Which QM interpretation (Bohm, Copenhagen, MWI) best supports the resolution of Hardy's Paradox?
They all do.
To answer which is the "best" is highly subjective. (For me, Bohm is the best.)
But I thought Bohm's model is based on particles having definite locations and maintaining existence whether observed or not, yet recent experiments seem to indicate that although one can make statements about past events when not observed, the particle does not actually exist in the traditional sense. Can you explain what is meant by this?
That is true.
Can you specify what experiments do you have in mind?
The recent 09' study by Lundeen and Steinberg. It seems to me that if particle positions and objective reality are true, then the two particles would have destroyed each other whether observed or not.
This is a good point. Demystifier (among others) believes that the Bohmian formalism leads to equivalence with the orthodox interpretation of QM. However, I wonder if this is like having your cake and eating it too. The benefit of Bohmian theories is that they retain realism, thus dispensing with the perceived fuzzy characteristics of QM (i.e. the measurement problem/collapse).
And yet Hardy's paradox is intended to weed out realistic interpretations, even non-local ones. And there are others as well (such as Leggett, GHZ, entanglement of particles that have never interacted, etc.) I personally do not understand how a realistic interpretation survives experiments like Lundeen and Steinberg (although Demystifier makes a good case and his ideas are worth listening to).
In his paper Phys. Rev. Lett. 68, 2981 (1992), Hardy states rather clearly that, in his opinion, reality is not compatible with locality and Lorentz invariance. As I can see, he never states that even non-local realistic interpretations are ruled out.
There is another more recent paper (discussed several times on this forum) by Zeilinger and others that a wide class of non-local realistic theories are ruled out, but even THEY explicitly say in their paper that the Bohmian theory is not ruled out.
It is in fact trivial to qualitatively explain how nonlocal realistic theories may be compatible with the results of Hardy, GHZ and others. Simply, by changing the type of measurement one performs, hidden variables send information to each other that the experiment setting has been changed and that consequently the hidden variables have to change (instantaneously) their objective properties. It may look as a conspiracy, but the Bohmian interpretation explains that "conspiracy" in a remarkably simple way.
Anyway, I don't know about the Lundeen and Steinberg experiment, so can someone give me a link/reference?
Experimental Joint Weak Measurement on a Photon Pair as a Probe of Hardy's Paradox by J. S. Lundeen and A. M. Steinberg (Phys. Rev. Lett. 102, 020404 (2009))
First, let me thank to Cthugha who gave me the reference to the paper of Lundeen and Steinberg, so that I can make the explanation that follows.
The crucial fact about this experiment is that it is based on WEAK measurements. Namely, it is known that a value obtained by a weak measurement does not need to coincide with the value predicted by Bohmian mechanics. However, as even the theorists who discovered the concept of weak measurement explicitly say in some of their papers, it does not mean that Bohmian mechanics is not consistent. Namely, in a sense, a weak measurement is not a true measurement. Instead, it is an indirect conclusion about the value of some variable that has not been "really" (i.e., strongly) measured. Such an indirect conclusion about that value can be considered "natural" or "naive", depending on the view. From the Bohmian point of view, it is naive. An example of a weak measurement is to "measure" the PATH of the particle (along one of the paths allowed by a beam splitter) by actually (i.e., strongly) measuring the FINAL POSITION of the particle in one of the detectors at the end of the path. The path "measured" this way does not need to coincide with the path predicted by Bohmian mechanics.
Anyway, if we take weak measurements seriously, then it can also be viewed as a good news for Bohmian mechanics. Namely, weak measurements allow to perform a simultaneous measurement of position and velocity of a particle. It turns out that such a measurement gives the same values as those predicted by Bohmian mechanics:
http://arxiv.org/abs/0706.2522 [New J. Phys. 9 165 (2007)]
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