Simple violation of Bell inequalities

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Simple violation of Bell inequalities

Postby gill1109 » Tue Jul 02, 2019 10:17 pm

Jarek wrote:Indeed, while our intuition demands it, there are now no doubts that "local realism" is incorrect.

The question is how to repair it without referring to magic - like building models based on physical assumptions, which are also able to violate such inequalities - by the way pointing where our "local realism" intuition is wrong.
My point here is that this missing assumption is time/CPT symmetry, which is at heart of (Lagrangian mechanics) theories we use in all scales: from QFT, unitary QM to GRT, but is against our natural intuition: which is very time-asymmetric.

Using time-symmetric "4D local realism" instead: in space-time, the basic object is no longer particle, but its trajectory - continuous for 4D locality.
Ensembles of such objects: Feynman in QM, or statistical physics: Boltzmann in MERW, for example, have strong Anderson localization - like real physics, unlike standard diffusion - which is local in standard sense and often very wrong, while MERW is nonlocal in a standard sense ... but is local in the 4D sense: is just path ensemble.
And the constructions here show that we get also other nonintuitive quantum properties from "4D local realism": using path ensembles - Born rule and resulting Bell violation.

What do think about such "4D local realism: path ensembles" explanation of quantum "spookiness"? Do you know a better explanation?

I think there is a better explanation. It was discovered by Slava Belavkin (RIP) and called "eventum mechanics". It admits that time is asymmetric and it puts time and causality into the QM picture, getting a true synthesis of the Born law and the usual "unitary" QM. Born law is not an uncomfortable add-on, but an intrinsic part of the dynamics. Belavkin's programme was not followed up and he had an untimely death. However, we know that the framework is compatible with Lorentz invariance. It embodies irreducible randomness and, for want of a better word, spooky action at a distance. (But it could better be called more "passion" than "action"; it is not malevolent or scary, one could better call it "angelic").

https://arxiv.org/abs/0905.2723

Schrödinger's cat meets Occam's razor
Richard D. Gill

Unpublished, incomplete
(I'm looking for a co-author to help me finish it!)

We discuss V.P. Belavkin's approach to the measurement problem encapsulated in his theory of eventum mechanics (as presented in his 2007 survey). In particular, we show its relation to ideas based on superselection and interaction with the environment developed by N.P. Landsman (1995, and more recent papers).
Landsman writes "those believing that the classical world exists intrinsically and absolutely [such persons later termed by him B-realists] are advised against reading this [his, 1995] paper". He adopts a milder position, calling it that of an A-realist: we live in a classical world but to give it special status is like insisting that the Earth is the centre of the universe. The B-realists are accused of living under some kind of hallucination. Landsman presents arguments pointing in a particular direction to a resolution of the measurement problem which at least would satisfy the A-realists. We point out in this paper that the theory earlier developed by Belavkin (surveyed in his 2007 paper) seems to complete Landsman's program or at least exhibits a "realisation" satisfying his desiderata. At the same time it seems that this completion of the program ends up giving both A- and B-realists equal licence to accuse the others of living under hallucinations.

https://arxiv.org/abs/1207.5103

Statistics, Causality and Bell's Theorem
Richard D. Gill

Journal reference: Statistical Science 2014, Vol. 29, No. 4, 512-528
DOI: 10.1214/14-STS490

Bell's [Physics 1 (1964) 195-200] theorem is popularly supposed to establish the nonlocality of quantum physics. Violation of Bell's inequality in experiments such as that of Aspect, Dalibard and Roger [Phys. Rev. Lett. 49 (1982) 1804-1807] provides empirical proof of nonlocality in the real world. This paper reviews recent work on Bell's theorem, linking it to issues in causality as understood by statisticians. The paper starts with a proof of a strong, finite sample, version of Bell's inequality and thereby also of Bell's theorem, which states that quantum theory is incompatible with the conjunction of three formerly uncontroversial physical principles, here referred to as locality, realism and freedom. Locality is the principle that the direction of causality matches the direction of time, and that causal influences need time to propagate spatially. Realism and freedom are directly connected to statistical thinking on causality: they relate to counterfactual reasoning, and to randomisation, respectively. Experimental loopholes in state-of-the-art Bell type experiments are related to statistical issues of post-selection in observational studies, and the missing at random assumption. They can be avoided by properly matching the statistical analysis to the actual experimental design, instead of by making untestable assumptions of independence between observed and unobserved variables. Methodological and statistical issues in the design of quantum Randi challenges (QRC) are discussed. The paper argues that Bell's theorem (and its experimental confirmation) should lead us to relinquish not locality, but realism.
gill1109
Mathematical Statistician
 
Posts: 1653
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Simple violation of Bell inequalities

Postby Jarek » Tue Jul 02, 2019 11:19 pm

Thank you, interesting - I will have to study, but there are also other phenomena which are natural for (time symmetric) path ensembles - equivalent with QM in Feynman's path integrals.
For example rho ~ sin^2 stationary probability distribution for [0,1] infinite potential well, or more generally Anderson localization - which seems impossible to obtain with random walk which is local in standard sense, but is natural for 4D local MERW: path ensemble.
This is a much deeper problem than of e.g. redefining measurement ...

