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The difficulty with these semi-classical interpretations of quantum phenomena is that they tend to work nicely for a few very simple cases and fall to bits when

The difficulty with these semi-classical interpretations of quantum phenomena is that they tend to work nicely for a few very simple cases and fall to bits when things get more complex. Bohm's quantum potential works almost perfectly for single electron atoms, in which the quantum potential simply holds the electron still, but falls apart for multi-electron atoms, which require a higher dimensional space for the quantum potential to live. Although Bell did defend pilot wave theory--which is taught in every introductory QM course and covered in every introductory QM text--he himself did not see it as anything more than an inspiration for a more complete interpretation, which would necessarily be non-local in accordance with the theorem that bears his name. My own belief is that pilot waves cannot account for quantum statistics, and therefore cannot account for the heat capacity of solids: http://www.tjradcliffe.com/?p=470 http://www.tjradcliffe.com/?p=470 There is a claim that pilot wave theory somehow deals with this, but the argument is focused on the decay of radioactive particles rather than thermodynamics, which seems to be odd, because the thermodynamic argument is the fundamental one: the heat capacity of solids is an unequivocal way of counting available states, and if hidden variables (such as the "true" positions and momenta of the piloted particles) exist then they break the symmetry under exchange that gives rise to the statistics we observe, and create additional states that would... hmmm... OK, having thought about it for a bit I'm no longer entirely convinced it's impossible that pilot waves might preserve the symmetry while also preserving identity. It would require that exchanging the labels on the pilot waves precisely compensate for the labels on the particles. Would that be enough? I'm going to have to think more about this before forming a more firmly held opinion on it.

