Bohmian interpretation and schroedingers cat

[confusedashell]

What happens to the cat in the Bohm interpretation?
If I've got it right:
In MWI it splits, dead in one universe, alive in another.
In CI it's not decided until observed.
In TI both these absurd concepts are escaped and it's just either dead or alive(I cannot remember the details)

but in Bohmian mechanics what does happen to the poor cat?

Btw, was Schroedinger allergic to cats ?:P

 

[colorSpace]

I think both in more modern forms of CI, as well as in Bohmian mechanics, measurements and measurement-like interactions are likely to end superposition in such situations rather quickly.

 

[confusedashell]

Bohmian kills off observer role, CI brought it in.

i didn't understand you, what happens to the cat? layman terms
does it die/not die? and why is it dead/not dead?

 

[colorSpace]

Bohmian kills off observer role, CI brought it in.

i didn't understand you, what happens to the cat? layman terms
does it die/not die? and why is it dead/not dead?

My understanding is that many physicists who today say they support CI, have replaced 'conscious observation' with measurement-and measurement-like interactions which leave a trace of information. That is, a superposition of positions is ended when the position is measured, or when the objects in superposition have an interaction with other objects that would leave a trace of information about the position.

I would assume, without knowing the details, that in Bohmian mechanics this is very similar, however here there is a mathematical model for this process that defines precisely the kind of situation which will end superposition (although I'm not sure whether this can be expressed in a way that would be intuitively understandable, rather than only mathematically).

So for both interpretations, I'd assume that superposition ends before it reaches the cat, and that the cat will be either one or the other in the common sense.

 

[vanesch]

Bohmian kills off observer role, CI brought it in.

i didn't understand you, what happens to the cat? layman terms
does it die/not die? and why is it dead/not dead?

In BM, this is in fact ambiguous. You have to know that BM has TWO dynamics to it:
one is the unitary evolution of the quantum state, without any "projection" or so, exactly as in MWI. But on the other hand, there is a "particle dynamics" which is Newtonian, and in which a potential appears, which is derived from the wavefunction. Note hence that the wavefunction dynamics has an influence on the particles (through the quantum potential) but that the particles don't have any influence on the quantum dynamics which leads its own life, just as in MWI (and not CI, because there's no "projection" at any point).

So the QUANTUM states of the cat happen as in MWI, there is a "live" and a "dead" quantum state of the cat which will continue to exist. But the PARTICLES will follow one or the other (as they had statistical distributions in their initial conditions), and the *particle cat* will end up, depending on initial conditions, in the live or dead state.

 

[confusedashell]

Ok so basically BM says that the cat is either or? and the opposite cancles out and don't exist?

 

[colorSpace]

In BM, this is in fact ambiguous. You have to know that BM has TWO dynamics to it:
one is the unitary evolution of the quantum state, without any "projection" or so, exactly as in MWI. But on the other hand, there is a "particle dynamics" which is Newtonian, and in which a potential appears, which is derived from the wavefunction. Note hence that the wavefunction dynamics has an influence on the particles (through the quantum potential) but that the particles don't have any influence on the quantum dynamics which leads its own life, just as in MWI (and not CI, because there's no "projection" at any point).

So the QUANTUM states of the cat happen as in MWI, there is a "live" and a "dead" quantum state of the cat which will continue to exist. But the PARTICLES will follow one or the other (as they had statistical distributions in their initial conditions), and the *particle cat* will end up, depending on initial conditions, in the live or dead state.

I don't see the ambiguity, since there is only one particle. The elements of the "wavefunction dynamics" corresponding to the other possibility will become 'empty channels', and not influence the particle anymore. There are no other cats in those empty channels.

 

[confusedashell]

Agree'd.

Bohmian doesn't suggest any "branches" where the cat's state would survive.

 

[JesseM]

I would assume, without knowing the details, that in Bohmian mechanics this is very similar, however here there is a mathematical model for this process that defines precisely the kind of situation which will end superposition (although I'm not sure whether this can be expressed in a way that would be intuitively understandable, rather than only mathematically).

Bohmian mechanics doesn't involve any superpositions at all, the whole idea is that all particles have definite positions at all times, and there is a faster-than-light "pilot wave" coordinating their actions to account for the type of correlations seen in entanglement. You can read more about this interpretation here:

http://plato.stanford.edu/entries/qm-bohm/
http://www.math.rutgers.edu/~oldstein/papers/qts/node4.html
http://home.sprynet.com/~owl1/qm.htm#IV

 

[colorSpace]

I think in addition to the guiding quantum potential and the guided particle, one needs to understand the process of measurement in BM (which I don't, I've read the term "von Neumann" measurement), in order to have a good picture of what happens here, and to understand BM in general, since the position of the particle is not directly measurable. It seems to me that the common descriptions of BM (including my little attempts) completely miss an important element there.