Image

Image
Jarek
 
Posts: 140
Joined: Tue Dec 08, 2015 1:57 am

Re: Simple violation of Bell inequalities

Postby gill1109 » Wed Jul 03, 2019 1:50 am

Jarek wrote:Thank you, interesting - I will have to study, but there are also other phenomena which are natural for (time symmetric) path ensembles - equivalent with QM in Feynman's path integrals.
For example rho ~ sin^2 stationary probability distribution for [0,1] infinite potential well, or more generally Anderson localization - which seems impossible to obtain with random walk which is local in standard sense, but is natural for 4D local MERW: path ensemble.
This is a much deeper problem than of e.g. redefining measurement ...

I think that redefining measurement is a problem which needs to be solved before proceeding to attempt to unify QM and GR. So that is a quite deep problem, too.
gill1109
Mathematical Statistician
 
Posts: 1653
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Simple violation of Bell inequalities

Postby Jarek » Wed Jul 03, 2019 2:52 am

GR is extremely time-symmetric theory, time direction is just chosen locally fourth dimension, e.g. switches with spatial under black hole horizon ... or, at least in theory, there can be constructed non-orientable spacetime, e.g. Klein-bottle-like wormhole, in which going through a loop literally switches past and future lightcones.
Time asymmetry is in thermodynamics - statistical physics, effective theory - is only a property of a concrete solution we are living in. Like symmetry of equations governing lake surface can be broken if throwing a rock - this rock in our physics is our Big Bang: when everything was localized, hence entropy was low - creating entropy gradient and starting reason-result chains leading to us.
"Proofs" of entropy growth in time symmetric models make no sense as we could switch time sign and proof the opposite ... but e.g. Boltzmann H-theorem ( https://en.wikipedia.org/wiki/H-theorem ) does it - by using very subtle uniformity assumption: Stosszahlansatz. Kac ring is a great model to understand this assumption: http://www.maths.usyd.edu.au/u/gottwald ... c-ring.pdf

Anyway, to unify GR with QM we again need time-symmetry.
And QM already has it: in Feynman's path integrals, in unitary evolution.
Asymmetric is wavefunction collapse, but it is imagined as being a result of interaction with environment - considering "Wavefunction of the Universe", there is no longer environment - only unitary/time symmetric evolution.

ps. I see you again focus of CHSH in your paper, which is quite subtle - can you also handle this much more crude: P(A=B) + P(B=C) + P(A=C) >=1" inequality: "tossing 3 coins, at least 2 are equal"?
Jarek
 
Posts: 140
Joined: Tue Dec 08, 2015 1:57 am

Re: Simple violation of Bell inequalities

Postby gill1109 » Wed Jul 03, 2019 10:35 pm

Jarek wrote:GR is extremely time-symmetric theory, time direction is just chosen locally fourth dimension, e.g. switches with spatial under black hole horizon ... or, at least in theory, there can be constructed non-orientable spacetime, e.g. Klein-bottle-like wormhole, in which going through a loop literally switches past and future lightcones.
Time asymmetry is in thermodynamics - statistical physics, effective theory - is only a property of a concrete solution we are living in. Like symmetry of equations governing lake surface can be broken if throwing a rock - this rock in our physics is our Big Bang: when everything was localized, hence entropy was low - creating entropy gradient and starting reason-result chains leading to us.
"Proofs" of entropy growth in time symmetric models make no sense as we could switch time sign and proof the opposite ... but e.g. Boltzmann H-theorem ( https://en.wikipedia.org/wiki/H-theorem ) does it - by using very subtle uniformity assumption: Stosszahlansatz. Kac ring is a great model to understand this assumption: http://www.maths.usyd.edu.au/u/gottwald ... c-ring.pdf

Anyway, to unify GR with QM we again need time-symmetry.
And QM already has it: in Feynman's path integrals, in unitary evolution.
Asymmetric is wavefunction collapse, but it is imagined as being a result of interaction with environment - considering "Wavefunction of the Universe", there is no longer environment - only unitary/time symmetric evolution.

ps. I see you again focus of CHSH in your paper, which is quite subtle - can you also handle this much more crude: P(A=B) + P(B=C) + P(A=C) >=1" inequality: "tossing 3 coins, at least 2 are equal"?

What do you mean, can I deal with it? Yes I can deal with it. CHSH is more general. So in dealing with CHSH I also dealt with your inequality. It is not “more crude”, it’s a special case. Please read my Statistical Science paper.

