Thoughts on Bohmian Mechanics?

[pantheid]

Hi, I'm an undergraduate in college, majoring in physics, and I just finished a course in Quantum Mechanics. I was left very disappointed with the interpretation presented, and this winter I am starting to do research with a professor in the field of Bohmian Mechanics. However, I am finding different opinions on the validity of the subject; many students and professors say that its complete BS, Griffiths seems to have a reasonable proof against it, but its supporters claim that the interpretation is perfectly reasonable if it is properly understood. Can I get your opinions on Bohmian Mechanics?

 

[atyy]

There is no question that Bohmian mechanics does solve the measurement problem by providing hidden variables for non-relativistic quantum mechanics.
http://arxiv.org/abs/quant-ph/0209123
http://arxiv.org/abs/quant-ph/0308039
http://arxiv.org/abs/quant-ph/0308038

For relativistic quantum mechanics, the picture is less clear, and the subject of current research.
http://arxiv.org/abs/1205.1992
http://arxiv.org/abs/1307.1714

Bohmian mechanics does leave problems, but it converts the problems of interpretation to those of classical equilibrium statistical mechanics. In so doing, it suggests that there may be a non-equilibrium regime, which would result in violations of quantum mechanics, and this results in "beyond the standard model" research.
http://arxiv.org/abs/1306.1579

The overall importance of Bohmian mechanics is not its specific equations, but as an example of a solution to the measurement problem for some quantum mechanical theories. It is not unique, and often "Bohmian mechanics" is used to indicate classes of hidden variable theories which solve the measurement problem in a similar spirit. The papers by Valentini, for example, use different dynamics from Bohm's, which is why he prefers the term "de Broglie - Bohm theory". See the introduction of http://arxiv.org/abs/0706.2522 .

 

[dextercioby]

There are numerous discussions here about BM. Demystifier is one of its greatest supporters, he might give you an overview and offer reading reccomendations.

 

[bhobba]

Its not my personal interpretation, but its perfectly valid, and as correct, or incorrect, as any any interpretation. Choices of interpretations, since there is no way to experimentally distinguish any of them, are purely made on aesthetically what appeals to you.

BM, along with Copenhagen and Many Worlds, is one of the principle interpretations people hold to, so it is far from fringe. The reason I personally eschew it is this inherently unobservable pilot wave which is, to me, highly reminiscent of the old idea of an aether - but on the positive side it allows a much more usual view of reality than other interpretations. Its all a matter of taste and opinion - but opinions are like bums - everyone has one - it doesn't make it correct - even my opinion - no especially mine. In science what we want are experiments to decide things - not opinions.

That said it still is interesting understanding and comparing interpretations of QM - providing you realize in a certain sense until it makes contact with experiment its reminiscent of the arguments about the number of angels dancing on a head of a pin - a bit like that anyway.

Here is a good article explaining BM:
http://arxiv.org/pdf/quant-ph/0611032v1.pdf

But I also encourage you to learn about bog standard QM as much as possible before being caught up in the quagmire of interpretations. I like Ballentine - Quantum Mechanics - A Modern Development:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

Here you will find it developed from just two axioms, and can understand exactly the key points on where interpretations differ.

Thanks
Bill

 

[pantheid]

Thanks for the responses! I've done some more reading on the interpretations of Quantum Mechanics, and it seems to me that each of them has some sort of flaw. My understanding (and please, correct me if I'm wrong), is that BM's main flaw is that it makes predictions that violate special relativity. But then again, haven't QM experiments (such as entanglement) shown that SR is violated anyway?

 

[atyy]

No, SR has not yet been violated. What's happening in entanglement is that there is nonlocality, but of a form consistent with SR. Entanglement cannot be used to send classical information faster than light so it does not violate SR.

I'm not sure that BM cannot be extended to relativistic quantum theory. There are proposals I linked to in post #2, and in the reference by Passon that bhobba linked to discuss other proposals for relativistic BM. I don't know if there is yet consensus on the subject, so it's being researched.

I think one advantage of BM is that it points beyond QM (and possibly beyond SR). By the same token the chief advantage of many-worlds is that it suggests that QM can be complete. The naive textbook interpretation allows both possibilities.