 

[colorSpace]

Bohmian mechanics doesn't involve any superpositions at all, the whole idea is that all particles have definite positions at all times, and there is a faster-than-light "pilot wave" coordinating their actions to account for the type of correlations seen in entanglement.

Hmm, yes, I was more thinking of "something that can cause interference patterns" than of "superposition". That's why I mentioned that one needs to understand how measurement and measurement-like interactions work in BM. Not all questions of how BM replaces CI-collapse might be answered by the concept of guided particles alone.

 

[vanesch]

I don't see the ambiguity, since there is only one particle. The elements of the "wavefunction dynamics" corresponding to the other possibility will become 'empty channels', and not influence the particle anymore. There are no other cats in those empty channels.

This is correct, but these terms in the wavefunction continue to exist, and this wavefunction, in BM, is "just as real" as the particles: it is the "other half" of the universe, which consists on one hand of a particle dynamics, and on the other, of a wavefunction dynamics. The particle dynamics depends on the wavefunction dynamics, but not in the other way. I know that in BM, one has tendency to give emphasis to the particle dynamics, but unfortunately, it is not autonomous (from the particle states alone, one cannot predict nor the particle evolution, nor the wavefunction). So the wavefunction is a part of reality in BM (is a genuine real "field" in hilbertspace), just as much as the particles are.

So the "ghosts of the cat" continues to exist in the "wavefunction part" of reality, but only one "particle cat" will exist in the "particle part" of reality.

 

[colorSpace]

This is correct, but these terms in the wavefunction continue to exist, and this wavefunction, in BM, is "just as real" as the particles: it is the "other half" of the universe, which consists on one hand of a particle dynamics, and on the other, of a wavefunction dynamics. The particle dynamics depends on the wavefunction dynamics, but not in the other way. I know that in BM, one has tendency to give emphasis to the particle dynamics, but unfortunately, it is not autonomous (from the particle states alone, one cannot predict nor the particle evolution, nor the wavefunction). So the wavefunction is a part of reality in BM (is a genuine real "field" in hilbertspace), just as much as the particles are.

So the "ghosts of the cat" continues to exist in the "wavefunction part" of reality, but only one "particle cat" will exist in the "particle part" of reality.

Oh, the cat has multiple ghosts? :) What difference does that make?

 

[confusedashell]

vanesch that makes no sense, so your saying that BM is MWI without actually other real universes? just "ghost universes" ?

That must on the microscopical level, not macroscopic.

 

[vanesch]

Oh, the cat has multiple ghosts? :) What difference does that make?

Let us not forget (what is often done in BM), that we need TWO dynamical elements in BM: the wavefunction dynamics, and the particle dynamics. What happens is that the wavefunction dynamics is the unitary quantum mechanics one, just as in MWI. But ON TOP of that, there is the particle dynamics, and in BM, one often gives the impression that that is all there is. A bit as if in classical electrodynamics, we had charged particles, and the EM field, but we pretended that there were in fact only the particles, and not the EM field. But the analogy doesn't work entirely, because in this example, the particles DO influence the EM field, while this is not the case in BM.

So it is as if we have, say, an electron, and a coulomb field around that electron. Afterwards, the electron interacts with something, and the electron goes LEFT in that interaction, but we now have two coulomb fields: one centered on the electron going left, and one going right, but with no electron in it. Of course, that's not how things work in classical EM: the EM field "goes with" the particle. But not so in BM: the wavefunction evolves independently of what happens to the particles.

So we have in BM reality:

"particle world": { cat particles with a statistical uncertainty on the initial position}

"wavefunction world": |cat - in - box state>

After the famous experiment, we'd have:

"particle world": {cat particles in a living cat} (randomly choosen because of initial condition uncertainty)

"wavefunction world": |living cat> |stuff> + |dead cat> |otherstuff>

So there are now two terms in the wavefunction: the first term is "centered on" the particles, while the second term is "living on its own" independent of the particles.

It is true that we can, concerning the *particle dynamics*, just as well forget about the second term, it will not influence much the dynamics of the particles anymore. But it still exists in the "wavefunction world". So it looks a bit like our "coulomb field going to the right, without an electron in its center" (which, again, cannot happen in classical EM, it is just an image of what goes on here).

 

[vanesch]

Bohmian mechanics doesn't involve any superpositions at all, the whole idea is that all particles have definite positions at all times, and there is a faster-than-light "pilot wave" coordinating their actions to account for the type of correlations seen in entanglement.

Well, the superposition still holds for the "pilot wave" dynamics, because it is the same as the usual quantum dynamics...

