Bell's theorem and local realism

[harrylin]

[...]
The problem is not the " particle" concept in the hidden layer, in the physics behind the scenes, it is the discreteness of the manifest outcomes. Click or no-click. +1 or -1. Within a time interval of fixed duration.

Me thinks that you are in disagreement with Neumaier:

"the traditional hidden variable assumption only amounts to a hidden classical particle assumption.
And the experiments demonstrating their violation only disprove classical models with particle structure. [..]
We conclude that classical field theory models for a quantum phenomenon are not excluded by traditional no-go theorems for hidden variables."
- http://arnold-neumaier.at/ms/lightslides.pdf

As you are an expert in statistics and he is an expert in QFT (and I'm an expert in neither), I don't know...

The recent paper needs more looking at http://arxiv.org/abs/1307.2981. [..] as far as I can see there is no spatial dimension. They are measuring at the same time different observables "in the same place". [..]

With "nonlocal" they ( http://arxiv.org/abs/1307.2981) clearly mean a spatial separation, just like everyone else:

"Let us now consider the situation where the quadrature phase components of two correlated and spatially separated light fields are measured. [..] The strength of the correlations increases with n(m), asymptotically reaching the limit of perfect correlations as n becomes very large [..] This feature thus further corroborates our earlier results of increase in Bell violations for larger orbital angular momentum of LG beams."

 

[gill1109]

Me thinks that you are in disagreement with Neumaier:

"the traditional hidden variable assumption only amounts to a hidden classical particle assumption.
And the experiments demonstrating their violation only disprove classical models with particle structure. [..]
We conclude that classical field theory models for a quantum phenomenon are not excluded by traditional no-go theorems for hidden variables."
- http://arnold-neumaier.at/ms/lightslides.pdf

As you are an expert in statistics and he is an expert in QFT (and I'm an expert in neither), I don't know...


With "nonlocal" they ( http://arxiv.org/abs/1307.2981) clearly mean a spatial separation, just like everyone else:

"Let us now consider the situation where the quadrature phase components of two correlated and spatially separated light fields are measured. [..] The strength of the correlations increases with n(m), asymptotically reaching the limit of perfect correlations as n becomes very large [..] This feature thus further corroborates our earlier results of increase in Bell violations for larger orbital angular momentum of LG beams."

Yes I disagree strongly with Neumaier. He needs to read "Bertlmann" so that he understands the issues. This is not a matter of QFT vs statistics. This is a matter of ignorance of basic logic, basic facts.

OK good that the Indian gentlemen do have space in their picture. Next then is to check out the (non-standard) Bell inequality for continuous variables they are using: is there also a Bell theorem based on that inequality? Is the experiment they have in mind loophole-free? A lot of work to do. I am sceptical: there hasn't yet been done a successful loophole-free Bell-type experiment in the quantum physics lab yet, after 50 yrs trying. I doubt that classical optics can give a successful experiment. I conclude that the Indian gentlemen know a lot about optics, little about Bell's theorem (ie that's my working assumption. Sceptical = scientific. Extraordinarily radical scientific claims require extraordinarily strong scientific evidence).

 

[harrylin]

Yes I disagree strongly with Neumaier. He needs to read "Bertlmann" so that he understands the issues. This is not a matter of QFT vs statistics. This is a matter of ignorance of basic logic, basic facts.

It's of course not a matter of QFT vs statistics; I suppose that one cannot teach QFT without a reasonably good understanding of statistics! Indeed, it appears that he understands the issues, see also his publication list here: http://arnold-neumaier.at/papers/physpapers.html. In that list I now found an older, rather unpolished paper of him in which he explains his conclusions in more detail:

http://lanl.arxiv.org/abs/0706.0155

It looks like implicit advice to De Raedt to change his modelling approach...

