Why is the pilot-wave theory controversial ? Is it?

[ZapperZ]

Please note an important part in the PF Rules:

References that appear only on http://www.arxiv.org/ (which is not peer-reviewed) are subject to review by the Mentors. We recognize that in some fields this is the accepted means of professional communication, but in other fields we prefer to wait until formal publication elsewhere.

Topics in QM are still heavily dependent on peer-reviewed publication. So please use only such sources and not unpublished ones.

Zz.

 

[Fredrik]

Ah yes that makes more sense.

EDIT: on the other hand, since QM is a non-relativistic theory, why should anyone use relativistic arguments in discussions about its interpretation?

It sounds like what you have in mind when you say "QM" is the quantum theory of a single spin-0 particle in Galilean spacetime. ("The Schrödinger equation and stuff"). But "QM" can also refer to the mathematical framework in which quantum theories are defined ("Hilbert spaces and stuff"), and it can certainly handle special relativistic theories.

Edit: I see that there are almost a hundred posts after the one I replied to, so someone has probably said this already.

 

[Demystifier]

Jklasers, what essay are you referring to?

 

[Cthugha]

That post by jklasers was a full quote from some of the first google hits on pilot wave theory. As the other posts from the same user looked similar, I suppose it is a spambot which was not allowed to post his links yet.

 

[bohm2]

What is Seevinck criterion?

I've read a few of his papers and I have trouble understanding his arguments. Seevinck appears to argue that Bohmian mechanics, at least, the DGZ version (where ψ is nomological) is not "holistic". But I don't believe Seevinck has looked closely at the different interpretations of pilot wave theories although he does acknowledge this possibility in a footnote. He writes:

Indeed, in Section 4 classical physics and Bohmian mechanics are proven not to be epistemologically holistic, whereas the orthodox interpretation of quantum mechanics is shown to be epistemologically holistic without making appeal to the feature of entanglement, a feature that was taken to be absolutely necessary in the supervenience approach for any holism to arise in the orthodox interpretation of quantum mechanics...It was shown that all theories on a state space using a Cartesian product to combine subsystem state spaces, such as classical physics and Bohmian mechanics, are not holistic in both the supervenience and epistemological approach. The reason for this is that the Boolean algebra structure of the global properties is determined by the Boolean algebra structures of the local ones.

Holism, physical theories and quantum mechanics
http://mpseevinck.ruhosting.nl/seevinck/gepubliceerde_versie_Holism.pdf

 

[Demystifier]

I don't see why it is even important whether it is holistic or not.

 

[bohm2]

I don't even understand the difference between nonseparability versus holism. I always assumed that the two meant the same thing. But it seems there are different types/degrees of non-separability/holism and different degrees of non-locality as suggested in the paper I posted above and also in the Stanford piece by Richard Healey:

Holism and Nonseparability in Physics
http://plato.stanford.edu/entries/physics-holism/

And where does non-local "directional" quantum "steering" fit into the picture? I'm guessing this is a very "weak" form of non-locality? So in terms of controversial from most to least:

strong non-locality>weak non-locality> steering>non-separability/holism

I still don't understand how some authors can argue that Bell's inequality excludes not just local but even weakly non-local theories while others argue that it only rules out separability/non-holism.

 

[audioloop]

I 't even understand the difference between nonseparability versus holism. I always assumed that the two meant the same thing. But it seems there are different types/degrees of non-separability/holism and different degrees of non-locality as suggested in the paper I posted above and also in the Stanford piece by Richard Healey:

Holism and Nonseparability in Physics
http://plato.stanford.edu/entries/physics-holism/

And where does non-local "directional" quantum "steering" into the picture? I'm guessing this is a very "weak" form of non-locality? So in terms of controversial from most to least:

strong non-locality>weak non-locality> steering>non-separability/holism

I still don't understand how some authors can argue that Bell's inequality excludes not just local but even weakly non-local theories while others argue that it only rules out separability/non-holism.

Holism is more than Non-Separability as Contextuality is more than Non-Locality
---
"a physical theory is holistic if and only if it is impossible in principle to infer the global properties,
as assigned in the theory, by local resources available to an agent, there is no way we can find out about it using only local means, i.e., by using only all possible non-holistic resources available to an agent. In this case, the parts would not allow for inferring the properties of the whole, not even via all possible subsystem property determinations that can be performed"
Seevinck. (Epistemological Holism, physical property holism).
unlike of Ontological Holism, Nonseparability.


how, when and what it can posit the cause of explanation (determination) of values
or are values just "parts" of a single fact or process (as matter of fact, not so composed) ?Hierarchical Status

Holism -> Non separability -> Contextuality -> Nonlocality

Syntactical Reality .

 

[Demystifier]

Sure, it's really a nice little idea. From the little I know of quantum gravity, it seems the interest originates from there, in an attempt to derive the time-dependent Schrödinger equation from a time-independent universal wavefunction, this by treating spacetime as a macroscopic quantity.

Let's keep it simple, keeping the idea clear: the set-up is a two-particle system, the first with coordinates q, the latter with coordinates Q. The "universal" wavefunction is the time-independent $\Psi(Q,q)$ satisfying $E \Psi = \hat H \Psi$. We now suppose that the Q-particle is macroscopic, such that we know its (Bohmian) position Q(t) at all times. We now want to treat the subsystem q quantum-mechanically. To do this, it is logical to define the conditional wavefunction $\psi(q,t) := \Psi(Q(t),q)$. Note that the conditional wavefunction is now time-dependent since we've evaluated the universal wavefunction in the Bohmian trajectory for the macroscopic particle. It's not hard to prove/see that this conditional wavefunction and the universal wavefunction predict the same physics for the small particle.

Now due to the postulates of pilot-wave theory we know $\dot Q(t)$ in terms of $\Psi$. Consequently, using the chain rule, we can calculate $i\partial_t \psi(q,t)$. One gets that in highest order of M, being the mass of the macroscopic particle Q, we get that $i\partial_t \psi = \hat H' \psi$ where $\hat H'$ denotes the appropriate Hamiltonian for the subsystem. The math is a bit cumbersome, however I worked it out in a bachelor (i.e. undergraduate) project I made; I will PM it to you.

Summarizing, in the case of a time-independent Schrödinger equation, we can derive the time-dependent Schrödinger equation for a subsystem in case the environment is macroscopic.

Another, in my view less compelling, approach is taken by Goldstein in e.g. http://arxiv.org/pdf/quant-ph/0308039v1.pdf (page 21). The above approach, the one I outlined, I haven't seen as such in print. I think perhaps Kittel talks about it in his quantum gravity book, but I'm really not sure, this is more of a guess. Anyway I don't claim priority on this one, the suggestion mainly came from my advisor for the project (Ward Struyve), and I don't know where he got his juice, although there is a link with Tejinder Pal Singh as I outline in my project. I'll send the PM in a moment. (Anyone else interested is free to PM me, of course.)

These beautiful ideas are now further further elaborated in
http://arxiv.org/abs/1209.5196