An argument against Bohmian mechanics?

[Demystifier]

Well, if you decide that non-local is compatible with local there seems to be not much more room for discussion. I would say that if non-local hidden variables are made compatible with relativistic locality they are actually local hidden variables.
Maybe you should define what you mean by local and nonlocal before claiming incorrectness. The locality I'm referring is no FTL signal transmission allowed, and the non-locality I refer to is FTL signal transmission allowed. Now the only way the nonlocality in Bohmian interpretation could be different that my definition would be if it was not a realistic/deterministic interpretation, which it is claimed that it is by its proponents...

Bohmian mechanics is non-local in way which does not allow FTL signal transmission. For a simple explanation see e.g.
https://www.physicsforums.com/threa...ctual-definiteness.847628/page-2#post-5319182

 

[vanhees71]

Some of the arguments about interpretations of quantum mechanics are just about philosophical preferences, but I think some of them are genuine technical disputes, which presumably have technical answers, and are not just a matter of opinion. It's hard to tease apart the nuggets that are objective, though. But in this particular case, I think there is a technical question that you are assuming one answer to, and that others are assuming a different answer, and that is: to what extent does the classical world emerge from the quantum world by (mere) coarse-graining?

I use the word "mere" to mean "without adding additional assumptions about wave function collapse". I do not believe that the world that we see, in which macroscopic things have approximately definite positions and momenta at all times, follows by coarse-graining the microscopic description. The microscopic/macroscopic cut makes a bigger difference than that: on the microscopic side, we have deterministic evolution of quantum amplitudes, and on the macroscopic side, we have nondeterministic evolution according to the probabilities given by the Born rule. It seems to me not simply a matter of interpretation or metaphysics, but a technical question that should have a technical answer: Is the macroscopic side derivable from the microscopic side? (Many-Worlds seems like an attempt to do that) Or does the macroscopic side require additional assumptions (something akin to a collapse hypothesis, or something akin to the Bohmian assumption that particles have definition positions at all times)?

But there is no cut, as far as we know. If you are able to prepare macroscopic objects carefully enough and keep them sufficiently isolated from uncontrollable influence "from the environment" they show quantum behavior, and as soon as you cease this isolation you get quickly into classical behavior through the very efficient mechanism of decoherence, which in a way is "coarse graining" in the sense that many quasi random interactions through coupling to the environment average over many microscopic degrees of freedom. A nice example is Zeilinger's double slit experiment with buckyballs which can be seen as pretty large ("mesoscopic") systems. It's already enough not to cool them down too much to have almost classical behavior through the emission of "thermal photons".

 

[vanhees71]

Yes, of course if you believe that, then Bohmian Mechanics, Consistent Histories, Many Worlds and other approaches that attempt to solve the measurement problem are pointless. However, the standard view (LL, Dirac, Weinberg) is that you are wrong (ie. it is not a matter of taste, you are simply wrong - your averaging does not work). LL mentions the Heisenberg cut in his QM text (p3 of the 1977 English translation, 3 ed, Pergamon), Weinberg mentions the Heisenberg cut in section 3.7 of his 2013 QM text.

Where is the minimal interpretation disproven, i.e., why is it wrong to say that there is no cut? Where is it proven that the classical behavior of macroscopic objects are due to dynamics that contradicts the standard quantum dynamics? Where is the measurement problem, i.e., is there an real-world experiment that cannot be described by minimally interpreted QT?

 

[vanhees71]

Some of the arguments about interpretations of quantum mechanics are just about philosophical preferences, but I think some of them are genuine technical disputes, which presumably have technical answers, and are not just a matter of opinion. It's hard to tease apart the nuggets that are objective, though. But in this particular case, I think there is a technical question that you are assuming one answer to, and that others are assuming a different answer, and that is: to what extent does the classical world emerge from the quantum world by (mere) coarse-graining?