OK good that the Indian gentlemen do have space in their picture. Next then is to check out the (non-standard) Bell inequality for continuous variables they are using: is there also a Bell theorem based on that inequality? Is the experiment they have in mind loophole-free? A lot of work to do. I am sceptical: there hasn't yet been done a successful loophole-free Bell-type experiment in the quantum physics lab yet, after 50 yrs trying. I doubt that classical optics can give a successful experiment.

I have similar questions as you, but "only" a successful semi-classical model is desired...

I conclude that the Indian gentlemen know a lot about optics, little about Bell's theorem (ie that's my working assumption. Sceptical = scientific. Extraordinarily radical scientific claims require extraordinarily strong scientific evidence).

I agree; note that I regard "Bell's theorem" (the math plus its usual metaphysical interpretation) to be such an "extraordinarily radical scientific claim".

 

[TrickyDicky]

The problem is not the " particle" concept in the hidden layer, in the physics behind the scenes, it is the discreteness of the manifest outcomes. Click or no-click. +1 or -1. Within a time interval of fixed duration.

Let's give some context. It is not that the theorem introduces any "particle" concept as its premise. It is about the conclusions from the theorem given certain assumption that is virtually shared by the whole physics community, namely atomism, the atomic theory as explanation of matter(the fundamental building blocks narrative) . Now the thing is atomism implies realism. So if one assumes the atomic theory(and I have yet to meet any physicist in academia that doesn't, then logically with Bell's theorem one is discarding any theory that includes objects with particle properties(locality) as able to explain quantum correlations experiments.

Now it is true that there are physicists that when it comes to QM claim not to be realists in order to keep locality, but if they follow the atomic theory they are realists even if they don't know it so they are simply not being logical, and then it begs the question why they would consider Bell's theorem which is based on logic.

Now I have to say that I disagree with Neumaier that Classical field theory like electrodynamics as understood at least since Lorentz, violates Bell's inequalities as a theory. The reason is that electrodyamics includes classical particles. So it is both local and realistic.

 

[billschnieder]

http://lanl.arxiv.org/abs/0706.0155

It looks like implicit advice to De Raedt to change his modelling approach...

The conditional probability of detecting a photon which is in state λ and passes through filter k when Ak = A and A3−k = 0 is pk(A, λ).

Did no one else see the contradiction in talking about "probability of detecting" a photon, and yet saying LHV theories can not reproduce the QM predictions. There are of examples of LHV models doing just that with individial particles (rather than "classical fields", See De Raedt's own model for example). But I guess it could all be dismissed as "detection loophole" as though it makes sense to talk of "probability of detection" (different from unity), when everything is detected.

 

[stevendaryl]

Let's give some context. It is not that the theorem introduces any "particle" concept as its premise. It is about the conclusions from the theorem given certain assumption that is virtually shared by the whole physics community, namely atomism, the atomic theory as explanation of matter(the fundamental building blocks narrative) . Now the thing is atomism implies realism. So if one assumes the atomic theory(and I have yet to meet any physicist in academia that doesn't, then logically with Bell's theorem one is discarding any theory that includes objects with particle properties(locality) as able to explain quantum correlations experiments

I'm not sure what all you are lumping into the concept of atomism. I also don't understand where you think that atomism comes into play in discussions of Bell's theorem. What Bell's local realism amounts to--as described already by Richard Gill--is basically the idea that any fact about the universe can be factored into facts about tiny little regions of the universe, together with facts about how neighboring regions fit together. Facts about each tiny region can either be continuous (the values of fields) or discrete (the locations, momenta, angular momenta, charges, etc. of particles within the region). There is a second component to local realism that is added by relativity, which is that the evolution of one little region cannot depend on facts about distant regions.

The violation of Bell's inequality implies (in one way of looking at, at least) that there are facts about the universe that don't factor into facts about the little regions making up the universe. I don't see the connection with atomism, though.

Now, there are nonlocal facts about the universe. In particular, it's topology can't be determined just by looking at little regions--it's a fact about how all the little regions are glued together to make a whole. On the other hand, since topology doesn't suddenly change in normal physics, topology is not a likely candidate for explaining nonlocal correlations. Contrary to what Joy Christian seems to believe, I don't think that you can use topology to violate Bell's inequality (unless you suppose a really weird topology, such as every point is connected to every other point).