anigbrowl 12y ago
It's hard to think about this given that the Copenhagen school has had decades of effort lavished on it, while De Broglie's concepts seem to have had very little development. I've always been a little interested in them because I like underdogs, but have assumed as a lay person that the Copenhagen approach was correct. The oil drop experiment is certainly thought-provoking.
- lmm 12y ago
  The most obvious, naive extrapolation of ordinary quantum mechanics (that is, assume the experimenter is an ordinary quantum system behaving in the ordinary way) comes out as the many-worlds interpretation. There are arguments for others, but many-worlds should be your "default".
  - tim333 12y ago
    The trouble with many worlds, for me at any rate, is say you have a mirror where the photons go one way 94% of the time, the other 6% of the time. How does that work? 94 worlds of one type and 6 of the other? Everett did some hand wavy, we assign a probability P to each outcome stuff but you still wonder how on earth that works physically. If the universe branches with one version of you seeing it go one way and one the other is one of you more existy or what?
    - ajuc 12y ago
      I thought there are 94 you (and universes) that seen one result and 6 that seen the other. Then there are irrational probabilities :)
    - lmm 12y ago
      The only thing that's fundamental, that's physically "real", is the wavefunction. So you have your mirror and your photon and you, and all that's described according to some wavefunction |P(t)>, evolving according to the laws of quantum mechanics. Now we observe that after the photon passes through the slit, we can decompose the function as |P(t)> = sqrt(0.94)|Q(t)> + sqrt(0.06)|R(t)> where Q and R are independent, each individually evolving according to the laws of quantum mechanics. This is already derived rather than fundamental, but the phenomenon is real, because the causality relation is real. Our neurons under Q (and of course a "neuron" isn't really fundamental, it's an interpretation of a particular group of particles behaving in a particular way, i.e. of particular aspects of the wavefunction) have no effect on our neurons in R and vice versa. All that is physically real; the only remaining question is what we should expect to subjectively experience. Since our neurons in Q have no effect on our neurons in R and vice versa, it seems like we'd experience either being in Q or being in R. With what probability? Well, whatever it is it had better be conserved; it makes no sense to say that we'd experience R with 4% probability in 5 minutes and then 8% probability in 10 minutes. If we send another photon through in Q, splitting the wavefunction further into |S(t)> + |T(t)> + |R(t)> where Q = S + T, then our subjective probabilities should be such that the probability we find ourselves in S or T = the probability that we found ourselves in Q before sending the second photon. What's the probability-like quantity that's conserved by quantum evolution of a system? Why, it's the norm, ||P>|^2. I guess that's what we'd expect to be the subjective probability then.
jessriedel 12y ago
> ...pilot wave theory--which is taught in every introductory QM course and covered in every introductory QM text... Having assisted in teaching intro QM courses, I can say this is very incorrect -- unless you replace "every" with "many" and "taught/covered" with "mentioned off hand". I just pulled the very popular "introduction to quantum mechanics" by Griffiths off my shelf. It contains nothing about pilot waves except for a single footnote in an appendix used as an example of "a number of hidden variable theories [proposed over the years]".
- tjradcliffe 12y ago
  OK, "every GOOD intro QM course" and "every GOOD intro QM text" :-) I shall now walk away mumbling about the degenerate state of today's youth...
  - Osmium 12y ago
    Griffiths happens to be the most accessible while-still-rigorous QM book I've read, so I'd be careful with the criticism ;) it is concise though, which is probably the main reason it doesn't really discuss pilot waves.
  - TTPrograms 12y ago
    A book not containing a fringe, weak theory does not make it bad.
  - vanderZwan 12y ago
    Sure thing, True Scotsman ;)
- cshimmin 12y ago
  Agreed... I managed to finished all my courses towards a PhD in high-energy physics without ever having heard of pilot wave theory before. I'm an experimentalist but we still have to take all the same standard QM/QFT courses as the theory guys.
yummyfajitas 12y ago
As far as I'm aware, pilot wave theories designed for thermodynamics explicitly occur on the state space R^N mod SN (where SN is the appropriate group, depending on fermion or boson).
deleted 12y ago
[deleted]
trevelyan 12y ago
I can see how it works in 2D, with things bouncing into the air where there is no resistence, but how is that supposed to work in a 3D field? Wouldn't any movement push the particle up against a barrier that would force it back into the center?
mkempe 12y ago
Francis Fer, friend and colleague of de Broglie, wrote a 2-volume treatise on thermodynamics in the early 70s, with an introduction by de Broglie, so if you are interested in a treatment of the subject that would be close to his views, you may want to look it up.
jostylr 12y ago
Bohmian mechanics has a very elegant way of dealing with identical particles. I know as I am a coauthor on such papers. The idea is that instead of R^3N with its labels, we use a space with no labels on particles. The only relevant data are the locations of the particles, not some extrinsic numbering. This immediately gives us bosons. Fermions take a little more work, essentially using a vector bundle approach analogous to Mobius strips. One can then prove that in 3 dimensions and for scalar wave functions, that is all the possibilities. For 2D, you also get anyons; this is all about the topology of the natural configuration space. For spin, one has to realize that it is modeled well by wave functions that take on vectors as values. When moving to multiple particles with spin, we tensor (kind of multiply) those vectors together. But the key point is that we tensor based on the spatial location. So instead of tensoring over particle 1 and particle 2, we tensor over their positions. This gives us complicated vector bundles. It opens a lot more possibilities, but when you look at general quantum dynamics, the only stable ones in 3D are the bosons and fermions. Thus, not only can Bohmian mechanics account for it, it actually provides a very natural explanation. It is completely rooted in considering what the configuration space is. Where Bohmian mechanics shines is that what the configuration space is comes from what the theory itself is concerned with, namely particles with definite positions. And just as a side note, the standard formalism of quantum mechanics emerges in a mathematically rigorous way from Bohmian mechanics. Everything in non-relativistic quantum mechanics is completely accounted for and you get a clear foundation for extending it to other spaces and more general questions. As for relativity and quantum field theory, that is still a work in progress, but the main stumbling block is actually having a well-defined evolution of the wave function in interacting cases. If we had that, then the Bohmian additions are easily handled for the most part. Research has been done and is being done. A simple (layperson) reference for this is sadly lacking, but you can try either http://arxiv.org/pdf/quant-ph/0506173.pdf http://arxiv.org/pdf/quant-ph/0506173.pdf or my thesis (chapter 5) at http://jostylr.com/thesis.pdf http://jostylr.com/thesis.pdf Hopefully they are somewhat accessible to this audience.
- tehwalrus 12y ago
  I never understood why other physicists always argued so strongly against QM being the measurable outcomes from a system that was deterministic underneath. Thanks for the references, I'll see if I can understand them! One question - What aether/field do the pilot waves travel in? E? B? something else?
eevilspock 12y ago
Another example of the scientific community's natural resistance to paradigm shifts, per Thomas Khun's The Structure of Scientific Revolutions?

