. So, the problem does not exist. You have to add Einstein causality to derive something nontrivial about any spin. But once Einstein causality is not valid, no such problem arises.

 

[Paul Colby]

A measured spin "component" is definitely the outcome of disturbing the system. It's therefore doubtful to consider that as an "element of reality" of the the undisturbed system, as intended by EPR and understood by Bell

Help me out here. A system in an eigenstate of observable $A$ has this mythical "element of reality" prior to measurement but only if $A$ is an measurement is performed? Once performed, the system is disturbed yielding the eigenvalue $\alpha$ of $A$. I guess one must make an exception for an eigenstate and give the disturbance thing a pass? So, what exactly is the additional content associated with "element of reality"?

 

[Ilja]

A measured spin "component" is definitely the outcome of disturbing the system.It's therefore doubtful to consider that as an "element of reality" of the the undisturbed system, as intended by EPR and understood by Bell.
Coincidentally, I read yesterday that a measured spin component is certainly not an "element of reality" of the electrons in the DBB interpretation - once more, http://arxiv.org/abs/1305.1280 "The Pilot-Wave Perspective on Spin" -Norsen

The problem is that in the EPR-Bell experiment you have no possibility, if you believe in fundamental relativity or Einstein causality, to claim that a decision what to measure by Alice can distort the outcome measured by Bob.

In dBB, the decision of Alice immediately influences the measurement made by Bob. So the EPR criterion, indeed, gives nothing. But dBB is not an Einstein-causal interpretation of quantum theory. It is only realistic and causal.

 

[Markus Hanke]

Interesting analogy, but there is one big difference. The property of being in motion is not a prerequisite for having other properties. The property of existing is. For how can something have any properties if it doesn't even exist? In other words, existence is elementary and motion is not. A non-elementary thing my be relative, but an elementary thing should be absolute.

Good point
But then again, this immediately brings to mind a finding from QFT in curved space-time : different observers may measure different numbers of particles within the same spacetime, depending on the observer's state of motion. If that is the case, then in what sense can the existence of particles be considered "real" or "elementary" ? Perhaps the very notion of "particle" isn't as fundamental as we tacitly take it for.

But you are right, this is very philosophical and leads too far away from the topic of this thread, so let's not take this any further. It is just fascinating to ponder these questions !

 

[Derek Potter]

I don't get it. How are x and y related to A, B and C?

Oh sorry, I was trying to say too much at once. x and y are just general members. I changed to x and y because I thought it was clearer than sticking with A B and C which you had already used in specifice examples :)

That does sound similar to relative states, but not to MWI. Relative states is not the same as MWI. MWI is the Wheeler's reinterpretation of the Everett's relative states.

Well I totally agree with *that* distinction. Not many people make it.

 

[stevendaryl]

The terms "physical" and "objective" are being used here for their emotional content.

No, they're not. I don't know what it is about QM that makes people say ridiculous things that they would never say if the subject were classical physics.

Let me illustrate the difference. Alice and Bob each draw a card from a standard 52-card deck, thoroughly shuffled. The objective facts are:

Alice has the ace of spades.
Bob has the three of hearts.

Alice might say: "Bob has a 49% chance of having a black card, and a 51% chance of having a red card."
Bob might say: "Alice has a 49% chance of having a red card, and a 51% chance of having a black card."

Those numbers are subjective--they are facts about Alice and Bob's knowledge. Actually, Bob definitely has a red card, and Alice definitely has a black card; the probabilities reflect their lack of information about the true state of affairs.

The distinction between subjective and objective is not a matter of emotional content. Sheesh.

 

[Paul Colby]

No, they're not. I don't know what it is about QM that makes people say ridiculous things that they would never say if the subject were classical physics.

Because it is very much not classical physics. The answer to the question I previously quoted is; yes, it's a fact.

Those numbers are subjective--they are facts about Alice and Bob's knowledge. Actually, Bob definitely has a red card, and Alice definitely has a black card; the probabilities reflect their lack of information about the true state of affairs.

The same holds in the QM measurement. If Alice measures and eigenvalue then the state of the unmeasured particle is known to Alice only and therefore subjective. Bob then makes a measurement and determines an outcome whose probability is know to Alice. So what?