I use the word "mere" to mean "without adding additional assumptions about wave function collapse". I do not believe that the world that we see, in which macroscopic things have approximately definite positions and momenta at all times, follows by coarse-graining the microscopic description. The microscopic/macroscopic cut makes a bigger difference than that: on the microscopic side, we have deterministic evolution of quantum amplitudes, and on the macroscopic side, we have nondeterministic evolution according to the probabilities given by the Born rule. It seems to me not simply a matter of interpretation or metaphysics, but a technical question that should have a technical answer: Is the macroscopic side derivable from the microscopic side? (Many-Worlds seems like an attempt to do that) Or does the macroscopic side require additional assumptions (something akin to a collapse hypothesis, or something akin to the Bohmian assumption that particles have definition positions at all times)?

What you usually need is the assumption that there is a separation of scales, i.e., that there are relevant macroscopic observables whose change with space and time are "slow" compared to the "rapid" fluctuations of microscopic observables, so that the macroscopic observables can be well described as spatio-temporal averages of macroscopically "small" but microscopical "large" domains. An example is the derivation of Boltzmann-like (semi-)classical transport equations from the full Kadanoff-Baym quantum dynamics via the gradient expansion.

 

[Demystifier]

I would try to figure it out. If I cannot, may be some else can. If no one can, then it should be called and viewed as an open problem. And there is nothing wrong with having open problems that stay unresolved for a long time. Look at Fermat's last theorem.

What you call a rational explanation in 5) to me seems to be just a guess. May be a good one, but still just a guess. If that's the case it should be considered a conjecture, not a solution to the problem.

Sure, in the mathematical language it can be called a conjecture. Nobody says that it is more than that. But mathematicians agree that conjectures have a mathematical value. No mathematician objects that there is no point of having a conjecture if you are not able to prove it.

Another way to think of it is in terms of mathematical logic. The textbook QM can be viewed as a set of axioms. But this set of axioms is not sufficient to assign a truth/false value to any meaningful statement. In pure math, the axioms of group theory are not sufficient to determine whether $gh=hg$ for any $g,h$. Likewise, the axioms of QM are not sufficient to determine whether observables have any values before measurements. To answer such questions, one must go beyond the axioms. One needs an interpretation of the axioms, or a model for the axioms. Real numbers with standard multiplication are one interpretation or one model for group-theory axioms. In this model, $gh=hg$ for any $g,h$. Likewise, Bohmian mechanics can be thought of as one interpretation or one model for QM axioms. In this model, the position observable has a value before measurement, but the spin observable has not.

Sometimes models are found with properties very different from the initially intended models. In pure math, non-standard analysis is an unexpected model of certain mathematical axioms; contrary to the widespread belief, it demonstrated that infinitesimal numbers are consistent with standard axioms of pure math. Likewise, Bohmian mechanics can be thought of as a non-standard model of QM axioms; contrary to a widespread belief it demonstrated that hidden variables are consistent with QM axioms.

Indeed, the status of Bohmian mechanics in physics is very much similar to the status of non-standard analysis in mathematics. It is rarely taught at universities, its usefulness is often disputed, and sometimes even its consistency is denied. Advocates argue that it is useful because it is intuitive, but the mainstream view is that it is counter-intuitive and more complicated than the standard approach. Non-experts often use some naive versions of it (naive infinitesimals, naive electron trajectories), mainstream experts tell them that infinitesimals and electron trajectories don't exist, but in a sense naive non-experts are not so totally wrong as mainstream experts think they are.

 

[RockyMarciano]

Bohmian mechanics is non-local in way which does not allow FTL signal transmission.

So that is an argument against Bohmian mechanics, besides the confusion that goes with trying to make nonlocality and locality compatible for a theory. Local according to the Bell terminology is equivalent to not allowing FTL signal transmission, and if Bohmian mechanics doesn't allow it and since it is a hidden variables theory that makes it a local hidden variables theory.
In any case it is not really important if you say that Bohmian mechanichs is local or nonlocal or both for my point, it is being deterministic in the classical sense what dooms this interpretation because that has been experimentally ruled out by the combination of EPR-type experiments and the empirical success of local QFT.

 

[martinbn]

So that is an argument against Bohmian mechanics, besides the confusion that goes with trying to make nonlocality and locality compatible for a theory. Local according to the Bell terminology is equivalent to not allowing FTL signal transmission, and if Bohmian mechanics doesn't allow it and since it is a hidden variables theory that makes it a local hidden variables theory.
In any case it is not really important if you say that Bohmian mechanichs is local or nonlocal or both for my point, it is being deterministic in the classical sense what dooms this interpretation because that has been experimentally ruled out by the combination of EPR-type experiments and the empirical success of local QFT.

