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.
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.
Bohmian mechanics is the new mechanics for point particles. In the equations for Bohmian mechanics there are parameters m 1 ,... ,m N which we shall call masses. We do so because in certain physical situations the particles will move along Newtonian trajectories and then these masses are Newtonian masses, and there is no point in inventing new names here. Although the theory is not at all Newtonian, it is nevertheless close in spirit to the Hamilton-Jacobi theory and an implementation of Born's guiding idea. The theory is in fact the minimal non-trivial Galilean theory of particles which move. We already gave the defining ingredients in the last chapter. Now we shall spell things out in detail.An N-particle system with "masses" m 1 ,... ,m N is described by the positions of its N particles Q 1 ,... ,Q N , Q i ∈ R 3 . The mathematical formulation of the law of motion is on configuration space R 3N , which is the set of configurations Q = (Q 1 ,... ,Q N ) of the positions. The particles are guided by a function
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