 

[gill1109]

Did no one else see the contradiction in talking about "probability of detecting" a photon, and yet saying LHV theories can not reproduce the QM predictions. There are of examples of LHV models doing just that with individial particles (rather than "classical fields", See De Raedt's own model for example). But I guess it could all be dismissed as "detection loophole" as though it makes sense to talk of "probability of detection" (different from unity), when everything is detected.

De Raedt has LHV models for every experiment done to date, which is possible since so far no experiment was loophole-free. In fact everyone knew (or should have known) that all those experiments had local-realistic explanations. Certainly Aspect, Weihs etc etc know that. Just last year there have been two photon polarisation experiments which overcome the detection loophole (Giustina et al; Christensen et al.). They don't have the required space-time constraints - fast rapid generation of new random settings, Alice's measurement result fixed before Bob's setting could arrive at Alice's place ... On the other hand, that constraint was achieved in the Aspect and Weihs experiments. So it really does look as though the experimenters are nearly there. And they think they'll be they in about a year. And then De Raedt will no longer be able to play his game. He and I discussed this a month ago. He agrees. He is already doing some rather different work, deriving the quantum correlations from informational and geometric axioms ...

 

[gill1109]

Now, there are nonlocal facts about the universe. In particular, it's topology can't be determined just by looking at little regions--it's a fact about how all the little regions are glued together to make a whole. On the other hand, since topology doesn't suddenly change in normal physics, topology is not a likely candidate for explaining nonlocal correlations. Contrary to what Joy Christian seems to believe, I don't think that you can use topology to violate Bell's inequality (unless you suppose a really weird topology, such as every point is connected to every other point).

If every point is connected to every other point ... this could be thought of as a violation of locality. A wormhole connecting Alice and Bob's measurement apparatus (or connecting the source with both their measurement devices) so that everything everywhere knows what is happening everywhere else... yes, that is a way you can explain the quantum correlations. Christian needs a random sign flip when transporting Alice's or Bob's outcome +/- 1 to a central location in order to calculate the correlation. Like a Möbius band. Nobody saw it happen before ...

 

[stevendaryl]

If every point is connected to every other point ... this could be thought of as a violation of locality. A wormhole connecting Alice and Bob's measurement apparatus (or connecting the source with both their measurement devices) so that everything everywhere knows what is happening everywhere else... yes, that is a way you can explain the quantum correlations. Christian needs a random sign flip when transporting Alice's or Bob's outcome +/- 1 to a central location in order to calculate the correlation. Like a Möbius band. Nobody saw it happen before ...

Well, a Mobius band seems to be an example of where topology can cause correlations to weaken with distance. On a Mobius strip, two objects initially with the same "handedness" will continue to have the same handedness if they stay close together, but if they get too far apart, their relative handedness can change.

That was actually one of my many objections to Christian's model. It seems to me that the difference between two different topologies--R^3 versus S^3, for example--would only come into play for experiments that take place over a large enough area. Localized experiments are not going to see a difference between the two. So it seems to me--without actually doing the calculations--that Christian's model couldn't possibly predict the same results as standard QM, that instead his model would predict a distance-dependency in the correlations where standard QM doesn't.

 

[bhobba]

Quantum mechanics is not in conflict with locality.

Hmmmm.

Certainly the cluster decomposition property is obeyed - but that only applies to non correlated systems. Correlated systems - well that's where the argument lies.

You can't use it to send information FTL - but that isn't quite the same as locality.

I personally believe QM violates both parts of naive reality - but that is just my view - you can have either - but not both.

Thanks
Bill

 

[gill1109]

Whether we say QM violates locality (or local realism) or not depends on our definitions. It seems nowadays *conventional* to say that Bell's theorem shows us that QM is in conflict with locality+realism+no-conspiracy. So if you want to stick with QM (and in particular, if Nature shows that she follows QM in a decisive experiment) we have to reject locality OR realism OR no-conspiracy (aka freedom).