To unify QM and GR we need to reconsider the basic objects of each theory, and the derived objects, and to reconsider the traditional associations between objects in one theory with objects in the other. I think there are some category mismatches.
gill1109
Mathematical Statistician
 
Posts: 1653
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Simple violation of Bell inequalities

Postby Jarek » Thu Jul 04, 2019 2:53 am

Regarding GR and QM unification, time in GR is just one of dimensions, already in special relativity this direction if not even fixed: changes with observer in Lorentz transform.
In contrast, in QM you would like to focus on evolution not only in a fixed time direction, but also in extremely time-asymmetric way: while past of spacetime is fixed, future does not exist yet.
From GR perspective it would mean that there is only half of spacetime: up to "now". But there isn't an objective "now" even in SR - it depends on observer, frame of reference. In GR under black hole horizon "now" becomes orthogonal ...
There is only one time philosophy compatible with GR: Einstein's block universe https://en.wikipedia.org/wiki/Eternalis ... hy_of_time) - that there is already some 4D spacetime satisfying Einstein's equation for curvature, like in action optimizing formulation of Lagrangian mechanics.
To unify it with QM you cannot use incompatible time philosophies: GR is time symmetric, so QM also needs to be treated this way.
E.g. Feynman's path ensemble is a compatible philosophy - in 4D spacetime even a perfect point particle is in fact its 1D trajectory.

Regarding Belavkin explanation, in your https://arxiv.org/pdf/1207.5103 I read for example:
The idea is to model the world in the conventional way with a Hilbert space, a quantum state on that space, and a unitary evolution. Inside this framework, we look for a collection of bounded operators on the Hilbert space which all commute with one an-other, and which are causally compatible with the unitary evolution of the space, in the sense that they all commute with past copies of themselves (in the Heisenberg picture, one thinks of the quantum observables as changing, the state as fixed; each observable corresponds to a time indexed family of bounded operators). We call this special family of operators the beables: they correspond to physical properties in a classical-like world which can co-exist, all having definite values at the same time, and definite values in the past too. The state and the unitary evolution together determine a joint probability distribution of these time-indexed variables, that is, a stochastic process. At any fixed time, we can condition the state of the system on the past trajectories of the beables. This leads to a quantum state over all bounded operators which commute with all the beables.

That is extremely abstract, I don't see how you define wavefunction collapse ... or construct Bell violation example.
And quantum weirdness is not only in measurement. For example normal particle in [0,1] infinite potential well should have rho=1 uniform distribution ... but in QM it has rho ~ sin^2 instead, or generally we have Anderson localization - e.g. making semiconductor an insulator, in contrast to standard diffusion in which it is always a conductor.
These are tough quantitative properties - abstract philosophy is not a sufficient explanation.
Jarek
 
Posts: 140
Joined: Tue Dec 08, 2015 1:57 am

Re: Simple violation of Bell inequalities

Postby gill1109 » Thu Jul 04, 2019 7:23 am

Jarek wrote:Regarding GR and QM unification, time in GR is just one of dimensions, already in special relativity this direction if not even fixed: changes with observer in Lorentz transform.
In contrast, in QM you would like to focus on evolution not only in a fixed time direction, but also in extremely time-asymmetric way: while past of spacetime is fixed, future does not exist yet.
From GR perspective it would mean that there is only half of spacetime: up to "now". But there isn't an objective "now" even in SR - it depends on observer, frame of reference. In GR under black hole horizon "now" becomes orthogonal ...
There is only one time philosophy compatible with GR: Einstein's block universe https://en.wikipedia.org/wiki/Eternalis ... hy_of_time) - that there is already some 4D spacetime satisfying Einstein's equation for curvature, like in action optimizing formulation of Lagrangian mechanics.
To unify it with QM you cannot use incompatible time philosophies: GR is time symmetric, so QM also needs to be treated this way.
E.g. Feynman's path ensemble is a compatible philosophy - in 4D spacetime even a perfect point particle is in fact its 1D trajectory.

Regarding Belavkin explanation, in your https://arxiv.org/pdf/1207.5103 I read for example:
The idea is to model the world in the conventional way with a Hilbert space, a quantum state on that space, and a unitary evolution. Inside this framework, we look for a collection of bounded operators on the Hilbert space which all commute with one an-other, and which are causally compatible with the unitary evolution of the space, in the sense that they all commute with past copies of themselves (in the Heisenberg picture, one thinks of the quantum observables as changing, the state as fixed; each observable corresponds to a time indexed family of bounded operators). We call this special family of operators the beables: they correspond to physical properties in a classical-like world which can co-exist, all having definite values at the same time, and definite values in the past too. The state and the unitary evolution together determine a joint probability distribution of these time-indexed variables, that is, a stochastic process. At any fixed time, we can condition the state of the system on the past trajectories of the beables. This leads to a quantum state over all bounded operators which commute with all the beables.