 

[colorSpace]

Let us not forget (what is often done in BM), that we need TWO dynamical elements in BM: the wavefunction dynamics, and the particle dynamics. What happens is that the wavefunction dynamics is the unitary quantum mechanics one, just as in MWI. But ON TOP of that, there is the particle dynamics, and in BM, one often gives the impression that that is all there is. A bit as if in classical electrodynamics, we had charged particles, and the EM field, but we pretended that there were in fact only the particles, and not the EM field. But the analogy doesn't work entirely, because in this example, the particles DO influence the EM field, while this is not the case in BM.

Yes, Bohm speaks of the classical potential and the quantum potential, and the classical force and the quantum force acting on the particle. He frequently uses the term "quantum field", and says the particle is alway accompanied by its field. However the field is merely a guiding principle, not a second part of the particle's (or the cat's) embodiment.

Here are a few quotes from a chapter in "The Undivided Universe" about the cat paradox:

"For the wave function corresponding to the live cat has no effect on the quantum potential acting on the dead cat or vice versa."

"Thus if we consider the system of firing device, plus gun, bullet and powder, it is clear that there is no overlap between the wavefunction [wavefunction-unfired] and [wavefunction-fired] (...). [Edit added:] Therefore the particles constituting this system will be either in the state corresponding to the firing or non-firing of the gun."

"In other words, once the electron has in effect been 'detected', everything proceeds in essentially the same way as it does in classical physics."

It is true that we can, concerning the *particle dynamics*, just as well forget about the second term, it will not influence much the dynamics of the particles anymore. But it still exists in the "wavefunction world". So it looks a bit like our "coulomb field going to the right, without an electron in its center" (which, again, cannot happen in classical EM, it is just an image of what goes on here).

Yes, those are called "empty channels" and become irrelevant.

 

[vanesch]

Yes, those are called "empty channels" and become irrelevant.

They become irrelevant for the *particle* dynamics, but they continue to exist in the wavefunction dynamics. What you seem to miss, is that the universe in Bohmian mechanics, contrary to what Bohmians often try to claim, doesn't consist just of a "particle universe", because it cannot explain the entire dynamics (you cannot reconstruct the wavefunction dynamics just from the particles). The Bohmian universe consists of a double universe: the particle universe (the one they like), and the wavefunction universe (identical to MWI). They need the wavefunction universe to have the particle dynamics right, so it "exists". And it is in this universe that the "ghost" branches continue to evolve, even though they won't act upon the particle universe anymore (due to a similar mechanism as in decoherence).

 

[colorSpace]

They become irrelevant for the *particle* dynamics, but they continue to exist in the wavefunction dynamics. What you seem to miss, is that the universe in Bohmian mechanics, contrary to what Bohmians often try to claim, doesn't consist just of a "particle universe", because it cannot explain the entire dynamics (you cannot reconstruct the wavefunction dynamics just from the particles). The Bohmian universe consists of a double universe: the particle universe (the one they like), and the wavefunction universe (identical to MWI). They need the wavefunction universe to have the particle dynamics right, so it "exists". And it is in this universe that the "ghost" branches continue to evolve, even though they won't act upon the particle universe anymore (due to a similar mechanism as in decoherence).

It is perhaps like the forces of gravitation (be it mediated by fields, waves or particles) extending beyond where there is matter in the universe, if that area didn't extend as well, without anything to act upon.

Or perhaps even like curved space extending beyond where there is anything to act upon.

 

[rkastner]

In Bohmian mechanics the cat has a definite fate (either alive or dead), depending on the initial position of the particles involved, but there is in principle no way to know those initial positions. So, apart from this initial epistemic uncertainty, the mechanics is totally deterministic and there is neither a "collapse" nor a branching of worlds. The "ghost" world does not really exist, it just represents an unrealized possibility. It is only the "particle cat" that exists and its fate, based on the initial particle positions, was determined from the beginning. But presumably only God knows that fate.

 

[vanesch]

In Bohmian mechanics the cat has a definite fate (either alive or dead), depending on the initial position of the particles involved, but there is in principle no way to know those initial positions. So, apart from this initial epistemic uncertainty, the mechanics is totally deterministic and there is neither a "collapse" nor a branching of worlds. The "ghost" world does not really exist, it just represents an unrealized possibility. It is only the "particle cat" that exists and its fate, based on the initial particle positions, was determined from the beginning. But presumably only God knows that fate.