This is just the present-day main-stream way of saying things. It is explained very nicely by Boris Tsirelson in the following encyclopedia article:
http://en.citizendium.org/wiki/entanglement_(physics )

One can say that it is then a matter of taste whether one should reject locality, realism, or freedom. I mean - it is completely optional. Cannot be decided by experiment. Is therefore a matter of taste or of philosophy. It's meta-physics.

Boris does explain very clearly in his article why he thinks that it is wise to keep locality and no-conspiracy but to reject realism. I agree with him; I find his arguments very pleasing. But sure - it is a matter of taste, of philosophy. It is not decidable by experiment. However philosophy is also important in physics since (I submit) the right philosophy generates the right frame of mind for uncovering exciting new physics.

To illustrate this remark: there was a generation of quantum physicists who were kind of brain-washed to think that you can kind of understand QM by simple classical physical notions. e.g. disturbing a system by observing it - nothing weird in that. However the really exciting experiments like Aspect's happened when people took QM seriously, ie took the amazing formalism seriously, and did not try to "explain away" by classical analogy what seemed at first revolutionary in the theory. Instead they embraced what seemed revolutionary in the theory, ie in the formalism, followed it up, and designed daring experiments which showed that it was "for real".

 

[TrickyDicky]

I'm not sure what all you are lumping into the concept of atomism. I also don't understand where you think that atomism comes into play in discussions of Bell's theorem. What Bell's local realism amounts to--as described already by Richard Gill--is basically the idea that any fact about the universe can be factored into facts about tiny little regions of the universe, together with facts about how neighboring regions fit together. Facts about each tiny region can either be continuous (the values of fields) or discrete (the locations, momenta, angular momenta, charges, etc. of particles within the region). There is a second component to local realism that is added by relativity, which is that the evolution of one little region cannot depend on facts about distant regions.

The violation of Bell's inequality implies (in one way of looking at, at least) that there are facts about the universe that don't factor into facts about the little regions making up the universe. I don't see the connection with atomism, though.

I thought I explained clearly that I was introducing atomism as a contextual element not related to the theorem itself but added to it since it is carried as a moreless implicit assumption by most physicist. Adding the two elements(theorem plus atomism) is what leads to what I concluded. Not the theorem by itself. Is it clearer now?

There are actually contrived ways to avoid this conclusion, for instance Bohmian mechanics, but they are usually considered to be basically ad hoc constructions.

 

[bhobba]

Whether we say QM violates locality (or local realism) or not depends on our definitions..

That I STRONGLY agree with.

Thanks
Bill

 

[gill1109]

I thought I explained clearly that I was introducing atomism as a contextual element not related to the theorem itself but added to it since it is carried as a moreless implicit assumption by most physicist. Adding the two elements(theorem plus atomism) is what leads to what I concluded. Not the theorem by itself. Is it clearer now?

There are actually contrived ways to avoid this conclusion, for instance Bohmian mechanics, by they are usually considered to be basically ad hoc constructions.

I would not call Bohmian mechanics contrived or ad hoc; it is wonderfully neat and very satisfying from several points of view ... but it is non-local, *and* it requires an "ether" (preferred reference frame) yet the predictions it makes about reality are independent of what that preferred reference frame is. And it predicts no more and no less than ordinary QM so one could say that it is superfluous. However it can provide mathematical tricks for getting the right answer faster. Just like we can prove things about the real numbers by embedding them in the complex numbers.

 

[bhobba]

it requires an "ether" (preferred reference frame) yet the predictions it makes about reality are independent of what that preferred reference frame is. And it predicts no more and no less than ordinary QM so one could say that it is superfluous.

My view exactly - I couldn't care less about locality - but that aether - that really bothers me.

Thanks
Bill

 

[bohm2]

I would not call Bohmian mechanics contrived or ad hoc; it is wonderfully neat and very satisfying from several points of view ... but it is non-local, *and* it requires an "ether" (preferred reference frame).

