Let's be fair, it's not true.bhobba said:That transformations between pure states should be continuous is highly intuitive
As an example say we analyze situation where two persons are in single room and we ask what is probability that one person or the other will come out first. There are two pure states: first person comes out first and second person comes out first. And we claim that there is transformation where half first/half second person comes out first.zonde said:And it is not intuitive that exact physical states should transform continuously.
Weirdness of entanglement does not go away if you think only about detection records of entangled particles as classical objects. Would you claim that detection records behave quantum mechanically (a la Schrodinger's cat)?rubi said:The weirdness of QM goes away as soon as one accepts that there are quantum objects. All instances of weirdness arise from thinking classically about things that behave quantum mechanically.
The detection records result from the ineraction of the detectors with quantum objects. Entangled particles just behave as they are supposed to do (because they are quantum objects) and therefore produce the observed detection records. If the detectors would interact with objects that behave sufficiently classically (like dice), the statistics of the detection records would of course be in agreement with classical statistics, but in the case of entangled particles, the detectors interact with quantum particles and therefore we observe the statistics that quantum objects are supposed to produce. Nothing is weird about the fact that (sufficiently) classical detectors interacting with quantum objects measure typtical quantum statistics. It would rather be weird if this weren't the case.zonde said:Weirdness of entanglement does not go away if you think only about detection records of entangled particles as classical objects. Would you claim that detection records behave quantum mechanically (a la Schrodinger's cat)?
The weirdness is in the fact that statistics calculated from classical detection records are inconsistent with locality.rubi said:Nothing is weird about the fact that (sufficiently) classical detectors interacting with quantum objects measure typtical quantum statistics.
You are using a concept of locality that is only adequate for classical physics. It requires that all observables can be modeled on the same probability space, which is not true in quantum mechanics. Just like there is no probability distribution ##P(x,p)## for non-commuting ##\hat x## and ##\hat p##, there isn't ##P(A,\lambda)## either, because certainly at least one observable in ##\lambda## won't commute with ##A##. The fact that the world is quantum mechanical requires us to refine our classical concepts. When you say that the statistics is inconsistent with locality, you use a locality concept that is ill-defined for quantum systems. It only makes sense in a purely classical world, which we know isn't true as soon as we accept that quantum objects exist. Yes, it is true that if the world were classical, then quantum statistics were weird. But the world isn't classical.zonde said:The weirdness is in the fact that statistics calculated from classical detection records are inconsistent with locality.
You assume I am referring to Bell theorem.rubi said:You are using a concept of locality that is only adequate for classical physics. It requires that all observables can be modeled on the same probability space, which is not true in quantum mechanics. Just like there is no probability distribution ##P(x,p)## for non-commuting ##\hat x## and ##\hat p##, there isn't ##P(A,\lambda)## either, because certainly at least one observable in ##\lambda## won't commute with ##A##. The fact that the world is quantum mechanical requires us to refine our classical concepts. When you say that the statistics is inconsistent with locality, you use a locality concept that is ill-defined for quantum systems. It only makes sense in a purely classical world, which we know isn't true as soon as we accept that quantum objects exist. Yes, it is true that if the world were classical, then quantum statistics were weird. But the world isn't classical.
Can you phrase your locality criterion in clear mathematical language and explain, why it follows from relativity? The fact that this "proof" comes from someone who writes about himself:zonde said:You assume I am referring to Bell theorem.
But I am not. Let me explain.
let me make a rather general conjecture that: For any QM prediction it is possible to have set of sequences of spacetime events (detection events) of any finite size that satisfy predicted relative frequencies given we don't have to introduce rounding errors. And I will include in this conjecture assumptions of locality and no superdeterminism.
And by locality assumption here I mean that given string of factual detection events at one side it is possible to have string of detection events at other side that reproduce prediction of QM exactly (neglecting rounding errors). You see, no probabilities here. We just cover all possibilities.
And here is counterexample to that general conjecture https://www.physicsforums.com/threads/a-simple-proof-of-bells-theorem.417173/#post-2817138
doesn't make me want to spend time on it. Maybe you can also refer me to a paper (not from Nick Herbert) that discusses this approach.NICK HERBERT is the author of "Quantum Reality", "Faster Than Light", "Elemental Mind" and a chapbook "Physics on All Fours". He invented the shortest proof of Bell's Theorem, had a hand in the quantum no-cloning theorem, recently discovered the quantum no-wedding theorem and "Nick's Theorem" which uses physics to derive limits on local psychic powers. Nick is currently obsessed with quantum tantra which he envisions as a brand new way of doing science and maintains a blog on these and other interests here.