 

[lightarrow]

Sorry for the naive reply.
Does we really need hidden variables, at least to have a more satisfying interpretation of the entanglement effect? Couldn't we assume that real properties (observables) of a quantum system does exist, but are not intrinsic to it, because they are destroyed by a measure of the complementary observable? For example, two entangled electrons opportunely preparad, of which we measure the spin component along z axis, would be measured as "spin-up" and "spin-down" because they really have spin-up and spin-down properties before the measurement, but these properties are destroyed if we measure the spin along x or y.

--
lightarrow

 

[Nugatory]

Sorry for the naive reply.
Does we really need hidden variables, at least to have a more satisfying interpretation of the entanglement effect? Couldn't we assume that real properties (observables) of a quantum system does exist, but are not intrinsic to it, because they are destroyed by a measure of the complementary observable? For example, two entangled electrons opportunely preparad, of which we measure the spin component along z axis, would be measured as "spin-up" and "spin-down" because they really have spin-up and spin-down properties before the measurement, but these properties are destroyed if we measure the spin along x or y.

Bell's theorem (google will find you many hits, including an excellent page maintained by our own DrChinese) shows that no such theory can match the quantum mechanical prediction and experimental results in all cases.

It's easy to make it work if you're only checking perfectly anti-correlated values like spin-up and spin-down, but if you are looking at three correlated values (for example, spin measured at zero, 120, and 240 degrees) there's no way of pre-assigning values that will work. Google will find you some examples pretty quickly.

 

[stevendaryl]

I'm a little uncertain (no pun intended) about Bohmian mechanics. The argument that it is experimentally equivalent to Copenhagen involves the assumption that particles are initially distributed with a density given by $\rho(x) = \psi^*(x) \psi(x)$. If that assumption is true initially, then it's true for all time.

However, I have a hard time understanding the meaning of that assumption when the number of particles is small--say, there is only one electron. In that case, the electron has a definite (if unknown) position at all times. So how does it make sense to say that the electron is distributed according to $\rho(x) = \psi^*(x) \psi(x)$?

I suppose you could say that $\psi$ refers, not to the actual electron, but an ensemble of electrons. But then you're basically moving into the ensemble interpretation, it seems to me.

 

[stevendaryl]

Bell's theorem (google will find you many hits, including an excellent page maintained by our own DrChinese) shows that no such theory can match the quantum mechanical prediction and experimental results in all cases.

Bell's theorem plus the assumption of lightspeed limit to interactions plus the rejection of superdeterminism.

 

[Demystifier]

For general physicists, my opinion about BM is that even practical physicists not interested in conceptual and philosophical foundations of QM should learn some basics of BM. Even if the main assumption of BM (the existence of objective continuous deterministic particle trajectories) is ultimately wrong, BM can be used as a thinking tool which transforms the otherwise very abstract quantum formalism into something much more intuitive.

In addition, some practical physicists exploit the ideas of BM to simplify the practical calculations in physics:
https://www.amazon.com/dp/9814316393/?tag=pfamazon01-20

 

[bohm2]

For myself, I find the fact that macroscopic quantum analogues of Debroglie-Bohm's (e.g. Couder's walking droplets) exist might lead to some important insights:

http://walkingdroplet.com/2013/02/
http://math.mit.edu/~bush/?page_id=484
http://math.mit.edu/~bush/?page_id=154

 

[pantheid]

I looked at the walking droplet stuff, and there was a video of "quantum tunneling" that was basically just the particle bouncing around. If this was a perfect analogy for tunneling, wouldn't we expect the particle to cross the barrier somehow? Otherwise, in what sense has tunneling occurred?

 

[bohm2]

I looked at the walking droplet stuff, and there was a video of "quantum tunneling" that was basically just the particle bouncing around. If this was a perfect analogy for tunneling, wouldn't we expect the particle to cross the barrier somehow? Otherwise, in what sense has tunneling occurred?

It does. See right at the end of that video.

 

[audioloop]

is perfectly reasonable if it is properly understood. Can I get your opinions on Bohmian Mechanics?

all interpretations are reasonable.
none stands out by itself.

relative state, objective reduction state, pilot wave (bm), modal models, time-symmetric theories.


.

 

[Dale]

With that, it is good to end this discussion of opinions.