Is the wavefunction ontological or epistemological?
What is wrong with Bohmian interpretation?
Now we are almost ready to introduce a new quantum mechanics interpretation. There is one more step to take: explain what is wrong with existing quantum mechanical interpretations. We start with Bohmian mechanics.
Let me clearly state that each and every existing quantum mechanics interpretation represent valuable contributions and provided new insight in quantum mechanics. Bohmian mechanics was a core incentive for
to develop his inequalities for example. But what is Bohmian mechanics? The
core idea is simple: the particle has a definite position at any single time
and it is guided by a “quantum potential”.
Since there are no local realistic models for quantum mechanics, one can see right away that the quantum potential must violate relativity. But can quantum mechanics and relativity coexists peacefully? What if we pick Nonlocality as an axiom for quantum mechanics? Popescu and Rohrlich considered such an idea http://arxiv.org/abs/quant-ph/9508009 . While this did not result in deriving quantum mechanics, it proved a fruitful idea and it led to the introduction of a hypothetical device called a PR box (PR from Popescu and Rohrlich). If classical resources can achieve the maximum correlation given by the
limit, quantum mechanics can achieve a higher correlation limit known as the
Tsirelson bound http://en.wikipedia.org/wiki/Tsirelson's_bound.
A PR box can go over the Tsirelson bound and achieve impressive feats http://arxiv.org/abs/quant-ph/0603017
Returning to Bohmian mechanics, there are internal inconsistencies regarding reality. We already encountered in the prior posts the problem of representing spin with a classical model. The biggest problem however is the fact that Bohmian mechanics is contextual. What does this mean? By Kolmogorov’s axioms, correlations cannot exceed
limit. The only way out is to demand different statistical contexts. Suppose
one measures three variables A, B, C with A and B compatible measurements and A
and C compatible measurements, but not B and C. Contextuality means that the
random variable associated with A in the context of A-B experiment is different than the random
variable associated with A in the context of A-C experiment. So much for “objective
Another problem I like to point out is the description of the hydrogen atom in Bohmian mechanics. If the electron does have a definite position, movement around the proton would radiate energy and the atom would be unstable. The solution in Bohmian mechanics is that the electron and proton are standing still at a fixed distance one from another. The problem is not that the electron is stationary despite electrostatic attraction (after all Bohmian mechanics is known for “surreal trajectories”) but the fact that this particular distance is distinguished from all other distances. This distance is completely ad-hoc with no possible explanation except “God made it so”. Compare this with the kinds of answers we get from quantum electrodynamics and it is clear why no quantum field theory was developed for Bohmian mechanics.