This is completely meaningless.

 

[Demystifier]

Local according to the Bell terminology is equivalent to not allowing FTL signal transmission,

No, that's not what "local" means according to the Bell terminology.

it is being deterministic in the classical sense what dooms this interpretation because that has been experimentally ruled out by the combination of EPR-type experiments and the empirical success of local QFT.

No, determinism has not been ruled out by EPR-type experiments and the empirical success of local QFT.

 

[Demystifier]

Look at Fermat's last theorem.

... just a guess. May be a good one, but still just a guess. If that's the case it should be considered a conjecture, not a solution to the problem.

A conjecture can be thought of as a conditional solution. To take example from pure math, consider the status of Fermat's last theorem before the work of Weil. If the Taniyama-Shimura conjecture is true, then the problem of proving the Fermat's last theorem is essentially solved. Analogously, if the conjecture that particles have Bohmian trajectories is true, then the measurement problem of QM is essentially solved.

 

[stevendaryl]

What you usually need is the assumption that there is a separation of scales, i.e., that there are relevant macroscopic observables whose change with space and time are "slow" compared to the "rapid" fluctuations of microscopic observables, so that the macroscopic observables can be well described as spatio-temporal averages of macroscopically "small" but microscopical "large" domains. An example is the derivation of Boltzmann-like (semi-)classical transport equations from the full Kadanoff-Baym quantum dynamics via the gradient expansion.

That's not the only issue with the classical/quantum split, though. It's not just a matter of averaging over small differences. If you have an amplification process, a small microscopic difference can lead to a huge macroscopic difference. Suppose I have a setup for measuring spins of an electron along the z-axis.

1. If the electron is spin-up, then a red light comes on, and I bet $1000 on some sports team.
2. If the electron is spin-down, then a green light comes on, and I bet $1000 on their opponents.

Then it follows from unitary evolution that if the electron is initially spin-up in the x-direction, then the entire system (electron + detector + me + the rest of the relevant universe) should evolve into a superposition of me winning $1000 and me losing $1000. Coarse-graining is not going to smooth out the differences between those two outcomes. It's not a matter of ignoring small fluctuations. In the macroscopic world, I see either one outcome or the other, not a superposition.

It seems to me that there are really only two sensible possibilities: (1) Something besides pure unitary evolution must be involved, or (2) something like many-worlds, where all possibilities exist simultaneously, must be true, and the appearance of classicality (that there is only one outcome that happens) someone arises.

 

[vanhees71]

The Stern-Gerlach experiment is the best example for something that can be understood by pure quantum-theoretical time evolution even analytically (under some simplifying assumptions). There's entanglement between the spin state and macroscopically defined position due to unitary time evolution.

 

[RockyMarciano]

This is completely meaningless.

A more accurate description would be that you just don't understand, then you have to ask what you don't understand in case you were interested in understanding ;)

 

[RockyMarciano]

No, that's not what "local" means according to the Bell terminology.No, determinism has not been ruled out by EPR-type experiments and the empirical success of local QFT.

I would expect from posters something more than just yes or no answers without further specific arguments to justify their position. Please define locality according to Bell's theorem, and why you think classical determinism has not been ruled out by EPR-type experiments and the empirical success of local QFT,

 

[stevendaryl]

Local according to the Bell terminology is equivalent to not allowing FTL signal transmission.

No, they are not equivalent according to Bell. Bell's notion of locality is stronger than simply saying that FTL communication is not possible.

Here's a counter-example. Suppose we have three subjects who are far, far away from each other: Alice, Bob and Carol. They perform the following experiment:

1. At an agreed-upon time, Alice picks a message either, "yes" or "no" and texts it to Bob using her magic cell phone.
2. Carol flips a coin, and gets either "heads" or "tails".
3. Bob checks his magic cell phone, where he either gets the message "yes" or "no".

When they do this experiment many times, they find the following pattern:

1. If Carol's coin flip resulted in "heads", then Bob's cell phone receives the message Alice sent.
2. If Carol's coin flip resulted in "tails", then Bob's cell phone receives the opposite of the message Alice sent.
3. Carol's coin produces "heads" or "tails" with equal likelihood.
   
