Assumptions of the Bell theorem

  • #851
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I consider causality the prerequisite of all science.
Sure, but Bohmian mechanics is also causal. The issue is whether causality should have a relativistic form, which is not a prerequisite of all science.

Another closely related prerequisite of all science, which Bohmian interpretation accepts but standard interpretation doesn't, is the Reichenbach common cause principle.

Last but not least, considering causality as a prerequisite of all science is a philosophical principle.
 
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  • #852
martinbn
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Sure, but Bohmian mechanics is also causal. The issue is whether causality should have a relativistic form, which is not a prerequisite of all science.
Not a prerequisite, but given that the other option is refuted by observation, it is the only possibility.
 
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  • #853
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given that the other option is refuted by observation, it is the only possibility.
But the other option is not refuted by experiment. Just as experiments of 18th century did not refute Einstein relativity, today experiments do not refute the possibility that Einstein relativity can be violated in some regime.
 
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  • #854
martinbn
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But the other option is not refuted by experiment. Just as experiments of 18th century did not refute Einstein relativity, today experiments do not refute the possibility that Einstein relativity can be violated in some regime.
Be careful you start to sound a lot like a crackpot. It is a slippery slope, once you go that way it is hard to go back. :wink:
 
  • #855
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Sure, but Bohmian mechanics is also causal. The issue is whether causality should have a relativistic form, which is not a prerequisite of all science.

Another closely related prerequisite of all science, which Bohmian interpretation accepts but standard interpretation doesn't, is the Reichenbach common cause principle.

Last but not least, considering causality as a prerequisite of all science is a philosophical principle.
Well, the empirical decision between the relativistic spacetime models with a limiting speed and the Newtonian spacetime model with no such limiting speed is overwhelmingly decided in favor of the former.
 
  • #856
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Be careful you start to sound a lot like a crackpot. It is a slippery slope, once you go that way it is hard to go back. :wink:
A crackpot says: Einstein was wrong.
A conservative scientist says: Experiments proved that Einstein was right.
An open minded scientist says: All existing experiments confirm that Einstein was right in the regimes where experiments have been performed, but we don't know whether Einstein was right in the regimes in which experiments have not been performed yet.
I try to be in the third category, even if, by superficial reading, it creates a risk of sounding like being in the first.
 
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  • #857
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Well, the empirical decision between the relativistic spacetime models with a limiting speed and the Newtonian spacetime model with no such limiting speed is overwhelmingly decided in favor of the former.
There is no such animal as "empirical decision" in a situation where both models have not been falsified by any experiment. In such situations you can only claim that relativity makes additional falsifiable predictions, in particular that no signals can be send faster than light. But this additional prediction of relativity is quite weak, given that classical ether theory has also speed limits for the sound waves of the ether, namely the speed of sound. So all we need to get the same prediction in a Newtonian context is that all the SM waves are sound waves of some universal ether.

On the other hand, the Newtonian model has also additional predictions, namely everything which follows from Reichenbach's common cause principle. Because if you accept Reichenbach's common cause principle in relativistic causality, you can prove Bell's theorem and it is falsified. How to live without the common cause principle is beyond me, because it is so much common sense that we use it implicitly without even thinking about it. (And that's why all those who propose this solution continue to use it without hesitation.)

Think about it: If there is a correlation, then the common cause principle requires some causal explanation. Say, if we observe some correlation between smoking and lung cancer, we require a causal explanation. Smoking causes lung cancer is one, others have been proposed, but the statistics show that if we control for these other explanations the correlation remains. So we conclude that smoking causes lung cancer. How to make this conclusion if correlations no longer require causal explanations?
 
  • #858
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Causality, space, time, locality, realism, common causes, correlations... are necessary macroscopic "accessories" to quantum fields.
Influences do not travel through an ether but through the respective relativistic electron, gluon, quark etc. field. This model explains pretty much all of reality at all scales, so far without gravity.
 
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  • #859
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There is no such animal as "empirical decision" in a situation where both models have not been falsified by any experiment. In such situations you can only claim that relativity makes additional falsifiable predictions, in particular that no signals can be send faster than light. But this additional prediction of relativity is quite weak, given that classical ether theory has also speed limits for the sound waves of the ether, namely the speed of sound. So all we need to get the same prediction in a Newtonian context is that all the SM waves are sound waves of some universal ether.
The Newtonian spacetime model is indeed empirically falsified with high significance. E.g., no accelerator for particles to relativistic speeds close to light would work if you'd use Newtonian mechanics to construct it. Also the GPS couldn't work without taking into account General Relativity etc. etc.