Yes, the PARTICLES. But the difficulty I always had with the Bohmians, is that the reality of the wavefunction is kind of suppressed, while it is an essential part of the dynamics. It seems as if only the "particles" are "really real" and the "wavefunction" is "just a guiding principle". Nevertheless, this "guiding principle" must be a genuinly real part of the world too in this light. I could just as well suppress the reality of the particles (whose dynamics is NOT essential!), consider them "tokens" or something, and say that the "wavefunction" is really real. When I look at the dynamical requirements, this wavefunction has "more" reality (it is an unsuppressable dynamically essential component) to it, than the particles. The wavefunction can live without the particles, but the particles don't know what to do without the wavefunction. So I've always been wary of why Bohmians seem to attach more reality to "half" of their world, which is the particle world, than to the other half (which is the wavefunction world).

EDIT: you see, as a metaphore, it seems almost as if Bohmians give more reality to a shadow than to the object that projects the shadow. The shadow dynamics can be derived from the object dynamics, but not vice versa.

 

[Demystifier]

Vanesch, why don't you think about BM in analogy with the Hamilton-Jacobi (HJ) formulation of classical mechanics? There, the function S satisfies the HJ equation and does not depend on the motion of the particle. The particle motion is determined by S. Yet, the particle is more physical, or "more real" if you like, than the function S. In fact, the analogy with HJ mechanics was the original motivation for introducing BM, both for Bohm and much earlier for de Broglie.

 

[akhmeteli]

When I look at the dynamical requirements, this wavefunction has "more" reality (it is an unsuppressable dynamically essential component) to it, than the particles. The wavefunction can live without the particles, but the particles don't know what to do without the wavefunction.

That's what I used to believe as well. It came as a surprise to me that this may not always be the case. In particular, in the standard (non-second-quantized) system of the interacting Klein-Gordon and Maxwell fields, the wavefunction can be eliminated in a natural way (in the unitary gauge), and the electromagnetic field evolves independently, so one can say that the electromagnetic field, not the wavefunction, plays the role of the guiding field of the Bohmian interpretation ( http://arxiv.org/abs/quant-ph/0509044 ). Conserved external currents can also be included in this scheme. I have not been able to obtain equally satisfactory results for the Dirac-Maxwell system though.

 

[vanesch]

Vanesch, why don't you think about BM in analogy with the Hamilton-Jacobi (HJ) formulation of classical mechanics? There, the function S satisfies the HJ equation and does not depend on the motion of the particle. The particle motion is determined by S. Yet, the particle is more physical, or "more real" if you like, than the function S.

Well, I would contest that then just as well ! To me, what is "real" is what is essential in the dynamics. In strictly Newtonian mechanics, you can limit yourself to the particles, because you can derive the future evolution of the particles by the current state of the particles (their relative positions give you the gravitational forces). You need as "current state" only the dynamical state of the particles, and you've "said everything". If you want to calculate gravitational potentials and so on, that's always possible, but the gravitational potential is not strictly needed. If you like it, you can give some "reality" to the gravitational potential, but that's arbitrary.
However, you cannot get rid of the particles, and replace them by just the potentials (and attribute what we call particles to the "evolution of the singularities in the potential" or something). So in this picture, the particles are essential, and the gravitational potential optional.

In Hamilton-Jacobi dynamics, what is essential is the field over phase-space. It's field equation is the HJ equation. What is also essential is the constants (usually called alpha and beta) of the "particles" which pick out the relevant paths in the phase flow over phase space. So in this "view", reality is a field over phasespace, with some specific points in it, picking out specific flow lines. So if you look upon it this way, the field S is very real !

This is BTW why this method isn't very useful in particle dynamics: we've replaced a particle dynamics by a field dynamics, which is usually mathematically much harder!

 

[colorSpace]

The exact roles of wavefunction vs. quantum potential vs particle don't seem clear yet.

1. In the 'Undivided Universe', Bohm & Hiley seem to be saying that the particle is not only guided by the quantum potential (which isn't exactly the wavefunction, but very related), but even more importantly, by the classical potential. The quantum potential is usually very small compared to the classical potential. As far as I understood.

2. In measurement, it would seem to me, the measurement device's visible output is (also) determined by the measured particle, not only the measured wavefunction. Measurement devices in BM are not special, they are physical objects like any other.

My question here: won't then the consequences also have an influence on the wavefunction, that is, even if the particle does not have an influence on its own wavefunction, won't it, via the measurement, which can potentially drive any decision? I haven't yet found a text in the above book that would be specific on this question (not looking at the mathematics).

3. In general, it seems that the quantum potential is a "guiding principle", but not "just" a guiding principle. As such, it plays a major role in the book. But I personally see this as similar to the stars and planets in relation to gravity. The "real" thing are the stars and planets, but that doesn't mean that gravity isn't also real and important. (Even though B&H don't use this example.)

4. It does appear, in BM, with its emphasis on ontology, that "Hilbert space" specifically is regarded an arbitrary mathematical tool to *describe* that which eventually leads to the quantum potential, rather than thought of as a real physical space. However the quantum potential is thought of as related to a physical "force".

