What do violations of Bell's inequalities tell us about nature?

bohm2

Yes, this is the heart of the issue for me. I think Einstein was very troubled by it, also. A very interesting paragraph by Belousek that summarizes this very nicely is the following:
Formalism, Ontology and Methodology in Bohmian Mechanics
http://www.ingentaconnect.com/conten...00002/05119217

Valentini tries to thread to a middle position something similar to yours (I'm guessing?) but there are problems with this also as Belousek notes:

ttn

Yes, I think we agree that this is an important and unsolved problem. My own best attempt to solve it (or at least indicate a direction for future work aimed at trying to solve it) is here:

http://arxiv.org/abs/0909.4553

The idea there is in some ways the idea that Belousek suggests, in the passage you quoted: break the 3N-space wave function up into N (or, as it turns out, in my example, a lot more than N) fields on 3-space. Belousek, though, seems to think there is some problem with doing this (associated with the different fields not really living in the same 3-space), but that particular worry makes no sense to me. The conditional wave function (CWF) is perfectly well-defined and there's no reason one cannot think of N such conditional wave functions (one for each particle) living in 3-space. (Just define the CWF for particle i as the wf, evaluated at the actual positions X_j of all particles other than the i'th, and evaluated at x_i = x, the position in physical space.) The problem (related to the recent PBR theorem, incidentally) is that these N CWFs are (radically) insufficient to generate the right dynamics for the particles (except for the unrealistic special case where the wave function is a product state). You need to somehow capture the whole structure of the wave function, including "entanglement", and the CWFs (alone) don't do this. My admittedly silly toy model above is a way to do this, albeit a way that even I can't really take too seriously.


I agree with Belousek's criticisms of Valentini here. I guess Valentini's views are similar to mine in that we both don't like the nomic interpretation of the wf. But where it seems he doesn't really think there's any problem with saying "the wf is a physically-real guiding-field that lives in configuration space", I am profoundly troubled by this. (Although, to be fair, it's possible Valentini sees no problem because, in fact, he thinks in terms of Albert's "marvellous point" picture. That, to be sure, solves some of the worries. But I think we'll agree it introduces others!)

But, interesting as all these issues are, one should keep in mind that they don't matter at all for a lot of important things -- such as whether Bell's theorem shows that nature is nonlocal!

audioloop

i agree, reality cannot be equated with values, values are just attributes of something (objects, entities, process etc).

stevendaryl

I read the paper "Against `Realism'" here: http://arxiv.org/abs/quant-ph/0607057

It's thought-provoking, and I think most of the points are well-taken, but I wasn't completely convinced by all of the arguments.

The point of the two-word phrase "local realism" is really, it seems to me, to distinguish between interpretations like the Bohm interpretation, which are realistic, but not local, and interpretations like Many-Worlds, which are local, but not realistic.

The argument in the paper against MWI is in some ways compelling, and in other ways not very. If I can oversimplify, MWI is a useless theory of physics, because the whole point of a physical theory is to predict outcomes of experiments (or the probabilities of various outcomes) while in the MWI, there are no definite outcomes (or all possible outcomes occur). MWI denies that there is any fact of the matter as to whether Alice measured an electron to have spin-up or spin-down relative to a particular axis. So it's not clear how to relate MWI with what we actually observe.

That sounds like a plausible reductio ad absurdum. But my feeling, based on the experience with many similar arguments, is that any piece of science or math can appear meaningless if you subject it to a withering enough philosophical examination.

The problem, it seems to me is that when we're talking about tiny little systems, such as electrons or atoms or molecules or photons, the recipe given by quantum mechanics seems perfectly meaningful (if weird). The quantum recipe tells us the likelihood for various observable outcomes for certain experimental setups, and we can actually repeat the experiment and gather statistics, and check the correctness of the quantum predictions. So quantum mechanics, with the usual recipe, clearly has empirical content.

Now, the way I see it, the only step you have to make to get to something like MWI is to consider: A human being, together with a macroscopic measuring device is just a huge collection of particles, all of which empirically obey the rules of quantum mechanics. Therefore, there is no reason not to treat macroscopic systems as quantum systems. But if you do that, you have to consider superpositions of macroscopically distinguishable states (cats that are a superposition of dead and alive). Either quantum mechanics is wrong (and there's no evidence of it being wrong), or it applies to macroscopic objects as well as microscopic objects.

