# Do nonlocal entities fulfill assumptions of Bell theorem?

Discussion in 'Physics & Math' started by Jarek Duda, Nov 3, 2015.

1. ### Jarek DudaRegistered Senior Member

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CHSH is a completely general inequality while asking about correlations between some 4 events: a, a', b, b'.
Here these events are measurements of light polarization (of the same beam) in 4 different angles - separated by pi/4.

I don't understand your problem - could you be more specific?

3. ### przyksquishyValued Senior Member

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Why should they fulfill CHSH? The situation is different than what CHSH was derived for and it isn't even the same kind of correlation, so why "should" they satisfy the same inequality?

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7. ### Fednis48Registered Senior Member

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Formally, it makes no sense to talk about correlations between "events", because events aren't numbers. Bell's Theorem, specifically, applies to correlations between scalar measurement outcomes. The experiment we're talking about does not look at the correlations between the measurements of the separate output beams; rather, it uses those measurements to find some derived quantities, then calculates the correlations between those. There is no reason to expect such correlations would satisfy Bell's inequality, classical or no. It sounds like you think Bell's Theorem is a bound on any correlation function between classical variables, and it's definitely not that general.

8. ### Jarek DudaRegistered Senior Member

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Correlations can be expressed by frequencies of events, they are measured as intensities in the discussed experiment - the energy of a single photon is not changed be a polarized, only their number - proportional to intensity.
There is nothing about "separate output beams" in derivation of Bell inequalities - this is an extremely universal derivation/inequality ... as you have already pointed me a few times at the beginning of this long thread.

However, these general equalities are violated in both QM and classical field here.
And it is not a surprise - just look at phonons in a crystal: https://en.wikipedia.org/wiki/Phonon
We can describe classical evolution of positions of atoms in a crystal lattice.
Alternatively, we can look at its normal modes as phonos - and describe them using quantum formalism - in a linear theory, sum of normal modes acts as superposition/entanglement.

Classical (lattice/field) and quantum pictures are just two equivalent descriptions of the same system.

9. ### przyksquishyValued Senior Member

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That doesn't answer the question I asked. Why should there be a hidden variable and model of the same mathematical form as Bell considered?

For Bell (from his 1964 paper), summarising EPR, the motivation was:

...and the type of hidden variable model that Bell goes on to consider is entirely motivated by this, i.e., it has the mathematical form it does because Bell was modelling locality and causality.

By contrast, the situation described in the Optica article doesn't involve distant correlations (so there's no opportunity to see anything that might challenge locality), and the supporting theory is based on classical electromagnetism, a theory that is already causal and local, so why should there be a hidden variable model for it that would imply their CHSH inequality?

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10. ### Jarek DudaRegistered Senior Member

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Analogous way of thinking leads to " ... as an argument that classical field theory could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality."
The discussed article shows that classical field theory has exactly the same problem as QM - like crystal can be described by classical positions, or by normal modes - "quantum" phonons.
Bell's inequalities are violated in both of them - hence, in contrast to classical mechanics, Bell's argument does not exclude field theoretic models of the reality.

This discussion is not going forward and I have a busy week - you can discuss your objections also here:

Last edited: Nov 17, 2015
11. ### Farsight

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Because you dismiss the hard scientific evidence bruce. Because you're a troll. As everybody can see by looking at your posts.

12. ### przyksquishyValued Senior Member

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No, that wouldn't work, since the Optica article doesn't deal with actual joint events (like EPR does) and there are no distances involved (so there is nothing to sensibly apply the relativistic causality principle to).

In fact, what you say doesn't even make sense, since classical electromagnetism is already compatible with relativistic causality and locality. There is nothing to "restore" in that case.

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13. ### Jarek DudaRegistered Senior Member

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Please show me where you need involvement of distance in derivation of CHSH?
https://en.wikipedia.org/wiki/CHSH_inequality#Derivation_of_the_CHSH_inequality

Electromagnetism is realistic and local (finite propagation, but its entities like waves are nonlocal) - hence some would say that you need to add there some magical superluminal data transmission to model reality ... while this article shows that it already violates CHSH - no additional magic and hand-waving is needed.

14. ### Fednis48Registered Senior Member

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True. And if the experiment actually looked at correlations between the intensities of different beams, then a Bell inequality violation would be surprising. Instead, the correlations are between derived quantities not expressable as the outcomes of different measurements, so Bell's Theorem need not apply.

Well, there's nothing about separate output beams, because Bell's Theorem doesn't just apply to beams. But the notion of correlations between two separate measurements plays a central role in every derivation of Bell's Theorem.

The crucial difference here is that quantum mechanics allow for complex amplitudes. It's true that any classical field can be expressed as a sum of amplitudes over its normal modes, but since these amplitudes are restricted to real numbers, there is no violation of Bell inequalities. If you don't believe me, try to come up with a counterexample; you'll find it can't be done. This is reflected in the inequalities themselves by the presence of 45-degree measurements, which in some sense rotate real numbers to complex ones.