[Edit: not exactly a "force" like others, but what B&H call "active information", something like radio signal telling a ship where to go, where the strength of the signal isn't important, only the content.]

 

[vanesch]

1. In the 'Undivided Universe', Bohm & Hiley seem to be saying that the particle is not only guided by the quantum potential (which isn't exactly the wavefunction, but very related), but even more importantly, by the classical potential. The quantum potential is usually very small compared to the classical potential. As far as I understood.

Yes, that is to say that in many cases, we can just do classical physics. The quantum potential is only important in those cases where we have a deviation between classical and quantum predictions.

2. In measurement, it would seem to me, the measurement device's visible output is (also) determined by the measured particle, not only the measured wavefunction. Measurement devices in BM are not special, they are physical objects like any other.

This is the circular thing in BM: by definition, one calls the "measurement output" as the *particle state* of the measurement apparatus. Its quantum state is as in MWI: that is: the wavefunction associated to the measurement act undergoes, just as in MWI, a superposition of outcomes. Only, the *particle state* of the measurement apparatus, which is a function of the wavefunction of the "device under test", its own wavefunction and its (unknowable) initial particle states, will go into a particular particle configuration. It is this particle configuration which is called "the outcome of measurement". If we would have called its wavefunction the "outcome of measurement" we would be in exactly the same situation as in MWI. It is the fact of focussing on the particle state of a measurement apparatus that we are able, in BM, to give a definite outcome to a measurement.

My question here: won't then the consequences also have an influence on the wavefunction, that is, even if the particle does not have an influence on its own wavefunction, won't it, via the measurement, which can potentially drive any decision? I haven't yet found a text in the above book that would be specific on this question (not looking at the mathematics).

No, the wavefunction is strictly independent of the particle world. The wavefunction in BM follows ALWAYS the schroedinger equation (just as in MWI), and never undergoes any "projection" (which would in that case give to BM exactly the same conceptual problems as in CI: why a "different" dynamics for a "measurement" than for a "physical interaction" ?).

But in BM, the wavefunction branches that are not "in resonance" with the particle state will not influence (in most cases) the particle dynamics anymore. So, concerning the particle dynamics, we can, after a measurement, just as well consider a projection: it won't influence the particle dynamics (the quantum potential) much.
This is a bit similar as considering the EM interaction of one charged particle upon another: the EM radiation that has been emitted "away" from the other particle won't influence it anymore, so in a calculation of the motion of the particles, we can just as well ignore this EM radiation. But does that mean that it doesn't exist ? I ask the same question to the Bohmians: does the fact that certain branches in the wavefunction have no influence anymore on the particle dynamics imply that they don't exist ?

3. In general, it seems that the quantum potential is a "guiding principle", but not "just" a guiding principle. As such, it plays a major role in the book. But I personally see this as similar to the stars and planets in relation to gravity. The "real" thing are the stars and planets, but that doesn't mean that gravity isn't also real and important. (Even though B&H don't use this example.)

It is stronger than this, because (at least in a Newtonian frame) the gravity interaction can be DEDUCED from the particle dynamics. There is no dynamical state to gravity itself. But not so for the wavefunction in BM: its dynamical state is NOT "recorded" in the particle states and hence, it lives its own life. But more so: in Newtonian dynamics, gravity is influenced by the particles. Not so in BM: the wavefunction is not influenced by the particles.

4. It does appear, in BM, with its emphasis on ontology, that "Hilbert space" specifically is regarded an arbitrary mathematical tool to *describe* that which eventually leads to the quantum potential, rather than thought of as a real physical space. However the quantum potential is thought of as related to a physical "force".

I know, but I think that this is a rethorical weakness of BM: IF one admits the ontological existence of the wavefunction itself, then the particle dynamics doesn't solve all of the conceptual difficulties of MWI, because that wavefunction with all its branches is "still out there". So in BM, one tries to minimise the ontology of the wavefunction and to maximize the particle ontology.

 

[ueit]

It is stronger than this, because (at least in a Newtonian frame) the gravity interaction can be DEDUCED from the particle dynamics. There is no dynamical state to gravity itself. But not so for the wavefunction in BM: its dynamical state is NOT "recorded" in the particle states and hence, it lives its own life. But more so: in Newtonian dynamics, gravity is influenced by the particles. Not so in BM: the wavefunction is not influenced by the particles.

I know, but I think that this is a rethorical weakness of BM: IF one admits the ontological existence of the wavefunction itself, then the particle dynamics doesn't solve all of the conceptual difficulties of MWI, because that wavefunction with all its branches is "still out there". So in BM, one tries to minimise the ontology of the wavefunction and to maximize the particle ontology.