Quite similar approach is used by Eberhard in his derivation of Bell type inequality [/PLAIN] http://dx.doi.org/10.1103/PhysRevA.47.R747[/URL]rubi said:doesn't make me want to spend time on it. Maybe you can also refer me to a paper (not from Nick Herbert) that discusses this approach.
I'm missing something in this argument. My understanding of "locality" (in the context of EPR, Bell's thm, etc) is that observables which have support only on mutually spacelike-separated regions necessarily commute. This seems different from the "enhanced" concept of locality you seem to be advocating above for the quantum context. Please give a precise definition of your enhanced concept of locality.rubi said:You [zonde] are using a concept of locality that is only adequate for classical physics. It requires that all observables can be modeled on the same probability space, which is not true in quantum mechanics. Just like there is no probability distribution ##P(x,p)## for non-commuting ##\hat x## and ##\hat p##, there isn't ##P(A,\lambda)## either, because certainly at least one observable in ##\lambda## won't commute with ##A##. [...]
You mean something like this?rubi said:Can you phrase your locality criterion in clear mathematical language
Hmm, I have to think about that.rubi said:explain, why it follows from relativity?
It's true that spacelike separated observables commute, but there are also observables that are not spacelike separated. For example the ##S_x##, ##S_y## and ##S_z## observables are not spacelike separated for Alice and Bobs individual particles. If you measure ##S_z## in a Bell test, the ##\lambda## observables would have to include ##S_x## and ##S_y## (and possibly many other observables) and there can't be a probability distribution ##P(S_x, S_y, S_z)## in quantum mechanics. Such combined probability distributions only exist for commuting observables. Whatever ##\lambda## is, in a quantum context, it certainly includes non-commuting observables that are localized in the same region as the one you are considering. That fact that Bobs variables are not among the ones that don't commute with Alices (and the other way around) doesn't help.strangerep said:I'm missing something in this argument. My understanding of "locality" (in the context of Bell's thm, etc) is that observables which have support only on mutually spacelike-separated regions necessarily commute.
I don't have an enhanced concept of locality. I'm just saying that the classical one doesn't apply anymore. It might as well be that in a quantum world, statistics just can't be used anymore to make conclusions about locality.This seems different from the "enhanced" concept of locality you seem to be advocating above for the quantum context. Please give a precise definition of your enhanced concept of locality.
zonde said:
Imho, this sounds more like an argument against local realism (meaning the notion that all possible observables have a value before being measured). It's not really an argument against (the standard notion of) "locality" per se.rubi said:It's true that spacelike separated observables commute, but there are also observables that are not spacelike separated. For example the ##S_x##, ##S_y## and ##S_z## observables are not spacelike separated for Alice and Bobs individual particles. If you measure ##S_z## in a Bell test, the ##\lambda## observables would have to include ##S_x## and ##S_y## (and possibly many other observables) and there can't be a probability distribution ##P(S_x, S_y, S_z)## in quantum mechanics. Such combined probability distributions only exist for commuting observables. Whatever ##\lambda## is, in a quantum context, it certainly includes non-commuting observables that are localized in the same region as the one you are considering. [...]
So, do you need explanation why Bell's or Eberhard's locality criterion follows from relativity?rubi said:but it still uses the same locality criterion as Bell.
You have misunderstood his derivation. He derives his inequality in presence of non-detections. But non-detections can be set to zero (there are no unpaired single detections) and of course derivation will remain valid. So his derivation is more general.rubi said:As far as I can tell, he only derives Bell's inequality in the presence of errors
A realistic theory is non-local if Bell's inequality is violated. But QM is not a realistic theory, so the violation of Bell's inequality doesn't imply that QM is non-local. Thus, Bell's criterion doesn't capture locality adequately for theories that are not realistic. Bell's factorization criterion can't even be formulated in the context of QM, since QM doesn't have the combined probability distributions, which are needed to write it down.strangerep said:Imho, this sounds more like an argument against local realism (meaning the notion that all possible observables have a value before being measured). It's not really an argument against (the standard notion of) "locality" per se.
I know it for Bell. I basically just want to know, why your definition of "locality" is appropriate, i.e. why it really captures the concept of locality appropriately.zonde said:So, do you need explanation why Bell's or Eberhard's locality criterion follows from relativity?