That is extremely abstract, I don't see how you define wavefunction collapse ... or construct Bell violation example.
And quantum weirdness is not only in measurement. For example normal particle in [0,1] infinite potential well should have rho=1 uniform distribution ... but in QM it has rho ~ sin^2 instead, or generally we have Anderson localization - e.g. making semiconductor an insulator, in contrast to standard diffusion in which it is always a conductor.
These are tough quantitative properties - abstract philosophy is not a sufficient explanation.

You can't unify two things while keeping them both the same. In order to unify GR with QM, one or both needs to be modified, expanded, or re-interpreted.

I'm sorry if you could not understand my little paper on the Belavkin approach. It does explain "wave function collapse" and gives us the Born law as an integral part of the theory. What do you mean by "construct the Bell violation example"? I think that that would now be an exercise for you, to "do the Bell experiment" in that framework. You will not get a new "interpretation" of that experiment. The framework simply reproduces the standard quantum predictions, avoiding paradoxes and self-contradictions.

I've told you that other researchers have already succeeded in creating Lorentz invariant collapse theories. I think that that is the way to go, but I am not the one who is equipped to do it. You could follow up the references I give in my Statistical Science paper. You could also try reading Belavkin's papers.

GR is going to need a huge overhaul. You have to stop clinging to the time reversibility. You have to face up to the real measurement problem: QM with collapse is *not* time reversible.

Cosmologists have wonderful simulation programs which simulate the evolution of the whole universe. Those simulations have a definite direction. They sometimes produce universes like ours, and sometimes they don't. They use pseudo-random generators to generate *random* universes. Their models are not local.
gill1109
Mathematical Statistician
 
Posts: 1653
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Simple violation of Bell inequalities

Postby Jarek » Thu Jul 04, 2019 11:31 am

You can't unify two things while keeping them both the same. In order to unify GR with QM, one or both needs to be modified, expanded, or re-interpreted.

Sure, but still some compatibility is needed.
GR says there is a 4D spacetme with intrinsic curvature governed by Einstein's equation.
Saying that past and future are completely different, you need to separate these halves in the spacetime.
Where is this separation? Remember that changing velocity literally modifies time direction in special relativity.
What is this difference between past and future in terms of Einstein's equation?
What's happening on their boundary?

ps. I have looked for "collapse" in your paper, but it wasn't helpful. Please just explain in a few sentences your belief.
Jarek
 
Posts: 140
Joined: Tue Dec 08, 2015 1:57 am

Re: Simple violation of Bell inequalities

Postby gill1109 » Fri Jul 05, 2019 4:43 am

Jarek wrote:
You can't unify two things while keeping them both the same. In order to unify GR with QM, one or both needs to be modified, expanded, or re-interpreted.

Sure, but still some compatibility is needed.
GR says there is a 4D spacetme with intrinsic curvature governed by Einstein's equation.
Saying that past and future are completely different, you need to separate these halves in the spacetime.
Where is this separation? Remember that changing velocity literally modifies time direction in special relativity.
What is this difference between past and future in terms of Einstein's equation?
What's happening on their boundary?

ps. I have looked for "collapse" in your paper, but it wasn't helpful. Please just explain in a few sentences your belief.

My belief is that "spooky action at a distance" does exist, but that we could better call it "angelic passion at a distance".

Collapse theories are theories like GRW, https://en.wikipedia.org/wiki/Ghirardi%E2%80%93Rimini%E2%80%93Weber_theory, in which something physical really does happen. Read recent papers like Fraulicher and Renner, or Brassard and Raymond-Robichaud. They discuss "unitary QM" (QM without collapse) such as many worlds theory, or QBism; and they define locality and realism. And show that this leads to paradoxes. And especially when one tries to derive or add Born's law to the picture.
gill1109
Mathematical Statistician
 
Posts: 1653
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Simple violation of Bell inequalities

Postby Jarek » Fri Jul 05, 2019 5:08 am

Both "spooky action at a distance" and "angelic passion at a distance" sound like from a domain of religion, not science - where we can not be satisfied with magical explanations, but need to pursue their solutions.
And there is no need for such mysticism: if only accepting time-symmetry of physics, use "4D locality" like in Feynman's path integrals instead of standard: "evolving 3D locality".
And there is https://en.wikipedia.org/wiki/CPT_symmetry in QFT, time symmetry in GR.

I agree with QM without collapse: as in Żurek's einselection ( https://en.wikipedia.org/wiki/Einselection ), collapse is a result of interaction with environment - not included e.g. in Schrodinger equation for single atom.
Considering Wavefunction of the Universe, there is no longer environment, wavefunction collapse - only unitary evolution, which again: is time-symmetric.
Jarek
 
Posts: 140
Joined: Tue Dec 08, 2015 1:57 am

Re: Simple violation of Bell inequalities

Postby gill1109 » Fri Jul 05, 2019 7:23 am

Jarek wrote:Both "spooky action at a distance" and "angelic passion at a distance" sound like from a domain of religion, not science - where we can not be satisfied with magical explanations, but need to pursue their solutions.
And there is no need for such mysticism: if only accepting time-symmetry of physics, use "4D locality" like in Feynman's path integrals instead of standard: "evolving 3D locality".
And there is https://en.wikipedia.org/wiki/CPT_symmetry in QFT, time symmetry in GR.