For the entire universe the wavefunction should be stationary because of energy conservation. In this case there is no dynamics associated with it. It is a constant, eternal field. Therefore BM could be completely described by the particle configuration.

It is also possible in this case that the universal wavefunction can be deduced from the particle configuration so one could do away with it.

 

[vanesch]

For the entire universe the wavefunction should be stationary because of energy conservation.

I don't see why the wavefunction of the universe should be an eigenfunction of the hamiltonian, and not a superposition of them.

 

[rkastner]

Vanesch: Re your post #21: yes, that's one reason I'm not a Bohmian anymore...

RK

 

[ueit]

I don't see why the wavefunction of the universe should be an eigenfunction of the hamiltonian, and not a superposition of them.

http://en.wikipedia.org/wiki/Ground_state" :

As an eigenstate of the Hamiltonian, a stationary state is not subject to change or decay (to a lower energy state). In practice, stationary states are never truly "stationary" for all time. Rather, they refer to the eigenstate of a Hamiltonian where small perturbative effects have been ignored. The language allows one to discuss the eigenstates of the unperturbed Hamiltonian, whereas the perturbation will eventually cause the stationary state to decay. The only true stationary state is the ground state.

For an infinitely old universe (presupposed by QM) I would expect to find it in its ground state. So, no wavefunction dynamics. The wavefunction for the ground state can also be determined from the particle configuration.

 

[colorSpace]

I think something here still isn't clear about BM. Perhaps, Vanesh, your description is then not fully describing the role of the particles.

Are the classical potentials (and thereby the classical forces between particles) determined by the particles, and independent of the wavefunction?

If not, what difference then would the particles make at all?

If yes, does it mean that the particle of the measured object has an influence on the measurement device which is independent of the wavefunction?

And it follows, our human experience, and the actions we then take, are based also on the particle positions, rather than the wavefunction alone.

 

[colorSpace]

[Continued from the previous message]

I don't think it is correct to say that in BM there is a disregard for the wavefunction.

For example, on page 58 of "The Undivided Universe", B & H write:

In our interpretation of the quantum theory, we see that the interaction of parts is determined by something that cannot be described solely in terms of these parts and their preassigned interrelationships. Rather it depends on the many-body wave function (which, in the usual interpretation, is said to determine the quantum state of the system). This many-body wave function evolves according to Schrödinger's equation. Something with this kind of dynamic significance that refers directly to the whole system is thus playing a key role in the theory. We emphasize that this is the most fundamentally new aspect of the quantum theory.

(The italics are original.)

However what is measured and humanly experienced are the positions of the particles. It is simply not true that these would be the "shadows" of the wave function, since the wave function leaves trillions and trillions of possibilities which multiply each second, and the particles would decide the single specific outcome. It would be like saying the chess rules completely determine each chess game, which isn't true even though the chess rules give only about 40 possibilities each move, very, very limiting compared to the wave function.

 

[vanesch]

However what is measured and humanly experienced are the positions of the particles.

INDEED. And this comes awfully close to MWI, where one says:
"what is measured and humanely experienced is ONE of the branches".

I admit directly that there is a difference: the Bohmian view allows for a "single, common, objective" experience, while MWI needs to lock them up in different "subjective" experiences.

It is simply not true that these would be the "shadows" of the wave function, since the wave function leaves trillions and trillions of possibilities which multiply each second, and the particles would decide the single specific outcome. It would be like saying the chess rules completely determine each chess game, which isn't true even though the chess rules give only about 40 possibilities each move, very, very limiting compared to the wave function.

I know. The difference between BM and MWI is that in BM, there is one unique "token" (branch indicator!) for all subjective experience, which consists of "the particles" (which are branch indicators in fact). While in MWI, each subjective experience "traces its own" path throughout the branchings (its "consistent history").

Even probability-wise there are similarities:
while BM has some difficulties indicating (although there is work in this direction, I know) why the "probability distribution of the particles" must initially be in agreement with the norm of the wavefunction, or the Born rule in position representation (a very strange "initial condition"), MWI has some difficulties telling us why the probabilities of "an individual experience" must be distributed according to the Born rule, and just posits it (although, here too, there is work in progress).

 

[Fra]

MWI has some difficulties telling us why the probabilities of "an individual experience" must be distributed according to the Born rule, and just posits it

But I think this is an issue for foundational QM itself right? Regardless of interpretation and is IMO one of the challanges in trying to understand QM at the next level. Unlike the interpretation only-issues, I find this interesting.

They way I see it, this contains two issues.

1) How is "probability" defined in this context. (Ie. how can we apply the probability formalisms from mathematics to physics).

2) Given that the first problem is solve, prove that the born rule holds.

But I think the two issues are entangled and need to solved together.

