What were Newton's thoughts on non-locality?

[Derek P]

[Moderator's note: spun off from another thread.]

Only with force at a distance!

And yet modern physicists accept non-locality which is far worse :)
Do you know where Newton expressed his misgivings? It would be interesting to know exactly what he thought.

 

[A. Neumaier]

modern physicists accept non-locality which is far worse :)

The bad thing is not nonlocal correlations (which is an experimental fact, and not against relativity) but nonlocal information flow (which would contradict relativity, but which has not the slightest experimental basis). See the discussion in another current thread starting about here.

 

[Derek P]

The bad thing is not nonlocal correlations (which is an experimental fact, and not against relativity) but nonlocal information flow (which would contradict relativity, but which has not the slightest experimental basis). See the discussion in another current thread starting about here.

Well, the thread that you have referred to is labelled "A" and I would find it a serious struggle. So what is the "take away" concept?

No the bad thing is non-local causality. You cannot avoid something from Alice getting to Bob FTL, whether you call it information or not. If you accept the story of definite events, that is!

 

[A. Neumaier]

the bad thing is non-local causality. You cannot avoid something from Alice getting to Bob FTL

There is nothing acausal about Bell-type experiments. Alice cannot influence the statistics of Bob in a faster than light way. Extended causality - the kind of causality following from relativistic quantum field theory, is always satisfied in Bell-type experiments.

 

[Derek P]

There is nothing acausal about Bell-type experiments. Alice cannot influence the statistics of Bob in a faster than light way. Extended causality - the kind of causality following from relativistic quantum field theory, is always satisfied in Bell-type experiments.

The link doesn't seem to go anywhere useful. Anyway I disagree. Alice chooses a setting and gets a result. Bob's statistics depend on these two. Bell's theorem proves that these statistics cannot be explained locally in any theory be it QFT or science fiction. Therefore some function of Alice's setting and result influences Bob's statistics. No amount of redefining causality can alter the "macroscopic" cause and effect.

 

[A. Neumaier]

The link doesn't seem to go anywhere useful.

I improved the link.

Bob's statistics depend on these two.

No. Bob's statistics (i.e., what quantum mechanics predicts about what Bob can conclude without knowing what Alice did) is exactly the same no matter what Alice does. Only the joint (Alice,Bob) statistics depends on what Alice does, and this is of course reasonable. Moreover, the joint statistics is observable only at a time in the intersection of the future cone of both Alice's and Bob's actions, hence there is no causality problem.

 

[Derek P]

I improved the link.

No. Bob's statistics (i.e., what quantum mechanics predicts about what Bob can conclude without knowing what Alice did) is exactly the same no matter what Alice does. Only the joint (Alice,Bob) statistics depends on what Alice does, and this is of course reasonable.

Not if it breaks the Bell Inequality it isn't.

Moreover, the joint statistics is observable only at a time in the intersection of the future cone of both Alice's and Bob's actions, hence there is no causality problem.

That's a fair point - if you are willing to accept that the reality of the events is held in limbo until the news reaches Charles. I feel that Bob might disagree and quite reasonably claim that his memory of the detection event makes it at least as real as Charles's second-hand information. But it's overkill to play fast and loose with the reality of events, you just need to say that the outcome is indefinite despite appearences. Which is what MWI explains using unitary QM.

 

[A. Neumaier]

Not if it breaks the Bell Inequality it isn't.

The Bell inequalities are a statement about classical dynamics only. Therefore whether or not they hold has no impact at all on question of causality.

it's overkill to play fast and loose with the reality of events

My argument has nothing to do with the reality of events, or with memory. Bob knows his statistics only and will from his observations not notice anything Alice has done before she shares her secrets with him (or Charles).

 

[Derek P]

[Moderator's note: spun off from another thread.]

... and upgrading it from "B" to "I" in the process

And yet modern physicists accept non-locality which is far worse :)
Do you know where Newton expressed his misgivings? It would be interesting to know exactly what he thought.

 

[Derek P]

The Bell inequalities are a statement about classical dynamics only. Therefore whether or not they hold has no impact at all on question of causality.