 

[Markus Hanke]

It is only realistic and causal.

Ok, so what would happen if I was to turn the question on its head ? We have discussed how macroscopic observers make measurements on quantum systems, and interpret the results and correlations. You say that quantum systems ( such as our EPR pairs ) can best be understood in a realistic and causal way; if that is the case we should be able to change the question, and ask how the quantum system itself would see/measure the rest of the universe ? Essentially, in analogy to riding rays of light in Special Relativity ( or at least playing catch-up with them ), I am wondering what it would be like to ride a quantum object ? How would I perceive the rest of the universe ? What would it be like for me to be entangled with another quantum object ? If QT is both realistic and causal, then it should be possible and meaningful to ask this question, no ?

 

[Derek Potter]

Please don't ask me anything about MWI. I'm unable to explain something about MWI using only decent language. It is simply inconsistent as an interpretation. Probabilities make sense only as a plausible expectation about what happens. If everything happens, it makes no sense at all.

I don't see why probabilities only make sense that way. You can only confirm your expectation by doing a run of similar experiments. So everything happening - mostly in other worlds - doesn't affect your measurement of the distribution in *your* world. In other words the observed distribution is identical to that of a true probability distribution even though it's actually caused by deterministic branching.

MWI rejects every argumentation once it does not like the results (that means, in particular, Bell's theorem) but on the other hand uses common sense postulates from the justification of Bayesian probability theory to justify the claim that they can somehow derive the Born rule. IMHO not more than an actual illustration how one can derive everything from a theory with contradictions.

Since when does MWI reject Bell's theorem? I thought it just rejected one of the conditions for the theorem to apply. Or are you just talking about the Wheeler interpretation (see comment by Demystifier) and not talking about relative states?

 

[Derek Potter]

Because it is very much not classical physics. The answer to the question I previously quoted is; yes, it's a fact.

The same holds in the QM measurement. If Alice measures and eigenvalue then the state of the unmeasured particle is known to Alice only and therefore subjective. Bob then makes a measurement and determines an outcome whose probability is know to Alice. So what?

So what - the eigenvalue is of an operator that Alice has only just that moment chosen. For your argument to be valid, Bob's particle would have to be in an eigenstate of all possible operators at once.

 

[Paul Colby]

So what - the eigenvalue is of an operator that Alice has only just that moment chosen. For your argument to be valid, Bob's particle would have to be in an eigenstate of all possible operators at once.

Only if you ignore the way things work. Alice knows the component of the entangled state once the eigenvalue of her particle is revealed. Knowing this she knows the state of the particle that Bob will then measure. This isn't a classical probability problem, it's a QM one. This is the fundamental nature of quantum states and observables.

 

[stevendaryl]

Help me out here. A system in an eigenstate of observable $A$ has this mythical "element of reality" prior to measurement but only if $A$ is an measurement is performed?

No, the whole point of the EPR criterion for being an element of reality is that the value of a property at time t can't depend on what happens after time t.

Let me make an analogy: Suppose I give you some powder and tell you that if you burn it, it will produce green smoke. That implies something about the chemical composition. If you decide NOT to burn it, it won't produce green smoke, but the chemical that would have produced the green smoke is still there.

 

[Paul Colby]

Okay, I can see that you have nothing to contribute to this discussion.

That's a subjective fact well known to me before I commented. People simply refuse to give up on classical pictures and struggle with the unavoidable consequences. Most people here feed on these discussions. This really shouldn't bother me but it leads to language being introduced that adds no content and often misleads. Should a simple classical mind friendly "interpretation" (i.e. model without content) be found, I really doubt it will be used. If a model beyond QM is found as a result, then I very much doubt it will be a return to classical ideas. More than likely it will be even less comprehendible than what came before.

 

[Demystifier]

But then again, this immediately brings to mind a finding from QFT in curved space-time : different observers may measure different numbers of particles within the same spacetime, depending on the observer's state of motion. If that is the case, then in what sense can the existence of particles be considered "real" or "elementary" ?