I agree with QM without collapse: as in Żurek's einselection ( https://en.wikipedia.org/wiki/Einselection ), collapse is a result of interaction with environment - not included e.g. in Schrodinger equation for single atom.
Considering Wavefunction of the Universe, there is no longer environment, wavefunction collapse - only unitary evolution, which again: is time-symmetric.

OK, then forget those slogans.
There is a simple neuro-linguistic explanation: what we mean by "understand" is conditioned by our brains, which through evolution, have some basic modules of logical thought, which we call "understand". We cannot "understand" QM as many of the really great physicists (Feynmann,...) very well knew. All we can do is get used to the formalism and maybe even gain mathematical intuition inside the formalism or any mathematically equivalent formalism.

Zurek's Einselection is logically flawed and does not explain anything. It is a "FAPP" explanation, ie it hides the paradoxes in a lot of words, and helps people sleep easy at night, and just get on and calculate.

Considering the wave function of the universe, nothing happens and nothing is real. The cosmologists who simulate the universe do not merely unitarily evolve the wave function of the universe. No: they have practical collapse theories which are moreover non-local but it doesn't matter since they get beautiful results.

The only good solution I know is Belavkin's eventum mechanics but everyone is so indoctrinated by physicist's present dogmas that they don't even start to look at it. Some basic laws of physics are time-symmetric but that does not mean that there is no arrow of time.

Belavkin’s solution has a breathtaking simplicity. There is a wave function of the universe and there it does undergo a unitary evolution. Yet, in the Heisenberg picture, it is a unitary endomorphism, not a unitary isomorphism. This restablishes causality and a direction if time, and make the Born law a consequence of the basic structural assumptions, not an uneasily co-existing add-on, or a source of paradox.

Nothing mystic about this. Very hard, sensible, pure mathematics. Very fruitful, too. Unjustly ignored, mainly because of prejudice and ignorance.
gill1109
Mathematical Statistician
 
Posts: 1653
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Simple violation of Bell inequalities

Postby Jarek » Fri Jul 05, 2019 8:29 am

To "understand" rules governing our world, the minimum is that there exists some objective situation. Also we use fields everywhere from QFT to GR, which have finite propagation speed - locality.
However, we know that "local realism" is incorrect - the question is how to repair it.
And using "4D local realism" instead, like path ensembles, can repair this disagreement.

However, you disagree with time-symmetry it requires, even though time/CPT symmetry is also central in QFT, GR, and unitary QM.
But I haven't seen any meritorious argument why do you disagree with time symmetry?
Because of thermodynamics? But this is statistical physics - effective not fundamental theory. All fundamental we use are symmetric. Fundamentally symmetric lake surface gets to solution without this symmetry when throwing a rock.

Wavefunction of the Universe is only an abstraction for including environment into considered quantum system to avoid decoherence.
If you agree with unitary evolution, so what is the difference if evolving after switching t -> -t ?
Jarek
 
Posts: 140
Joined: Tue Dec 08, 2015 1:57 am

Re: Simple violation of Bell inequalities

Postby gill1109 » Fri Jul 05, 2019 10:31 am

Jarek wrote:But I haven't seen any meritorious argument why do you disagree with time symmetry?

The collapse of the wave function in conventional QM is not time-symmetric, and all attempts to "derive" Born's law from unitary QM are failures.

Belavkin's eventum mechanics keeps exactly the symmetry which we want as well as giving us Born's law as a consequence of basic causality principles.

And nothing is spoilt of your own favourite approach. It remains a valid computational and conceptual tool. What's the problem? Your approach, and Belavkin's approach, solve different problems. They are compatible with one another.
gill1109
Mathematical Statistician
 
Posts: 1653
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Simple violation of Bell inequalities

Postby Jarek » Fri Jul 05, 2019 11:43 am

Regarding wavefunction collapse, one example is atom deexcitation: electron drops to a lower orbital producing a photon ... its time-symmetric analogue is excitation of this atom by photon absorption.
Idealization of measurement is Stern-Gerlech: magnetic dipole precesses in strong magnetic field, unless having parallel or anti-parallel alignment - strong magnetic field makes the dipole analogous to excited atom: falling to lowest energy and producing photon ... but this is time symmetric - it could analogously absorb such photon and change direction of magnetic dipole for a moment.
Generally, particle processes can be decomposed into ensemble of Feynman diagrams, which are CPT symmetric in QFT e.g. using https://en.wikipedia.org/wiki/Antiparti ... rpretation
One could think that random walk is not time symmetric, but our information is: knowing position of a particle in a given moment, you loose this information analogously if shifting time toward future or toward past.
We don't have time symmetric analogue of breaking an egg, but this is a solution issue: we have reason-results chains producing an egg only from past direction ... like for throwing a rock into a lake - in theory it could be reversed, but producing initial condition for such reversed solution is much more difficult.