Hrvoje Nikolic has published a Bohmian model compatible with relativity. He does it by treating time on an equal footing with space and his model does not involve a preferred Lorenz frame. Some of his stuff can be found here:

Slide Presentation:
Making Bohmian Mechanics compatible with Relativity and Quantum Field Theory
http://www.tcm.phy.cam.ac.uk/~mdt26/tti_talks/deBB_10/nikolic_tti2010.pdf

Relativistic Quantum Mechanics and Quantum Field Theory
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/nikolic_2010d.pdf

Making nonlocal reality compatible with relativity
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/nikolic_2010a.pdf

 

[gill1109]

Hrvoje Nikolic has published a Bohmian model compatible with relativity. He does it by treating time on an equal footing with space and his model does not involve a preferred Lorenz frame. Some of his stuff can be found here:

Slide Presentation:
Making Bohmian Mechanics compatible with Relativity and Quantum Field Theory
http://www.tcm.phy.cam.ac.uk/~mdt26/tti_talks/deBB_10/nikolic_tti2010.pdf

Relativistic Quantum Mechanics and Quantum Field Theory
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/nikolic_2010d.pdf

Making nonlocal reality compatible with relativity
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/nikolic_2010a.pdf

Nice! Recently also the CSL model has been made relativistically invariant and this means that the same can be done for Belavkin's "eventum mechanics". So the apparent defects of the first versions of these three classes of models were not fundamental, they were just "first rough guesses" which needed careful refinement. I will find the reference later (guy at Imperial college, London).

 

[morrobay]

In this paper: Correlation Functions, Bell's Inequality and Fundamental Conservation Laws.
They are equating the Bell's test experimental outcomes with particles that are realistic objects.
P(a,b)_QM = P(a,b)_C = - cosø

arxiv.org/pdf/quant-ph/0407041.pdf

 

[gill1109]

In this paper: Correlation Functions, Bell's Inequality and Fundamental Conservation Laws.
They are equating the Bell's test experimental outcomes with particles that are realistic objects.
P(a,b)_QM = P(a,b)_C = - cosø

arxiv.org/pdf/quant-ph/0407041.pdf

Here's the abstract:

Correlation functions, Bell's inequalities and the fundamental conservation laws

C. S. Unnikrishnan (Tata Institute, Mumbai)

I derive the correlation function for a general theory of two-valued spin variables that satisfy the fundamental conservation law of angular momentum. The unique theory-independent correlation function is identical to the quantum mechanical correlation function. I prove that any theory of correlations of such discrete variables satisfying the fundamental conservation law of angular momentum violates the Bell's inequalities. Taken together with the Bell's theorem, this result has far reaching implications. No theory satisfying Einstein locality, reality in the EPR-Bell sense, and the validity of the conservation law can be constructed. Therefore, all local hidden variable theories are incompatible with fundamental symmetries and conservation laws. Bell's inequalities can be obeyed only by violating a conservation law. The implications for experiments on Bell's inequalities are obvious. The result provides new insight regarding entanglement, and its measures.

Europhys.Lett. 69 (2005) 489-495
arXiv:quant-ph/0407041

De Raedt has jus done something similar: symmetry + some information principle implies quantum correlation hence incompatible with local realism.

One can't have all attractive fundamental principles at same time. My personal choice: accept fundamental (irreducible) quantum randomness as "real"; reject "realism" = the reality of outcomes of unperformed measurements (rather idealistic, isn't it!?). In particular, give up looking for a LHV theory.