Vanesch, I I'm not into MWI, but parts of what you say is in line with my thinking too, and you seem to more or less adhere to a kind of "relational view" of QM (or?), and that makes me wonder:

Doesn't you find the the whole standard construction of the frequentist interpretation of probability, to sort of at least conceptually or philosophically, clash with the relational thinking? I mean, it means there must be someone (or something) that is physically responsible for the event counting? And this something must be able to ultimately be able to encode a lot of information right?

Ie. the question is wether the whole concept of probability as used in standard QM, is relationally designed? I think it's not.

Do you agree or disagree?

/Fredrik

 

[colorSpace]

My understanding is that BM explains the probabilities as resulting from the dynamics of chaotic motion (referring to Brownian motion as an example in some respects).

BM therefore, in theory, does not have to state the probabilities as an assumption, and also allows for the possibility that under very specific (unknown) circumstances these might be different than in standard QM.

 

[vanesch]

My understanding is that BM explains the probabilities as resulting from the dynamics of chaotic motion (referring to Brownian motion as an example in some respects).

Nope. BM is strictly deterministic: it is Newtonian dynamics with added forces! The only probabilistic aspect in BM (which make it coincide with the statistical predictions of QM) is that one needs to consider the *initial conditions* (the positions of the particles) as distributed statistically according to the norm squared of the initial wavefunction. If you don't do that, BM is blatantly in contradiction with QM. And if you do so, you can show that this statistical sample evolves and has the same statistical properties as predicted by QM. In other words, if (by hand) you put in the initial statistical distribution of the particles in agreement with the norm squared of the wavefunction in position representation, then this property is conserved under Bohmian dynamics.

The "wiggles" you see in typical Bohmian particle traces are not random Brownian motion, but are very precise Newtonian-like dynamics.

However, and maybe this is what you are referring to, there has been some work (don't have a reference handy but there are articles on the arxiv about this) that shows that even if you start from different initial distributions, that after a long time the probability distributions of the particles seem to evolve in the direction of those given by the reduced density matrices for sub-systems. That's very interesting because that's what is also at the basis of classical statistical mechanics: that one can make the equiprobability hypothesis because any initial particle distribution will quickly evolve for its low-order correlation functions into an ensemble that is compatible with the equiprobability hypothesis.

BM therefore, in theory, does not have to state the probabilities as an assumption, and also allows for the possibility that under very specific (unknown) circumstances these might be different than in standard QM.

Normally not! If you do not make the assumption of an initial statistical uncertainty in agreement with QM, you get blatantly different results out, and BM would be easily rejected. At least, naively in a simple application. If you take into account a long evolution, and you only look at subsystems, then there is, as I said, some work that indicates that we get out the same statistics as QM.

 

[colorSpace]

Nope. BM is strictly deterministic: it is Newtonian dynamics with added forces! The only probabilistic aspect in BM (which make it coincide with the statistical predictions of QM) is that one needs to consider the *initial conditions* (the positions of the particles) as distributed statistically according to the norm squared of the initial wavefunction. If you don't do that, BM is blatantly in contradiction with QM. And if you do so, you can show that this statistical sample evolves and has the same statistical properties as predicted by QM. In other words, if (by hand) you put in the initial statistical distribution of the particles in agreement with the norm squared of the wavefunction in position representation, then this property is conserved under Bohmian dynamics.

The "wiggles" you see in typical Bohmian particle traces are not random Brownian motion, but are very precise Newtonian-like dynamics.

Wrong. While BM is deterministic (without being strict about it), this is not in contradiction to what I said. "The Undivided Universe" tells a different story than you.

Here a quote from B & H:

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"What we have to explain then is why P should tend to approach |ψ|2 in typical situations that are currently treated in physics (i.e. situations in which the quantum laws are valid). In this chapter [Chapter 9] we shall give such an explanation showing that one can understand how an arbitrary probabilistic density, P, may approach |ψ|2 even on the basis of our deterministic theory because the latter leads to chaotic motion under a wide range of conditions. We shall then show how the overall statistical approach may be generalised to include, not only what are usually called pure states, but also what are usually called mixed states (which are at the basis of quantum statistical mechanics). Finally we shall extend this study and show how the approach of P to |ψ|2 could further be justified on the basis of an underlying stochastic process in the movement of particles."
-------

Also, you seem to get confused about the deterministic nature of BM by the mention of Brownian motion. The relevant quote:

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"We have thus far been explaining quantum probabilities in terms of chaotic motions that are implied by the quantum laws themselves, with pure ensembles representing chaotic motions of the particles and mixed ensembles bringing in also chaotic variations in the quantum field. Whenever we have statistical distributions of this kind, however, it is always possible that these chaotic motions do not originate in the level under investigation, but rather that they arise from some deeper level. For example, in Brownian motion, small bodies which may contain many molecules undergo chaotic velocity fluctuations as a result of impacts originating at a finer molecular level. If we abstract these chaotic motions and consider them apart from their possible causes we have what is called a stochastic process which is treated in terms of a well-defined mathematical theory [5]."
-------