I don't think that decoherence really changes the picture much. The way I understand decoherence is that it's a matter of realizing that the "system" in the case of a macroscopic object like a cat is not just the cat, but also electromagnetic and gravitational fields. So you don't have a universe in which a cat is in a superposition of dead and alive, you have the whole universe being in a superposition of a state in which the cat is dead and a state in which the cat is alive. It seems to me that decoherence is not an alternative to MWI--the MWI concept of the entire universe being in a superposition of states is an inevitable consequence of decoherence.

So even though I agree that MWI has disturbing philosophical implications, it seems that once you've accepted that quantum mechanics applies to electrons and photons and atoms, the MWI interpretation is an inexorable conclusion.

The alternative of considering some kind of "pilot wave" theory I don't think is philosophically any better, and I really don't think that it ends up being any different than MWI. The reason I say that is because even though a Bohm-style interpretation assumes that particles have definite positions, which sounds philosophically more acceptable, there is something weird about the trajectories of these particles. No, I'm not actually talking about the nonlocal interactions (even though that is pretty weird itself for someone who has spent a lot of time with Special Relativity). I'm talking about the fact that particles don't affect each other! The trajectory of a particle is determined, in a Bohm-type theory, by the wave function. The wave function evolves deterministically according to Schrodinger's equation (or Dirac, or whatever), completely independently of the locations of the particles. So the wave function influences the particles, but is not influenced by them. In this way, the particles are not really participants in the physics, they are just actors following a script provided by the wave function, and have no influence on each other.

To me, that's as big of a philosophical disaster as MWI is. We might be comforted that an electron really does have a location at each moment, but its location now has no causal effect on anything in the future. In a pilot-wave theory, it's still the case that all the action, and all the physics, is in the wave function, rather than in the particles. And the wave function evolves smoothly and doesn't hesitate to allow a dead cat's wave function to be in superposition with an alive cat's wave function.

DrChinese

That is a fair assessment of the paper. ttn and others (including myself) have debated this many times. Not surprisingly, Bohmians tend to agree with the conclusion more often than others.

I, being mostly a non-realist, reject his thesis. I find that Bohmian representations of such experiments as delayed choice entanglement swapping (DCES) are unsatisfactory. Those seem to me to require a non-realistic interpretation of some kind. I realize that Bohmians do not agree however, but you can judge for yourself.

ttn

Thanks for taking the time to read it and for your thoughtful comments. I'll resist the temptation to get into a huge discussion of all the issues raised, but just make a couple brief remarks.

1. Yes, clearly, that is the overall intent of people who speak of "local realism". But it doesn't really help clarify *exactly* what the "realism" in "local realism" is supposed to mean. Recall that there are some senses in which e.g. the Bohm interpretation is "realistic" and some senses in which it isn't. So just saying "theories like the Bohm interpretation are realistic" doesn't help much. We need a crisp statement of what "realism" means, and then a crisp identification of where, exactly, any such assumption is made in Bell's derivation -- and here I mean the *full* derivation: (Bell writes, footnote 10 of B's Sox) "My own first paper on this subject starts with a summary of the EPR argument *from locality to* deterministic hidden variables. But the commentators have almost universally reported that it begins with deterministic hidden variables."

2. It is hardly as clear as you imply that MWI is local. I know everybody claims this, but in so far as MWI has *only* the wave function in its ontology, and insofar as the wave function doesn't live in physical space (but instead some high-dimensional configuration space), it seems that MWI doesn't posit any physically real stuff in ordinary physical space at all. And so I literally have no idea what it would even mean to say that it's local, i.e., that the causal influences that propagate around between different hunks of stuff in physical space do so exclusively slower than the speed of light. It's ... a bit like saying that Beethoven's 5th symphony is local. It's not so much that it's non-local, but just that it's not even clear what it could mean to make *either* claim. Incidentally, there is a really nice and interesting paper that suggests a way for MWI to posit some local beables, i.e., some physical stuff in 3-space. The authors end up concluding (correctly I think) that this theory is actually non-local:

http://arxiv.org/abs/0903.2211


The main difference with (traditional formulations of MWI), to me, is that the pilot-wave theory provides a way to have a fundamental/microscopic theory that actually accounts for the macroscopic stuff we observe: there are trees and tables and planets and people in the theory (namely, tree-shaped, table-shaped, etc., collections of particles in 3-space) and also the pointers on lab equipment are predicted to move the way, and with the statistics, we observe them to actually move in experiments. That's quite an achievement compared to virtually all other contenders. Ordinary QM only gets familiar macroscopic stuff by separately positing it, and then making up special ad hoc dynamical rules for how it interacts with the microworld. MWI, as I pointed out above, doesn't seem to have any "stuff" in 3-space at all, so evidently there are no trees, planets, etc. -- instead just tree-ish and planet-ish delusions in peoples' minds.


