Contours of a New Theory
I began my search for a new theory as a student of physics and philosophy at UC Berkeley in the 1960s. My undergraduate mentor, the iconoclastic philosopher Paul Feyerabend, introduced me to the long-standing, unresolved debates about quantum foundations.2 Under Feyerabend’s supervision, I wrote my senior thesis on the Copenhagen interpretation and its discontents. The paper was heavily influenced by David Bohm’s understanding of quantum mechanics as an approximation to a deeper theory, analogous to the way the macro laws of thermodynamics approximate the collective behavior of gaseous molecules.3 In graduate school, I shut-up-and-calculated by day and mused about alternative quantum formulations by night.
I tell the tale of my fateful encounter with the charismatic Paul Feyerabend at https://paulraskin.info/encounters/luminaries/#paul-feyerabend
Three design considerations guided this exploration: realism, stochasticity, and testability. First, I sought a theory compatible with philosophical realism, the idea that physics should describe an objective world. Second, to describe quantum phenomena, the theory should be probabilistic as a statistical approximation to underlying processes. Third, the theory should be testable. New interpretations that replicated Schrödinger’s equation but made no additional predictions were vulnerable to the criticism that they were operationally meaningless. The burden of proof falls on the challengers to the entrenched paradigm.
The first criterion—philosophical realism—suggested classical physics, the epitome of objective science, as a point of departure. Of course, Newtonian physics is unable to account for the discrete transitions at atomic scales and must be superseded. But if the classical picture could be modified in a straightforward, intuitive manner, Copenhagen’s radical rejection of realism would not have been necessary. The path taken by modern physics was contingent, at least in part, on the idiosyncratic propensities of influential personalities, while other paths remained unexplored.
The second criterion—the new theory should make probabilistic predictions—drew my attention to Brownian motion. In classical Brownian motion, a particle placed in a medium undergoes small, random fluctuations caused by collisions with molecules in the surrounding fluid or gas comprising the medium. Such “stochastic” motion is described statistically, for example, by a probability function that gives the likelihood of finding the particle at a specific location.
In SET, a simple modification of classical physics generates quantum theory and then some. The stochastic electron model has two components: classical motion plus Brownian motion due to an unknown source (Figure 1). The combined particle-medium system moves through space like a flying jumping bean. The particle moves stochastically relative to the medium, which is the source of the fluctuations, while acted upon by external classical forces.
I published an early version of the theory “Short-time Stochastic Electron,” Foundations of Physics 8 (1977): 31–44.
The third criterion—testability—plays a critical role in SET. Explaining how requires a brief review of classical descriptions of Brownian motion. In 1905, Einstein wrote a pathbreaking paper (one of several in his annus mirabilis) on Brownian motion, in which he computed the probability distribution of finding the particle at a given location (actually, he computed the “mean squared displacement,” or square of the distance traveled). Einstein’s derivation approximated the Brownian motion as a sequence of discrete, independent jumps (“Markov process”).
Later, Ornstein and Uhlenbeck introduced a more precise description of Brownian motion in which the particle moves along a continuous, differentiable path. Notably, the predictions of Ornstein-Uhlenbeck and Einstein differ by transient terms only. That is, the difference between the two solutions vanishes after sufficient time passes, specifically for times much greater than a characteristic “relaxation time” associated with the medium.
Consequently, in SET the fluctuating component of motion (position vector in Figure 1) relies on the Ornstein-Uhlenbeck description. Figure 2 illustrates the relationships among the theories. In analogy to classical Brownian motion, as transient terms die out, SET converges to Schrödinger’s equation. In this way, the theory reproduces quantum mechanics predictions while raising the possibility of detecting short-time deviations. Mathematical demonstrations of these claims are presented in the next section.