However, and maybe this is what you are referring to, there has been some work (don't have a reference handy but there are articles on the arxiv about this) that shows that even if you start from different initial distributions, that after a long time the probability distributions of the particles seem to evolve in the direction of those given by the reduced density matrices for sub-systems. That's very interesting because that's what is also at the basis of classical statistical mechanics: that one can make the equiprobability hypothesis because any initial particle distribution will quickly evolve for its low-order correlation functions into an ensemble that is compatible with the equiprobability hypothesis.

Why would you mention this as an "however" ?

Normally not! If you do not make the assumption of an initial statistical uncertainty in agreement with QM, you get blatantly different results out, and BM would be easily rejected. At least, naively in a simple application. If you take into account a long evolution, and you only look at subsystems, then there is, as I said, some work that indicates that we get out the same statistics as QM.

So you agree that BM, in theory, does not have to state the probabilities as an assumption, and also allows for the possibility that under very specific (unknown) circumstances these might be different than in standard QM ?

 

[Demystifier]

But Brownian motion is also fundamentally deterministic, isn't it?

 

[colorSpace]

BTW, Vanesh, since you like Hilbert space, you might find this quote interesting, in chapter 15.8 of TUU:

"We are now ready to extend the model of a particle in our interpretation so that it can be included within the framework of Hilbert space."

:)

 

[vanesch]

So you agree that BM, in theory, does not have to state the probabilities as an assumption, and also allows for the possibility that under very specific (unknown) circumstances these might be different than in standard QM ?

Well, it is not clear to me in how much that this is still ongoing research, or a final established result, that "most of the time" starting with just ANY distribution, you arrive onto the QM distributions.

However, consider the following. We already KNOW that IF you start with initial distributions given by the quantum distributions, that you THEN always follow the quantum distributions (that's about the basic theorem that justified BM in the beginning: IF you take as initial distributions the initial wavefunction norm squared, then this remains conserved through dynamics).

Now, IF it would turn out that with a DIFFERENT initial distribution you obtain a DIFFERENT "midway" statistical distribution than that given by QM, that would mean that your "midway" statistical distribution is SENSITIVE to the initial distribution (because we already know that IF it has the QM distribution from the start, it cannot deviate from it midway). So I don't see what would be the importance of a result showing that your distribution is sensitive to initial conditions...
The most interesting result (and I know that some work has been done on that, but I don't know how conclusive it is) would be that we are essentially INDEPENDENT of the initial distribution. In that case, it cannot be anything else but the quantum distribution (given that we already know ONE initial condition where this is going to be the case, namely the initial quantum distribution).

 

[Fra]

If you take into account a long evolution, and you only look at subsystems, then there is, as I said, some work that indicates that we get out the same statistics as QM.

I always try to seek similarities, rather than differences, and I can help thinking this sounds very familiar, and I wonder if this BM view may connect to how I like to think of it - although the clothing of words, and thinking is different.

In a relational view as I see it, the prior information to which everything relates (in that view), is formed from it's interaction history ~ evolution. This prior structure is what is partially retained from the interaction history. And in a sense I think of this as an equilibration process, which "selects" the most favourable prior.

In principle, and in the general I case I think the prior is also dynamical. And in this view I see ordinary QM, as the idealisation where the implicit prior is in equilibrium with the environment. It means that the local environment are all in a limited "agreement", which also explains why the expectations in such case happen to be exact. Because the local group of "observers" has developed a collective - semiobjective - reference.

If it is not, then I doubt ordinary QM formalism would make sense - like, if the evolved prior is not yet in equilibrium with the environment, then it's expectations will be wrong, which results in a further deformation of the observers microstructure. But due to the thinkg works in reality, we are highly unlikely to observe such "extremely far from equilibrium" states in normal situations. Except possible in very extreme and twisted situations. Planck domain physics and similar stuff maybe?

Ie. if consider that statistics is always conditional on the structure of the underlying event space, then maybe ordinary QM statistics corresponds to the case where the underlying event space or probabiltiy space is equilibrated. But in the cases where it's not, the normal formalism fails. this seems to be at the root of some of QM assumptions, we assume that there exists a well defined and objective hilbert space and event space.

If the bohmians object to this, in the general case - for reasons I may not comlpetely understand - I think I might share their "conclusion" by other ways of reasoning?

Then maybe a solution to the sound "bohmian objections" may have a satisfactory possible resolution in the relational view?

/Fredrik