Sure, the trajectories are "weird". I understand the discomfort about the particles responding to, but not in turn affecting, the wave function. Sometimes people talk about this as a violation of Newton's third law -- the particles don't react back on the wf. So, sure, maybe that's "weird", but who said Newton's third law has to be respected?


If you think that, it makes me think you haven't appreciated exactly why MWI is so "philosophically" (I would say: "physically"!) disasterous.


Seriously, the main value of the particles having definite positions is not that it makes you feel good (compared to feeling queasy about indefinite/fuzzy positions in ordinary QM or whatever), but that if you get a whole bunch of electrons (and other particles) together, into a macroscopic thing, then the macroscopic thing will actually have some definite shape, be at some definite place, etc., -- without the need to wave your arms and make up special rules and extra postulates. The macroscopic world (that we know about directly through sense perception) just comes out, just emerges, from the microscopic picture, without any philosophical mumbo jumbo.

stevendaryl

If the particles don't affect the wave function, and the only thing that affects the particles is the wave function, then the particles aren't really participants in the physics. I know that the usual way of doing one-particle Bohmian mechanics has an ordinary Newtonian-type force term, and then an additional term due to the "quantum potential", which can be viewed as a small correction to the Newtonian prediction. But in the actual world, there is no "external" potential, there is only interactions with other particles. So a many-particle analog to the quantum potential is all there is to affect particle trajectories.

No, I think I understand exactly why MWI is conceptually a nightmare, when it comes to understanding the relationship between theory and experience. But I don't think a "pilot wave" theory is any better. It just supplements the universal wave function with particles that carry out a pantomime of actual physical interactions.

It seems equally full of mumbo jumbo to me. The particles are just putting a do-nothing mask on the wave function.

Suppose you arrange a bunch of atoms into a solid brick wall. Then a Bohmian type of theory would predict that the wall would continue to exist for a good long time afterward, giving a reassuring sense of solidity. But now, you take a baseball (another clump of atoms arranged in a particular pattern) and throw it at the wall. What happens then?

The question for a Bohmian type theory is what wave function are you using to compute trajectories? The full wave function describes not the actual locations of the particles of the ball and the wall, but a probability amplitude for particles being elsewhere. If, as you seem to agree, the wave function affects the particles, but not the other way around, then the fact that you've gathered atoms into a wall doesn't imply that the wave function is any more highly peaked at the location of the wall. So if it's the wave function that affects the trajectory of the ball, then why should the ball bounce off the wall?

The principle fact that Bohmians use to show that Bohmian mechanics reproduces the predictions of quantum mechanics is that if particles are initially randomly distributed according to the square of the wave function, then the evolution of the wave function and the motion of the particles will maintain this relationship. That's good to know in an ensemble sense, but when you get down to a small number of particles--say one electron--the wave function may say that the electron has equal probabilities of being in New York and in Los Angeles, but the electron is actually only in one of those spots. So either the wave function has to be affected by the actual location (in a mechanism that hasn't been demonstrated, I don't think) or there has to be the possibility of an electron having a location that is in no way related to the wave function (except in the very weak sense that if the electron is at some position, then the wave function has to be nonzero at that position).

So either you have to have a "wave function collapse" or some other way for the wave function to change that doesn't involve evolution according to the Schrodinger equation, or you have the possibility that the trajectories of physical objects are unaffected by the locations of other physical objects. Which is certainly contrary to experience.

ttn

You raise a number of important and interesting points... far more interesting than the lab reports I should probably be grading instead of writing this! =)

Now this is a very strange statement. I think it reflects a view which your other comments also seem to reflect -- namely that you are accustomed (from ordinary QM or whatever) to thinking of the wave function as the thing where, so to speak, "the action is". So to you, if the wave function of a particle is split in half, with part in LA and part in NY, then there's going to be a 50/50 chance of detecting it in LA/NY, according to all the usual QM rules. And then you assume that this is still the case in Bohm's theory, such that the "real particle position" that supplements the wf is a kind of pointless epiphenomenon that "doesn't participate in the physics". If you want to understand the Bohm theory, though, you have to accept that it just doesn't work this way. You have to retrain yourself to think in a different way. In particular, you have to accept that the physical stuff we interact with in real life (particles, brick walls, balls, apparatus pointers, etc.) is not "made of" wave function, but is instead made of particles. This is hard for people to even understand as an option, because in ordinary QM (which everyone always learns first), there is only the one thing -- the wave function -- so *of course* that is where all the physics is. But in Bohm's theory there are really *two* things, the wave *and* the particle. So there is a legitimate and meaningful and important question: which one are things like tables and chairs made of? And the answer (that you have to provisionally accept if you want to understand the Bohmian view of the world at all) is that stuff is made of *particles*. Despite what the traditional terminology suggests, it's actually the *wave function* that is the "hidden variable" in Bohm's theory -- the particles are right there, visible, in front of your eyes when you look out on and interact physically with the world; whereas the wave function is this spooky ethereal invisible thing that is sort of magically acting behind the scenes to make the particles move the way they move.