I'm aware of that. One can derive Bell type inequalities for more realistic situations, where detectors don't have 100% efficiency. Nevertheless, the derivations always assume Bell's factorization property somewhere and this is the one that supposedly encodes locality.You have misunderstood his derivation. He derives his inequality in presence of non-detections. But non-detections can be set to zero (there are no unpaired single detections) and of course derivation will remain valid. So his derivation is more general.
rubi said:I know it for Bell. I basically just want to know, why your definition of "locality" is appropriate, i.e. why it really captures the concept of locality appropriately.
rubi said:A realistic theory is non-local if Bell's inequality is violated. But QM is not a realistic theory, so the violation of Bell's inequality doesn't imply that QM is non-local.
As I understand concept of locality, spacelike separated regions are independent as tested by "external" parameters ("external" parameters from one region can not influence what happens in the other region).rubi said:I know it for Bell. I basically just want to know, why your definition of "locality" is appropriate, i.e. why it really captures the concept of locality appropriately.
I understand this concept of locality, but zonde claims to be using a different one.stevendaryl said:I think that Bell explained his notion of locality in his essay about "Local Be-ables". Let me try to paraphrase, rather than repeat him.
Let's focus on a measurement event that takes place in a small region of spacetime. For example, we set up a Stern-Gerlach device for measuring the spin of an electron. Before the measurement takes place, we can figure out a set of possible outcomes for the measurement. Now, if we know more about the history of the universe prior to that measurement event, we may use that knowledge to narrow down the set of possibilities. For example, if we know that the electrons were produced in the spin-up state along some axis (and that there are no fields present between the source and the device), then we know that the device will definitely not measure spin-down along that axis. Bell's locality criterion is that the set of possibilities should be determined by local conditions. If information about conditions in distant regions of space allow you to narrow down the set of possibilities beyond what can be deduced from local conditions, then the theory is nonlocal in Bell's sense. The sense of "nonlocal" is pretty straight-forward: the best (most accurate) prediction about what happens in one region of space requires information about distant regions of spacetime.
Non-local correlations are not problematic though, as the example of Bertlmann's socks shows. People claim that Bell violations are a sign for non-local causation, which doesn't follow. It is true that non-local correlations between quantum objects can be more severe than non-local correlations between classical objects. But concluding that QM is non-local (i.e. it features non-local causation rather than just non-local correlations) is not possible, since Bell's argument for non-local causation in the case of inequality violation makes crucial use of the realism of the underlying theory and therefore doesn't apply to QM. In other words: If the world were classical, then a Bell violation excludes a common cause for the non-local correlations. Since, the world is quantum mechanical, a common cause cannot be excluded, so the non-local correlations needn't be problematic.And the EPR experiment is definitely nonlocal in this sense. A pair of anti-correlated spin-1/2 particles are produced. Alice measures the spin of one particle along axis [itex]\vec{A}[/itex] and finds it is spin-up along that axis. Far, far, away, Bob measures the spin of the other particle along the same axis. Then it is definitely the case that Bob will measure spin-down, but there is no local information that would allow him to predict this. But there is nonlocal information: the fact that Alice already measured spin-up along that axis.
This notion of nonlocality is about nonlocality of inference, rather than causality. The mere fact that Alice can predict Bob's result doesn't say anything about whether there is a causal influence between the two measurements. But it does say that there is nonlocal information. Any correlation between distant events that doesn't factor into facts about local regions is a nonlocal correlation in Bell's sense. As to whether that's the "appropriate" notion of locality, it depends on what you mean: appropriate for what?
As I said, non-local correlations are not problematic even in a local theory. It would only be problematic if there were no common cause that could explain them, because that would hint at non-local causation. I'm only arguing that Bell violations can't be used to exclude a common cause in the past in the case of a non-realistic theory.stevendaryl said:It seems clear to me that QM is nonlocal, in the sense that it makes nonlocal predictions. In a spin-1/2 EPR experiment, QM predicts that if Alice and Bob both measure spins of their particles along the same axis, they will get opposite results. That's a nonlocal fact about those results. The point about hidden variables is that such nonlocal facts can arise in classical probability through ignorance about local hidden (unknown) variables. So classically, nonlocal facts can be accounted for by local facts, and so the nonlocality is seen to be an artifact of our ignorance, rather than an objective fact about the world. But in contrast, QM appears to involve nonlocal facts that can't be accounted for by local facts. So it's nonlocal, in Bell's sense. I don't see how realistic versus nonrealistic is relevant to the conclusion.