anigbrowl 12y ago

It's hard to think about this given that the Copenhagen school has had decades of effort lavished on it, while De Broglie's concepts seem to have had very little development. I've always been a little interested in them because I like underdogs, but have assumed as a lay person that the Copenhagen approach was correct. The oil drop experiment is certainly thought-provoking.

lmm 12y ago
The most obvious, naive extrapolation of ordinary quantum mechanics (that is, assume the experimenter is an ordinary quantum system behaving in the ordinary way) comes out as the many-worlds interpretation. There are arguments for others, but many-worlds should be your "default".
- tim333 12y ago
  The trouble with many worlds, for me at any rate, is say you have a mirror where the photons go one way 94% of the time, the other 6% of the time. How does that work? 94 worlds of one type and 6 of the other? Everett did some hand wavy, we assign a probability P to each outcome stuff but you still wonder how on earth that works physically. If the universe branches with one version of you seeing it go one way and one the other is one of you more existy or what?
  - ajuc 12y ago
    I thought there are 94 you (and universes) that seen one result and 6 that seen the other. Then there are irrational probabilities :)
  - lmm 12y ago
    The only thing that's fundamental, that's physically "real", is the wavefunction. So you have your mirror and your photon and you, and all that's described according to some wavefunction |P(t)>, evolving according to the laws of quantum mechanics. Now we observe that after the photon passes through the slit, we can decompose the function as |P(t)> = sqrt(0.94)|Q(t)> + sqrt(0.06)|R(t)> where Q and R are independent, each individually evolving according to the laws of quantum mechanics. This is already derived rather than fundamental, but the phenomenon is real, because the causality relation is real. Our neurons under Q (and of course a "neuron" isn't really fundamental, it's an interpretation of a particular group of particles behaving in a particular way, i.e. of particular aspects of the wavefunction) have no effect on our neurons in R and vice versa. All that is physically real; the only remaining question is what we should expect to subjectively experience. Since our neurons in Q have no effect on our neurons in R and vice versa, it seems like we'd experience either being in Q or being in R. With what probability? Well, whatever it is it had better be conserved; it makes no sense to say that we'd experience R with 4% probability in 5 minutes and then 8% probability in 10 minutes. If we send another photon through in Q, splitting the wavefunction further into |S(t)> + |T(t)> + |R(t)> where Q = S + T, then our subjective probabilities should be such that the probability we find ourselves in S or T = the probability that we found ourselves in Q before sending the second photon. What's the probability-like quantity that's conserved by quantum evolution of a system? Why, it's the norm, ||P>|^2. I guess that's what we'd expect to be the subjective probability then.

jessriedel 12y ago

> ...pilot wave theory--which is taught in every introductory QM course and covered in every introductory QM text... Having assisted in teaching intro QM courses, I can say this is very incorrect -- unless you replace "every" with "many" and "taught/covered" with "mentioned off hand". I just pulled the very popular "introduction to quantum mechanics" by Griffiths off my shelf. It contains nothing about pilot waves except for a single footnote in an appendix used as an example of "a number of hidden variable theories [proposed over the years]".

