Bohm Interpretation

1. Apr 12, 2009

JustinLevy

I do not understand why (apparrently) so many people on this board prefer the Bohm interpretation. To have more meaningful discussion, I tried to refresh my memory on the details and read some about it. Unfortunately, Bell's "unspeakable in quantum mechanics" book was not very helpful to me. Even stranger was the wikipedia page which, if it's definitions are correct, leads Bohmian mechanics to be distinguishable from QM since it defines the momentum operator differently.

In non-relativistic QM, the state of a system can be represented by the wavefunction, which can be written as a function of all the particles positions (well, and spins). The norm of the wavefunction is defined to be the probability density, and the wavefunction evolves according to the Schrodinger equation.

In Bohmian mechanics, there is also a wavefunction (pilot wave) which evolves according to the Schrodinger equation. ADDITIONALLY, there are particles which move according to the classical Hamiltonian with an additional "quantum potential" determined by the pilot wave.

Please note: I provided that information to give a 'snapshot' of my current level of understanding Bohmian mechanics and its contrasts with QM. What I wish is for someone to succinctly, and precisely (with math) define and explain what Bohmian mechanics is.

In particular these things confuse me:
What are the "pilot waves" functions of for BM? (since the particles have a definite position and momentum, they can't be functions of that)
And while the particle evolution is effected by the pilot wave, how do the particles effect the pilot wave?
In fact, how do the particles effect anything? Do they effect the potential for other particles, or measurement (which means they would have to affect particles somehow), etc?

2. Apr 12, 2009

Staff Emeritus
Because the vast majority of people on the board are amateurs. Amateurs worry about such things.

Professionals, after having spent 3 or more years studying QM in graduate school usually adopt the principle that "QM says if I set up measurement X, I will obtain an ensemble of measurements {X}", rather than worrying about creating a narrative that explains what elements of pre-QM physics survive and what elements do not: i.e. an "interpretation".

Rarely a calculation comes around that looks easy if you think about one interpretation (I am thinking of asymmetric B factories, which is simplest to understand in terms of Copenhagen), and the working physicist will analyze it in terms of whatever works best. Since all interpretations - by definition - give the same answer, they are all equally "real" (and equally unreal).

3. Apr 12, 2009

Dmitry67

Well, I am pure amateur but I prefer MUH and hence MWI.

But whats about Demistifyer and Ilja? For me they do not look like as amateurs: they have articles submiited to arhiv and they both have/work on some complicated theories.

4. Apr 12, 2009

QuantumBend

You make 11 dimension and get string theorums. Bohm need pilots mathematics.

5. Apr 12, 2009

zenith8

There's a good Cambridge University course on the internet http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" [Broken]. See lecture 1 for a succinct summary.

If he was talking about any other subject Vanadium50 would get penalized for rudeness by the moderators for this - but sadly it's not going to happen. This is what Bohmists have to put up with - for no really good reason other than people following the herd and therefore feeling safe insulting people. Lecture 7 in the course above is quite amusing on this topic. Don't let people like him put you off (though from your tone I suspect you're one of them already, and you're just looking for a quick reason to dismiss it? )..

I think the point is that while you get the same results as regular QM, all the 'weirdness' and 'paradoxes' disappear, and you can derive stuff (like Born's rule) that otherwise have to be postulates. Things like double slit experiments become 'understandable' (in ways that Feynman said no-one could do) and therefore not confusing to students. You might say so what? But how much hot air has been wasted on weirdness discussions over the decades..?

Also, the whole thing about Bell's theorem, nonlocality, the Aspect experiments etc. came out of a study of the Bohm interpretation by Bell (so saying that it's not important to think about interpretations is just nonsense).

Essentially physicists love pretending to be mysterious because it impresses women (substitute previous word with appropriate gender if required). The interpretation offered by pilot-wave theory is so prosaic that the women would think you were a massive nerd and start looking for fighter pilots or reality TV stars instead.