Regarding Born rules, there are these two types of probabilistics:
1) Standard, intuitive: probability of alternative of disjoint events is sum of their probabilities,
2) Born rules: probability of alternative of disjoint events is proportional to sum of squares of their amplitudes.
Bell inequalities are derived using 1), hence models satisfying 2) might/can violate them.
Please show construction how non time-symmetric model can satisfy 2) ?
For time-symmetric models, 2) is just natural: one psi comes from past direction, the second from future:
Image
Jarek
 
Posts: 140
Joined: Tue Dec 08, 2015 1:57 am

Re: Simple violation of Bell inequalities

Postby gill1109 » Fri Jul 05, 2019 8:55 pm

Jarek wrote:Regarding Born rules, there are these two types of probabilistics:
1) Standard, intuitive: probability of alternative of disjoint events is sum of their probabilities,
2) Born rules: probability of alternative of disjoint events is proportional to sum of squares of their amplitudes.
Bell inequalities are derived using 1), hence models satisfying 2) might/can violate them.
Please show construction how non-time-symmetric model can satisfy 2) ?

Dear Jarek
I have shown how a non-time-symmetric model can satisfy 2) in my paper https://arxiv.org/abs/0905.2723 "Schrödinger's cat meets Occam's razor".

The mathematics is rather easy. Notice that the *only* refinement to standard unitary QM is that we assume that the unitary evolution is an endomorphism, not an isomorphism. It is one-to-one, but not "onto". It is injective, not surjective. (I take here the Heisenberg picture where observables "now" are mapped to observables "yesterday"). Please read it carefully. "Eventum mechanics" contains conventional unitary QM. Born's rule is a *consequence* of the standard assumptions. Everything you say remains true remains an option. If your way of thinking helps you to understand and or helps you to compute stuff, then, by all means, use it.


Schrödinger's cat meets Occam's razor
Richard D. Gill

We discuss V.P. Belavkin's approach to the measurement problem encapsulated in his theory of eventum mechanics (as presented in his 2007 survey). In particular, we show its relation to ideas based on superselection and interaction with the environment developed by N.P. Landsman (1995, and more recent papers).

Landsman writes "those believing that the classical world exists intrinsically and absolutely [such persons later termed by him B-realists] are advised against reading this [his, 1995] paper". He adopts a milder position, calling it that of an A-realist: we live in a classical world but to give it special status is like insisting that the Earth is the centre of the universe. The B-realists are accused of living under some kind of hallucination. Landsman presents arguments pointing in a particular direction to a resolution of the measurement problem which at least would satisfy the A-realists. We point out in this paper that the theory earlier developed by Belavkin (surveyed in his 2007 paper) seems to complete Landsman's program or at least exhibits a "realisation" satisfying his desiderata. At the same time, it seems that this completion of the program ends up giving both A- and B-realists equal licence to accuse the others of living under hallucinations.

N.P. Landsman (1995), Observation and superselection in quantum mechanics, SHPMP 26, 1355–2198.
https://arxiv.org/abs/hep-th/9411173

V.P. Belavkin (2007), Eventum Mechanics of Quantum Trajectories: Continual Measurements, Quantum Predictions and Feedback Control.
https://arxiv.org/abs/math-ph/0702079
https://www.maths.nottingham.ac.uk/plp/vpb/publications/emmpc-rmp.pdf

See also Belavkin's inaugural lecture in Nottingham, 2000, "Quantum Probabilities and Paradoxes of the Quantum Century"
https://www.maths.nottingham.ac.uk/plp/vpb/inaugural/index.htm
https://www.maths.nottingham.ac.uk/plp/vpb/inaugural/sld001.htm
gill1109
Mathematical Statistician
 
Posts: 1653
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Simple violation of Bell inequalities

Postby Jarek » Sat Jul 06, 2019 1:00 am

Dear Richard,
Careful studying of all these materials would need a month - I would need a good motivation first, which is still missing.
The belief of magic/spookiness/angelicness behind QM is caused mainly by Bell violation, which requires Born rules.
It seems absolutely obvious that "probability of alternative of disjoint of events is sum of their probabilities" ... but somehow QM allows to insert square there - to break the spell we need a good understanding of this square.
My current belief is that it comes from time-symmetry e.g. in Feynman's path/diagrams ensembles: one psi is from the past, second from future, like in two state vector formalism of QM: https://en.wikipedia.org/wiki/Two-state ... _formalism

You disagree, but I still didn't see any serious argument for your disbelief.
Microscopic physics is time/CPT symmetric (and also GR) ... macroscopic e.g. a mug breaking in space vacuum - giving all these floating pieces exactly opposite momentum and angular momentum, they should combine into the mug ... but it is just much simpler for us to produce mug in a different way: using intuitive for us reason-result chains started in our Big Bang - like rock breaking symmetry of surface of a lake, our broken time symmetry is of a specific physics solution we live in: in vicinity of low entropic Big Bang in our past.