 

[stevendaryl]

Hrvoje Nikolic has published a Bohmian model compatible with relativity. He does it by treating time on an equal footing with space and his model does not involve a preferred Lorenz frame. Some of his stuff can be found here:

Slide Presentation:
Making Bohmian Mechanics compatible with Relativity and Quantum Field Theory
http://www.tcm.phy.cam.ac.uk/~mdt26/tti_talks/deBB_10/nikolic_tti2010.pdf

Relativistic Quantum Mechanics and Quantum Field Theory
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/nikolic_2010d.pdf

Making nonlocal reality compatible with relativity
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/nikolic_2010a.pdf

Here's a question that occurred to me while reading the second paper. The author points out that nonlocal interactions are consistent with relativity and causality, provided that the notion of causality is with respect to the scalar parameter s rather than coordinate time. My question is this: What is the difference, conceptually, between (1) N particles moving through 4 dimensional spacetime, and (2) 1 particle moving through 4N dimensional spacetime? It seems to me that locality is the only difference. A single particle through 4N dimensional spacetime can be subject to forces that depend on 4N numbers x^\mu_a, (where a ranges over the particles), while in the case of local interactions, N particles in 4 dimensional spacetime, each particle is subject to a force that depends only on 4 coordinates, its own location in spacetime. If you generalize to allow nonlocal forces, then it seems to me that the number of spacetime dimensions is no longer particularly meaningful. In a sense, it is locality that determines (or at least, gives significance to) the number of dimensions of spacetime.

 

[billschnieder]

De Raedt has jus done something similar: symmetry + some information principle implies quantum correlation hence incompatible with local realism.

Are you referring to this article:

http://arxiv.org/abs/1303.4574
Annals of Physics 347, 45 (2014)

It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the observed events are robust with respect to small changes in the conditions under which the experiments are carried out.

...

In the present paper, we demonstrate that the basic equations of quantum theory directly follow from logical inference applied to experiments in which there is
(i) uncertainty about individual events,
(ii) the stringent condition that certain properties of the collection of events are reproducible, meaning that they are robust with respect to small changes in the conditions under which the experiments are carried out.

I did not see a claim by them that their results were incompatible with realism. Unless it's a different paper.

 

[gill1109]

Are you referring to this article:

http://arxiv.org/abs/1303.4574
Annals of Physics 347, 45 (2014)


I did not see a claim by them that their results were incompatible with realism. Unless it's a different paper.

Yes this is the paper I meant. No they don't claim that. Bell's theorem says that. They don't say that Bell was wrong. Bell's theorem (which is a bit of elementary calculus and probability theory) has stood up for more than 50 years now.

Note: de Raedt and Michielsen's many papers on event based simulations of famous experiments do not contradict Bell's theorem, because so far, no experimentalist has actually done (was able to do) the experiment which needs to be done. But they are now at last getting close.

 

[gill1109]

My question is this: What is the difference, conceptually, between (1) N particles moving through 4 dimensional spacetime, and (2) 1 particle moving through 4N dimensional spacetime? It seems to me that locality is the only difference.

Good question. I think your answer is correct. What we mean by locality determines the difference between (1) and (2).

 

[billschnieder]

My question is this: What is the difference, conceptually, between (1) N particles moving through 4 dimensional spacetime, and (2) 1 particle moving through 4N dimensional spacetime? It seems to me that locality is the only difference.

Uhm, the difference is that you have one particle in one case and 4 in the other? 4 separate particles have 4 separate N-dimensional states, while 1 particle will have a single joint 4N-dimentional state. Surely you may have the exact same number of parameters, but the relationships between the parameters and the degrees of freedom involved will be wildly different.

 

[gill1109]

Nice! Recently also the CSL model has been made relativistically invariant and this means that the same can be done for Belavkin's "eventum mechanics". So the apparent defects of the first versions of these three classes of models were not fundamental, they were just "first rough guesses" which needed careful refinement. I will find the reference later (guy at Imperial college, London).

D. Beddingham (2011). Relativistic State Reduction Dynamics. Foundations of Physics 41, 686–704. arXiv:1003.2774

 

[gill1109]

A recently published paper on classical optics seems to make similar suggestions, if I understand correctly what the authors are saying:
" [..] we have presented the first study of nonlocal correlations in classical optical beams with topological singularities. These nonlocal correlations between two different light modes are manifested through the violation of a Bell inequality using the Wigner function for this system of classical vortex beams. [..]
Clearly, the violation of the Bell inequality for classical light fields and the existence of nonlocal correlations bring out totally new statistical features of the optical beams. [..] "
Phys. Rev. A 88, 013830 (2013) - [PLAIN]http://arxiv.org/abs/1307.29...of different continuous outcome measurements.