That's the overview point. Now let me try to explain exactly how some of your comments exhibit this confusion about how to understand the "roles" of the two things, the wave and the particles...


This is really an aside, but actually the "usual way of doing ... bohmian mechanics" does *not* involve any "quantum potential". Yes, Bohm and a few others like to formulate the theory that way, as was discussed in the thread above. But (I think at least) it is much better (and certainly these days more standard) to forget the silly quantum potential, and just let the ordinary wave function be the thing that "guides" or "pilots" the particles. The quantum potential is a big bloated pointless middle man, at best. Better to just get rid of it and define the theory in terms of (a) the wave function obeying the usual Sch eq, and (b) the particles obeying the guidance law, basically v = j/rho (where j and rho are what are usually called the probability current and density respectively).


Here you assume that the "actual physical interactions" are happening in the wave function, so that the particles are (at best) pantomiming some one small part of the physics. But that's not the right way to think about it. If what we mean by "physical" is stuff like balls crashing into brick walls, then that is particles. What you call a ball or a brick wall is, in bohm's theory, a collection of *particles*.


It'll bounce off the wall. The theory predicts this. Here is how to think about it. Pretend the brick wall and the ball are each just single particles, and assume that they have an interaction potential which is basically zero for r>R, and basically infinite for r<R. Call the wall's coordinate "x" and the ball's "y". The configuration space is now the x-y plane. Suppose the wall is initially at rest near x=0, i.e., its initial wf is some sharply peaked stationary packet centered on x=0. The ball starts at some negative value of y, say -L, and has a positive velocity; so take its initial wf to be an appropriate packet. Now the wave function for the 2 particle system -- which we assume is a product state of the two one-particle wf's just described -- is thus a little packet located at (x=0, y=-L) and moving with some group velocity toward the origin (x=0, y=0). What Schroedinger's equation says now is that the packet (in the 2d config space) will propagate up, bounce off the big potential wall at (x=0,y=0), and reflect back down. (I assume here that the mass of the wall particle is large compared to the mass of the ball particle.) So much for the wave function.

What about the actual/bohmian particle positions? Well, at t=0, the wall has some actual position in the support of its wf, and likewise for the ball. And then the actual configuration point just moves along with the moving/bouncing packet in configuration space. So the story you'd tell about the two particles in real space is: the wall particle just sits there the whole time, while the ball particle comes toward it, bounces off, and heads away.

Now you want to ask: what happens if, instead of initially being in a (near) position eigenstate, the wall is initially in a superposition of two places? It's a good question, but if you think it through carefully, you'll find that the theory says exactly what anybody would consider the right/reasonable thing. So, just recapitulate the above, but now with the initial wf for the wall being a sum of two packets, one peaked at x=0 and one peaked at x=D. Now (I'm picturing all of this playing out in the x-y plane, and hopefully you are too) the initial 2-particle wave function in the 2D config space has *two* lumps: one at (x=0, y=-L), and the other at (x=D, y=-L). So then run the wf forward in time using the sch eq: the two lumps each propagate "upward" (i.e., in the y-direction). Eventually the first lump reaches the potential wall near (x=0,y=0) and bounces back down. Meanwhile the other lump continues to propagate up until it reaches the potential wall near (x=D,y=D) at which point it too reflects and starts propagating back down. So much for the wave function.

What about the particles? The point here is that in bohm's theory the *actual configuration* is in one, or the other, of the two initial lumps. If (by chance) it happens to be in the first lump, then the story is *exactly* as it was previously -- the other, "empty" part of the wave function (corresponding to the wall having been at x=D) is simply irrelevant. It plays no role whatever and could just as well have been dropped. On the other hand, if (by chance) the actual positions are initially in the second lump, then the story (of the particles) is as follows: the ball propagates toward the wall (which is at x=D) until the ball gets to x=D, and then it bounces off. That is, there is some fact of the matter about where the wall actually is, and the ball bounces off the wall just as one would expect it to.