4. This effect is undiminished by distance---so even if Alice, Bob and Carol are lightyears apart (so that it is impossible for any of them to communicate in the length of the time to perform one round of the experiment), the same pattern holds.

It's impossible for Alice to use her magic cell phone to communicate to Bob, because Bob's message always has a 50/50 chance of being "yes" or "no", regardless of Alice's message. But it's also impossible to implement this setup using only local interactions. So it violates Bell's notion of locality, but doesn't allow FTL communication.

 

[stevendaryl]

I would expect from posters something more than just yes or no answers without further specific arguments to justify their position. Please define locality according to Bell's theorem, and why you think classical determinism has not been ruled out by EPR-type experiments and the empirical success of local QFT,

Bell's notion of locality is not about FTL. It's about factorizability of probability. A local theory, according to Bell, has the property that for any measurement, the outcome of the measurement (whether deterministic or not) depends only on conditions at the location where the measurement took place. What this means is that whenever there is a correlation between distant measurements, that correlation must be mediated by local state variables (which may be hidden).

 

[martinbn]

I would expect from posters something more than just yes or no answers without further specific arguments to justify their position. Please define locality according to Bell's theorem, and why you think classical determinism has not been ruled out by EPR-type experiments and the empirical success of local QFT,

No, this is an A-level thread, posters need not explain basic notions.

 

[stevendaryl]

No, they are not equivalent according to Bell. Bell's notion of locality is stronger than simply saying that FTL communication is not possible.

Here's a counter-example.[deleted]

There is a much simpler counter-example. Suppose that Alice and Bob are far away from each other, and they are both flipping coins. It happens to be the case that Alice's result is always the same as Bob's result. That's a nonlocal correlation, even though it can't be used for communication between Alice and Bob.

 

[martinbn]

A conjecture can be thought of as a conditional solution. To take example from pure math, consider the status of Fermat's last theorem before the work of Weil. If the Taniyama-Shimura conjecture is true, then the problem of proving the Fermat's last theorem is essentially solved. Analogously, if the conjecture that particles have Bohmian trajectories is true, then the measurement problem of QM is essentially solved.

I understand your point, and I guess I'll take your word about BM being analogous. By the way it is Wiles, Weil is related in a different way. And at the time it wasn't known that it implies Fermat nor that it is related, that came a bit later.

 

[stevendaryl]

But there is no cut, as far as we know. If you are able to prepare macroscopic objects carefully enough and keep them sufficiently isolated from uncontrollable influence "from the environment" they show quantum behavior, and as soon as you cease this isolation you get quickly into classical behavior through the very efficient mechanism of decoherence, which in a way is "coarse graining" in the sense that many quasi random interactions through coupling to the environment average over many microscopic degrees of freedom. A nice example is Zeilinger's double slit experiment with buckyballs which can be seen as pretty large ("mesoscopic") systems. It's already enough not to cool them down too much to have almost classical behavior through the emission of "thermal photons".

Well, it seems to me that without a classical/quantum cut, then you're in the same boat as "many-worlds" when it comes to explaining why we only see one outcome when we perform a measurement. If we view the entire universe as a quantum system, and an electron is in a superposition of spin-up and spin-down, and we measure the spin, then the entire universe should be in a superposition of "measured spin-up" and "measured spin-down". Which is basically many-worlds.

 

[Demystifier]

I understand your point, and I guess I'll take your word about BM being analogous. By the way it is Wiles, Weil is related in a different way. And at the time it wasn't known that it implies Fermat nor that it is related, that came a bit later.

Thanks for the corrections. (I knew it was Wiles, but I often have problems with mixing up similar names. For instance, at one occasion I was explaining to someone the "Cartan diagonalization" as the proof that reals are not countable.) By the way, how do you like my analogy with non-standard analysis?

 

[Demystifier]

No, this is an A-level thread, posters need not explain basic notions.

Brilliant answer, I should use it more frequently!

