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In Bohmian Mechanics, it assumes a universal wave field in which particle's motion can be calculated using Newton's law of motion:

\begin{equation} m\frac{d^{2}x}{dt^{2}} = - \nabla(V+U) \end{equation}

where $V$ is the classical potential and $U$ is the 'quantum potential'.

In this way, Bohm showed that his theory can recover all the prediction made by the Copenhagen interpretation. However, I feel a bit confused about his explanation to the EPR paradox. We know from Bell's inequality that the value of observable does not take a definite value prior to the measurement and an instantaneous interaction exists between two particles. In Bohm's view, particle behaves in a deterministic way. So I feel in Bohm's theory the particle should be in a certain state before measurement which shouldn't be right according to Bell's inequality. If so, in its explanation of the EPR paradox (Bohm 1952), where does the superposition of states come from?

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  • $\begingroup$ "the quantum potential can develop unstable bifurcation points, which separate classes of particle trajectories according to the "channels" into which they eventually enter and within which they stay. This explains how measurement is possible without "collapse" of the wave function, and how all sorts of quantum processes, such as transitions between states, fusion of two states into one and fission of one system into two, are able to take place without the need for a human observer." Bohm et al '87. $\endgroup$
    – Cosmas Zachos
    Commented Feb 16, 2020 at 19:13
  • $\begingroup$ I think in Bohm's derivation of quantum measurement. He expanded the wave function as a superposition of its eigenstates and showed that the 'apparatus coordinate' will finally enter one of 'channels' you said. But as a deterministic theory, how can the wave function be expanded as a superposition of eigenstates at the first place instead of being already in a certain eigenstate? $\endgroup$
    – Winniebear
    Commented Feb 16, 2020 at 20:55
  • $\begingroup$ How do you get interference? Have you accepted his double slit picture? $\endgroup$
    – Cosmas Zachos
    Commented Feb 16, 2020 at 20:59

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