The only thing that could possibly confuse anybody about this is that they are thinking: but the wall really *isn't* in one or the other of the definite places, x=0 or x=D, it's in a *superposition* of both! Indeed, that's what you'd say in ordinary QM. And then you'd have to make up some story about how throwing the ball at the wall constitutes a measurement of its position and so collapses its wave function and thus causes it (the wall) to acquire a definite position, just in time to let the ball bounce off it. But all of this is un-bohmian. In bohm's theory everything is just simple and clear and normal. The wall (meaning, the wall PARTICLE) is, from the beginning, definitely somewhere. Maybe we don't know, for a given run of the experiment, where it is, but who cares. It is somewhere. The ball bounces off this actual wall when it hits this actual wall. Simple.



Well, it certainly implies that there's some kind of "peak" (at the point in configuration space corresponding to the arrangement of atoms you just made). But you're right -- this is just one peak in a vast mountain range, so to speak. There are lots of other peaks. But these, as it turns out, are totally irrelevant. They don't affect the motion of the particles (because, so to speak, the evolution of the actual configuration -- the actual particle positions -- only depends on the structure of the wave function around this actual configuration point... the theory is "local in configuration space"). Of course, there can be interference effects, and so on, but the theory again perfectly agrees with the usual QM predictions -- it just does so without extra ad hoc philosophical magic postulates about what happens during "measurements".


Because that's what the theory's fundamental laws (the Sch eq and the guidance equation) say will happen.


I'm not seeing what you think the problem is. Let a single particle come up to a 50/50 beam splitter, and "split in half". Half of the wf goes to LA and half to NY. Ordinary QM says now if you make a measurement of the position (in LA, say) and (say) you actually *find* that the particle is there, that is because some magic happened -- the intervention by the measurement device pre-empted the normal (schroedinger) evolution of the particle's wave function, and made it collapse so that now *all* of its support is in LA, with the "lump" over in NY vanishing. According to Bohm's theory it's much simpler. Particle position detectors don't do anything magical -- they just respond to where the particles is (just like the ball above responds to the actual location of the wall). And note, the word "particle" there means "particle" -- as opposed to the wf! Got that? Particle detectors detect *particles*, not wave function. So the particle detector clicks or beeps or whatever if (as might have been the case with 50% probability) the particle was in fact already actually there in LA. Simple.

You are missing some important points about how the theory works. Hopefully the above clarifies. Note that there is certainly no "collapse postulate" in the axioms of bohm's theory -- the wf (of the universe, basically) obeys the sch eq *all the time*.

HOWEVER, there is a really cool and important thing about bohm's theory -- you can meaningfully define a wave function of a *sub-system*. Take the wall/ball system above. The wave function is a function \psi(x,y). But we also have in the picture the actual wall position X and the actual ball position Y. So we can construct a mathematical object like \psi(x,Y) -- the "universal" wave function, but evaluated at the point y=Y. This is called the "conditional wave function for the wall": \psi_w(x) = \psi(x,Y). And likewise, \psi_b(y) = \psi(X,y) is called the "conditional wave function of the ball".

Now here's the amazingly beautiful thing. Think about how the conditional wave function of the wall, \psi_w(x), evolves in time. To be sure, it starts off having two lumps, one at x=0 and one at x=D. But if you think about how \psi(x,y) evolves in time (with the two lumps becoming *separated* in the y-direction, because one of them reflects earlier than the other), you will see that \psi_w(x) actually "collapses" -- after all the reflecty business has run its course, \psi_w(x) will be *either* a one-lump function peaked at x=0, *or* a one-lump function peaked at x=D. Which one happens depends, of course, on the (random) initial positions of the particles.

The point is -- and this is really truly one of the most important and beautiful things about Bohm's theory -- the theory actually *predicts* (on the basis of fundamental dynamical laws which are simple and clear and which say *nothing* about "collapse" or "measurement") that *sub-system* wave functions (these "conditional wave functions") will collapse, in basically just the kinds of situations where, in ordinary QM, you'd have to bring in your separate measurement axioms to make sure the wfs collapsed appropriately. So not only does bohm's theory make all the right predictions (contrary to what I think you are worrying), it actually manages to *derive* the weird rules about measurement that are instead *postulated* in ordinary QM.

stevendaryl

I'm not questioning what it's "made of", I'm questioning what it means to "interact with" something physical. In ordinary Newtonian physics it means, for example, that a ball will bounce off a wall. How, in Bohm's theory, is such an interaction modeled? Well, the original one-particle model is not really applicable, because it had "external" fields that interacted with particle. In a many-particle version of Bohm's theory (which I haven't seen written down, but I assume that such a thing exists), the only forces are those due to particle-particle interactions (such as electromagnetic interactions). The question is: What kind of force acts on an electron due to other electrons, in the Bohm theory? Is there an inverse-square law based on the positions of electrons? I don't think so---such an interaction would not (I don't think) reproduce the same predictions as orthodox quantum mechanics. Instead, what I think would be the case is that the "force" on one electron would depend not on the positions of other electrons, but on the shape of the wave function.