It's a statement about the statistics of definite events. A well designed EPR experiment enforces a causal order which, if interpreted as definite events, results in an impossible violation.

My argument has nothing to do with the reality of events, or with memory. Bob knows his statistics only and will from his observations not notice anything Alice has done before she shares her secrets with him (or Charles).

That's trivially true and has no bearing on the question of causality operating on the earlier events.

 

[A. Neumaier]

If the BI is broken then Bell's theorem applies.

Bells theorem says that the inequalities hold under certain classical conditions. It says nothing about quantum systems, no matter whether or not these satisfy the inequalities. The violation only implies that the violating quantum system cannot be simulated with Alice and Bob living in some classical world prescribed by Bell's assumptions. Thus it just tells about limitations in classical understanding of quantum behavior.

 

[Mentz114]

The violation only implies that the violating quantum system cannot be simulated in the classical way prescribed by Bell's assumptions.

The experiment and the violation can be simulated by a code which assumes information sharing between the photons.

 

[A. Neumaier]

The experiment and the violation can be simulated by a code which assumes information sharing between the photons.

But not with communicating computers Alice and Bob situated at the distance required to make the Bell violations also violate classical relativity.

Simulation at one local computer of course respects even classical causality, no matter how much the Bell inequalities are violated in the simulation.

 

[Mentz114]

Simulation at one local computer of course respects even classical causality, no matter how much the Bell inequalities are violated in the simulation.

The non-locality is easily simulated inside one program. When it is inactivated all the correlations go to zero. I have a calculation that shows that the singlet state is faithfully emulated.

 

[A. Neumaier]

The non-locality is easily simulated inside one program. When it is inactivated all the correlations go to zero. I have an algebraic calculation that shows that the singlet state is faithfully emulated.

Yes, but there is no conflict with classical causality simulating Bell-violations inside one program. You can do it only because the program communicates over tiny distances only, just pretending they are large.

To have bearing on the causality problem even from a classical point of view you'd have to simulate with two computers as far apart as Alice and Bob are, with each computer doing only one partner's tasks.

 

[Mentz114]

To have bearing on the causality problem even from a classical point of view you'd have to simulate with two computers as far apart as Alice and Bob are, with each computer doing only one partner's tasks.

What you describe is an actual EPR experiment.
The transmission of information can be simulated in logic with the correct outcomes. I'd go so far as to say that I can get close to proving it.

 

[wle]

For people interested in Bell's theorem, I would heavily recommend reading Bell's "La Nouvelle Cuisine" if you can get a hold of it, since it's probably the essay where Bell gives the most careful explanation of why he was concerned with "locality", why he settled on the definition he did, and why he was not satisfied with some other possible definitions like the no-signalling principle (the point that Bob's local statistics are independent of Alice's measurement choice in quantum physics). It's been a while since I read it, but I think some of the key points that are worth understanding about Bell's views (even if you disagree with them) are:

• Bell was obviously dissatisfied with the standard ("textbook") formulation of quantum physics, particularly emphasising the apparent fundamental role attributed to "measurement" in the theory (i.e., what is nowadays called the "measurement problem").
• Bell was familiar with the Bohm hidden-variable interpretation and seemed to view it as the most likely way to resolve the measurement problem. He seemed to be hoping (before disproving the possibility) that there could be a local hidden-variable model that would do for relativistic quantum field theory what the Bohm interpretation does for nonrelativistic quantum theory.
• Bell criticised the no-signalling principle as a definition of "locality" for more-or-less the same reason, since it relies on assuming a distinction between "controllable" physical states (like the physical orientation of a Stern-Gerlach magnet or polarisation filter which determines a "measurement") and "uncontrollable" ones (like where a dot appears on a detection screen near the Stern-Gerlach magnet -- the outcome of a "measurement"), which Bell did not see a good fundamental justification for. (So, can you have a well-defined no-signalling principle in a theory that does not have a measurement problem like QM?)

So I think what you make of Bell's theorem is going to depend on how much you agree with Bell's motivations. E.g., if you're someone who thinks the standard textbook formulation of quantum physics is fine the way it is or you think some interpretation like MWI or QBism already solves everything, then you won't necessarily have much reason to be concerned if quantum theory is "nonlocal" according to some definition Bell made up. You could just see it as an interesting factoid about quantum theory in that case.

