I listened to your podcast titled “Dialectical Materialism, Marxist Realism and Quantum Mechanics" and would like to clarify some confusion about Bohmian mechanics. The Bohmian or ontological interpretation of non-relativistic quantum mechanics is a deterministic theory. It is ontological because it states that there are particles with well-defined position and momenta in nature, it is also realistic for this reason. We can see this by considering the theory, starting with the position-representation of wavefunction in polar form

After some algebraic manipulations, we separate into real and imaginary parts to get the following set of coupled differential equations

And taking the gradient of Equation (4) to get

Figure 1 : Quantum trajectories for a free Gaussian wave packet

Figure 2 : Classical trajectories corresponding to the free Gaussian wave packet

The equations of motion were numerically solved using the Quantum Trajectory Method of Robert Wyatt. We see that the quantum potential causes the trajectories to spread through their evolution. So, I hope you have learned about Bohmian mechanics through this letter.

Kind regards,

P