If that's not the case, I would like to see a simple example worked out; for example, a Bohmian model of two point-masses interacting through a harmonic oscillator potential. That seems simple enough that it could be worked out explicitly. Maybe I'll try myself.

It's not a matter of "how to think about" it. It's a matter of what the theory says about how particles interact. Yes, I agree, a brick wall is a collection of particles, and a ball is another collection of particles, and all the particles are following some pilot wave. It's a quantitative, not a philosophical, question of what happens when the actual ball is far away from the central part of the wave function representing the amplitude for the ball's position. Does the ball behave in a classical way, bouncing off the wall, regardless of the shape of the wave function? It's not a philosophical question, but a technical question.

ttn

Did you actually read my last post? All of it? I spent a long time and actually explained in detail exactly how you'd model this. It's a two-particle system, just the kind of thing you say here you "haven't seen written down". Anyway, I get now that you're raising a slightly different sort of issue than what I addressed before, but please do read what I wrote before carefully, because it will help you understand the theory.



Yes and no. The main point is just that the particles don't really interact directly with one another, in the (classical) way you're thinking of here. The theory instead works like this: one puts the usual interaction terms in the Hamiltonian (whatever one would do in ordinary QM for the situation under study, so, maybe an inverse-square-law coulomb type force if we are really trying to talk about two electrons scattering off each other) and then has the usual schroedinger equation in which these interaction terms influence how the wave function behaves. Then, as you pointed out earlier, the particles come along for the ride, surfing as it were on the wave function. So the fact that one has inverse-square-law (or whatever) forces in the Hamiltonian, will end up making the particles tend to repel each other, etc. (In some appropriate classical limit, they would just behave like classical particles interacting directly via 1/r^2 forces... but of course more interesting things can happen when one isn't in the classical limit.) But it's not like the particles experience two kinds of forces: the ones that the wave function exerts on them, and then also the 1/r^2 coulomb forces that they exert directly on each other. That's just not what the theory says. The particles *only* experience the "forces" (and really "force" is not at all the right word for it, since the relevant law is *nothing like* F=ma, but leave that aside here) exerted on them by the wave function. That's it. So it's not exactly that the particles don't exert forces on each other, but rather that their (coulomb, whatever) interaction is completely mediated by the wave function.

Notice that your wrong way of thinking it should work is actually kinda/sorta the way you might talk about it in the quantum potential formulation of the theory, which I don't like -- partly because it invites this kind of thinking, that "really", the theory is just "classical physics but with an extra quantumish force". But it's not. That's really just a wrong and misleading way to try to understand it.



Sure, play with it. But actually there's not much to work out. You'd do all the standard things to understand how the wave function works (e.g., probably, switch to relative/average coordiantes so it decouples into free motion of the cm plus a 1-particle-type problem, which can be solved easily, for the relative coordinate). Then you make up some initial conditions and figure out what the time-dependent wave function will be. That is all totally standard and not at all bohmian. The bohmian part is now easy. Given the solution of the sch equation, i.e., given the time-dependent wf, see how the particles will move for various possible initial conditions.


Not sure if this is exactly what you want, but take a single particle in 1D, with a gaussian initial wf. As we all know, sch's eq implies that the gaussian wf will remain gaussian but spread in time. The bohmian trajectories will just spread with it. For example, if the particle happens to start right in the middle, it'll just sit there, but if it instead starts a little bit off to the right, it'll *accelerate* to the right (such that its distance from the middle increases, and indeed increases nonlinearly, with time), and if it starts a little to the left it'll accelerate to the left.

nanosiborg

No, I don't think that Bell's theorem leaves us a choice of giving up locality OR giving up hidden variables. I think it rules out any local hidden variable theory or interpretation of QM solely because of the locality condition. Further, I agree with what I take to be your position that, whether realistic or hidden variable or nonrealistic or whatever, no explicitly local theory of quantum entanglement can match all the predictions of QM or all the experimental results.