 

[PeterDonis]

The transmission of information can be simulated in logic

Yes, but so what? The simulation does not meet the conditions of the actual experiment: the events inside the computer that simulate spacelike separated measurements are not themselves spacelike separated. So the simulation does not tell you anything useful about any underlying "mechanism" in the actual experiment.

 

[A. Neumaier]

What you describe is an actual EPR experiment.
The transmission of information can be simulated in logic with the correct outcomes. I'd go so far as to say that I can get close to proving it.

Sure. But logic is independent of causality.

The point I wanted to make is that Bell's theorem is not about quantum mechanics, but about classical assumptions regarding intuition and rules. It nowhere uses Hilbert spaces, state vectors, or operators. Thus it cannot say anything intrinsic about the quantum world.

On the other hand it uses classical assumptions, hence says something about what can happen in a hypothetical world in which sufficiently many classical rules hold. In this hypothetical world, the Bell inequalities cannot be violated. Since they are violated in nature, this proves that nature is not any of these hypothetical classical worlds. Nothing else. Thus such a classical world cannot realize the experiment under otherwise equal conditions (i.e., Alice and Bob doing exactly the same at exactly the same locations and times, with exactly the same value of the speed of light, etc.). This is what I meant with ''cannot simulate''.

On the other hand, a simulation program pretends only to realize a (quantum) world. In place of performing real experiments, sending real objects to far away places where they are observed, they just simulate the mathematics. None of the computed events and correlations are produced with faster than light speed, so nothing violates any causality restrictions. Now Derek P claimed that Bell violations imply causality violations - but your simulated Bell violations imply nothing, only that the mathematics used was not faulty.

 

[Mentz114]

Yes, but so what? The simulation does not meet the conditions of the actual experiment: the events inside the computer that simulate spacelike separated measurements are not themselves spacelike separated. So the simulation does not tell you anything useful about any underlying "mechanism" in the actual experiment.

Obviously, in the computer program the entangled photons share a memory location for their polarization. When the one is changed so is the other. What is learned from the emulation is that the classical event ordering (A or B being projected first etc) AND the distinction between 00 and 11 coincidences must both be jettisoned by averaging over those variates. What is left is the singlet state.

It is not true to say that data which is exactly like that from EPR expriments cannot be simulated. I've done it many times.

 

[Mentz114]

Sure. But logic is independent of causality.

The point I wanted to make is that Bell's theorem is not about quantum mechanics, but about classical assumptions regarding intuition and rules. It nowhere uses Hilbert spaces, state vectors, or operators. Thus it cannot say anything intrinsic about the quantum world.

So, do you think non-local hidden variables can explain EPR results ? Or is that just a distraction ?

.. - but your simulated Bell violations imply nothing, only that the mathematics used was not faulty.

They shed light on what information needs to be passed.

 

[A. Neumaier]

data which is exactly like that from EPR expriments cannot be simulated.

Yes, the data can be simulated, assuming the Rules of Quantum Mechanics. But their simulation proves nothing about causality and nature. It is just a computational check of the simple lemma that there are quantum mechanical states violating the Bell inequalities. Thus if it proves anything it proves the consistency of a few lines of straightforward logical arguments.

So, do you think non-local hidden variables can explain EPR results ?

I don't care in the context of the problem under discussion - here it doesn't matter. There is no logical relation between a theorem with classical assumptions and a world governed by quantum mechanics.

Hidden variables only matter if you insist on a classical description of some sort - which I think is completely misguided. For example, Bohmian mechanics explains EPR with non-local hidden variables. But its assumptions are in another way so weird that it is no improvement over standard quantum mechanics.

 

[Mentz114]

Yes, the data can be simulated, assuming the Rules of Quantum Mechanics. But their simulation proves nothing about causality and nature. It is just a computational check of the simple lemma that there are quantum mechanical states violating the Bell inequalities. Thus if it proves anything it proves the consistency of a few lines of straightforward logical arguments.

Yes, I agree.

I don't care in the context of the problem under discussion - here it doesn't matter. There is no logical relation between a theorem with classical assumptions and a world governed by quantum mechanics.