Right there at the start, just under the Bell's 1971 derivation heading. "We start with the standard assumption of independence of the two sides..." If the two sides (i.e. measurements) are separate from each other, we expect them to be independent because of locality. If they are instead two derived quantities from the same physical quantity, there is no reason to make the standard assumption.

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15. ### przyksquishyValued Senior Member

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It's used to justify the mathematical factorisation condition (written there as $E(a, b) = \int \underline{A}(a, \lambda) \underline{B}(b, \lambda) \rho(\lambda) d\lambda$) that the derivation starts with.

The article by Norsen (arXiv:0707.0401 [quant-ph]) and one of the essays by Bell (available from here) that I linked to in my first post in this thread explain this in detail.

Last edited: Nov 18, 2015
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16. ### SchmelzerValued Senior Member

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There are, yet, no two different speeds, thus, also no need for two ethers. If in some future there appears such a necessity, so what? We have already examples - speed of sound together with speed of light inside a usual piece of condensed matter.
You have the equations of the most fundamental theory - quantum mechanics - in the variant with the dBB interpretation, which contains a formula for the velocity $\dot{q}$ of a given configuration $q$. A "how" question about the most fundamental theory will always remain unanswered - the answer will always be a more fundamental theory, which allows to derive the previous theory as some approximation, and in this way explains how it works. So, wait for a subquantum theory if you want to understand how the QM equations work.
This is what Great Manitou told you, or how you have obtained such information about subquantum theory? Same question for all the other mentioned "problems" too.

The point being? Up to now, I'm not aware that quantum effects have been observed for distances much larger than one astronomical unit, which is small in comparison with the universe. Or have I missed something? I'm also very sorry for you that your brain seems to use dumb spherical wavefronts to distribute information, my brain uses, afaik, a neuronal network, scnr.
Signalling has been used successfully to explain everything in the classical domain, including Newtonian gravity, which also contained, in Newton's version, infinite speed. There is no reason to reject old successful explanations, especially in situations where nothing better is available. Giving up realism and causality in favor of mysticism and astrology is, of course, always a possibility, but, sorry, I'm prejudiced against this possibility.

17. ### Q-reeusValued Senior Member

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????? You have many times this forum and elsewhere claimed a signalling speed v >> c as reasonable (quasi dBB basis), just as long as v is not actually infinite.
The 'so what' is not merely to explain what kind of 2nd 'ether' could support propagation speeds v >> c. It's all the rest that's required - 'smart signalling' without energy-momentum expenditure or attenuation with distance etc.
You know better than that. Standard dBB requires instantaneous connections over any distance. Modifying that at all is to reject dBB in favour of a dBB look-alike.
Speculation about some subquantum theory is moot. Any such will have to deal with the same basic objections as for standard QM 'signalling' issues.
Great Manitou told me something? Where did that one get pulled out from? Resorting to senseless derision will not win an argument. Signals that have physical effect but require no expenditure or back-reaction needs quite some justification. I say there is none on offer. Well maybe Susskind-style magical 'micro-wormholes' will appeal. But then iirc you like me reject such entities outright. What else then?
Why pick 1 AU? That's already an enormous separation wrt purported signalling requirements. As indeed is merely the length of a typical laboratory bench in fact.
Is that some kind of sarcastic humour? Or meant to convey something objectively relevant and 'deep'? If the latter, explain the basics of this 'neuronal network' - presuming it relates to OP issue and not brain physiology (i.e. sarcastic humour).
Really? Last time I checked, Newtonian gravity was an instantaneous action-at-a-distance theory that just 'was' and Newton and all since never talked of 'signals' being instantaneously exchanged in order for it to work.
Now you're being silly. As someone familiar with GR you know very well Newtonian instantaneous action-at-a-distance gravity is inconsistent with e.g. GW's and various aspects of binary pulsar data etc, in addition to e.g. incorrect prediction for gravitational deflection of starlight.
I have no greater inclination to accepting mysticism but substituting one variety for another is not the way out.

Last edited: Apr 26, 2017
18. ### iceauraValued Senior Member

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27,099
Violations of Bell's Inequality, implying entanglement and consistent with the predictions of QED, have been observed in starlight from a much greater distance than 1 AU: https://phys.org/news/2017-02-physicists-loophole-bell-inequality-year-old.html

19. ### iceauraValued Senior Member

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Causality is of course a derived, rather than fundamental, feature of the universe; a useful mental shortcut, never more than approximately descriptive of a real situation. A useful crutch for a limited brain.

It is far too useful and reliable a concept to be abandoned casually, or for lesser concepts of little use, but if the best theories require that it be modified or even set aside in order to understand what is going on, in order to register and think about what our virtual sensory mathematics has shown us, then that is what is going to have to be done.

Realistically speaking.