Physicists have been trained to believe that 'no-one understands quantum mechanics' so pilot-wave theory can't be true - but believe me, if one could dismiss it that easily it would have been by now. Remember it was invented almost in its entirety by 1927 (with Bohm adding a few tweaks about measurement theory in 1952) which is why these days one should refer to it as 'pilot-wave theory' rather than Bohmian mechanics or whatever. It was thus invented before Copenhagen itself and came within an ace of being adopted by the mainstream (but unfortunately Bohr and Heisenberg and other leaders were slaves to the logical positivism fashionable at the time and thus did not allow themselves to believe that particles could have 'trajectories' between position detection events).

Last edited by a moderator: May 4, 2017
6. Apr 12, 2009

Ilja

First about the momentum operator: Momentum measurements have the same results as in quantum theory. But they do not measure mass times velocity of the trajectory, but something else. These two things become identical only in the classical limit.

The wave function is a function on the configuration space Q, that means, the space of all possible configurations of the universe (or the particular toy universe of the given theory).

Then, the action equals reaction symmetry does not hold: The configuration (the particles) is influenced by the wave function, but not reverse. The particles influence each other because the position q_1 of particle 1 appears in the guiding equation for particle 2

$$\frac{d}{dt} q_2 = \frac{d}{dq_2} \Im\hbar\ln \Psi(q_1,q_2)$$

The most important thing "influenced" by the "particles" are we ourself: Our own configuration is part of the configuration of the universe.

7. Apr 12, 2009

QuantumBend

Why neutrinas go through WHOLE WORLD not banging? No good.

8. Apr 12, 2009

malawi_glenn

What? Can you please specify what banging means in physical terms?

9. Apr 12, 2009

malawi_glenn

How/can does Bohm Interpretation and formulation result in Quantum Field Theories? Is there relativistic formulations of Bohm-quantum mechanics?

As far as I know, this is where Bohm becomes really "nasty".

Also according to what I know, Bohm must use a different notation of probability so that Occam's razor can't be applied to it.

But I am really considering to follow that course that zenith8 proposed, seems to be really good.

10. Apr 12, 2009

QuantumBend

OK, It better crashes when neutrinas go through EARTH. Not crashing 10000000000 atom.

11. Apr 12, 2009

Ilja

For field theories, it seems most natural to use a field ontology. We have not particles, but fields, elements of some space of field configurations. The trajectory is, then, a field on space depending on time. For canonical field theories, this is a straightforward construction, even in the relativistic domain. The problematic parts is not relativity, but theories which do not have a canonical space of field configurations. In particular fermions. There are several different proposals how to handle fermions.

My own proposal is to use canonical quantization for fermion fields too - contrary to standard wisdom, this appears possible, as I have shown in ilja-schmelzer.de/papers/clm.pdf (published in Foundations of Physics this year). For this quantization scheme, the straightforward Bohmianization scheme works.

The problems are metaphysical. Existing proposals (except my own;-))) are not really beautiful. Empirical evidence is, instead, almost unproblematic. (One does not even need a Bohmian theory for fermions, because all what one needs is that macroscopic states differ. But they already differ if one considers only the EM field.)

Your remark about Bohm's notion of probability I do not understand, there is nothing special about it. There is some quantum equilibrium, which can be derived in analogy to thermodynamics, and which has, from point of view of probability theory, the same status.

12. Apr 12, 2009

malawi_glenn

what in the name of God are you speaking of?

NEUTRINOS have a low probability to interact with matter since they only do so with the weak force.

can you please try to write greater precision so that one can understand what you are saying and what the points of your arguments are.

13. Apr 12, 2009

Staff: Mentor

Please, people, let's keep this discussion civil, without disparaging "snipes" at interpretations that you don't like, or at people who favor them. Otherwise we'll be tempted to ban discussion of QM interpretations, just like we ban discussion of religion.

14. Apr 12, 2009

Staff Emeritus
Go ahead, click "report", if you think I have crossed a line.

