What's the current status of Bohm's hidden variable theory? Does it stand up in light of the Bell test (I was under the impression that the Bell results suggest an arbitrary number of hidden variables would be necessary)?
> What's the current status of Bohm's hidden variable theory? Does it stand up in light of the Bell test
In "normal" quantum mechanics we have the wave-particle dualism. A particle behaves also like a wave, whatever that means.
In Bohm's hidden variable theory, also known as "pilot wave theory" the wave and the particles are separate. The pilot wave is a wave of unknown making (the theory does not say what it would be made of), and this wave follows the normal quantum mechanical behaviour. Then particles "ride" on this wave. So all the quantum mechanical wave effects happen in the pilot wave, and then the classical particle-like particles just follow theirs paths, already laid out by the wave.
Although "spooky action at a distance" is also experimentally verified, explaining this by postulating a wave that fills the whole universe, and explicitly reacts spookily over distances, makes the whole "spooky action at a distance" uncomfortable explicit in this theory, so it doesn't appeal to most physicists.
"The de Broglie–Bohm theory makes the same (empirically correct) predictions for the Bell test experiments as ordinary quantum mechanics. It is able to do this because it is manifestly nonlocal."
What's the current status of Bohm's hidden variable theory? Does it stand up in light of the Bell test?
Yes. Bell's theorem doesn't forbid hidden variable theories (in fact, he has a publication preceding his famous result explicitly demonstrating a hidden variable theory that could reproduce QM measurements on a two-level system), just local hidden variable theories. In his collected papers, Bell often remarks that he feels Bohm's interpretation should be more widely studied.
It's a good question why it's not. My understanding, though I'm not well versed in the subject, is that there are some pretty severe shortcomings to it, particularly when you start considering systems with many particles. I've read some of Bohm's writings to try to understand it and as far as I got I found it pretty underwhelming; it seemed more like a bookkeeping trick than any sort of real insight.
Try reading some of the stuff from http://www.bohmian-mechanics.net/ I was a student of Sheldon Goldstein of that group and can attest that it has no problems with many particles.
In fact, part of my thesis was explaining how identical particles are handled in Bohmian mechanics. Basically, one considers a configuration space whose points are sets of points in physical space rather than some arbitrarily ordered points. One then immediately gets bosons and there is a principle which guides one to fermions. This works beautifully with spin as well, where the spin is associated with the physical point in space, not with the particle label as is usually done. I find it to be very elegant.
There is also an extension to quantum field theory in which the particle creation and annihilation operators actually represent those events with the Bohm particles. So that is not a problem either. It becomes an indeterministic theory at that point (creation is a random event while annihilation is simply when the particles collide).
The main conceptual question is dealing with instantaneousness of the theory. It is a merit of BM that it brings this to the forefront. One can always put in an arbitrary (hidden) foliation of space-time to deal with it, but it is a bit distasteful even if, as there are, foliations that can be derived the other existing structures.
One final note is that Bell was a very strong proponent of Bohmian mechanics even when Bohm had forgotten about it for a time. Bell's formulation was based on the first order probability flow and not the quantum potential. Bell's version works for spin while the quantum potential does not (sadly for numerical work).
I don't know and don't keep track. I lost interest after realizing that it can be made compatible with any possible observation.
I'm personally a fan of the Everett interpretation. Also called the many worlds. Which is what you get if you assume that quantum mechanics applies to the observer. Then the act of observation throws the observer into a superposition of possible states where different things were observed. And those states cannot meaningfully interact later for thermodynamic reasons.
Unless someone comes up with good reason to believe that quantum mechanics does not describe humans, I see no reason not to accept it. And if quantum mechanics is replaced by something different, to the extent that quantum mechanics is an accurate description of us, that interpretation remains correct.
There's a problem with with many-worlds that I haven't seen convincingly refuted: when collapsing superposition of two states you might need to (or rather almost always) need the ratio of worlds with outcome A to worlds with outcome B to be irrational. So unless you create a continuum of new worlds each time it won't work.
The wavefunction is a superposition of n independent wavefunctions at different amplitudes, like you can divide a piano's sound into a bunch of pure sine waves. "From the inside" each feels like a self-contained world (in a physically rigorous sense), but the ratio between their amplitudes and phases can be an arbitrary complex number - just as even if you're only playing a C and a G, the ratio of their amplitudes can be anything.