Good to know.

Hidden variables only matter if you insist on a classical description of some sort - which I think is completely misguided. For example, Bohmian mechanics explains EPR with non-local hidden variables. But its assumptions are in another way so weird that it is no improvement over standard quantum mechanics.

Understood.

I should say that actually thinking out the emulation taught me that it will only work by ditching some classical assumptions - which actually supports your points. One of the things that is gone is the time ordering of some events. So that denies classical causality also.

Thanks for for replying in such detail.

 

[PeroK]

The link doesn't seem to go anywhere useful. Anyway I disagree. Alice chooses a setting and gets a result. Bob's statistics depend on these two. Bell's theorem proves that these statistics cannot be explained locally in any theory be it QFT or science fiction. Therefore some function of Alice's setting and result influences Bob's statistics. No amount of redefining causality can alter the "macroscopic" cause and effect.

This is not correct. Nothing Alice does affects Bob's statistics. What experiments show is that nature doesn't make up her mind in each case until a measurement is made. Bells inequality is the way to distinguish this pure QM from a simple hidden variables.

You could interpret this as nature having a non-local FTL mechanism behind the scenes. But, unless you find and tap into that mechanism you can't invoke FTL.

You certainly can't send a message FTL by simply measuring something at your end. That just tells you what nature has decided in that case. The overall statistics are governed by the initial entangled state and not by what is measured.

 

[PeterDonis]

It is not true to say that data which is exactly like that from EPR expriments cannot be simulated.

Of course you can simulate the data. You just can't conclude anything about a echanism underlying the actual experiments from the simulation.

 

[Mentz114]

Of course you can simulate the data. You just can't conclude anything about a mechanism underlying the actual experiments from the simulation.

I think it might be possible to rule out certain things by logic alone but I agree it does not have the force of an experiment.
The most interesting thing about the data, emulated or otherwise, is that whichever way it is analysed the probability estimates look like random coin tossing - except when coincidences are counted, when huge correlations appear. Like random clouds lining up and spelling out ones name - but only from a certain angle.

 

[Derek P]

You certainly can't send a message FTL by simply measuring something at your end. That just tells you what nature has decided in that case. The overall statistics are governed by the initial entangled state and not by what is measured.

I suppose it was inevitable that someone would start talking about sending messages by entanglement sooner or later. But nobody, not @PeterDonis, not @A. Neumaier, not @wle, not @Mentz114, not @Derek P... none of us have come close to suggesting that it is possible. So can we please not discuss it?

 

[PeroK]

I suppose it was inevitable that someone would start talking about sending messages by entanglement sooner or later. But nobody, not @PeterDonis, not @A. Neumaier, not @wle, not @Mentz114, not @Derek P... none of us have come close to suggesting that it is possible. So can we please not discuss it?

Your posts imply FTL communication. For example:

Anyway I disagree. Alice chooses a setting and gets a result. Bob's statistics depend on these two. ...Therefore some function of Alice's setting and result influences Bob's statistics. No amount of redefining causality can alter the "macroscopic" cause and effect.

If this is true, then it is obviously very easy for Alice to send a message to Bob FTL. At a pre-arranged time, Alice does measurement A or B on a set of particles which affect Bob's statistics. Bob then (a short time later) does his measurements and his statistics tell him whether Alice did measurement A or B. That is then a message from Alice to Bob FTL.

In any case, Bob has a certain collection of particles and his statistics are independent of what anyone else does.

 

[Derek P]

it is obviously very easy

It may be obvious to you, it is not obvious to me.

 

[A. Neumaier]

It may be obvious to you, it is not obvious to me.

He spelled out in the sentence directly afterwards how to send one bit of information if your assertion were correct.

His final statement then states what is actually the case (which doesn't allow this kind of bit-sending).

 

[stevendaryl]

If this is true, then it is obviously very easy for Alice to send a message to Bob FTL. At a pre-arranged time, Alice does measurement A or B on a set of particles which affect Bob's statistics. Bob then (a short time later) does his measurements and his statistics tell him whether Alice did measurement A or B. That is then a message from Alice to Bob FTL.

