MWI, EPR and Deutsch: Exploring Quantum Mechanics

[matteo210]

Hello,

i have a question regarding the Many World Interpretation of quantum mechanics and how it explains the entanglement of two particles..

From my understanding, entangling two particles so that an observable of one (es. spin of z axis) is correlated with the same observable of the other particle, is described by MWI as a correlation of the relative states of the particles, so that their joined state is described by the same wave-function.
In this way, the wave function can determine the probabilities of the outcome of the measurement and can keep the results of the measurements correlated without implying faster than light communication (no info is transmitted, the particles only share the wave-function) or hidden variables. On the other hand, and this is the question, this seems to me to imply a physical reality of the wave-function (as opposed as a tool scientists use to compute probabilities).
So, how can the physical reality of the wave-function be described?
According to (my understanding of) David Deutsch (the fabric of reality), mwi does not need to imply abstract realms where the particles or their histories interact with themselves creating interference effects before being "realized" in our universe after a measurement. Quite simply, every possible story is realized and these actual worlds interact with each other time-simmetrically, as can be seen in interference effects.
Reading Deutsch's book, i had the impression that mwi was the only qm interpretation that could be seen as a fully "materialistic" and self-consistent interpretation. But, thinking twice about it, even mwi imply an abstract but real world of the wave function. Is this correct? And where would that world be? It can't be part of our space-time, nevertheless is real, so "where" is it?

 

[Demystifier]

On the other hand, and this is the question, this seems to me to imply a physical reality of the wave-function (as opposed as a tool scientists use to compute probabilities).

True, wave function is physically real in MWI.

Reading Deutsch's book, i had the impression that mwi was the only qm interpretation that could be seen as a fully "materialistic" and self-consistent interpretation.

Not true. MWI is not the only fully "materialistic" and self-consistent interpretation of QM.

But, thinking twice about it, even mwi imply an abstract but real world of the wave function. Is this correct?

Yes it is.

And where would that world be? It can't be part of our space-time, nevertheless is real, so "where" is it?

It is in the Hilbert space. (Alternatively, it can also be viewed to be in the configuration space.)

 

[matteo210]

thanks Demystifier for your answer.

MWI is not the only fully "materialistic" and self-consistent interpretation of QM.

Which interpretation of QM is fully "materialistic"? I can only think of Bohm's interpretation but, just because (in my understanding) it assumes the reality of the wave-function in the physical world (maybe even inside space-time?), i don't like the strong non-locality it implies.
Do you mean there are other interpretations that can be seen as "materialistic" except for being based on an Hilbert space?
From my layman understanding, i am reluctant to call "materialistic" any theory based on an abstract and purely mathematical configuration space (and that includes all interpretations of QM except maybe for bohm's, i think). Am i wrong? Why? does an Hilbert space have an actual (physical, therefore "material") existence on his own?

It is in the Hilbert space. (Alternatively, it can also be viewed to be in the configuration space.)

True, wave function is physically real in MWI.

What does it mean the wave function is physically real? If it means it does exist in the Hilbert space, what does that mean, in laymen's terms? "Where" is the Hilbert space other than in the mind of mathematicians? To a non-mathematician like me saying that "the wave-function is in the hilbert space" is not different than saying "3 belongs to the natural numbers'set". It doesn't mean that "3" is physically real (in contrast with the mathematics usually used in physics, es. in Einstein, where every mathematical equation represents physical entities, as energy, matter, pressure, space-time, etc..).
In short, how does Hilbert space relates to physical existence?

 

[Demystifier]

Which interpretation of QM is fully "materialistic"? I can only think of Bohm's interpretation but, just because (in my understanding) it assumes the reality of the wave-function in the physical world (maybe even inside space-time?), i don't like the strong non-locality it implies.
Do you mean there are other interpretations that can be seen as "materialistic" except for being based on an Hilbert space?
From my layman understanding, i am reluctant to call "materialistic" any theory based on an abstract and purely mathematical configuration space (and that includes all interpretations of QM except maybe for bohm's, i think). Am i wrong? Why? does an Hilbert space have an actual (physical, therefore "material") existence on his own?

It's about terminology. If theories formulated in the abstract configuration space count as materialistic, then MWI, Bohmian, and objective collapse (GRW) interpretations are materialistic. If such theories do not count as materialistic, then probably no materialistic interpretation of QM is known.