One possible interpretation is that relativity is not fundamental, there is a preferred Lorentz frame, so only particles defined with respect one frame are elementary, while those defined with respect to other frames are not much more than clicks in a detector. Another interpretation is that particles are not elementary at all, i.e. they are just clicks irrespective of the frame.

 

[Derek Potter]

Only if you ignore the way things work. Alice knows the component of the entangled state once the eigenvalue of her particle is revealed. Knowing this she knows the state of the particle that Bob will then measure. This isn't a classical probability problem, it's a QM one. This is the fundamental nature of quantum states and observables.

How on Earth does she know what Bob is going to measure in the future? Different polarizer angles are different bases. Bob hasn't chosen his yet.

It is this dependency on *both* angles (actually their difference) that makes it quite impossible to explain the violations of Bell's Inequality by local variables. The inequality doesn't have anything to do with how you describe the state. You can make Bob's state a herd of fairies waving their magic wands over it if you want to - as long as nothing from Alice can reach Bob (even by magic), it is impossible for the violations to occur unless either local causality is violated or Alice's outcome is not unique (as in RSF/MWI).

 

[Ilja]

I don't see why probabilities only make sense that way. You can only confirm your expectation by doing a run of similar experiments. So everything happening - mostly in other worlds - doesn't affect your measurement of the distribution in *your* world. In other words the observed distribution is identical to that of a true probability distribution even though it's actually caused by deterministic branching.

There is no well-defined process of branching and no well-defined history - which would be equivalent to a Bohmian trajectory, even if splitted (which one would have in a stochastic interpretation too). There is nothing which clearly distinguishes a branch - except the completely vague idea that it is something like an isolated wave packet, but it is doubtful that real wave functions split into localized packages instead of something very smooth. Roughly, you have nothing. Except a wave function. And whatever else from common sense one decides to use for some particular purpose.

Since when does MWI reject Bell's theorem?

They claim to be a realistic and Einstein-causal interpretation. But Bell's theorem holds for realistic Einstein-causal theories. So, they have to use some form of creative naming conventions or so (many words interpretation) to avoid Bell's theorem.

 

[Paul Colby]

How on Earth does she know what Bob is going to measure in the future? Different polarizer angles are different bases. Bob hasn't chosen his yet.

Bob's polarizer will react as if the particle was in a state which is now known by Alice. Bob still thinks the state is in a general entangled one and is none the wiser. I get that you find this mysterious. I don't because I've accepted QM as fundamental. QM states possessing their very own unique properties that aren't classical properties. When I was first confronted with the fact that the speed of light is independent of frame I had similar (identical) conceptual problems. But, the logic which 100% based on observations, dictate that space-time has this property. I got over it. QM very well (and almost assuredly is) just as fundamental. When I ask why is accepting SR so different than QM the replies boil down to because it doesn't conform to the way we think (or in some cases define) the world should work. I would suggest that people just accept the rules as fundamental for a week just as an exercise. If you find yourself asking but how did bob's measurement know...the answer is this is how the known state reacts to that measuring device.

 

[Paul Colby]

It is this dependency on *both* angles (actually their difference) that makes it quite impossible to explain the violations of Bell's Inequality by local variables.

Okay.

 

[Ilja]

You say that quantum systems ( such as our EPR pairs ) can best be understood in a realistic and causal way;

I say that to understand requires to describe it in a realistic and causal way. Everything else is mysticism, not understanding.

What would it be like for me to be entangled with another quantum object ? If QT is both realistic and causal, then it should be possible and meaningful to ask this question, no ?

I don't know, and I don't think so. What would it be like to be attracted by Newtonian gravity for a particle? I don't know, even if I know Newtonian gravity IMHO good enough.

 

[Derek Potter]

There is no well-defined process of branching and no well-defined history - which would be equivalent to a Bohmian trajectory, even if splitted (which one would have in a stochastic interpretation too). There is nothing which clearly distinguishes a branch - except the completely vague idea that it is something like an isolated wave packet, but it is doubtful that real wave functions split into localized packages instead of something very smooth. Roughly, you have nothing. Except a wave function. And whatever else from common sense one decides to use for some particular purpose.

