An argument against Bohmian mechanics?

[Demystifier]

That's indeed interesting. Is there any chance to observe these consequences?

I don't know. Personally I don't find it very interesting, because the assumed initial violation of equilibrium is too ad hoc. The initial equilibrium can be violated in an infinite number of different ways, and Valentini assumed one particular form without any good reason.

 

[Demystifier]

(as I still lack to understand what's the merit of BM in the non-relativistic context either)

Only because you refuse to explain to yourself why do you attempt to explain the magic tricks even when you don't check your ideas experimentally.

 

[vanhees71]

Hm, out of curiosity of course, but when I can't check my ideas experimentally, I'm not doing of much value for science. Of course I mean that I make an assumption or claim which doesn't lead to observable consequences even in principle. Of course, it's a great thing that Einstein predicted gravitational waves 100 years before physicists were able to really detect them, but that it took so long was due to the technical difficulty to get the result, and gravitational waves are observable predictions of GR (of course, Einstein was himself not sure about this for a while; of course, he got the waves in the weak-field limit of GR, but then he couldn't find wave-like solutions for the full non-linear theory, and that stayed for quite a while this way, but that's another story).

 

[vanhees71]

I don't know. Personally I don't find it very interesting, because the assumed initial violation of equilibrium is too ad hoc. The initial equilibrium can be violated in an infinite number of different ways, and Valentini assumed one particular form without any good reason.

Then the question is, whether there's a reason for the universe to start in "quantum equilibrium" and not in another state. Of course, a lot about cosmology is pure speculation, like the puzzle concerning the matter-antimatter asymmetry. It's always assumed that the universe started with a symmetric state (i.e., equal amount of matter and antimatter), but that's an assumption (although a pretty "natural" one). Also inflation is an ad-hoc assumption to solve some puzzles like the flatness and horizon problems, but it's in no way verified today by observations.

 

[atyy]

I've no clue, how to repair BM for the relativistic case. Sometimes I hear the claim, there is something similar as for non-relatvistic ("first quantization") QM for relativistic QFT, but I've not seen this worked out in a detaile mathematical way yet.

One way to repair BM for the relativistic case is to use lattice gauge theory - which is non-relativistic, but for small enough lattice spacing will be consistent with experiment. Also, given the Wilsonian viewpoint, we can use lattice gauge theory as the basis of QED.

This is only a partial solution, as there is no lattice standard model due to the chiral fermion problem.

 

[atyy]

Then the question is, whether there's a reason for the universe to start in "quantum equilibrium" and not in another state. Of course, a lot about cosmology is pure speculation, like the puzzle concerning the matter-antimatter asymmetry. It's always assumed that the universe started with a symmetric state (i.e., equal amount of matter and antimatter), but that's an assumption (although a pretty "natural" one). Also inflation is an ad-hoc assumption to solve some puzzles like the flatness and horizon problems, but it's in no way verified today by observations.

The universe should not start in quantum equilibium, however, under certain dynamics, equilibrium can be rapidly reached - so BM makes QM analogous to statistical mechanics.

 

[ShayanJ]

Is there anything in BM that can disturb the quantum equilibrium?

 

[atyy]

Again, I don't understand this. The Born rule is applied everywhere, where QT is applied to describe observed phenomena. Nobody talks about a cut. You have some preparation procedure (e.g., the bunches of protons running in the LHC) and measurement devices (e.g., the big detectors ATLAS, CMS, LHCb, and ALICE). Then as much "statistics" is taken as possible (i.e., you make a lot of pp collisions at the LHC energy and observe a lot of things with the detectors to measure spectra, cross sections, etc. etc.). I don't need new artificial words like beable or the like. Physics is just what's done in the lab, the evaluation of the data by experimentalists and the description (aka modeling/simulating) in terms of QT by theoreticians.

Who is "nobody"? Landau and Lifshitz? Weinberg? I hate to argue from authority, but you are simply wrong that nobody talks about a cut when two of the most distinguished quantum mechanics textbooks mention it.

 

[atyy]

Is there anything in BM that can disturb the quantum equilibrium?

Quantum equilibrium is analogous to thermodynamic equilibrium, so yes, it can be disturbed.