Instead you believe in a different solution - I am mostly interested in Born rules, and searching these materials for "Born" keyword, I have only found it in Landsman's paper - but like in QM, it is assumed not derived.
To break the spell - understand the magic, we need to derive it.
Please just explain in a few sentences what is your understanding of source of this highly non-intuitive square:
Born rules: probability of alternative of disjoint events is proportional to sum of squares of their amplitudes.
Jarek
 
Posts: 140
Joined: Tue Dec 08, 2015 1:57 am

Re: Simple violation of Bell inequalities

Postby gill1109 » Sat Jul 06, 2019 3:52 am

Jarek wrote:Dear Richard,
Careful studying of all these materials would need a month - I would need a good motivation first, which is still missing.
The belief of magic/spookiness/angelicness behind QM is caused mainly by Bell violation, which requires Born rules.
It seems absolutely obvious that "probability of alternative of disjoint of events is sum of their probabilities" ... but somehow QM allows to insert square there - to break the spell we need a good understanding of this square.
My current belief is that it comes from time-symmetry e.g. in Feynman's path/diagrams ensembles: one psi is from the past, second from future, like in two state vector formalism of QM: https://en.wikipedia.org/wiki/Two-state ... _formalism

You disagree, but I still didn't see any serious argument for your disbelief.
Microscopic physics is time/CPT symmetric (and also GR) ... macroscopic e.g. a mug breaking in space vacuum - giving all these floating pieces exactly opposite momentum and angular momentum, they should combine into the mug ... but it is just much simpler for us to produce mug in a different way: using intuitive for us reason-result chains started in our Big Bang - like rock breaking symmetry of surface of a lake, our broken time symmetry is of a specific physics solution we live in: in vicinity of low entropic Big Bang in our past.

Instead you believe in a different solution - I am mostly interested in Born rules, and searching these materials for "Born" keyword, I have only found it in Landsman's paper - but like in QM, it is assumed not derived.
To break the spell - understand the magic, we need to derive it.
Please just explain in a few sentences what is your understanding of source of this highly non-intuitive square:
Born rules: probability of alternative of disjoint events is proportional to sum of squares of their amplitudes.


Jarek: a careful study of those materials should only take *you* two days. One day to read, and look up a few things on wikipedia, and one day to think about it.

If you are not prepared to take those couple of days, I don't see why I should feel obliged to follow up your ideas, which would cost me a lot more effort. I am not a physicist. There is a lot of hard mathematical physics which I don't know much about. And I don't have any professional need to learn that stuff. I'm a retired statistician! I have a nice little consulting business. I'm interested in data and in causality!

But, you asked for a couple of sentences on the source of that square:

Born rules: there are two basic ways to find probabilities in nature (positive numbers which add up to one).

One way is by taking the unit interval and breaking it into pieces. That is Kolmogorov probability.

The other way is by looking at the squares on the two short sides of a right-angled triangle whose hypotenuse has length one. That's Von Neumann (quantum) probability.

Kolmogorov and von Neumann, about the same time, came up with these two solutions of Hilbert's sixth problem (to axiomatize those branches of physics in which mathematics is prevalent). The Born rule comes from the second solution. The "local hidden variables" programme is an attempt to find Kolmogorov "behind" von Neumann. It is easy to do as long as you don't insist on locality (Bell), or more generally, on non-contextuality (Kochen-Specker).
gill1109
Mathematical Statistician
 
Posts: 1653
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Simple violation of Bell inequalities

Postby Jarek » Sat Jul 06, 2019 5:30 am

Dear Richard,
I am directly writing explanations here, but I understand you mostly don't even try to read them - being focused on advertising your approach, you want me to understand a hundred of pages of abstract algebra ... which barely touches the main problem of quantum mysticism I am interested in: Born rules.
I am also mainly statistics, information theory person and so are my arguments (and the question of such squares) - like just uniform distribution among paths, leading to rho ~ psi^2 in two lines in the diagram above or e.g. in https://en.wikipedia.org/wiki/Maximal_e ... derivation
That's all, Born rules directly come from time symmetry assumption: one psi from past, second from future, like in TSVF formulation of QM: https://en.wikipedia.org/wiki/Two-state ... _formalism
And we know well that all fundamental physics has time symmetry - you disagree, but didn't give any serious argument.