I had been thinking that it would be pointless to make a local nonrealistic theory, since the question, following Einstein (and Bell) was if a local model with hidden variables can be compatible with QM? But a local nonrealistic (and necessarily nonviable because of explicit locality) theory could be used to illustrate that hidden variables, ie., the realism of LHV models, have nothing to do with LHV models' incompatibility with QM and experiment.

Your coin-flip model, insofar as it would incorporate a λ representing the coin-flip, would be a hidden variable model. But because the coin-flip won't change the individual detection probability, λ can be omitted. (?) We can do that with Bell's general LHV form also, because in Bell tests λ is assumed to be varying randomly and therefore has no effect on the individual detection probability -- ie., rate of individual detection remains the same no matter what the setting of the polarizer, so the inclusion of a randomly varying λ is superfluous. (?) Bell only includes it (I suppose) because that's the question he's exploring. That is, it's because the inclusion of a λ term is a major part of an exercise aimed at answering whether a local hidden variable interpretation of standard QM is possible.

In the course of doing that it's been shown as well that a local interpretation of QM is impossible. So, it should be clear that I agree with you (and Bell) that it's all about the locality condition.

Thanks. I like your writing style. It's very clear and clearly organized. Just that sometimes things get a bit complicated, and some of it (eg., in the scholarpedia article) is momentarily a bit over my head. But I expect to have everything sorted out for myself after another dozen or so slow readings of it and your papers.
Ok.
Ok.
Ok.
Thanks.
I'd put it like this. Bell's formulation of locality, as it affects the general form of any model of any entanglement experiment designed to produce statistical dependence between the quantitative (data) attributes of spacelike separated paired detection events, refers to at least two things: 1) genuine relativistic causality, the independence of spacelike separated events, ie., that the result A doesn't depend on the setting b, and the result B doesn't depend on the setting a. 2) statistical independence, ie., that the result A doesn't alter the sample space for the result B, and vice versa. In other words, that the result at one end doesn't depend in any way on the result at the other end.

The problem is that a Bell-like (general) local form necessarily violates 2 (an incompatibility that has nothing to do with locality), because Bell tests are designed to produce statistical (ie., outcome) dependence via the selection process (which proceeds via exclusively local channels, and produces the correlations it does because of the entangling process which also proceeds via exclusively local channels, and produces a relationship between the entangled particles via, eg., emission from a common source, interaction, 'zapping' with identical stimulii, etc.).

Ok, I don't think it has anything to do with Jarrett's idea that "Bell locality" = "genuine locality" + "completeness", but rather the way I put it above, in terms of an incompatibility between the statistical dependence designed into the experiments and the statistical independence expressed by Bell locality.

Is this a possibility, or has Bell (and/or you) dealt with this somewhere?

ttn

Well, you'd only convince the kind of person who voted (b) in the poll, if you somehow managed to show that *no* "local nonrealistic" model could match the quantum predictions. Just showcasing the silly local coin-flipping particles model doesn't do that.

But I absolutely agree with the way you put it, about what the question is post-Einstein. Einstein already showed (in the EPR argument, or some less flubbed version of it -- people know that Podolsky wrote the paper without showing it to Einstein first and Einstein was pissed when he saw it, right?) that "realism"/LHV is the only way to locally explain the perfect correlations. Post-Einstein, the LHV program was the only viable hope for locality! And then Bell showed that this only viable hope won't work. So, *no* local theory will work. I'm happy to hear we're on the same page about that. But my point here is just that, really, the best way to convince somebody that "local non-realistic" theories aren't viable is to just run the proof that local theories aren't viable (full stop). But somehow this never actually works. People have this misconception in their heads that a "local non-realistic" theory can work, even though they can't produce an explicit example, and they just won't let go of it.

Since it so perfectly captures the logic involved here, it's worth mentioning here the nice little paper by Tim Maudlin

http://www.stat.physik.uni-potsdam.d...Bell_EPR-2.pdf

where he introduces the phrase: "the fallacy of the unnecessary adjective". The idea is just that when somebody says "Bell proved that no local realist theory is viable", it is actually true -- but highly misleading since the extra adjective "realist" is totally superfluous. As Maudlin points out, you could also say "Bell proved that no local theory formulated in French is viable". It's true, he did! But that does not mean that we can avoid the spectre of nonlocality simply by re-formulating all our theories in English! Same with "realism". Yes, no "local realist" theory is viable. But anybody who thinks this means we can save locality by jettisoning realism, has been duped by the superfluous adjective fallacy.