Right, but how does this imply the locality criterion of Nick Herbert (for instance), which says something about errors rather than spacelike separated regions? Why is the statement about errors the same as a statement about spacelike separated regions?zonde said:As I understand concept of locality, spacelike separated regions are independent as tested by "external" parameters ("external" parameters from one region can not influence what happens in the other region).
I reread your post #123 and I think it's worth returning to it.rubi said:I understand this concept of locality, but zonde claims to be using a different one.
Let's say we have polarization entangled photons and two non-commuting probability spaces for H/V detections and +45/-45 detections. Let's say Alice and Bob both measure photons in H/V basis so they use H/V probability space and observe perfect correlations. If they would measure photons in +45/-45 basis they would use +45/-45 probability space and would observe perfect correlations. Is this approximately your idea of non-commuting probability spaces?rubi said:It requires that all observables can be modeled on the same probability space, which is not true in quantum mechanics.
It's not my idea, it's Andrei Khrennikov's or Fine's I think. You have the following spaces: ##\Omega_1 = \{\uparrow,\downarrow\}## and ##\Omega_2 = \{\leftarrow,\rightarrow\}##, and probabilities on them, but you don't have ##\Omega_1\times\Omega_2##, since the events in that space cannot occur due to the non-commutativity of observables. In a quantum system, it is just impossible in principle to measure the system in the state ##(\uparrow,\leftarrow)## for example, because an eigenstate of ##S_z## is never an eigenstate of ##S_x## at the same time. There is a probability ##P_1(\uparrow)## and a probability ##P_2(\leftarrow)##, but no combined probability ##P_{12}(\uparrow,\leftarrow)##.zonde said:Let's say we have polarization entangled photons and two non-commuting probability spaces for H/V detections and +45/-45 detections. Let's say Alice and Bob both measure photons in H/V basis so they use H/V probability space and observe perfect correlations. If they would measure photons in +45/-45 basis they would use +45/-45 probability space and would observe perfect correlations. Is this approximately your idea of non-commuting probability spaces?
Are you trying to guess my next question?rubi said:It's not my idea, it's Andrei Khrennikov's or Fine's I think. You have the following spaces: ##\Omega_1 = \{\uparrow,\downarrow\}## and ##\Omega_2 = \{\leftarrow,\rightarrow\}##, and probabilities on them, but you don't have ##\Omega_1\times\Omega_2##, since the events in that space cannot occur due to the non-commutativity of observables. In a quantum system, it is just impossible in principle to measure the system in the state ##(\uparrow,\leftarrow)## for example, because an eigenstate of ##S_z## is never an eigenstate of ##S_x## at the same time. There is a probability ##P_1(\uparrow)## and a probability ##P_2(\leftarrow)##, but no combined probability ##P_{12}(\uparrow,\leftarrow)##.
Alice and Bobs observables commute, so if they make a choice of basis, then the occurring events can be modeled on a combined probability space. But that is not my point. The point is that Bell's factorization criterion must hold for local observables and it can only sensibly be written down if all observables commute. Bell requires you to be able to specify a set of local observables ("beables"), modeled on a combined probability space, that determines the local physics completely. Such a set cannot exist in quantum mechanics.zonde said:Are you trying to guess my next question?
Because I was asking about both parties measuring their entangled photons in the same commuting basis: H/V or +45/-45 that re analog to your ##\Omega_1 = \{\uparrow,\downarrow\}## and ##\Omega_2 = \{\leftarrow,\rightarrow\}##
Well, you see the problem is that if Alice measures her photons in H/V basis and Bob measures his in +45/-45 basis (yes you guessed my next question right) their detection records commute. If we use two channel detection scheme under ideal conditions all detection events are still perfectly correlated between Alice and Bob in time domain.rubi said:Alice and Bobs observables commute, so if they make a choice of basis, then the occurring events can be modeled on a combined probability space. But that is not my point. The point is that Bell's factorization criterion must hold for local observables and it can only sensibly be written down if all observables commute. Bell requires you to be able to specify a set of local observables ("beables"), modeled on a combined probability space, that determines the local physics completely. Such a set cannot exist in quantum mechanics.
You can of course model the statistics of the detection records on a combined probability space. I never claimed something different. This is not relevant though. In order to conclude something about locality from the measured statistics, you need to derive an inequality and this derivation makes use of local hidden variables that can be modeled on a combined probability space. As you saw in the example of ##S_x## and ##S_y##, this requirement isn't satisfied. In a quantum theory, not all local observables can be modeled on the same probability space and therefore a derivation of Bell's inequality is not possible. If the world is quantum mechanical, the statistics therefore cannot be used to make conclusions about non-locality.zonde said:So what non-commuting spaces you can propose for factual physical detection records?