Why is this a problem? This complaint looks to me much like someone complaining about the Pythagorean theorem because it results in irrational numbers. (And yes, historically there were such complaints. And no, that is not a good reason to discard that theorem.)
A system described by physics evolves according to the laws of physics. We find the result surprising. But that is because we have bad intuition, not because physics is fundamentally broken.
> when collapsing superposition of two states you might need to (or rather almost always) need the ratio of worlds with outcome A to worlds with outcome B to be irrational. So unless you create a continuum of new worlds each time it won't work.
Has this been shown? I would want any such proof inspected for hidden continuum assumptions existing in the probability calculations, thus leading to irrational probabilities.
Try reading http://arxiv.org/pdf/0903.2211.pdf This basically presents many worlds as a mass density obtained by integrating out the wave function. The worlds we see can be traced through the evolution, like two videos overlain on each other can be deduced over time.
The Everett Interpretation is best thought of as the idea that collapse just doesn't happen. Which means that there aren't discrete integer worlds but only higher and lower amplitudes. If you had discrete worlds that would also be a problem because you could change how many worlds you had by how you did the math.
>good reason to believe that quantum mechanics does not describe humans
One simple idea is that the more energy and matter you shove into the wave function, the easier it is to collapse, so that at the macro level quantum effects are rendered impossible.
The problem is that there is absolutely no experimental or theoretical reason to believe that quantum states ever collapse. And there is an explanation for why we would perceive collapse even if there is none.
If you take those ideas seriously, you're forced into the Everett interpretation.
But the "explanation" assumes what it sets out to prove.
If there is no reason to believe in collapse, there is no reason to believe that we can only be conscious of our state of entanglement with one component of a wavefunction rather than both.
That is, the Everret interpretation assumes that for some unknown reason we can only be conscious of the classical world, and uses this assumption to "explain" that we are conscious only of the classical world.
Consider a polarizing beam splitter with detectors in either arm. We are only ever conscious of a photon being detected in one arm or the other. But why not both, since the matter of our brain is necessarily entangled with both components of the photon wavefunction?
All Many Worlds does is push the central mystery around, from "Why do photons prepared in the same initial state collapse into different final states?" to "Why aren't we conscious of being entangled with both photon polarization states rather than just one?" It won't do to simply say, "Well, consciousness doesn't work that way." We know it doesn't. The question is, given the otherwise completely continuous physics describing the world, why is the physics of the brain such that it can't generate consciousness of that world?
Decoherence and similar approaches have the same problem, because they assume that for some reason the brain is unable to detect the quantum world without the aid of such classical phenomena as interference patterns in photon detection, but there is simply no warrant for that assumption.
If you restrict your description of the universe to non-collapsing QM you would never guess at the existence of the classical world. Ergo, a brain fully-described by non-collapsing QM is a quantum brain, and there is no particular reason why it shouldn't be in all states at once. That is it not in all states at once is manifestly true, but the question is "Why not?" It won't do to simply assume it, as all these alternative interpretations of QM do.
Getting the brain to be aware of only a single classical world is exactly the same problem as getting a wavefunction to collapse. It has just moved the problem around, not solved it.
If there is no reason to believe in collapse, there is no reason to believe that we can only be conscious of our state of entanglement with one component of a wavefunction rather than both.
Absolutely true. The process of cognition is addressed by science. Consciousness, not so much.
That is, the Everret interpretation assumes that for some unknown reason we can only be conscious of the classical world, and uses this assumption to "explain" that we are conscious only of the classical world.
No such assumption is made. In fact you are the one adding an implicit assumption that consciousness obeys classical rules, when we have no data suggesting that such is the case.
Consider a polarizing beam splitter with detectors in either arm. We are only ever conscious of a photon being detected in one arm or the other. But why not both, since the matter of our brain is necessarily entangled with both components of the photon wavefunction?
This is a non-issue if consciousness can exist in non-interacting superpositions? Indeed there is indirect evidence that this is the case.
While science is currently unable to explain the phenomena of consciousness, we are able to say a lot about the process of cognition. And to date nobody has ever demonstrated that we can be conscious of something we did not learn about through physically understood processes. (If you have such a demonstration, there is a million dollar prize waiting for you, courtesy of James Randi.)