They claim to be a realistic and Einstein-causal interpretation. But Bell's theorem holds for realistic Einstein-causal theories. So, they have to use some form of creative naming conventions or so (many words interpretation) to avoid Bell's theorem.

I didn't say anything about actual branching. Can we backtrack a bit and make the distinction which Demystifier brought up, between relative states and Wheeler's reinterpretation? I am happy to agree to the term MWI being reserved for Wheeler's nonsense, but in that case everything I've just said applies to relative states. You still get different "worlds" in RSF, the difference being that you, the commentator, not the observer, decompose a state in whatever basis you fancy. Often it will be sensible to use whatever the experiment sets out to measure, or else use the emergent preferred basis, but fundamentally you can use anything you like.

I don't see that MWI (unless you still mean Wheeler's version) rejects Bell's theorem. It is after all a theorem. It would be like rejecting 2 + 2 = 4. However for the theorem to be applicable, the kind of realism required is that "When I see a dog, it's a dog, not a ****ing kangaroo!" - which is, to put it mildly, a big assumption when we are dealing with a theory a) of observations and b) in which superposition is fundamental. Do you not agree?

 

[Derek Potter]

Bob's polarizer will react as if the particle was in a state which is now known by Alice. Bob still thinks the state is in a general entangled one and is none the wiser. I get that you find this mysterious. I don't because I've accepted QM as fundamental. QM states possessing their very own unique properties that aren't classical properties. When I was first confronted with the fact that the speed of light is independent of frame I had similar (identical) conceptual problems. But, the logic which 100% based on observations, dictate that space-time has this property. I got over it. QM very well (and almost assuredly is) just as fundamental. When I ask why is accepting SR so different than QM the replies boil down to because it doesn't conform to the way we think (or in some cases define) the world should work. I would suggest that people just accept the rules as fundamental for a week just as an exercise. If you find yourself asking but how did bob's measurement know...the answer is this is how the known state reacts to that measuring device.

I really don't know where you get the idea that I or anyone else here does not agree that QM is fundamental. It is a total waste of time explaining that we need to accept what we already accept.

 

[Ilja]

Can we backtrack a bit and make the distinction which Demystifier brought up, between relative states and Wheeler's reinterpretation? I am happy to agree to the term MWI being reserved for Wheeler's nonsense, but in that case everything I've just said applies to relative states.

Its hard, I have never seen an MWI variant which made sense for me, and so I have to acknowledge that I have not tried hard to distinguish the variants. My main criticism was that they need additional structure to make sense at all, but that I have never seen a variant which really specifies the additional structure(s) which are required.

I don't see that MWI (unless you still mean Wheeler's version) rejects Bell's theorem.

They claim "MWI is a realist, deterministic, local theory" even on the Wiki level. Its not my job to make their claims compatible with Bell's theorem.

But what I have seen, they can simply claim that Bell's theorem is not applicable, and it is hard to question this given that Bell's theorem requires a meaningful notion of probability theory, and this is nothing one can reasonably claim that it exists.

On the other hand, they use some common sense postulates to argue they have enough probability theory to prove the Born rule.

 

[Paul Colby]

It is a total waste of time explaining that we need to accept what we already accept.

If this is accepted then why do you ask,

How on Earth does she know what Bob is going to measure in the future? Different polarizer angles are different bases. Bob hasn't chosen his yet.

because in QM, which you claim to accept, she knows the STATE of bob's particle and therefore may answer all statistical questions regarding Bob's eventual choice of polarizer before Bob chooses. What's not to understand?

 

[Markus Hanke]

I don't know, and I don't think so. What would it be like to be attracted by Newtonian gravity for a particle? I don't know, even if I know Newtonian gravity IMHO good enough.

I think it is a perfectly reasonable question to ask what it would be like to "ride" a classical test particle under the influence of Newtonian gravity, and an easy to answer one too. If one assumes both realism and causality, it should likewise be possible to wonder what it would be like to "ride" a quantum particle ( never mind the entanglement thing for now ), and what the rest of the universe would look like from that perspective. I don't know the answer either, but it is an interesting question, though possibly not meaningful. I don't know.

