What is the wave function about?

bohm2

Does the wave function represent the physical state of the system (MW) or merely our information about the system (orthodox interpretation)? If it represents something in between (Bohmian), what does that imply? Furthermore, if QM is supposed to be more “fundamental” than classical physics, does this suggest that configuration space is more "fundamental" than normal 3-space or (4 dimensional space-time)? If it’s more fundamental, why does the world appear to evolve in 3-space or (4 dimensional space-time)? I mean what is the nature of this configuration space where the wave function lives in? Goldstein writes:

A second point is that for a multi-particle system the wave function (q) = (q1 ,..., qN ) is not a weird field on physical space, its a weird field on configuration space, the set of all hypothetical configurations of the system. For a system of more than one particle that space is not physical space. What kind of thing is this field on that space?


http://philsci-archive.pitt.edu/1272/
http://users.ox.ac.uk/~sfop0257/papers/Finding.pdf


If one takes the quasi-objective (in between) view as in the Bohmian model, what does the necessary non-locality/non-separability imply? Moreover, how is it possible that the wave function acts upon the positions of the particles but it is not acted upon by the particles? So that in,

Bohmian mechanics there’s no back action, no effect in the other direction, of the configuration upon the wave function, which evolves autonomously via Schrodinger’s equation, in which the actual configuration Q does not appear.

Furthermore, there are problems with treating the wave function as nomological (denoting a law of nature) as in Bohm's model because, "laws aren’t supposed to be dynamical objects, (as) they aren’t supposed to change with time, but the wave function of a system typically does...(since), we can in (a) sense control the wave function of a system. But we don’t control a law of nature. This makes it a bit difficult to regard the wave function as nomological."

http://math.rutgers.edu/~oldstein/papers/rrwf.pdf

bayak

I think that the wave function represents the congruence of trajectories of one particle (simple case) in the compactified Minkowski spacetime.
http://socionet.ru/publication.xml?h=repec:rus:gulthb:1

wuliheron

This is a false dichotomy. The wave function represents what we observe and the latest theories imply what we observe depends on the context.

bohm2

It's in Russian? Is there a full English version?

This should read one of the Bohmian models as originally presented by Durr, D., Goldstein, S. and Zanghi, N. (1992):

We propose that the reason, on the universal level, that there is no action of configurations upon wavefunctions, as there seems to be between all other elements of physical reality, is that the wavefunction of the universe is not an element of physical reality. We propose that the wave function belongs to an altogether different category of existence than that of substantive physical entities, and that its existence is nomological rather than material. We propose, in other words, that the wavefunction is a component of physical law rather than of the reality described by the law.

But this version of the pilot wave seems to have been abandoned. In the present form of pilot-wave theory, ψ is regarded as ontological treated as "a new kind of causal agent acting in confguration space." I think this is how Bohm originally interpreted it.

http://www.tcm.phy.cam.ac.uk/~mdt26/...008_denial.pdf

bayak

There is the old English version (http://www.ptep-online.com/index_fil...8/PP-13-18.PDF ). But there are not wave function. There are only complex probability density function.

skippy1729

If you try to give quantum mechanics a naive realist interpretation, like Bohm or Everett, you find yourself contorting yourself beyond belief with things that are unobservable, bring forth no new results and still have gaping big holes. But these girls tell it better than I can:

http://www.youtube.com/watch?v=saWCyZupO4U

On a more serious note, this short paper in Physics Today by Asher Peres and Chris Fuchs might be interesting:

http://citeseerx.ist.psu.edu/viewdoc...=rep1&type=pdf

Skippy

bohm2

I'm not sure I would describe Bohm's or Everett's version as "naive". One can argue that there is nothing naive about the concepts of non-locality/non-separability or multiple universes/branches. Moreover, I think the epistemic view argued for by Peres and Fuchs is, in the final analysis, also just another interpretation. And there's arguably even less motivation to take their interpretation any more seriously than any of the others. In fact, one might have less motivation because to view physics as the "science of meter reading" doesn't look particularly rewarding, I think.

wuliheron

For that matter viewing physics as the "science of long shots" doesn't look particularly rewarding either. After 85 years of producing nothing useful Bohmian mechanics are about as big a long shot as they get.

skippy1729

Perhaps "naive" was a poor choice of words. I should have said "clever and sophisticated theories desperately clinging to a naive classical reality".