Quantum mechanics predicts that entanglement will cause that physical system to separate into a superposition of non-interacting states. And therefore all evidence is that there is no way for your consciousness of one state to affect cognition and therefore any awareness of any other.
Most of this is me thinking out loud. Feel free to ignore it.
With regard to consciousness, I meant only that we are only conscious of the classical universe. This is not an assumption but a statement of fact. It is why QM seems weird to us, because we are only aware of quantum effects via inference from statistical distributions, not a conscious awareness of the wavefunction in the way we are we are conscious of rocks.
I'm not concerned with nor do I need to make any claim about the mechanisms of consciousness, but only rely on the factual and uncontroversial observation that "We are consciously aware of only the classical world". There is a case to be made that this defines the classical world.
> Quantum mechanics predicts that entanglement will cause that physical system to separate into a superposition of non-interacting states.
This is actually a vastly more coherent way (as it were) of putting the argument than it is usually stated. I don't find it immediately convincing for a variety of reasons, but it is at least a testable claim. I'm particularly concerned about the role of weak measurements in breaking the "non-interacting" aspect, and the potential for delayed-choice measurements. But even without those there is trouble.
There are also the usual conservation concerns: how is it that both states end up with all the mass, energy, charge and other quantum numbers we normally consider to be conserved? That is, what is the ontology of these non-interacting states?
Consider an ion and a photon that interact such that they are entangled. The ion has a net charge as well as a mass and angular momentum. For fun, let's say that the photon starts out unpolarized, as does the ion, which is in a magnetic field. The ion has spin 1/2 and the interaction is such that the photon goes from right to left circularly polarized and the atom goes from Jz = -1/2 -> 1/2, or vice versa. So we end up with states that look like |L 1/2> and |R -1/2>.
The claim is that no future evolution of the system will allow these states to ever interact with each other. But we know this is not the case. We could easily pass the photon through a beam-splitter and 1/4-wave plates to interfere with each other. We can do anything we like to the ion--pass it through a dipole, accelerate it, whatever, and it will not change this. So long as we don't "measure" it (whatever that is) it will be possible to get the components of the photon wavefunction to detectably interact. But it won't do to talk about "measurement" in such a context, because that's what we're trying to avoid.
The question is: what is the condition such that the components of the individual particle wavefunctions may never be brought back together to show an interference pattern again? "Thermalization" (entanglement with a heat bath) is the usual claim, but I'm unconvinced that this is not simply hiding the quantum mystery behind a thermodynamic one (and the thermodynamic mystery would require a proof of something like Boltzmann's H-theorem to actually work.)
Nor does this answer the real question, which is: why is it that we are aware of all this only via inference from interference patterns? The quantum state formalism captures that fact, but does not explain it (Note to self: I need to formulate more clearly what I would consider an "explanation" in this regard.)
Ah, but macro-level systems can amplify quantum effects. For instance, the human eye -- under the right conditions -- is sensitive to individual photons.
A packet of energy absorbed and exciting a molecule in my eye, causing a cascade through a complex system still feels entirely classical. I'm not sure merely invoking "photon" is enough to imply quantum effects. It's when the behavior breaks from deterministic to probabilistic (independent of initial conditions) that we switch paradigms.
In "normal" quantum mechanics we have the wave-particle dualism. A particle behaves also like a wave, whatever that means.
In Bohm's hidden variable theory, also known as "pilot wave theory" the wave and the particles are separate. The pilot wave is a wave of unknown making (the theory does not say what it would be made of), and this wave follows the normal quantum mechanical behaviour. Then particles "ride" on this wave. So all the quantum mechanical wave effects happen in the pilot wave, and then the classical particle-like particles just follow theirs paths, already laid out by the wave.
Although "spooky action at a distance" is also experimentally verified, explaining this by postulating a wave that fills the whole universe, and explicitly reacts spookily over distances, makes the whole "spooky action at a distance" uncomfortable explicit in this theory, so it doesn't appeal to most physicists.
"The de Broglie–Bohm theory makes the same (empirically correct) predictions for the Bell test experiments as ordinary quantum mechanics. It is able to do this because it is manifestly nonlocal."
http://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory#...