I don't understand what you mean here. For the usual case of two spin-entangled spin-1/2 particles, the sample space for Bob's measurement is just {+,-}. This is certainly not affected by anything Alice or her particle do. So if you're somehow worried that the thing you call "2) statistical independence" might actually be violated, I don't think it is. But I don't think that even matters, since I don't see anything like this "2) ..." being in any way assumed in Bell's proof. But, basically, I just can't follow what you say here.

Huh???

The closest I can come to making sense of your worry here is something like this: "Bell assumes that stuff going on by Bob should be independent of stuff going on by Alice, but the experiments reveal correlations, so one of Bell's premises isn't reflected in the experiment." I'm sure I have that wrong and you should correct me. But on the off chance that that's right, I think it would be better to express it this way: "Bell assumes locality and shows that this implies a certain limit on the correlations; the experiments show that the correlations are stronger than the limit allows; therefore we conclude that nature is nonlocal". That is, it sounds like you are trying to make "something about how the experimental data should come out" into a *premise* of Bell's argument, instead of the *conclusion* of the argument. But it's not a premise, it's the conclusion. And the fact that the real data contradicts that conclusion doesn't invalidate his reasoning; it just shows that his *actual* premise (namely, locality!) is false.

morrobay

Reading underlying parameter = hidden variable. Then nonvarying underlying parameters produces perfect correlations for spin measurements along parallel directions for spin - entangled particles. And a varying underlying parameter would produce spin measurements when directions are not parallel. Bell proved that a local deterministic hidden variable model does not explain the measurements when detector settings are not parallel.So this would be the challenge: To show a local hidden variable model with varying and nonvarying underlying parameters- that does explain the measurements.

audioloop

well well said....

they counfuse real with counterfactual definiteness


real come from Latin res, thing, object just that.
values are just attributes of objects, quality, characteristics, attributes, values are just secondary aspects of objects, i.e properties of objects.


reality: the state of things as they actually exist.

DrChinese

I guess Einstein was one of those muddle-heads. He believed (but could not prove) that particles had pre-existing values for non-commuting observables, and said that any other position was unreasonable. He defined elements of reality and realism quite specifically.

ttn, no need for us to debate the point again; this is just the opposition's placard. Although by looking at the poll results as of now, it looks like you are losing 6-12.

ttn

As usual, you suggest here that Einstein/EPR simply came out and said "we feel like believing in pre-existing values for non-commuting observables; we feel like anything else is unreasonable." In other words, you suggest that there was no *argument* for this *conclusion*. But, of course, there was. And (to quote Bell) it was an argument "from locality to" these pre-existing values. That is, what Einstein showed (and this was admittedly somewhat obscured in the EPR paper that Podolsky wrote and published before even showing it to Einstein!) was that believing in these pre-existing values is the only way to locally explain the perfect correlations.

To be sure, Einstein was wrong about something. In particular, he simply assumed that locality was true. Then, applying his perfectly valid *argument* "from locality to" pre-existing values (or "hidden variables" or "realism" or CFD or whatever anybody wants to call it), he *concluded* that these pre-existing values really existed. (Which of course in turn implies that the QM description, which fails to mention any pre-existing values, is incomplete.) Now it turns out locality is false. So Einstein was wrong to assume it. The EPR argument can no longer be used as a proof for the existence of pre-existing values since we now know that its premise (locality) is actually false! But none of this undermines in the slightest bit the validity of the argument "from locality to" these pre-existing values. That is, it remains absolutely true that pre-existing values are the only way to locally explain the perfect correlations -- whether locality is true or not.

I no longer consider it possible to convince you of any of this, so, yes, we don't need to debate it. But I think re-hashing the points can help others make a better and more informed judgment about the subject of this poll.

Let me urge you to put up a better, or at least additional, placard. So far your placard amounts to "nuh uh". Your position, though, is clear. You think that, by saying there are no pre-existing values, we can consistently maintain locality. That is, you do not accept that Einstein/EPR validly argued "from locality to" pre-existing values. That is, you think that it is possible to explain the perfect correlations locally but without pre-existing values. This is precisely why I issued "ttn's challenge" in my first post in this thread: please display an actual concrete (if toy) model that explains the perfect correlations locally without relying on pre-existing values.

To not do this is to confess that your position (your vote for (b) in the poll) is indefensible.



Luckily, truth is not decided by majority vote. So far -- since nobody has risen to answer my challenge -- all the results prove is that 12 people hold a view that they have no actual basis for.

audioloop

amazing ! travis norsen, in person....
travis, do you believe in CFD ?