Classical aether theory agrees with (special) relativity up to order ##\beta=v/c## and differs beyond that. Of course, the "empirical decision" is in agreement with relativity, not with aether theory, and that's why we all learn relativity in the 1st semester at university and nothing about aether theory (except the professor bothers to make some historical remarks about this hypothesis and its empirical refutation).
 
  • #860
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A crackpot says: Einstein was wrong.
A conservative scientist says: Experiments proved that Einstein was right.
An open minded scientist says: All existing experiments confirm that Einstein was right in the regimes where experiments have been performed, but we don't know whether Einstein was right in the regimes in which experiments have not been performed yet.
I try to be in the third category, even if, by superficial reading, it creates a risk of sounding like being in the first.
I think you'd be more likely to be mistaken for crackpot, by the conservative types than other open minded types ;)

IMO, the whole notion and meaning of causality, becomes fuzzy end ambigous when spacetime itself does. This is why I think that looking at the foundations of QM (which for some people, involves also the relation to gravity), can not too conservatively stick to the paradigm outside it's domain.

In some agent pictures, one can consider another typer of "causality", that does not refer to 4D spacetime, but a more abstract information space. This in principle then means, that the ordinarty meaning of light cone causailty, may be relaxed from another perspective beucase spacetime itself becomes relaxed. If Causality is a property of 4D spacetime, what is the "generalized meaning" of causality prior to 4D formation?

If we refuse to ponder about relaxing physical laws, how can we ever hope to find a deeper explanatory understanding?

/Fredrik
 
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  • #861
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Classical aether theory agrees with (special) relativity up to order ##\beta=v/c## and differs beyond that.
The Newtonian spacetime model is indeed empirically falsified with high significance. E.g., no accelerator for particles to relativistic speeds close to light would work if you'd use Newtonian mechanics to construct it.
Have you really never heard about the Lorentz ether? It is based on the Newtonian spacetime model, but makes the same predictions as SR.

Also the GPS couldn't work without taking into account General Relativity etc. etc.
And the extension of the Lorentz ether to gravity which gives the same predictions as GR is also well-known here:

Schmelzer, I. (2012). A Generalization of the Lorentz Ether to Gravity with General-Relativistic Limit. Advances in Applied Clifford Algebras 22(1), 203-242, resp. arxiv:gr-qc/0205035
Of course, the "empirical decision" is in agreement with relativity, not with aether theory, and that's why we all learn relativity in the 1st semester at university and nothing about aether theory (except the professor bothers to make some historical remarks about this hypothesis and its empirical refutation).
No, you learn relativity because the extension of the Lorentz ether to gravity was unknown for a long time and, given there was a relativistic theory of gravity but no comparable ether theory of gravity, it was reasonable to favor GR - unknown theories cannot participate in the competition. And once on anyway for gravity has to teach GR, it makes sense to teach SR even if the classical Lorentz ether is equivalent.

After the generalization to gravity is known, the two theories are empirically on equal foot. For those who ignore it, GR remains the preferred theory, whatever its singularities and quantization problems. Probably forever, independent of what happens in science, given that ignorance is a universal tool and can be always applied to get rid of what one does not like.
 
  • #862
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Why should one use a more complicated scheme for the same physics. Occam's razor is a very useful tool!
 
  • #863
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Why should one use a more complicated scheme for the same physics. Occam's razor is a very useful tool!
Because simplicity is a subjective category. What one person finds simpler another person finds more complicated, and vice versa. For instance, when I solve problems in quantum physics, I often first solve it conceptually with the Bohmian picture in my mind (because that's simpler for me) and then translate the results into a standard "Copenhagen" picture (because that's simpler for most intended readers of the paper I eventually write).
 
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  • #864
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Why should one use a more complicated scheme for the same physics. Occam's razor is a very useful tool!
A Newtonian background simplifies a lot of things. For example, it gives local conservation laws. For example, think about the "topological foam".

A notion of causality which is predefined and independent of the physical configuration simplifies also a lot, especially in comparison with a notion of causality depending on the gravitational field if the gravitational field becomes, because of quantum effects, uncertain.
 