But @Derek P was not claiming that Alice could send information about her measurement choice to Bob. He was claiming that information about the combination measurement and result affected Bob.

Alice's measurement and result is a pair $(\alpha, A)$ where $\alpha$ is her orientation choice, and $A$ is her result, $\pm 1$.

The relevant question is not: "Can Bob learn something about $\alpha$?" For Derek's claim, the relevant question is: "Can Bob learn something about the pair $(\alpha, A)$?" The answer is certainly "yes". If Bob measures the spin of his particle along the z-axis, and gets result +1, then he knows afterward that $(\alpha, A) \neq (\hat{z}, +1)$. He didn't know that, previously. So he learns something about the combination of Alice's measurement + result. Which is what Derek was talking about.

Learning something about a pair of variables does not imply that you've learned anything about either variable, separately.

 

[PeroK]

But @Derek P was not claiming that Alice could send information about her measurement choice to Bob. He was claiming that information about the combination measurement and result affected Bob.

Alice's measurement and result is a pair $(\alpha, A)$ where $\alpha$ is her orientation choice, and $A$ is her result, $\pm 1$.

The relevant question is not: "Can Bob learn something about $\alpha$?" For Derek's claim, the relevant question is: "Can Bob learn something about the pair $(\alpha, A)$?" The answer is certainly "yes". If Bob measures the spin of his particle along the z-axis, and gets result +1, then he knows afterward that $(\alpha, A) \neq (\hat{z}, +1)$. He didn't know that, previously. So he learns something about the combination of Alice's measurement + result. Which is what Derek was talking about.

Learning something about a pair of variables does not imply that you've learned anything about either variable, separately.

That is correlation. Not "cause and effect", as is being claimed.

The results are correlated, but the statistics on one particle are not influenced by the choice of measurement on the other. Bob has no way to tell, without communication from Alice, a) whether she has measured anything or b) what she has chosen to measure.

I don't believe @Derek P agrees with this last statement.

 

[A. Neumaier]

then he knows afterward that

Only if Alice actually measured something. If she instead took a nap, or if her detector failed because of a power outage, Bob concluded something wrongly.

Bob gets conditional information only, of the kind: ''Should Alice have measured $\alpha=\hat z$ then her result was $-1$.'' Because Bob doesn't know whether the hypothesis holds, he knows nothing. Having about tomorrow's whether the conditional information that ''Should there be no clouds it will not rain'' tells in fact nothing useful about the weather tomorrow, unless we have information about tomorrows clouds.

In any case, whatever statistics from data collected by Bob can be made (by Bob or Charles) before Alice's choices or results become available to them will be completely unaffected by the behavior of Alice and her detector. Thus there are no causality violations, in contradiction to the claim of @Derek P:

No the bad thing is non-local causality. You cannot avoid something from Alice getting to Bob FTL, whether you call it information or not.

This something is called ''conditional information''. But nothing in relativity forbids conditional information to be passed faster than light. For example, we know lots of conditional information about what can or cannot happen inside black holes although no information can flow out from there. Conditional information is what we can get from theory independent of observation, but theoretical conclusions apply instantaneously and have no speed limit.

Causality only demands that information flow is limited by the speed of light. Thus causality is not violated in Bell-type experiments.

 

[Derek P]

This something is called ''conditional information''. But nothing in relativity forbids conditional information to be passed faster than light. For example, we know lots of conditional information about what can or cannot happen inside black holes although no information can flow out from there. Conditional information is what we can get from theory independent of observation, but theoretical conclusions apply instantaneously and have no speed limit.
Causality only demands that information flow is limited by the speed of light. Thus causality is not violated in Bell-type experiments.

The required information is unconditional - namely Alice's actual setting and Alice's actual result.

 

[Derek P]

In any case, whatever statistics from data collected by Bob can be made (by Bob or Charles) before Alice's choices or results become available to them will be completely unaffected by the behavior of Alice and her detector. Thus there are no causality violations, in contradiction to the claim of @Derek P:

Well that is highly ambiguous. If you are saying that the events CANNOT be affected because of relativity, causality etc then of course I would agree. But in a well-designed EPR experiment the observations ARE affected.