 

[ShayanJ]

Quantum equilibrium is analogous to thermodynamic equilibrium, so yes, it can be disturbed.

Technological limits aside, can you think of any experimental setup that is able to probe quantum non-equilibrium?

 

[Demystifier]

Hm, out of curiosity of course, but when I can't check my ideas experimentally, I'm not doing of much value for science.

Then, by the same token, I think about Bohmian mechanics out of curiosity too, with the same caveat on the value for science. So whenever someone tells you that he likes to think about BM, just tell yourself: "Aaa, I get it, that's not really science but just curiosity, the same thing I am doing when I think about magic tricks. "

 

[Demystifier]

Quantum equilibrium is analogous to thermodynamic equilibrium, so yes, it can be disturbed.

Unless the whole universe is in the equilibrium, in which case the disturbance is only possible as a small-probability fluctuation.

 

[vanhees71]

Who is "nobody"? Landau and Lifshitz? Weinberg? I hate to argue from authority, but you are simply wrong that nobody talks about a cut when two of the most distinguished quantum mechanics textbooks mention it.

Well, where in these books is this idea ever really used, and where is it necessary to be used? I just take a measurement apparatus and measure something. I don't need a cut to use it to check the predictions of quantum theory.

 

[atyy]

Well, where in these books is this idea ever really used, and where is it necessary to be used? I just take a measurement apparatus and measure something. I don't need a cut to use it to check the predictions of quantum theory.

They use it when they do not include the measurement apparatus in the quantum state.

 

[rubi]

As someone who likes to explain magic tricks, I still find the comparison to BM a bit outrageous. It's a terrible analogy. If your explanation requires invisible pink unicorns that are spread over the whole universe and need to conspire over cosmic distances in order to make the rabbit appear, then I would reject the explanation immediately, even though I would have to admit that technically, it's not excluded by observations. Just because something is an explanation, it doesn't mean it's a rational explanation. BM is possibly one of the least rational explanations that people have come up with in the history of science.

 

[vanhees71]

They use it when they do not include the measurement apparatus in the quantum state.

Where concretely use my experimenter colleagues the cut when they analyze an experiment at the LHC? As far as I now they use a data file provided by the detectors, which are real-world measurement devices to register particles. The corresponding outcomes of measurements are compared to the (probabilistic) predictions of quantum theory. Nowhere do they need to assume a cut to design their experiments and evaluate the data in terms of cross sections, predicted by QT.

 

[Jilang]

For experimentalists the location of the cut is unimportant. There is a mathematical formalism that wraps up the whole thing. That said it is most unsatisfying if you believe there is cut. The model doesn't distinguish between states pre and post cut as far as I can tell, making our formulaism a shorthand.

 

[atyy]

Where concretely use my experimenter colleagues the cut when they analyze an experiment at the LHC? As far as I now they use a data file provided by the detectors, which are real-world measurement devices to register particles. The corresponding outcomes of measurements are compared to the (probabilistic) predictions of quantum theory. Nowhere do they need to assume a cut to design their experiments and evaluate the data in terms of cross sections, predicted by QT.

Concretely, the cut is used when they claim to have made an observation. You can tell they have made a cut if they claim certain observations are consistent with quantum mechanics, and they have used the Born rule.

 

[atyy]

As someone who likes to explain magic tricks, I still find the comparison to BM a bit outrageous. It's a terrible analogy. If your explanation requires invisible pink unicorns that are spread over the whole universe and need to conspire over cosmic distances in order to make the rabbit appear, then I would reject the explanation immediately, even though I would have to admit that technically, it's not excluded by observations. Just because something is an explanation, it doesn't mean it's a rational explanation. BM is possibly one of the least rational explanations that people have come up with in the history of science.

But you like Consistent Histories, which means your dislike of BM is only a matter of tase - unlike vanhees71, which is a technical disagreement. If we apply vanhees71's view, Consistent Histories is also pointless.

 

[atyy]

Technological limits aside, can you think of any experimental setup that is able to probe quantum non-equilibrium?

Valentini has done some work on this, but it has limitations that were discussed by Demystifier in his posts above.

Anyway, the basic idea is that unless there is fine tuning, it is unlikely the universe was created in equilibrium. If the universe was created in non-equilibrium, there may still be some signatures of that nonequilibrium observable today.