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  • #865
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Because simplicity is a subjective category. What one person finds simpler another person finds more complicated, and vice versa.
I think simplicity can be relative even in a more formal sense, if you consider different ways for an agent(observer) to represent and process information about past, in order to predict the future for the benefit of it's survival. Then it seems obvious that what is the best or simplest way, depends on the agents capacity at hand. So occams razor for an atom may be different from th occams razor for the lab frame where creatures doing QM lives. This would even make noise relative. An agent with higher capacity of decoding information may find information in what a less capacble agent can. I think is interesting and this relativity of simplicity is not just about us humans I think.

/Fredrik
 
  • #866
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A Newtonian background simplifies a lot of things. For example, it gives local conservation laws. For example, think about the "topological foam".

A notion of causality which is predefined and independent of the physical configuration simplifies also a lot, especially in comparison with a notion of causality depending on the gravitational field if the gravitational field becomes, because of quantum effects, uncertain.
You have nearly as many conservation laws from relativistic (Minkowski) spacetime symmetries as from Galilei-Newtonian spacetime. In fact the Galilei group is a bit more complicated than the Poincare group, particularly when it comes to quantum theory. I can't say anything about quantum gravity, because there's no consistent quantum theory of the gravitational interaction.
 
  • #867
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Why should one use a more complicated scheme for the same physics. Occam's razor is a very useful tool!
Because simplicity is a subjective category. What one person finds simpler another person finds more complicated, and vice versa.
Occam's razor is important for discouraging overfitting. If one model has to introduce additional parameters to be able to reproduce predictions (hopefully consistent with observations) for which another model needs no such parameters, then it is less simple as far as Occam's razor is concerned.

But for comparisons between models with isomorphic parameters that make identical predictions, Occam's razor doesn't help, it is dull so to speak.
 
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  • #868
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You have nearly as many conservation laws from relativistic (Minkowski) spacetime symmetries as from Galilei-Newtonian spacetime. In fact the Galilei group is a bit more complicated than the Poincare group, particularly when it comes to quantum theory.

The issue with conservation laws is without doubt not a problem of SR. I have thought that you talk about GR vs. generalized Lorentz ether, where we have indeed some essential differences like background independence vs. Newtonian background, and no local conservation laws vs. well-defined conservation laws.

I can't say anything about quantum gravity, because there's no consistent quantum theory of the gravitational interaction.
Quantum gravity as an effective field theory exists:

Donoghue, J.F. (1994). General relativity as an effective field theory: The leading quantum corrections. Phys Rev D 50(6), 3874-3888;
Donoghue, J.F. (1996). The Quantum Theory of General Relativity at Low Energies, Helv.Phys.Acta 69, 269-275, arXiv:gr-qc/9607039.

It works mathematically equivalent to the generalized Lorentz ether. Namely, it uses the field theory version of GR, thus, fixes a flat background. It is done in harmonic coordinates, so that general covariance has to be broken.

Once it is defined as an effective field theory, all one needs to gain a consistent quantum theory is to define one consistent regularization around or beyond the critical length. A lattice regularization will do it. There may be some problems showing the large distance limit of that regularization is indeed the original theory, but consistency will not be a problem.
 
  • #869
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Necessary assumptions:
[...]
I think one is missing - or it is formulated implicitly.

If your express the concept of local realism via local hidden variables and specify that outcome must be an isolated function only depending on those and the detector setting, you rule out any outside interaction. So you do not consider any local realistic theory that models measurement as an (superluminar) interaction - i.e. almost non-locally.

On the other hand if you allow local interaction, then hidden variables could interact through local means but required always an non zero amount of time for that interaction. So if measurement process itself wasn't instantaneous but there is time between the start of the process and end when it settles for a value, than this gives hidden variables some room to interact - if only in a superluminar way to meet the strict time restrictions. An instant measurement therefore also rules out the option of local interaction which always needs non zero time to take place.

Not sure if that is just a formal observation, but the non-locality is technically bound to disabling interaction and if you were to relax that, the instant measurement.
 
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  • #870
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Think about it: If there is a correlation, then the common cause principle requires some causal explanation. Say, if we observe some correlation between smoking and lung cancer, we require a causal explanation. Smoking causes lung cancer is one, others have been proposed, but the statistics show that if we control for these other explanations the correlation remains. So we conclude that smoking causes lung cancer. How to make this conclusion if correlations no longer require causal explanations?