20. ### SchmelzerValued Senior Member

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Yes, it is reasonable. But, yet, we do not have these two speeds. In dBB the signal speed is infinite. Similar to Newtonian theory. In some future, dBB may be replaced by some more fundamental theory, which has some larger limiting speed. Or not. We will see, if we survive up to this moment.
Of course, dBB is not the final theory, thus, will be rejected. Without doubt. It has, last but not least, its own infinities (the velocity near wave function zeros becomes infinite). If the result will be a dBB look alike or not we will see. Is GR an NT look-alike? Hardly. I'm sure that it will be a realistic and causal theory, supporting usual logic and probability theory (which is the logic of plausible reasoning). And it will have the equations of GR/ QT as some limit/approximation. Everything beyond that is guess.
Ok, so why you speculate about problems where speculation is moot?
Simply rhetorics, don't whine. There is nothing which enforces this. Conservation laws are, in the Noether approach, a consequence of translational invariance of the theory, together with the Langrange formalism. Same for action equals reaction, it follows from the Lagrange formalism. Who told you that the next more fundamental theory will have such a formalism? And, if not, why would you think that classical conservation laws play a role?
Why 1 AU? Just for fun (and to avoid that you find an experiment which really reached this dimension). I could have used as well one 1 OUD (Observable Universe Diameter). So, yes, some kind of sarcastic humor. Numbers in physics are anyway unimaginable large or small in comparison with human imagination. So such feelings are irrelevant. (Or should better be irrelevant - you know, all those mainstream physics talking about the Great Accuracy of the predictions of GR and SM seem to think that this matters, as an argument that some properties of our actually best theories are really fundamental.)
Of course you can send a signal with infinite speed in NT. And there have been computations and measurements of the speed of gravity before GR. With the result that the speed of gravity is much greater than c. (I don't care about what people have talked about, so maybe you are right about the language they used, who knows.)
Sorry, you misunderstood me. Of course, I do not propose to return to NT. I have a much better ether theory of gravity, as you know. But NT is simply an example that a theory with infinite signalling speed can be explained as the limit of a theory with finite signalling speed. This possibility is known, and simple, and something similar may happen with the infinite signalling speed of dBB theory too. And therefore I see no reason to worry a lot about infinite signalling speed in dBB theory.
I'm working on getting rid of the really serious mainstream-accepted elements of mysticism in physics. And I think I'm very successful in this. No need for a mystical four-dimensional curved spacetime, where a simply ether evolving in normal space does the job, even better given that we know how to quantize this ether. Now my main interest is quantum interpretation. And there is also no need for mainstream mysticism, like many worlds, quantum logic, Schroedinger's cats or (in)consistent histories. And certainly no reason to give up realism, logic, probability theory, or causality, in all their classical beauty. This does not mean that understanding QT is a finished job, and nothing mystical remains. But infinite signalling speed is simply not the point to worry about.
No. In the experiment, starlight from far away has simply been used as a random number generator, to avoid the loophole that the choice of the experimenters what to measure was already fixed at the time of creation of the pair, and could have somehow influenced the creation process. They could have used completely classical properties of that starlight for this experiment, all they needed that it was random, and the source of randomness far far away. The real quantum part of the experiment was the usual one, "they shot the entangled photons out in opposite directions, toward detectors located in buildings several city blocks awayâ€”the Austrian National Bank and a second university building."

Sorry, but I have never seen any derivation of causality which makes sense. Of course, causal connections in one theory will be usually explained by deeper and more complex causal connections of a more fundamental theory.

There is also a wide range of rather informal used of the word "causal", and some of these uses may be, indeed, derived. But what is relevant here is only a very special meaning of causality, the one connected with probability theory by Reichenbach's principle of common cause. Not the many other "causal influences" used in evolution theory or teleological descriptions of human behavior.
Feel free to speculate about this possibility. But it is nothing which has actually happened. With Bell's theorem we have simply a case where relativists don't want to accept that their theory is empirically falsified, and are ready to sacrifice even realism and causality to defend their beloved mystical idea of fundamental relativistic symmetry.

21. ### Q-reeusValued Senior Member

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I have no issue per se with possible failures of such formalisms. Having for instance found long ago stock standard classical EM field equations predict results that violate the very definitions of two of the ME's. And other areas of physics where similar issues arise. But there are what may be called reasonable vs unreasonable violations/discrepancies/modifications - pick a term to taste. The issues I earlier raised re QM 'signalling' come under the hugely unreasonable category imo.

22. ### SchmelzerValued Senior Member

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Your claim about the EM equations sounds, as formulated, like complete self-contradictory nonsense, sorry. What remains is nothing I could comment, because "unreasonable imo" is nothing what could be criticized.

23. ### Q-reeusValued Senior Member

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To you it would given what a formal physics training has instilled inside the cranium. Yet the conundrum is easy enough to show. Which will not be done here or any time soon elsewhere.
It's what you pointedly never addressed earlier - my pointing out the necessary characteristics of any 'signalling' that could possibly work. Defying every reasonable physical principle to do so. You opt for mysticism no less than the others that drop realism or both locality and realism. Maybe there is no escape from mysticism of some sort.

Last edited: Apr 27, 2017