Universal wave function, 17.2

Relativity

Pilot wave theory is explicitly nonlocal. As a consequence, most relativistic variants of pilot wave theory need a foliation of space-time. While this is in conflict with the standard interpretation of relativity, the preferred foliation, if unobservable, does not lead to any empirical conflicts with relativity.

The relation between nonlocality and preferred foliation can be better understood as follows. In de Broglie–Bohm theory, nonlocality manifests as the fact that the velocity and acceleration of one particle depends on the instantaneous positions of all other particles. On the other hand, in the theory of relativity the concept of instantaneousness does not have an invariant meaning. Thus, to define particle trajectories, one needs an additional rule that defines which space-time points should be considered instantaneous. The simplest way to achieve this is to introduce a preferred foliation of space-time by hand, such that each hypersurface of the foliation defines a hypersurface of equal time.

However, this way (which explicitly breaks the relativistic covariance) is not the only way. It is also possible that a rule which defines instantaneousness is contingent, by emerging dynamically from relativistic covariant laws combined with particular initial conditions. In this way, the need for a preferred foliation can be avoided and relativistic covariance can be saved.

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There has been work in developing relativistic versions of de Broglie–Bohm theory.

— Wikipedia on De Broglie–Bohm theory

2012.04.18 Wednesday ACHK