This reasoning is basically circular. If correlations require a common cause, and the common cause principle requires causality... then of course correlations require causality. But this is the quantum world! You can't make such sweeping assertions!!

Simply put: There is no time ordering required by quantum predictions (I'm thinking of the various array of Bell tests). You can in fact entangle pairs *after* they are measured, by the same mechanism as you would entangle them before they are measured (swapping). Completely consistent with quantum theory are the various acausal/adynamical and time symmetric interpretations. In those, a future measurement setting is part of an overall context. No single component of the overall context can be considered to be the "cause" of the final correlated outcome(s). See for example:

Time Symmetric Quantum Mechanics:
https://arxiv.org/abs/0706.1232

Relational BlockWorld:
http://philsci-archive.pitt.edu/3247/1/RBW_FPP_2007.pdf

As far as anyone knows, these are not inconsistent with relativity. You can't assume classical causality, except by personal preference.
 
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  • #871
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This reasoning is basically circular. If correlations require a common cause, and the common cause principle requires causality... then of course correlations require causality. But this is the quantum world! You can't make such sweeping assertions!!

Simply put: There is no time ordering required by quantum predictions (I'm thinking of the various array of Bell tests). You can in fact entangle pairs *after* they are measured, by the same mechanism as you would entangle them before they are measured (swapping). Completely consistent with quantum theory are the various acausal/adynamical and time symmetric interpretations. In those, a future measurement setting is part of an overall context. No single component of the overall context can be considered to be the "cause" of the final correlated outcome(s). See for example:

Time Symmetric Quantum Mechanics:
https://arxiv.org/abs/0706.1232

Relational BlockWorld:
http://philsci-archive.pitt.edu/3247/1/RBW_FPP_2007.pdf

As far as anyone knows, these are not inconsistent with relativity. You can't assume classical causality, except by personal preference.

First, causality goes beyond classical thinking (false dichotomy) and second, correlations cant be arbitrary.
 
  • #872
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First, causality goes beyond classical thinking (false dichotomy) and second, correlations cant be arbitrary.
But correlations can be quite arbitrary. Think of the most simple case of two random variables with some joint probability distribution ##\rho(x_1,x_2)##. Expectation values (first order), variances and correlations (second order), skews and all higher order of that distribution are just a the coefficients of a series decomposition much like Taylor is. When the random variables live in a space-time, then there are also coordinates to play with, including time. Ah and yeah, simultaneity isn't well defined here as well.

What's the causality of that? I don't think that is makes sense to apply causality everywhere.

Causality implies a strict order. So it makes only sense where that is the case, i.e. systems with entropy that have a visible direction of time.
 
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  • #873
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This reasoning is basically circular. If correlations require a common cause, and the common cause principle requires causality... then of course correlations require causality. But this is the quantum world! You can't make such sweeping assertions!!

Simply put: There is no time ordering required by quantum predictions (I'm thinking of the various array of Bell tests). You can in fact entangle pairs *after* they are measured, by the same mechanism as you would entangle them before they are measured (swapping). Completely consistent with quantum theory are the various acausal/adynamical and time symmetric interpretations. In those, a future measurement setting is part of an overall context. No single component of the overall context can be considered to be the "cause" of the final correlated outcome(s). See for example:

Time Symmetric Quantum Mechanics:
https://arxiv.org/abs/0706.1232

Relational BlockWorld:
http://philsci-archive.pitt.edu/3247/1/RBW_FPP_2007.pdf

As far as anyone knows, these are not inconsistent with relativity. You can't assume classical causality, except by personal preference.
Here is our book on acausal explanation resolving the mysteries of modern physics: Beyond the Dynamical Universe, and here is our most recent paper on it: Beyond Causal Explanation: Einstein's Principle Not Reichenbach's. Accordingly, explanation is fundamentally about 4D constraints and dynamical/causal explanation follows when appropriate. For example, Fermat's Principle is a 4D constraint and Snell's Law is the dynamical counterpart. Typically, people believe the converse is true and that's what causes so many mysteries in modern physics (origin of the universe, grandfather paradox for closed timelike curves, entanglement, measurement problem, ... ). What we argue in the book and paper is that sometimes there just isn't a reasonable dynamical/causal counterpart to the fundamental 4D constraint. Another one that we're all familiar with is the relativity principle applied to the measurement of the speed of light c. Today, we (most of us anyway) just accept that "principle explanation" of time dilation and length contraction without requiring a causal mechanism ("constructive counterpart") a la the luminiferous aether. If you apply the relativity principle to the measurement of Planck's constant h, you get the difference between quantum probability theory and classical probability theory to include Bell state entanglement. Here is a paper on that: Answering Mermin's Challenge with Conservation per No Preferred Reference Frame. Here is an argument using Information Invariance & Continuity per quantum information theory (still under review) that makes the point more generally: The Relativity Principle at the Foundation of Quantum Mechanics.