What does it mean the wave function is physically real? If it means it does exist in the Hilbert space, what does that mean, in laymen's terms? "Where" is the Hilbert space other than in the mind of mathematicians? To a non-mathematician like me saying that "the wave-function is in the hilbert space" is not different than saying "3 belongs to the natural numbers'set". It doesn't mean that "3" is physically real (in contrast with the mathematics usually used in physics, es. in Einstein, where every mathematical equation represents physical entities, as energy, matter, pressure, space-time, etc..).
In short, how does Hilbert space relates to physical existence?

These questions are too philosophical for my taste, so I am not able to give a cogent answer.

 

[matteo210]

Thanks again Demistyfier,

i would rather not mess with philosophy, but i think this is one of those cases that stands at the boundaries and can't be ignored. The way i see it, the wave-function has no actual physical counterpart and yet it has an active physical role per sé in entanglement (at least in MWI and similar interpretations). So it is clearly more than just a tool humans use or a mathematical representation of a physical entity(or maybe it is, but in this case what is the physical entity it represents?). It seems to me like it is the physical entity itself. But if it is a physical entity, where is it? How can there be a physical entity outside space-time? Maybe a deeper understanding of information theory and cosmic holography could help us answer this question?

 

[Demystifier]

Thanks again Demistyfier,

i would rather not mess with philosophy, but i think this is one of those cases that stands at the boundaries and can't be ignored. The way i see it, the wave-function has no actual physical counterpart and yet it has an active physical role per sé in entanglement (at least in MWI and similar interpretations). So it is clearly more than just a tool humans use or a mathematical representation of a physical entity(or maybe it is, but in this case what is the physical entity it represents?). It seems to me like it is the physical entity itself. But if it is a physical entity, where is it? How can there be a physical entity outside space-time? Maybe a deeper understanding of information theory and cosmic holography could help us answer this question?

Instead of giving an answer, let me ask you some questions:
In CLASSICAL mechanics is Hamiltonian real? If it is real, where Hamiltonian is? If it is not real, can you remove it from the theory without replacing it with something equally problematic?

My point is the following. In the Bohmian interpretation (which is somewhat similar to MWI) of QM, the wave function plays a similar role to the role of the Hamiltonian in classical mechanics.

 

[matteo210]

It took me some time to reply, mainly because i am not well acquainted with maths and mechanics.
Anyway, from what i understood of hamiltonian mechanics, in a classical world i could describe it as a way to compute the physical proprieties (dependant on the transition from/to potential/kinetic energy) of a system, based on the principle of least action. I don't see particular contraddictions between maths and physics, as there's a way to justify from the physical point of view the principle of least action. Ironically, the principle is justified physically by quantum mechanics (Feynman's path integral).
So i can answer that the Hamiltonian is (abstract but) real and its reality is due to the principle of least action, which takes us back to the wave function that describes all possible "actions" of a system.
So in my view the quantum wave function/path integral is what justifies the reality of the hamiltonian in classical mechanics.
Can i also say that the wave function is (abstract but) real? this takes me back to my original question, wave function (if it is real) should have a physical reality too to explain non-local entanglement effects. It couldn't be abstract but real because there is nothing else we can use to physically explain the phenomenon of non-local entanglement (as far as i am aware).
So either the wave function is real and "physical", or the wave function is not real and nothing but a mathematical tool humans use, just as they used the epicyclic model of Ptolemy to compute planetary motions even in the absence of the correct cosmological background.
i think the answer may lie on the boundary/surface of our universe, where the "quantum action" is likely to take place, and when we will have a better cosmological background than what we have now, we should find a better and "physical" way to describe what we now call the wave function.
Being a layman with only a superficial knowledge of the matter, i am not completely sure what i just wrote makes sense or not, and i am still on my long and hard way to understand reality, so i am grate to anyone that can help me correct/improve/enhance my thoughts. so, to restate my question in a clearer way, is there a physical explanation of non-local entanglement? I've read about ontological (Bohm), relative states (Everett-DeWitt-Deutsch), consistent histories (Omnes, Hartle, Gell-Mann), Copenhagen (Bohr and Born) and information theory (Zeilinger) interpretations, but i still haven't found a physical explanation of non-local entanglement (except for Bohm's ontological interpretation, that has nonetheless other major flows from my point of view).