I also don't think "science of meter reading" is an accurate description of searching for understanding of the universe without the baggage of accepting unobservable entities as a matter of faith.

Skippy

Demystifier

How about this book?
Applied Bohmian mechanics:
http://www.amazon.com/Applied-Bohmia.../dp/9814316393
http://europe.uab.es/xoriols/Books?a...&target=Flayer

wuliheron

Never read it. Perhaps you'd like to explain just how useful Bohmian mechanics are compared to the standard theory....

Demystifier

Let me quote from the introduction of the book:
"... we believe that Bohmian mechanics can help us make progress with our real problems.
There are, at least, three clear reasons why one could be interested in studying quantum
problems with Bohmian mechanics:

(1) Bohmian explaining: Even when the Copenhagen mathematical machinery is
used to compute observable results, the Bohmian interpretation ofently offers
better interpretational tools. We can find descriptions of electron dynamics
such as “an electron crosses a resonant tunneling barrier and interacts with another
electron inside the well”. However, an electron crossing a tunneling region is not
rigourously supported within orthodox quantum mechanics, but it is within
the Bohmian picture. Thus, in contrast to the Copenhagen formulation, the
Bohmian interpretation allows for an easy visualization of quantum phenomena
in terms of trajectories that has important demystifying or clarifying consequences.
In fact, Bohmian mechanics allows for a simultaneous description
and interpreation of quantum mechanics within the same theoretical framework.
In particular, it provides a single-event description of the experiment,
while Copenhagen quantum mechanics accounts for its statistical or ensemble
explanation. We will present several examples in chapters 2 and 3 emphasizing
all these points.

(2) Bohmian computing: Although the predictions of the Bohmian interpretation
reproduce the ones of the orthodox formulation of quantum mechanics, its
mathematical formalism is different. In some systems, the Bohmian equations
might provide better computational tools than the ones obtained from the orthodox
machinery, resulting in a reduction of the computational time, an increase
in the number of degrees of freedom directly simulated, etc. We will
see examples of these computational issues in quantum chemistry in chapters
4 and 5, as well as in quantum electron transport in Chap. 6.

(3) Bohmian thinking: From a more fundamental point of view, alternative formulations
of quantum mechanics can provide alternative routes to look for the
limits and possible extensions of the quantum theory. As we will discuss later,
the work of John Bell on non-locality is a clear example of the unquestionable
utility of understanding quantum phenomena with Bohmian mechanics.
In particular, Chap. 7 presents the route to connect Bohmian mechanics with
geometrical optics and beyond opening the way to apply the powerful computational
tools of quantum mechanics to classical optics, and even to electromagnetism.
The natural extension of Bohmian mechanics to the relativistic
regime and to quantum field theory are presented in Chap. 8, while Chap. 9
discusses its application to cosmology."

For more details, you need to get the book itself.

wuliheron

Sorry, not interested in what people believe might be possible. After 85 years of speculation its not unreasonable to demand some concrete results.

ThomasT

They're naive in the sense that they involve/entail nonempirical fantasies.

Or one can argue that there is. And ultimately they offer no demonstrable insights about the underlying reality that can't be inferred from standard QM.

Yes, the most sophisticated one.

I like it because I think that, despite what some might see as apparent superficiality, it's actually deeper than either the Bohmian or Everettian interpretations. I think that's why, imo, most physicists would agree with Peres' and Fuchs' take on QM, as opposed to the alternatives.

Bohmians and MWIers are reading the same meters and predicting the same probabilities as standard 'uninterpreted' QMers. They're just carrying some unwarranted philosophical baggage along with that.

Demystifier

The results in item (2) of my post above are very concrete. In some cases, Bohmian trajectories are a much more efficient method (but equivalent to the standard method) to compute some measurable predictions of QM.

ThomasT

Yes, there is that. As well as some other aspects of BM that make it attractive. But then there's BM's nonlocality.

wuliheron

Being more efficient in some cases without making any new predictions just isn't terribly useful. I'm sure we could say the same thing about any number of other theories including phlogiston theory. It needs to prove itself uniquely useful in some significant way.