I don't think the word "amateur" is rude - it means someone who does something for the love of it, rather than for pay, and derives from the latin amat, (s)he loves. I believe that that statement is true.

As far as the second half of my statement goes, there are thousands of pages written on QM and its applications every month in journals. (About 1500 such articles are submitted every month on QM or applications). Far less than 1% of these papers are about interpretations (0.1% or so in 2009 have the word "interpretation" in the title, and a good fraction of those - perhaps half - are written by people without giving their affiliation), which contrasts with maybe 30% on the QM section of PF. One cannot help but draw the conclusion that this is a topic that amateurs find far more interesting than professionals.

15. Apr 12, 2009

DrChinese

You've probably already seen these, if not:

Passon (2006): What you always wanted to know about BM...

Nikolic (2006): QM: Myths and facts (supports BM)

Passon (2004): Why isn't every physicist a Bohmian?

I have followed your comments about the philosophical issues around the study of Bohmian/dbb/Pilot Wave theories, and I think they match very closely my own thoughts. That is why I have tried to engage some of the knowledgeable members of this board to teach me more. This school is very dedicated, and the results of Bell experiments *could* be considered as pointing us towards a non-local theory (see Norsen reference below). But I can't believe, in the long run, it makes sense to construct an interpretation that gives identical results as what is already taught in textbooks. So my interest is to find some delta, and I personally think a truly different interpretation will yield a different - and hopefully testable - prediction eventually. That is why I wonder about radioactive decay, virtual fields, etc.

Norsen (2006): Against 'Realism' This article is one that I am in strong disagreement with, and Norsen and I have debated this point endlessly on this board in the past. Nonetheless, if you accept Norsen's argument, then the Bohmian viewpoint makes infinitely more sense. However, I completely reject the idea that Bell's Theorem does not include Realism as an assumption as it is easily to point to. Unfortunately, Bell did not clearly label it in his original paper and his book (Speakable... etc) is very vague on this subject (as Bell had obviously moved closer towards Bohmian ideas by that time). But none of that changes anything, and I can't think of any non-Bohmian that agrees with Norsen's hypothesis. And certainly I can't think any anyone actually doing experimental work in this area (a la Zeilinger and many others) who have ever mentioned that Bell's Theorem presumes non-locality.

16. Apr 12, 2009

QMessiah

DrChinese, what interpretation do you "believe" in?
I hate how intepretations have become like a religion...but, which do you prefer?

I think Norsen's arguments are pretty sound, this paper was also published in peer reviewed Foundations of Physics.

17. Apr 12, 2009

Staff Emeritus
I think that question points out exactly why professionals aren't interested in this at the level amateurs are. If the various interpretations give identical results, there is no scientific basis for distinguishing between them. Indeed, who's to say that only one can be right? It's like asking whether you believe in configuration space or momentum space: both will give the same answers. Often one is less work than the others.

18. Apr 12, 2009

samalkhaiat

19. Apr 12, 2009

p764rds

I am sure you are correct, but I need educating on this:

1 Apple = 10 Apples - (a flying virtual elephant ate 9)
Its mathematically correct but cannot be physically correct. Why are we allowed to do it? (e.g. let time go backwards and subtract the effects out at the end, or lets have some virtual particles that may not exist).

Last edited: Apr 12, 2009
20. Apr 12, 2009

feynmann

Do you think Gell-Mann and Weinberg are amateurs? They both disagree with Bohr's <Copenhagen interpretation>

Niels Bohr brainwashed a whole generation of physicists into believing that the problem (of the interpretation of quantum mechanics) had been solved fifty years ago. ( Murray Gell-Mann, Noble Prize acceptance speech, 1976)

Steven Weinberg in "Einstein's Mistakes", Physics Today, November 2005, page 31, said:
Bohr's version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wave function (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?
Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wave function, the Schrödinger equation, to observers and their apparatus.

Last edited: Apr 12, 2009