 

[Derek Potter]

Its hard, I have never seen an MWI variant which made sense for me, and so I have to acknowledge that I have not tried hard to distinguish the variants. My main criticism was that they need additional structure to make sense at all, but that I have never seen a variant which really specifies the additional structure(s) which are required.

Okay. To my simple understanding of relative states it makes sense without any additional structure.

They claim "MWI is a realist, deterministic, local theory" even on the Wiki level. Its not my job to make their claims compatible with Bell's theorem.

But what I have seen, they can simply claim that Bell's theorem is not applicable, and it is hard to question this given that Bell's theorem requires a meaningful notion of probability theory, and this is nothing one can reasonably claim that it exists.

On the other hand, they use some common sense postulates to argue they have enough probability theory to prove the Born rule.

MWI has probability - the expectation of particular statistics. What it does not have is absolute outcomes - typically a measurement results in an entanglement. I don't see the problem with having emergent probability whilst asserting an ontic model which precludes applying Bell's Theorem. It's not as if it claims to violate the theorem, only that the necessary conditions are not met.

 

[Derek Potter]

If this is accepted then why do you ask,

because in QM, which you claim to accept, she knows the STATE of bob's particle and therefore may answer all statistical questions regarding Bob's eventual choice of polarizer before Bob chooses. What's not to understand?

Ah yes, my bad. She knows the STATE of Bob's particle. Oops.

But that does not alter anything. She *knows* the state, no mystery. But she also has had a causal influence on it. From a distance instantly. And that is a serious problem.

Saying "that's just the way QM is" does not get around the fact that the EPR correlations are impossible given local causal definite-realism. If you are happy that at least one of them has to go because "that's just the way QM is" then fine, let's leave it at that. I prefer to ask what does this tell us is going on a bit deeper than "shut up and let me calculate the probabilities" :)

 

[Ilja]

Okay. To my simple understanding of relative states it makes sense without any additional structure.

Even a subdivision into system and observer is already additional structure.

MWI has probability - the expectation of particular statistics.

I see no base for such expectations. Maybe I'm blind, but I don't see it.

I don't see the problem with having emergent probability whilst asserting an ontic model which precludes applying Bell's Theorem.

I don't see any probability emerging.

It's not as if it claims to violate the theorem, only that the necessary conditions are not met.

Claiming they are somehow realist and have a probability, but the EPR criterion of reality is somehow not applicable.

 

[Paul Colby]

But that does not alter anything. She *knows* the state, no mystery. But she also has had a causal influence on it. From a distance instantly. And that is a serious problem.

Alice's measurement is on the entangled state. The result of her measurement produces a pair in a product state. At this the measurement process is the exactly the same as measuring a $z$-polarized particle along $x$. Now, a common assumption is that the $x$-measurement device physically kicks or "disturbs" each spin along $z$ into a spin along $\pm x$ kind of at random. That this is a deeply flawed classical imagining of the measurement process is amply underscored by exactly the class of argument you reference. For practical reasons one cannot measure things without some form of interaction with the thing being measured. However, I do not believe it is this unavoidable measurement interaction causes the selection of an individual eigenvalue.

 

[Derek Potter]

Even a subdivision into system and observer is already additional structure.

I see no base for such expectations. Maybe I'm blind, but I don't see it.

I don't see any probability emerging.

Claiming they are somehow realist and have a probability, but the EPR criterion of reality is somehow not applicable.

You mentioned the factorization problem once before in terms of state space. I didn't get it then and I still don't. Which could easily be because I am not mathematical though I am trying to follow the principles that people mention! So let's cut to the chase. If we can take an arbitrary subspace of the global system's state space, what structure is needed to justify the assumption that at least one such (not every such) subspace is the state space of an observer? What is it about observer state spaces that makes it necessary to add something to QM in order for them to exist?

I do appreciate that a quantitative derivation of the Born Rule is controversial. But a qualitative emergence of probability is trivial. A sequence of observation yields a frequency for each outcome. That's all the probability one needs. Isn't it?

 

[Derek Potter]

Alice's measurement is on the entangled state. The result of her measurement produces a pair in a product state. .

I don't understand you. If the two electron state is |u>|d> + |d>|u> then Alice's measurement creates an entanglement of exactly the same form except that the first ket is now Alice's state not her electron's state. That's not a product. Neither can it be made into one without changing the basis from local variables like spin to non-local ones like two-electron entangled spins!