I still don't see how your criterion relates to locality. You have just defined a criterion and named it locality, but does it really deserve that name? I can't make this connection and I'm asking for clarification.And this question is important because my counterexample (and Eberhards derivation) is based on assumption that we can analyze detection records within the same domain and that QM predictions are applicable to statistics of these detection records (as experiments confirm).
I don't think anyone has a problem with that, even people who say QM is non-local. What makes them to say QM is non-local is something you actually didn't consider at all in your post. Its about collapse!rubi said:The world is quantum mechanical. Someone in the past generated a pair of entangled quantum objects and sent one to Alice and the other one to Bob. This is the common cause that explains the non-local correlations.
No, the collapse is not a problem here, since it is only ever important if you make sequantial measurements. The statistics of a Bell-test experiment, however, are the same, whether there is a collapse or not. All statistics of Bell-test experiments can be computed from the uncollapsed state.Shyan said:I don't think anyone has a problem with that, even people who say QM is non-local. What makes them to say QM is non-local is something you actually didn't consider at all in your post. Its about collapse!
In a Bell-type experiment, at first we have one two-spin system in the state ## \frac{1}{\sqrt{2}} ( |\uparrow \downarrow \rangle-|\downarrow\uparrow \rangle) ## and this system can be as extended(in space) as you want. But suddenly, after A measures her spin, the one two-spin system collapses to two one-spin systems. This collapse is a consequence of A's measurement and the fact that A's measurement(which is a local event) is causing a non-local event (the collapse of a state which is describing a system not not wholly confined in a region of space), is what makes people say that QM is non-local.
Actually I should say the mere presence of a state like ## \frac{1}{\sqrt{2}} ( |\uparrow \downarrow \rangle-|\downarrow\uparrow \rangle) ## that couldn't care less about the spatial-extension of the system its describing means that QM is non-local.
My counterexample and Eberhard's derivation don't use local hidden variables. Only factual detections (Eberhard) and plus all possible counterfactual detections allowed by predictions of QM and locality criterion(my counterexample).rubi said:In order to conclude something about locality from the measured statistics, you need to derive an inequality and this derivation makes use of local hidden variables that can be modeled on a combined probability space.
Let's start with this definition.rubi said:I still don't see how your criterion relates to locality. You have just defined a criterion and named it locality, but does it really deserve that name? I can't make this connection and I'm asking for clarification.
Is it OK. Probably I have to add that results of tests are represented by records of some spacetime events.zonde said:As I understand concept of locality, spacelike separated regions are independent as tested by "external" parameters ("external" parameters from one region can not influence what happens in the other region).
If that derivation doesn't ever make use of hidden variables, how can you exclude the possibility that the correlations can be explained by hidden variables?zonde said:My counterexample and Eberhard's derivation don't use local hidden variables. Only factual detections (Eberhard) and plus all possible counterfactual detections allowed by predictions of QM and locality criterion(my counterexample).
What is an external parameter? I would just put it like this: Events in one region of spacetime can only influence events in the forward lightcone of that region.Let's start with this definition.
Is it OK. Probably I have to add that results of tests are represented by records of some spacetime events.
If hidden variables are local then they are still subject to locality condition.rubi said:If that derivation doesn't ever make use of hidden variables, how can you exclude the possibility that the correlations can be explained by hidden variables?
"External" parameter is for example analyzer angle. I am putting "external" in quotes because we need no-superdeterminism assumption and satisfactory source (preferably several sources) of randomness.rubi said:What is an external parameter? I would just put it like this: Events in one region of spacetime can only influence events in the forward lightcone of that region.
rubi said:Non-local correlations are not problematic though, as the example of Bertlmann's socks shows.
People claim that Bell violations are a sign for non-local causation, which doesn't follow.
Edit: I'll explain it differently: Assume Alice has a red sock. Then she immediately knows that Bob has a Blue sock. Assume Alice has a spin-up partricle. Then she immediately knows that Bob has a spin-down particle. What is the difference? The difference is that the first case can be modeled by a local classical theory, in which there was a common cause of Alice and Bobs measurements.
rubi said:Edit: Or in other words: Bell's factorization criterion requires that all local observables that are needed to predict the local future can be modeled on a combined probability space.