Bohmian - The Theory - The Ontology

The Ontology

The ontology of de Broglie-Bohm theory consists of a configuration of the universe and a pilot wave . The configuration space can be chosen differently, as in classical mechanics and standard quantum mechanics.

Thus, the ontology of pilot wave theory contains as the trajectory we know from classical mechanics, as the wave function of quantum theory. So, at every moment of time there exists not only a wave function, but also a well-defined configuration of the whole universe. The correspondence to our experiences is made by the identification of the configuration of our brain with some part of the configuration of the whole universe, as in classical mechanics.

While the ontology of classical mechanics is part of the ontology of de Broglie–Bohm theory, the dynamics are very different. In classical mechanics, the accelerations of the particles are given by forces. In de Broglie–Bohm theory, the velocities of the particles are given by the wavefunction.

The wavefunction itself, and not the particles, determines the dynamical evolution of the system: the particles do not act back onto the wave function. As Bohm and Hiley worded it, "the Schrodinger equation for the quantum field does not have sources, nor does it have any other way by which the field could be directly affected by the condition of the particles the quantum theory can be understood completely in terms of the assumption that the quantum field has no sources or other forms of dependence on the particles". P. Holland considers this lack of reciprocal action of particles and wave function to be one "mong the many nonclassical properties exhibited by this theory". It should be noted however that Holland has later called this a merely apparent lack of back reaction, due to the incompleteness of the description.

In what follows below, we will give the setup for one particle moving in followed by the setup for particles moving in 3 dimensions. In the first instance, configuration space and real space are the same while in the second, real space is still, but configuration space becomes . While the particle positions themselves are in real space, the velocity field and wavefunction are on configuration space which is how particles are entangled with each other in this theory.

Extensions to this theory include spin and more complicated configuration spaces.

We use variations of for particle positions while represents the complex-valued wavefunction on configuration space.

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