 

[vanhees71]

But you like Consistent Histories, which means your dislike of BM is only a matter of tase - unlike vanhees71, which is a technical disagreement. If we apply vanhees71's view, Consistent Histories is also pointless.

Can you summarize, what Consistent Histories claims beyond the minimal interpretation? Perhaps, I'm too pragmatic to realize, where the problem with the minimal interpretation is, but I just don't get, why it should help to introduce any elements of interpretation that go beyond Born's rule, which establishes the meaning of the formalism concerning observable (and observed!) facts about nature.

 

[vanhees71]

Concretely, the cut is used when they claim to have made an observation. You can tell they have made a cut if they claim certain observations are consistent with quantum mechanics, and they have used the Born rule.

I still don't understand, where the cut is made. Experimentalists measure something by repeating for many times a preparation and measurement procedure and then analyze the experiment statistically. That's the way you "test hypotheses" in the sense of probability theory, and QT is just a probability theory for physical processes in nature, not more not less. There's no quantum-classical cut used anywhere. Also the construction of most measurement devices are based on QT nowadays since most are based on semiconductor technology, which is based on condensed-matter many-body QT. In other words, there is no clear boundary between classical behavior of macroscopic objects and quantum behavior of microscopic ones. The former is a more or less applicable approximation of the latter to describe macroscopic ("relevant") observables. It's no fundamental cut, but the application of an approximation.

Nobody talks about any "cut" when one uses non-relativistic approximations in classical mechanics or electrodynamics. There the non-relativistic treatment is a more or less applicable approximation to the fully relativistic one. That's the usual structure of physical theories: Different models or theories that are successful in describing certain phenomena can be approximations of each other. The more comprehensive theory tells us the range of validity of the approximations. The same holds for QT vs. classical approximations.

Historically the cut is due to the Heisenberg flavor of the Copenhagen interpretation and enters the game only because of the collapse hypothesis, which in my opinion is as superfluous and misleading as the introduction of a cut.

 

[stevendaryl]

I still don't understand, where the cut is made. Experimentalists measure something by repeating for many times a preparation and measurement procedure and then analyze the experiment statistically. That's the way you "test hypotheses" in the sense of probability theory, and QT is just a probability theory for physical processes in nature, not more not less. There's no quantum-classical cut used anywhere.

Yes, there is. The probabilities occur in quantum mechanics (or QFT) in the form of the Born rule:

When you perform a measurement on a system, the result is one of the eigenvalues of the corresponding operator and the probability of an outcome is the square of the amplitude for the system to be in the corresponding eigenstate.​

The use of probabilities involves a cut: You can describe it in several different ways:

1. The cut between the system, which is the thing being measured, and the observer, which is the thing being measured.
2. The cut between ordinary interactions, which are described by terms appearing in the Hamiltonian, and measurements, which are described by the Born rule. The system evolves smoothly and deterministically according to Hamiltonian dynamics in response to ordinary interactions, but measurements behave probabilistically.
3. The cut between microscopic systems, which are described by quantum amplitudes and which can be in superpositions of drastically different states, and macroscopic systems, which are observed to always have approximately definite values for quantities such as position. (By "approximately definite", let me illustrate by example: An automobile's position is subject to imprecision--you can't really say where it is with a precision much greater than the size of the automobile. But you would never say that it is uncertain whether an automobile is in London or New York City. So to within the limits of precision, its location is definite.)

To apply the Born rule, you must declare some aspect of the universe to be on the observer/measurement/macroscopic side of the cut.

This seems obvious to me. Certainly, if you consider two electrons interacting, does it make any sense to say that one electron is measuring the z-component of the spin of the other electron? Obviously not. The two electrons interact, and that interaction might depend on their spins, but there is never a point where one electron can be said to have measured the spin of the other. The Born rule can only be applied if there is a system that is macroscopic, that is capable of forming permanent records of past interactions. So it requires a "cut" between those parts of the universe that are treated using (reversible) microscopic dynamics and those parts that involve irreversible changes during a measurement interaction. If the measurement device is described by reversible dynamics, then there is nowhere to apply the Born rule.

