I was extremely happy to be invited to pay a tribute to David Bohm in the centenary year of his birth. Visiting Pari is always a pleasure. The people are so welcoming; the food is a delight. I wish I had more time to spend here with the wonderful people of Pari.
Let me start at the beginning. I first met David in 1961 on a fine sunny spring weekend at Cumberland Lodge in Great Windsor Park. My PhD with Cyril Domb, Mike Fisher and Martin Sykes was coming to an end. I had had a lot of fun working on the Ising model and applying some of the techniques to ferromagnets and the protein folding problem, but the time had come to move on to pastures new.
The Lodge was set up by Amy Buller as an institute where students could meet to explore the moral issues of the day and ‘to provide a safe space for “unsafe” discussions and to foster learning and critical thinking.’ This was an admirable venue to invite David Bohm to—to present his ideas on the meaning of quantum theory.
The atmosphere in the physics community at that time was one of total opposition, nay open hostility, to any proposals for an ontology that might underlie quantum mechanics, particularly when the words ‘hidden variables’ were mentioned. Bohr and Einstein had battled it out in 1935 and Bohr was perceived to be the victor. ‘There is only one interpretation possible’ were the words that Peierls used in a letter responding to a paper I was trying to get published. So, in the eyes of the orthodoxy of the day, Bohm was a heretic.
But why was he a heretic? All he had done was to split the Schrödinger equation into its real and imaginary parts under polar decomposition of the wave function, a process that sixth form students are taught to do1. The form of the resulting equations suggested an interpretation that did not fit in to the orthodoxy. However, if we read Dirac’s classic Quantum Mechanics carefully we find Dirac himself starting on the road Bohm later trod, but gave up because he felt it violated the Heisenberg uncertainty principle. Bohm showed it did not violate the uncertainty principle as I shall explain as I go along.
By assuming the Born probability postulate, the first equation corresponded to the conservation of probability. The form of the second equation had a strong resemblance to the classical Hamilton-Jacobi equation, if one assumed the classical canonical relation p = ∇S held when S was the phase of the wave function. This was a relation that Dirac uses and it was used later by Feynman2 in his ‘sum-over- paths’ approach. This second equation contains a term not present in the classical Hamilton-Jacobi equation. If one assumes the equation is still an expression for the conservation of energy, the term introduces a new quality of energy only present in quantum problems—the quantum potential energy.
Although we have plenty of illustrations of how this energy accounted for all quantum behavior, very few wanted to seriously consider it as a physical entity in its own right. Its appearance was a mystery! Never mind, take it seriously and ask, ‘What role does it play in the new interpretation?’ To answer this question, consider the classic two-slit interference experiment where we see “particles” behaving like ‘waves.’ However, the solution of the second equation gives rise to an ensemble of possible trajectories the particles would take to produce the fringes. These trajectories were presented in a paper by Philippidis, Dewdney, and Hiley3 and are shown in Figure 1. The trajectories to the right of the slits do not move in straight lines showing they
Figure 1: Bohm particle trajectories for two-slit interference.
must be subject to some force. That force has its origins in the quantum potential, shown in Figure 2 and this potential provides a straightforward explanation for the behavior of the particles.