 

[Demystifier]

I would expect from posters something more than just yes or no answers without further specific arguments to justify their position. Please define locality according to Bell's theorem, and why you think classical determinism has not been ruled out by EPR-type experiments and the empirical success of local QFT,

https://arxiv.org/abs/1303.2849

 

[stevendaryl]

Where is the minimal interpretation disproven, i.e., why is it wrong to say that there is no cut? Where is it proven that the classical behavior of macroscopic objects are due to dynamics that contradicts the standard quantum dynamics? Where is the measurement problem, i.e., is there an real-world experiment that cannot be described by minimally interpreted QT?

Well, that's why I said it was a technical problem, rather than a philosophical problem. You're not allowed to assume that a technical claim is true just because nobody has managed to prove it false. Whether the classical world, in which macroscopic objects have more-or-less definite positions and velocities, emerges from a minimal interpretation is a purely technical (mathematical) question, you can't decide it experimentally.

 

[stevendaryl]

The Stern-Gerlach experiment is the best example for something that can be understood by pure quantum-theoretical time evolution even analytically (under some simplifying assumptions). There's entanglement between the spin state and macroscopically defined position due to unitary time evolution.

Yes, but the part that is not described by unitary evolution is the transition from:

• The electron is in a superposition of being deflected to the left and being deflected to the right.
• The election was either deflected left or deflected right (with such-and-such probability).

 

[vanhees71]

Why should you wish for something like this? All you need to know are the probabilities to measure the electron at a certain place and then you also know it's spin state due to the entanglement provided by the SG apparatus (which is, in essence, just the inhomogeneous magnetic field). Then you put some detector (photoplate in the case of the original Frankfurt experiment) and check, whether the probabilities are predicted right. More isn't provided by QT here, and as far as we know, there's indeed no more to the phenomenon than that. You can of course ask what happens to the electron after it hit the photoplate, where it leaves a spot through the corresponding chemical reaction, but that's of course hard to describe. I'd say, it got simply absorbed and is not identifiable anymore for further investigations.

I think, it's just that we are so used to the classical worldview that we cannot emotionally accept that there's no more to know about the electron than the probabilistic content of the quantum formalism. Due to this classical prejudice it's hard to accept for us that the electron's properties are neve completely determined, and that this indeterminism is not just due to our ignorance due to some complexity which hinders us to gain complete knowledge about its state but that the complete knowledge about the quantum state doesn't imply determined values for all observables, but that's what QT is telling is with overwhelming persistence. Any experimental attempt to disprove this consequence of QT to our worldview was in vain, and QT always turned out to give the correct description. Also all theoretical attempts to "correct" for the supposed "shortcomings" of QT by modifying it are not very convincing. So you get a whole bunch of "interpretations", i.e., non-scientific but rather philsophical extensions, which however don't solve the apparent "problems" of QT, among them the measurement problem. From a scientist's point of view, however there are no principle problems, but QT is very successful in predicting what's observed, and that's what science is about. Let any speculations on "ontology" to philosophy, where it belongs to!

 

[RockyMarciano]

No, they are not equivalent according to Bell. Bell's notion of locality is stronger than simply saying that FTL communication is not possible.

Bell's notion of locality is not about FTL. It's about factorizability of probability. A local theory, according to Bell, has the property that for any measurement, the outcome of the measurement (whether deterministic or not) depends only on conditions at the location where the measurement took place. What this means is that whenever there is a correlation between distant measurements, that correlation must be mediated by local state variables (which may be hidden).

There is a much simpler counter-example. Suppose that Alice and Bob are far away from each other, and they are both flipping coins. It happens to be the case that Alice's result is always the same as Bob's result. That's a nonlocal correlation, even though it can't be used for communication between Alice and Bob.

https://arxiv.org/abs/1303.2849

There seems to be some miscommunication here. I am not referring to the "local realism" or "local hidden variables" whole concept, I made an effort in previous posts to analyze the usual splitting of "local realism" into a purely local part and a purely realistic part, I guess you missed it. When I refer to Bell's notion of local I mean the first part, not the whole concept of local realism that is opposed to the so called "nonlocal correlations" quantum behavior that I agree is broader.

 

[stevendaryl]

Why should you wish for something like this? All you need to know are the probabilities to measure the electron at a certain place.