 

[TrickyDicky]

The problem with BM and the rest of interpretations of QM, is that they are just that, interpretations, one may like one or another based on personal tastes but it doesn't make any difference in the end. BM and many-worlds are sometimes preferred over the rest on the grounds that they are more "realistic" than textbook QM because at least they claim that the wavefunction is something real. But quantum scholars such as Matzkin and Nurock("The Bohmian interpretation of quantum mechanics : a pitfall for realism") make a very good case that i.e BM is as antirealist as Copenhagen. And I see the same antirealism encrusted in many-worlds in the form of basic unfalsifiability of the existence of the other worlds.

All this is hardly surprising as they are just epistemological interpretations of a theory that is as far from scientific realism as they come.

Here is where Bell's theorem powerful tool enters telling us that any theory that explains the outcomes of quantum correlation experiments must be nonlocal. It narrows the possible theories one must consider.

 

[gill1109]

Here is what Bell's theorem powerful tool enters telling us that any theory that explains the outcomes of quantum correlation experiments must be nonlocal. It narrows the possible theories one must consider.

... if one does indeed want a theory which *explains* the outcomes in a "mechanistic" way. One can also choose not to explain the outcomes at all, but accept quantum randomness as a fundamental feature of nature. Not an emergent feature.

 

[TrickyDicky]

... if one does indeed want a theory which *explains* the outcomes in a "mechanistic" way. One can also choose not to explain the outcomes at all, but accept quantum randomness as a fundamental feature of nature. Not an emergent feature.

Sure, that is the usual non-realist "there is no quantum world" camp "a la Bohr".
The zillions of forum threads dedicated to interpretations of the quantum world are testimony that this view leaves many people unsatisfied, which in itself is not a compelling reason to think that it is not the correct way to view it.

 

[stevendaryl]

Uhm, the difference is that you have one particle in one case and 4 in the other? 4 separate particles have 4 separate N-dimensional states, while 1 particle will have a single joint 4N-dimentional state. Surely you may have the exact same number of parameters, but the relationships between the parameters and the degrees of freedom involved will be wildly different.

I don't think they are wildly different if you don't have locality. Let's do things classically, rather than quantum-mechanically. For simplicity, let's just consider 1-D space (so 2-D spacetime) and just two particles. Also, for simplicity, assume that the masses are equal. So the equations of motion are something like:

m \dfrac{d^2 x_1}{dt^2} = F_1(x_1, x_2)
m \dfrac{d^2 x_2}{dt^2} = F_2(x_1, x_2)

where x_1 is the position of particle 1 and x_2 is the position of particle 2, and F_1 is the force on particle 1, and F_2 is the force on particle 2.

Now, that pair of equations is exactly equivalent to a problem in 2-D space (3D spacetime) involving just one particle:

m \dfrac{d^2 \vec{x}}{dt^2} = \vec{F}(\vec{x})

where \vec{x} = (x_1, x_2) and \vec{F}(\vec{x}) = (F_1(x_1, x_2), F_2(x_1, x_2).

I don't see any difference at all. It's just a regrouping of parameters, and such a regrouping can't possibly have any physical significance.

If we insist on locality, then there is a big difference, because the force on particle 1 cannot depend on the location of particle 2 (unless they are co-located), and vice-verse. With that restriction, the equations for two particles in 1D space are:

m \dfrac{d^2 x_1}{dt^2} = F_1(x_1)
m \dfrac{d^2 x_2}{dt^2} = F_2(x_2)

which is not equivalent to a problem in 2D space. So I think that it's really locality that makes the dimensionality of spacetime meaningful.