ps. while writing this i stumbled on some attempts to physically, or at least geometrically/topologically define entanglement, in documents such as http://iopscience.iop.org/1742-6596/30/1/002/pdf/jpconf6_30_002.pdf?ejredirect=migration and http://www.fsr.ac.ma/GNPHE/ajmpVolume7N1-2009/ajmp0908.pdf and http://arxiv.org/abs/quant-ph/0108064 .Althought at the moment i don't have the needed mathematical skills to fully understand what's in it (es. are these geometric descriptions valid in QFT or they only apply on non-relativistic QM?), i think this papers enlight the directions i was trying to follow in the darkness of my mathematical ignorance thru my path to understanding reality.

pps. i also found a previous thread in a way related to mine discussing this paper http://arxiv.org/abs/quant-ph/9906086, https://www.physicsforums.com/showthread.php?t=112147

 

[Demystifier]

but i still haven't found a physical explanation of non-local entanglement (except for Bohm's ontological interpretation, that has nonetheless other major flows from my point of view).

I agree with you that the Bohm's interpretation provides the most physical explanation of non-local entanglement. In your view, what are the major flows of that interpretation?

 

[matteo210]

First i have to admit i haven't a comprehensive knowledge of Bohmian mechanics but, for what i know, i consider "dark spots" of the theory:

-probably the most common critic to the theory, the strong non-locality that implies, and that seems to contradict special relativity as it implies instantaneous actions and it is not Lorentz invariant. (i know there are some proposal to reconcile the two theories, es. http://arxiv.org/abs/quant-ph/0512065 but i really can't judge now their reliability).
-the concept of quantum equilibrium (that is used to justify the relation between probability density and "amplitude squared") seems to me to be taken for granted without a strong enough justification, but, then again, that could also be because i am not sufficently acquainted with the theory.
-in a similar way, i think that stating that particles necessarily have definite physical characteristic such as position etc indipendently from their state is taking to much for granted, without a convincing justification. For example, theories such as random discontinuous motion http://arxiv.org/abs/1001.5085 also propose a physical explanation for the "indefiniteness" of a particle position, and their justification looks more convincing to me.
I know there are some papers that try to address (maybe) all of my previous remarks, such as http://arxiv.org/abs/quant-ph/9512031v1 or http://arxiv.org/PS_cache/quant-ph/pdf/9511/9511016v1.pdf or more recently http://arxiv.org/abs/0903.2601 but i haven't read them all yet, so maybe there i can find the answers to my questions regarding Bohm's theory.

The above notwithstanding, i still think Bohm Mechanics is among my "all-time favourites" interpretations of QM, but i really need to get deeper in the theory to really understand it, and by that time maybe an updated, comprehensive and definitive theory of the quantum world will be present.

 

[Demystifier]

Matteo, your reservations about Bohmian mechanics are justified, and the references you quote are fine and well chosen. Reading them will certainly improve and sharpen your understanding of Bohmian mechanics.

Concerning the issue of compatibility between nonlocality and relativity, I believe it is better explained in a more recent paper
http://xxx.lanl.gov/abs/1002.3226
It contains some improvements with respect to the paper you mentioned, and contains a nontechnical part (Sec. 2) which should be easy to understand.

 

[yoda jedi]

i would rather not mess with philosophy, but i think this is one of those cases that stands at the boundaries and can't be ignored. The way i see it, the wave-function has no actual physical counterpart and yet it has an active physical role per sé in entanglement (at least in MWI and similar interpretations). So it is clearly more than just a tool humans use or a mathematical representation of a physical entity(or maybe it is, but in this case what is the physical entity it represents?). It seems to me like it is the physical entity itself. But if it is a physical entity, where is it? How can there be a physical entity outside space-time? Maybe a deeper understanding of information theory and cosmic holography could help us answer this question?

there are
ψ-epistemic view, ψ-complete, ψ-ontic view,
in the ψ-epistemic view the quantum state represent reality or our knowledge of reality, that is, a representation of an observer’s knowledge of reality rather than reality itself.
If the quantum state is a complete description of reality, its called ψ-complete view.
to Einstein the quantum state is not just incomplete, but epistemic.

and

ψ-complete → ψ-ontic

or its negation.

ψ-epistemic → ψ-incomplete.

Which interpretation of QM is fully "materialistic"?

any NONLINEAR QUANTUM MECHANICS; Singh or Elze or Tumulka or Zloshchastiev or Hansson and/or others (CSL models).