If someone later comes along with a "theory of the aether," it will not in anyway refute the already existing principle account (unless it changes Lorentz invariance or makes conflicting predictions). Likewise, for Bell state entanglement and the mysteries of quantum mechanics. It's been well over 100 years without seeing anything accepted along those lines for SR or QM, so we could be waiting a long time. In the meantime, we have the principle accounts based on empirical and mathematical facts :-)

 
  • #874
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This reasoning is basically circular. If correlations require a common cause, and the common cause principle requires causality... then of course correlations require causality. But this is the quantum world! You can't make such sweeping assertions!!
??????? Quantum theory is science. At least I hope so. Science has to follow scientific methodology. Once it is part of scientific methodology that correlations require causal explanations, causality is part of scientific methodology. Means, causality (the variant of it which includes the common cause principle) is part of scientific methodology. Means, quantum theory is obliged to follow the principles of causality. If some interpretation of quantum theory violates the principles of scientific methodology, it has to be rejected, that's all.

No circular reasoning here - except if you define scientific methodology as all what some scientists are doing. But this would be your personal [self-censored] decision, I do not support such [self-censored].

If you name this a "sweeping assertion" and add some !! this does not define an impressive argument. "Science" without the requirement to find causal explanations of observed correlations is not science, but something comparable with astrology.

Simply put: There is no time ordering required by quantum predictions (I'm thinking of the various array of Bell tests). You can in fact entangle pairs *after* they are measured, by the same mechanism as you would entangle them before they are measured (swapping).
Whatever, all those predictions are compatible with a particular choice of time ordering. Take any time coordinate, and consider the dBB version of such experiments, and you will always find a picture with FTL influences but nonetheless causal.
Completely consistent with quantum theory are the various acausal/adynamical and time symmetric interpretations.
I can name also other nonsense which is "completely consistent with quantum theory". I have recently seen a paper discussing the compatibility of Hindu mysticism with quantum theory. Once scientific methodology requires causal explanations for correlations, interpretations which reject causality should be rejected as violating scientific methodology.

If there would be no interpretation of QT at all which would be compatible with the common cause principle, you could reasonably argue that there is something wrong with the common cause principle. It would be nonetheless a hard job for you, given that you would either have to present some replacement sufficient to replace causal reasoning in everyday life about smoking and lung cancer, or to reject all the up to now scientific conclusions based on the application of the common cause principle.

But actually we have causal interpretations of QT, starting with dBB as the most famous one. So there is no base at all for doubt.
In those, a future measurement setting is part of an overall context. No single component of the overall context can be considered to be the "cause" of the final correlated outcome(s). See for example:

Time Symmetric Quantum Mechanics:
https://arxiv.org/abs/0706.1232

Relational BlockWorld:
http://philsci-archive.pitt.edu/3247/1/RBW_FPP_2007.pdf

As far as anyone knows, these are not inconsistent with relativity. You can't assume classical causality, except by personal preference.
Same point - compatibility with relativity does not mean compatibility with the scientific methodology. Anti-scientific mysticism may be compatible as with quantum mysticism, as with relativistic mysticism.

Relativistic causality itself (Einstein causality) is compatible with classical causality as well as what scientific methodology requires - it does not reject the common cause principle, or anything else, but makes the stronger claim that causal influences can happen only inside the light cone. This notion of Einstein causality allows to prove the Bell inequalities, thus, has been empirically falsified.

Weakening it to "signal causality" does not save relativistic causality because it is not really a notion of causality, given that it does not contain the common cause principle. If it is nonetheless compatible with some relativistic version of mysticism or not is irrelevant.
 
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