De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial? (0811.0810v2)

Abstract: We reply to claims (by Deutsch, Zeh, Brown and Wallace) that the pilot-wave theory of de Broglie and Bohm is really a many-worlds theory with a superfluous configuration appended to one of the worlds. Assuming that pilot-wave theory does contain an ontological pilot wave (a complex-valued field in configuration space), we show that such claims arise from not interpreting pilot-wave theory on its own terms. Specifically, the theory has its own ('subquantum') theory of measurement, and in general describes a 'nonequilibrium' state that violates the Born rule. Furthermore, in realistic models of the classical limit, one does not obtain localised pieces of an ontological pilot wave following alternative macroscopic trajectories: from a de Broglie-Bohm viewpoint, alternative trajectories are merely mathematical and not ontological. Thus, from the perspective of pilot-wave theory itself, many worlds are an illusion. It is further argued that, even leaving pilot-wave theory aside, the theory of many worlds is rooted in the intrinsically unlikely assumption that quantum measurements should be modelled on classical measurements, and is therefore unlikely to be true.

• The paper systematically defends pilot-wave theory’s distinct ontology by refuting claims that it is merely a version of many-worlds.
• It critiques the misapplication of classical measurement analogies and emphasizes the unique role of configuration space in guiding particle trajectories.
• The paper highlights how quantum nonequilibrium states may reveal new physics beyond standard quantum mechanics.

De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial?

The paper by Antony Valentini critically assesses claims by some physicists that the de Broglie-Bohm pilot-wave theory is not a distinct interpretation of quantum mechanics but rather a incomplete version of the Everettian many-worlds theory. These assertions, put forth by Deutsch, Zeh, Brown, and Wallace, argue that the pilot-wave theory contains unnecessary complexity by introducing a physically real trajectory for particles that could be inferred efficiently through many-worlds theory. Valentini's paper systematically dissects these arguments and provides a detailed defense of the ontological independence of pilot-wave theory.

The pilot-wave theory, first proposed by de Broglie in 1927 and later reformulated by Bohm in 1952, suggests a deterministic formulation of quantum mechanics where particles have definite trajectories guided by a pilot wave. The theory posits that this pilot wave is a physically real entity in configuration space, driving the system's dynamics. A principal critique from the many-worlds perspective is that the pilot-wave interpretation implicitly assumes the existence of many universes, rendering the "real trajectory" superfluous. Valentini refutes this by demonstrating that these critiques arise from failing to understand pilot-wave theory within its own framework without incorporating assumptions from competing interpretations such as many-worlds.

Valentini argues that the apparent branching of universes in pilot-wave theory stems from a misunderstanding of its core dynamics and ontology. This misunderstanding is often fueled by inappropriate analogies to classical measurements, which, while rooted in obsolete classical physics assumptions, fail to apply to quantum phenomena. The author emphasizes that unlike classical fields, which exist in a 3-dimensional space, the pilot wave exists in configuration space, which does not directly translate to simultaneously existing multiple real-world states, as many-worlds theorists claim.

One of the haLLMark distinctions Valentini makes is between mathematical formalism and ontological claims. While many-worlds proponents interpret the mathematical structure of quantum mechanics as indicative of multiple simultaneous realities, pilot-wave theory distinguishes between the mathematical representation of potential trajectories and the one trajectory that is ontologically realized in our physical reality.

A critical aspect of Valentini's rebuttal is the role of quantum equilibrium and nonequilibrium states in pilot-wave theory. It highlights that pilot-wave theory, when understood on its own terms, suggests a broader physical framework where standard quantum mechanics is a special equilibrium state within a larger nonequilibrium domain. The theory of subquantum measurements introduced by pilot-wave theory proposes that nonequilibrium states could potentially reveal physics completely unknown to traditional quantum mechanics, providing new avenues for both theoretical investigation and empirical verification.

In examining the claims against pilot-wave theory, Valentini also posits a counterargument — the criticisms claiming that de Broglie-Bohm theory is a covert form of many worlds arise from an intrinsic misapplication of classical measurement logic to quantum processes. This misapplication leads to unnecessary postulates about the coexistence of multiple states or "worlds," whereas a correctly theoretical analysis should prioritize the singular, consistently observable reality described by the de Broglie-Bohm trajectories.

Thus, Valentini asserts that the de Broglie-Bohm theory is distinct and independent of the many-worlds interpretation. He argues for the legitimacy of considering pilot-wave theory as a superior paradigm in which quantum processes are deterministic and guided by ontological waves, differentiating it from probabilistic and non-deterministic interpretations presented in alternative quantum theories.

In conclusion, Valentini’s paper defends de Broglie-Bohm theory from mischaracterization by many-worlds proponents and asserts the necessity of evaluating quantum theories on their respective terms. Through a careful explication of both physical theory and theoretical implications, Valentini reinforces that pilot-wave theory remains a robust and substantial interpretation within the quantum domain, offering potential advancements for our understanding of subquantum phenomena.