 

[vanhees71]

But the interactions described by QT are the interactions between the measured object and the measurement apparatus, or at least there's no hint that only because something is constructed by men as a measurement device, all of a sudden different than the fundamental interactions described by QT are at work. This reminds me somehow at the old idea that there's a special "vis viva" at work disinguishing natural laws valid for living organisms vs. non-living matter (even there it's hard to clearly define a boundary, e.g., are viruses or prions living beings or not). That macroscopic devices are able to store information about the measured quantum system doesn't imply that there are other physical laws at work as those described by the Standard Model, i.e., QT.

 

[RockyMarciano]

It seems to me the discussion about the Heisenberg cut is not about its existence in the theory, but about whether that is a problem or not.
The cut is inherent to the construction of QM theory and in simple terms consists of the non-debatable coexistence in the formalism of classical observables and quantum probabilities per the Born rule. Whether one considers this a problem for the theory or just accepts it naturally like vanhees does should be a personal conclusion, not a source of dispute.

 

[stevendaryl]

But the interactions described by QT are the interactions between the measured object and the measurement apparatus,

But the additional rule, that a measurement result only results in an eigenvalue, with probabilities given by the square of the amplitude, applies only to measurements. So if you have a rule that only applies to some kinds of interactions, and not others, then you have a cut. You certainly can't apply that rule to the interaction between two electrons; you can't say that one electron is measuring something about the other electron, and will get such and such a result with such and such a probability.

What von Neumann first noted was that you can always move the cut to enlarge the part of the universe that is on the "microscopic" side, but you can't eliminate it. Without the cut, you don't have the Born rule. If you analyzed everything using microscopic dynamics, then there is suddenly no role for probabilities (unless the people trying to derive probabilities for Many Worlds succeed).

 

[RockyMarciano]

Also IMO the cut doesn't exist in nature, just in the QM formalism. In BM (and in MWI) the cut in the formalism is taken as real, and so it needs to build a classical ontology coexisting with the quantum phenomenology.

 

[stevendaryl]

It seems to me the discussion about the Heisenberg cut is not about its existence in the theory, but about whethertthat is a problem or not.
The cut is inherent to the construction of QM theory and in simple terms consists of the non-debatable coexistence in the formalism of classical observables and quantum probabilities per the Born rule. Whether one considers this a problem for the theory or just accepts it naturally like vanhees does should be a personal conclusion, not a source of dispute.

You can certainly say, as Von Neumann did, that there are two kinds of interactions: normal interactions that are described by Schrödinger's equation (or quantum field theory), and measurement interactions that involve a discontinuous change to a system. That's ugly, but it's coherent. What seems incoherent to me is accepting the practical advantages to the two types of interaction while also denying that there is anything special about measurement. That seems inconsistent, not just a matter of personal taste.

 

[stevendaryl]

Also IMO the cut doesn't exist in nature, just in the QM formalism. In BM (and in MWI) the cut in the formalism is taken as real, and so it needs to build a classical ontology coexisting with the quantum phenomenology.

Yes, but if the cut exists only in the formalism, that suggests (to me) that its appearance is due to not having the formalism figured out completely. Something analogous might be Special Relativity. The elegant way that SR is taught today makes no reference to a preferred rest frame. However, you can imagine an alternate history in which Einstein never came along, and we were stuck with an ad-hoc theory in which there is a preferred reference frame such that:

• In that frame, light travels at speed $c$ in all directions.
• Clocks (and other systems that change internal state with time) moving relative to this frame run slower.
• Physical objects moving relative to this frame are contracted in the direction of their motion.

You can make such an ad hoc theory to be observationally equivalent to SR, but you're stuck with an unobservable preferred rest frame. People could then speculate that this is only needed for the formalism, but isn't really part of nature.

 

[RockyMarciano]

You can certainly say, as Von Neumann did, that there are two kinds of interactions: normal interactions that are described by Schrödinger's equation (or quantum field theory), and measurement interactions that involve a discontinuous change to a system. That's ugly, but it's coherent. What seems incoherent to me is accepting the practical advantages to the two types of interaction while also denying that there is anything special about measurement. That seems inconsistent, not just a matter of personal taste.

Agreed. It is nevertheless an inconsistence that doesn't bother experimentalists(and a certain theorist which appears to have an experimentalist soul ;-)) in their applying the theory and it is no use trying to make them feel the inconsistence.