Quantum equilibrium and the origin of absolute uncertainty

Abstract

Abstract. The quantum formalism is a "measurement" formalism-a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schrödinger's equation for a system of particles when we merely insist that "particles" means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that an appearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by "ρ = |ψ| 2 ." A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.KEY WORDS: Quantum randomness; quantum uncertainty; hidden variables; effective wave function; collapse of the wave function; the measurement problem; Bohm's causal interpretation of quantum theory; pilot wave; foundations of quantum mechanics.

Active Information and Teleportation

“…It should be noted that the views expressed in our book differ very substantially from those of Dürr et al [14] who have developed an alternative theory. It was very unfortunately that they chose the term Bohmian mechanics' to describe their work.…”

“…We then find that this new energy, just like the energy of the gravitational field, is non-local. Contrary to the claims of Dürr et al [14], we are unable to give our approach a consistent mechanical interpretation. Rather we find it necessary to introduce the new notions of active and passive information [6] and [4].…”

“…It should, perhaps, be called 'quantum nonmechanics'" [15]. It would have been far better if Dürr et al [14] had chosen the term 'Bell mechanics'. That would have reflected the actual situation far more accurately.…”

Instability of quantum equilibrium in Bohm's dynamics

“…It might be asserted that the extended quantum equilibrium state (2.1) is 'absolute', in the sense of defining a preferred measure of 'typicality' for the initial conditions of the universe. An analogous claim has been made by some workers for the standard quantum equilibrium state (1.3) in the context of de Broglie's dynamics [25]. This last approach has been criticized on grounds of circularity [9,10].…”

Confusion about Bohm

“…It is also important to clarify that I use the term "Bohmian mechanics," as is now commonly done, to refer to the theory developed by Dtirr, Goldstein, et al, in the past 15-20 years as reflected by my reference to [2,5] rather than to Bohm's original papers. This theory is based on Bohm's work and can, I feel, be regarded as part of his scientific legacy; but it is not identical to his original formulation in every detail.1 Thus, nothing I said was a "comment on David Bohm's quantum mechanics" per se.…”