What you seem to be saying is that |u>|d> + |d>|u> appears to Alice to have collapsed to one or other of the products. But if the collapse is merely an appearence then there is no way you can say Bob's particle state has collapsed. It is in fact still entangled with the Alice system. But if you say the collapse is real and applies to Bob, then you have FTL propagation or causality.

 

[Ilja]

If we can take an arbitrary subspace of the global system's state space, what structure is needed to justify the assumption that at least one such (not every such) subspace is the state space of an observer?

The question is not that one can take some arbitrary subspace or not. The point is that one has to take it. And this choice of a subspace is necessary to define something which is claimed to have some status of reality - a split into different worlds. So, this choice of a subspace cannot be simply an arbitrary subjective and otherwise irrelevant thing, it has to be something real.

What is it about observer state spaces that makes it necessary to add something to QM in order for them to exist?

This is not the point. The point is that without additional structure nor observer state spaces nor system state spaces exist, but only a single global space without any structure.

The Copenhagen interpretation has, instead, a lot of additional structure, in the classical part it has a whole classical world full of it.

I do appreciate that a quantitative derivation of the Born Rule is controversial. But a qualitative emergence of probability is trivial. A sequence of observation yields a frequency for each outcome. That's all the probability one needs. Isn't it?

Which sequence? There are no sequences in a universe where everything always exists.

 

[Paul Colby]

I don't understand you. If the two electron state is |u>|d> + |d>|u> then Alice's measurement creates an entanglement of exactly the same form except that the first ket is now Alice's state not her electron's state. That's not a product.

If the state is $\vert u d\rangle+\vert d u\rangle$ and Alice performs a measurement on particle 1 obtaining a $u$ eigenvalue, then the resulting state for the pair is $\vert u d\rangle$ which is very much a product.

 

[Derek Potter]

The question is not that one can take some arbitrary subspace or not. The point is that one has to take it. And this choice of a subspace is necessary to define something which is claimed to have some status of reality - a split into different worlds. So, this choice of a subspace cannot be simply an arbitrary subjective and otherwise irrelevant thing, it has to be something real.

This is not the point. The point is that without additional structure nor observer state spaces nor system state spaces exist, but only a single global space without any structure.

The Copenhagen interpretation has, instead, a lot of additional structure, in the classical part it has a whole classical world full of it.

Which sequence? There are no sequences in a universe where everything always exists.

Okay, I haven't the faintest idea what any of that means. Thanks for trying.

 

[Derek Potter]

If the state is $\vert u d\rangle+\vert d u\rangle$ and Alice performs a measurement on particle 1 obtaining a $u$ eigenvalue, then the resulting state for the pair is $\vert u d\rangle$ which is very much a product.

Yes that theory(!) assumes that Alice's measurement collapses the wavefunction non-locally.

 

[Paul Colby]

What you seem to be saying is that |u>|d> + |d>|u> appears to Alice to have collapsed to one or other of the products. But if the collapse is merely an appearence then there is no way you can say Bob's particle state has collapsed. It is in fact still entangled with the Alice system. But if you say the collapse is real and applies to Bob, then you have FTL propagation or causality.

You bring much to what is being said that really hasn't been said by me. The EPR measurement (FTL propagation problem as you put it) assumes a causal connection that just isn't there. Viewing QM measurement as some form of random interaction is a flawed concept unsupported by experiment.

 

[Paul Colby]

Yes that theory(!) assumes that Alice's measurement collapses the wavefunction non-locally.

Yes, and I may owe the people here an apology. My interpretation of QM is quite "standard" at least from a 1960's view. I happen to hold the view that QM is quite strange, however, is quite consistent and doesn't need any help from additional interpretation. Reading the discussions here convince me even more of this position.

 

[Derek Potter]

You bring much to what is being said that really hasn't been said by me. The EPR measurement (FTL propagation problem as you put it) assumes a causal connection that just isn't there.

I cannot see how you can deny a causal connection when Bob's probabilities depend on Alice's basis and value.

Viewing QM measurement as some form of random interaction is a flawed concept unsupported by experiment.