tjradcliffe 12y ago
OK, "every GOOD intro QM course" and "every GOOD intro QM text" :-) I shall now walk away mumbling about the degenerate state of today's youth...
- Osmium 12y ago
  Griffiths happens to be the most accessible while-still-rigorous QM book I've read, so I'd be careful with the criticism ;) it is concise though, which is probably the main reason it doesn't really discuss pilot waves.
- TTPrograms 12y ago
  A book not containing a fringe, weak theory does not make it bad.
- vanderZwan 12y ago
  Sure thing, True Scotsman ;)
cshimmin 12y ago
Agreed... I managed to finished all my courses towards a PhD in high-energy physics without ever having heard of pilot wave theory before. I'm an experimentalist but we still have to take all the same standard QM/QFT courses as the theory guys.

yummyfajitas 12y ago

As far as I'm aware, pilot wave theories designed for thermodynamics explicitly occur on the state space R^N mod SN (where SN is the appropriate group, depending on fermion or boson).

deleted 12y ago

[deleted]

trevelyan 12y ago

I can see how it works in 2D, with things bouncing into the air where there is no resistence, but how is that supposed to work in a 3D field? Wouldn't any movement push the particle up against a barrier that would force it back into the center?

mkempe 12y ago

Francis Fer, friend and colleague of de Broglie, wrote a 2-volume treatise on thermodynamics in the early 70s, with an introduction by de Broglie, so if you are interested in a treatment of the subject that would be close to his views, you may want to look it up.

jostylr 12y ago

Bohmian mechanics has a very elegant way of dealing with identical particles. I know as I am a coauthor on such papers. The idea is that instead of R^3N with its labels, we use a space with no labels on particles. The only relevant data are the locations of the particles, not some extrinsic numbering. This immediately gives us bosons. Fermions take a little more work, essentially using a vector bundle approach analogous to Mobius strips. One can then prove that in 3 dimensions and for scalar wave functions, that is all the possibilities. For 2D, you also get anyons; this is all about the topology of the natural configuration space. For spin, one has to realize that it is modeled well by wave functions that take on vectors as values. When moving to multiple particles with spin, we tensor (kind of multiply) those vectors together. But the key point is that we tensor based on the spatial location. So instead of tensoring over particle 1 and particle 2, we tensor over their positions. This gives us complicated vector bundles. It opens a lot more possibilities, but when you look at general quantum dynamics, the only stable ones in 3D are the bosons and fermions. Thus, not only can Bohmian mechanics account for it, it actually provides a very natural explanation. It is completely rooted in considering what the configuration space is. Where Bohmian mechanics shines is that what the configuration space is comes from what the theory itself is concerned with, namely particles with definite positions. And just as a side note, the standard formalism of quantum mechanics emerges in a mathematically rigorous way from Bohmian mechanics. Everything in non-relativistic quantum mechanics is completely accounted for and you get a clear foundation for extending it to other spaces and more general questions. As for relativity and quantum field theory, that is still a work in progress, but the main stumbling block is actually having a well-defined evolution of the wave function in interacting cases. If we had that, then the Bohmian additions are easily handled for the most part. Research has been done and is being done. A simple (layperson) reference for this is sadly lacking, but you can try either http://arxiv.org/pdf/quant-ph/0506173.pdf http://arxiv.org/pdf/quant-ph/0506173.pdf or my thesis (chapter 5) at http://jostylr.com/thesis.pdf http://jostylr.com/thesis.pdf Hopefully they are somewhat accessible to this audience.

tehwalrus 12y ago
I never understood why other physicists always argued so strongly against QM being the measurable outcomes from a system that was deterministic underneath. Thanks for the references, I'll see if I can understand them! One question - What aether/field do the pilot waves travel in? E? B? something else?

eevilspock 12y ago

Another example of the scientific community's natural resistance to paradigm shifts, per Thomas Khun's The Structure of Scientific Revolutions?