Instability of quantum equilibrium in Bohm's dynamicsOn this basis we argue that, while de Broglie's dynamics is a tenable physical theory, Bohm's dynamics is not. In a world governed by Bohm's dynamics there would be no reason to expect to see an effective quantum theory today (even approximately), in contradiction with observation...
In our view Bohm's 1952 Newtonian reformulation of de Broglie's 1927 pilotwave dynamics was a mistake, and we ought to regard de Broglie's original formulation as the correct one. Such a preference is no longer merely a matter of taste: we have presented concrete physical reasons for preferring de Broglie's dynamics over Bohm's.
On quantum potential dynamicsIn deBroglie’s original formulation, the particle dynamics is given by a first-order differential equation. In Bohm’s reformulation, it is given by Newton’s law of motion with an extra potential that depends on the wave function—the quantum potential—together with a constraint on the possible velocities. It was recently argued, mainly by numerical simulations, that relaxing this velocity constraint leads to a physically untenable theory. We provide further evidence for this by showing that for various wave functions the particles tend to escape the wave packet. In particular, we show that for a central classical potential and bound energy eigenstates the particle motion is often unbounded.
bohm2 said:An interesting paper within the pilot-wave camp by Colin/Valentini arguing in favour of de Broglie dynamics over Bohmian mechanics:
Instability of quantum equilibrium in Bohm's dynamics
http://lanl.arxiv.org/pdf/1306.1576.pdf
akhmeteli said:As far as I understand, to accept Colin/Valentini's arguments, one has to (at least) agree with their statement:
"if de Broglie's pilot-wave theory is taken seriously it must be admitted that departures from the Born rule (3) are in principle possible -- just as departures from thermal equilibrium are obviously possible in classical dynamics",
because if such "departures" are not possible, it seems there is no more difference between what they call "de Broglie dynamics" and "Bohmian mechanics" than between, say, different formulations of classical mechanics.
Their statement does not seem obvious. Let me offer an analogy: it is well-known that the Maxwell equations contain a constraint, but we don't need to believe that departures from this constraint are possible to take the Maxwell equations seriously.
atyy said:In my understanding, dBB reduces the interpretive problems of QM to those of classical statistical mechanics, whose interpretive problems are solved by assuming it is incomplete. For example, why can we apply statistical mechanics to "the whole universe at a time"? What ensembles are there if there is only one universe? In statistical mechanics, this is not considered as intractable, because we believe statistical mechanics is an incomplete, effective theory. Also, from an aesthetic point of view, the point of dBB is that QM can be considered incomplete. Either way, if QM is incomplete, there must be departures from QM at some level.
akhmeteli said:I may agree or disagree with you that accepting Colin/Valentini's statement "reduces the interpretive problems of QM", but this "reduction" does not make their statement obvious. On the one hand, we don't have any experimental evidence of "departures", on the other hand, de Broglie's pilot-wave theory seems to be still valuable without allowing "departures", even if only a proof that QM allows a realistic interpretation in principle.
atyy said:Does this view also mean that you don't find classical statistical mechanics disturbing, given Newton's laws of motion?
akhmeteli said:I am not quite sure I understand how this is related to the discussion, but this is my take on classical statistical mechanics: I don't find it disturbing, as it is clear that it is just an approximation: e.g., while Newton's laws do not allow irreversibility, we can live with irreversibility of statistical mechanics regarding it as an approximation.
atyy said:I was thinking that if I believe in Newton's laws, I should just need to specify an initial condition for the universe, in which case the applicability of classical stat mech must presumably mean a initial condition was special. Similarly, if I believe in dBB dynamics, I should just need to specify an initial condition for the universe, and the wide applicability of quantum equilibrium must presumably mean something special about the initial condition. In the Newtonian case, it would mean that stat mech is only an approximation valid under some circumstances, and by analogy quantum equilibrium would be valid only under some circumstances.
akhmeteli said:Thank you, now I see the relation. However, I don't quite see why a "special" initial condition is impossible in general or incompatible with experimental data. Furthermore, as I said, classical statistical mechanics is just an approximation. I tend to believe that standard quantum mechanics (unlike unitary evolution, which is part of standard quantum mechanics) is also just an approximation, as evidenced by the measurement problem. Also see, e.g., http://arxiv.org/abs/1107.2138 (published in Phys. Rep.), where it is shown for a specific measurement model how deviations from the Born rule and projection postulate appear in the course of unitary evolution.
atyy said:Thanks for the reference! I'd actually come across it before. I was interested to find out that Hepp, one of the people they cite is a physicist. I know a little of his work in neurobiology:)
akhmeteli said:I don't think this is the same person.
atyy said:http://arxiv.org/abs/1107.2138, ref 12: K. Hepp, Helv. Phys. Acta 45, 237 (1972), one of the authors of the Coleman-Hepp model. The paper http://dx.doi.org/10.5169/seals-114381 says Klaus Hepp was at ETH
There's a Klaus Hepp in neurobiology, also at ETH:
http://www.ncbi.nlm.nih.gov/pubmed/17728448
http://www.ncbi.nlm.nih.gov/pubmed/11495962
http://www.ncbi.nlm.nih.gov/pubmed/8929435
http://www.ncbi.nlm.nih.gov/pubmed/16572152 (What?)
Wikipedia has a Klaus Hepp http://en.wikipedia.org/wiki/Klaus_Hepp, whose advisor was Fierz, and who worked in physics and neurobiology. I think that Wikipedia's Hepp is the author of the Coleman-Hepp model, because the Helv Phys Acta paper is dedicated to Fierz. I'm not sure he's the Hepp of the neurobiology papers I linked to, but I thought it was because Wikipedia says he worked on eye movements.
De Broglie dynamics fine and Bohmian dynamics untenable are two different interpretations of quantum mechanics, both of which aim to explain the behavior of particles at the subatomic level. These interpretations suggest that particles have a defined position and trajectory, contrary to the principles of the more widely accepted Copenhagen interpretation.
De Broglie dynamics fine and Bohmian dynamics untenable challenge the fundamental principles of quantum mechanics and have been met with skepticism from many scientists. They also have difficulty explaining certain phenomena, such as quantum entanglement and the uncertainty principle.
The Copenhagen interpretation states that particles do not have a defined position or trajectory until they are observed, whereas De Broglie dynamics fine and Bohmian dynamics untenable propose that particles have a predetermined position and trajectory at all times. Additionally, the Copenhagen interpretation does not require the existence of hidden variables, while De Broglie dynamics fine and Bohmian dynamics untenable do.
There is currently no direct experimental evidence that definitively supports or contradicts De Broglie dynamics fine and Bohmian dynamics untenable. However, some experiments have shown results that are more compatible with these interpretations than the Copenhagen interpretation.
Yes, there are ongoing efforts to design experiments that could potentially test the predictions of De Broglie dynamics fine and Bohmian dynamics untenable. However, due to the complex nature of these interpretations, it remains a challenging task to design experiments that can definitively confirm or refute them.