Well, if everything (including whatever device I used to detect an electron at a particular location) is described by unitary evolution, then why should the measurement result in a unique answer, as opposed to the universe being put into a superposition of

1. Detecting an electron on the left, and
2. Detecting an electron on the right

My problem is that if measurement is nothing but a complicated interaction of the type that individual particles undergo, then I don't see how there is any room for an additional assumption about measurements (that they give a definite result with particular probabilities). It's as if Newton's laws states that individual particles obey the three laws of motion, and then you add another law saying that snowflakes have six-fold symmetry. Either such a law is redundant (it is derivable from the laws of motion applied to the particles making up the snowflakes), or else it implies that there is something going on besides Newton's laws of motion.

 

[RockyMarciano]

No, this is an A-level thread, posters need not explain basic notions.

Brilliant answer, I should use it more frequently!

Please see my last post above.
I'll just ignore the trolling fragrance of your last remarks.

 

[stevendaryl]

When I refer to Bell's notion of local I mean the first part, not the whole concept of local realism that is opposed to the so called "nonlocal correlations" quantum behavior that I agree is broader.

I know you said that, but it's wrong. Bell's notion of "local" is not the same thing as "no FTL communication".

 

[RockyMarciano]

I know you said that, but it's wrong. Bell's notion of "local" is not the same thing as "no FTL communication".

So you find that locality split from realism is the same as local realism? What's the point of splitting the notion then? You might be missing a later paper by Bell after his famous 1964 one.

 

[vanhees71]

First of all what's a "realstic part". Note that after all these years in this forum, I still haven't get a clear-cut definition, what's meant by "realistic" in this context. As far as I can see, it's usually synonymous with deterministic.

Further in QT are correlations across large distances of parts of a quantum system, e.g., of the polarization of polarization-entangled photons measured at far distant places. That's what's usually termed imprecisely as "nonlocal correlations". Einstein used the much better term "inseparability" (my translation for the German "Nichtseparabilität").

Finally locality in relativistic QFT refers to the Lagrangian being a polynomial of the fields and its 1st derivatives at the same space-time point. Together with microcausality, i.e., the commutability of local observables at space-like separation of their arguments, particularly the Hamiltonian density, this excludes any FTL communication and the validity of the linked-cluster principle, as detailed in Weinberg, Quantum Theory of Fields, vol. I.

 

[RockyMarciano]

Hmmm... I'm saying the same thing Dr. Chinese has been saying for years but when I say it the reaction is different:interesting. I'll try and look up some quotes.

 

[DrChinese]

Hmmm... I'm saying the same thing Dr. Chinese has been saying for years but when I say it the reaction is different:interesting. I'll try and look up some quotes.

My summary of Bell:

No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

So I would say that Bohmian Mechanics is not ruled out by Bell. There may be reasons to rule it out, but a Bell test wouldn't be enough by itself.

 

[RockyMarciano]

First of all what's a "realstic part". Note that after all these years in this forum, I still haven't get a clear-cut definition, what's meant by "realistic" in this context. As far as I can see, it's usually synonymous with deterministic.

Further in QT are correlations across large distances of parts of a quantum system, e.g., of the polarization of polarization-entangled photons measured at far distant places. That's what's usually termed imprecisely as "nonlocal correlations". Einstein used the much better term "inseparability" (my translation for the German "Nichtseparabilität").

Finally locality in relativistic QFT refers to the Lagrangian being a polynomial of the fields and its 1st derivatives at the same space-time point. Together with microcausality, i.e., the commutability of local observables at space-like separation of their arguments, particularly the Hamiltonian density, this excludes any FTL communication and the validity of the linked-cluster principle, as detailed in Weinberg, Quantum Theory of Fields, vol. I.

The realistic part is indeed classical determinism. I agree with the rest of your post. I'm not sure if it was addressed to me, in any case I'm not sure if you are agreeing or disagreeing and about what?

 

[RockyMarciano]

My summary of Bell:

No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

So I would say that Bohmian Mechanics is not ruled out by Bell. There may be reasons to rule it out, but a Bell test wouldn't be enough by itself.

Sure, I'm not saying it is Bell by itself. It is basically Bell plus the cluster decomposition theorem from QFT plus their experimental confirmation of course.