In contrast, abstract algebra is very far from my interests - studying it would take me a long time, and I am generally skeptical to such common for modern physics approach: make up some abstract equations, process them, and finally give some magical interpretation to their result ... while it might look simple and natural, there are hundreds of assumptions hidden in such reasonings.
I prefer simple safe confirmed assumptions, like time-symmetry: already deeply in all fundamental theories we use, which is the only assumption I add to repair the "local realism" impossibility problem.

I understand we will not find a common language here. My suggestion is that if you want to convince people to your approach, beside many general papers, write a separate one focused on this most important problem: source of squares in Born rules.
Including explanation why we usually have first power, but sometimes we can have second: after summation over unmeasured variables.
Including identification of assumptions you use, and e.g. explanation of choosing one of two solutions in given types of situations - if it is already hidden in the materials you have suggested, extracting it would take me more than a month.

With best regards,
Jarek
Jarek
 
Posts: 140
Joined: Tue Dec 08, 2015 1:57 am

Re: Simple violation of Bell inequalities

Postby gill1109 » Sat Jul 06, 2019 5:56 am

Jarek wrote:Dear Richard,
I am directly writing explanations here, but I understand you mostly don't even try to read them - being focused on advertising your approach, you want me to understand a hundred of pages of abstract algebra ... which barely touches the main problem of quantum mysticism I am interested in: Born rules.
I am also mainly statistics, information theory person and so are my arguments (and the question of such squares) - like just uniform distribution among paths, leading to rho ~ psi^2 in two lines in the diagram above or e.g. in https://en.wikipedia.org/wiki/Maximal_e ... derivation
That's all, Born rules directly come from time symmetry assumption: one psi from past, second from future, like in TSVF formulation of QM: https://en.wikipedia.org/wiki/Two-state ... _formalism
And we know well that all fundamental physics has time symmetry - you disagree, but didn't give any serious argument.

In contrast, abstract algebra is very far from my interests - studying it would take me a long time, and I am generally skeptical to such common for modern physics approach: make up some abstract equations, process them, and finally give some magical interpretation to their result ... while it might look simple and natural, there are hundreds of assumptions hidden in such reasonings.
I prefer simple safe confirmed assumptions, like time-symmetry: already deeply in all fundamental theories we use, which is the only assumption I add to repair the "local realism" impossibility problem.

I understand we will not find a common language here. My suggestion is that if you want to convince people to your approach, beside many general papers, write a separate one focused on this most important problem: source of squares in Born rules.
Including explanation why we usually have first power, but sometimes we can have second: after summation over unmeasured variables.
Including identification of assumptions you use, and e.g. explanation of choosing one of two solutions in given types of situations - if it is already hidden in the materials you have suggested, extracting it would take me more than a month.

With best regards,
Jarek

Dear Jarek

I too am not interested in abstract algebra!

I am not interested in learning your stuff, right now. I will do that later. I do wish to advertise my approach because I found it very useful and I know it is badly neglected. Your approach, on the other hand, is well known, has been around for a long time, and has a lot of aficionados. Maybe I will study it too, sometime, but I have other things I need to do first (most of them nothing to do with physics at all - I am retired, have to take care of a wife, an old house which needs a lot of upkeep, a garden, children and grandchildren).

I don't ask you to understand a hundred pages of abstract algebra. I ask you to understand two or three. Even I, an applied statistician, did not find it difficult. I don't understand your prejudice against it. Sure, you want to sell your approach, and do not feel any need for another.

What you tell me about the origin of the Born rules is repeated, word for word, by Belavkin. It's mathematically equivalent. One wave from the future, one wave from the past.

There is nothing new under the sun. Neither of us believe in local realism. We both know that quantum mechanics defies human understanding, but one can get very well used to it. One does not understand new mathematics - one gets used to it.

Enough said.

Richard
gill1109
Mathematical Statistician
 
Posts: 1653
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Simple violation of Bell inequalities

Postby Jarek » Sat Jul 06, 2019 6:17 am

Dear Richard,
As written, I have searched for Born rules in the material you have provided, but without success - I interpret it is spread, would require studying a complete picture. But if you point me to a few pages focused on Born rules, I will try to understand it.
Sure time symmetric explanation is very far from something new, but allows to just remove the mist of magic from QM - which is still deeply there in the society. "If you think you understand QM, it means you don't understand QM" - extremely dangerous belief, which paralyzed physics from development - making that basic questions of physics are just ignored, like understanding the structure of EM field of particles - I am much more interested in, but it is nearly impossible to discuss about due to the quantum mystery ...
Best regards,
Jarek
Jarek
 
Posts: 140
Joined: Tue Dec 08, 2015 1:57 am

PreviousNext

Return to Sci.Physics.Foundations

Who is online

Users browsing this forum: Bing [Bot], Google [Bot] and 3 guests

CodeCogs - An Open Source Scientific Library