Well we agree on something then.

 

[Derek Potter]

Yes, and I may owe the people here an apology. My interpretation of QM is quite "standard" at least from a 1960's view. I happen to hold the view that QM is quite strange, however, is quite consistent and doesn't need any help from additional interpretation. Reading the discussions here convince me even more of this position.

Depends what you mean by "need". If you want to know what happens when you fire electrons through a double slit you can "shut up and calculate" - the formalism will give you everything you need. If you want to make sense of what's going on you need interpretation. That's why Bell's contribution is so profound. It places severe contraints on how you can interpret QM.

 

[Paul Colby]

If you want to make sense of what's going on you need interpretation.

Well, nature doesn't have to make sense in the way you define sense. There are other examples in physics where nature doesn't make sense. People have over the years redefined what makes sense means for these cases. People did it with both relativities and with electromagnetic fields requiring a medium for propagation. You could say, well these make sense to me, and I would accept your assessment without question. Even to this day there are people who dispute the relativities and those that still flog the ether concept. What these people miss is they need to view the observed rules of nature as fundamental and move on. So, have you thought about why relativity makes sense to you but QM doesn't? The non-local nature of some QM states may seem spooky but I think this is just a refusal to accept the vector nature of QM state and what measurements mean operationally.

 

[Derek Potter]

So, have you thought about why relativity makes sense to you but QM doesn't? The non-local nature of some QM states may seem spooky but I think this is just a refusal to accept the vector nature of QM state and what measurements mean operationally.

I have never said QM doesn't make sense to me. Not for several years anyway and certainly not here. What I say is that non-locality does not make sense. Ergo, you may deduce, I believe QM is local. Not classical but local.

 

[Paul Colby]

I have never said QM doesn't make sense to me. Not for several years anyway and certainly not here. What I say is that non-locality does not make sense. Ergo, yopu may deduce, I believe QM is local. Not classical but local.

We,agree on even more. So, electrons are fermions, photons bosons etc. How much of this seeming non-locality is really due to shabby treatment of the problem. After all we are assuming distinguishable particles in all that's written here.

 

[Derek Potter]

We,agree on even more. So, electrons are fermions, photons bosons etc. How much of this seeming non-locality is really due to shabby treatment of the problem. After all we are assuming distinguishable particles in all that's written here.

Well one of the particles is a detector called Alice with a big red label on it and it lives in the West wing of the building and the other is Bob with a big blue label and it lives in the East wing. That should be distinguishable enough.

 

[Paul Colby]

Well one of the particles is a detector called Alice with a big red label on it and it lives in the West wing of the building and the other is Bob with a big blue label and it lives in the East wing. That should be distinguishable enough.

Okay, what ever. Alice and Bob hear clicks and these are associated by time of flight coincidence. There are many details kind of glossed over that I usually find helpful in understanding what is actually observed. Bottom line is they are looking at excitations of field modes in highly correlated states. Does this help? Probably not. However, field theory is manifestly local as far as I understand. I'm guessing how this locality gets lost is likely in the skipped details.

 

[Derek Potter]

Okay, what ever. Alice and Bob hear clicks and these are associated by time of flight coincidence. There are many details kind of glossed over that I usually find helpful in understanding what is actually observed. Bottom line is they are looking at excitations of field modes in highly correlated states. Does this help? Probably not. However, field theory is manifestly local as far as I understand. I'm guessing how this locality gets lost is likely in the skipped details.

Strange. I am reliably informed that QFT is notoriously non-local.

In any case, as I have said before, the *observed* violations of Bell's Inequality do not depend on quantum theory. (Bell's Theorem says that the BI will be violated under QM, the BI itself is classical statistics of observed events.)

If QFT could explain the correlations locally, the field excitations would be local hidden variables so one of the other BI criteria would have to be wrong - causality, or reality. For the probability of an interaction at Bob to depend on what Alice does but not be caused by it would be odd to say the least, but perhaps no odder than Bob making reliable observations when there is nothing there to observe.

 

[Demystifier]

However, field theory is manifestly local as far as I understand.

Strange. I am reliably informed that QFT is notoriously non-local.

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