[Paper Review] A causal and continuous interpretation of the quantum theory: About an original manuscript by David Bohm sent to Louis de Broglie in 1951

Aurélien Drezet, Benjamin Stock|arXiv (Cornell University)|Feb 28, 2021

Philosophy and History of Science10 references4 citations

TL;DR

This paper reproduces and analyzes David Bohm's 1951 unpublished manuscript proposing a causal, continuous interpretation of quantum mechanics based on pilot-wave theory, where particles follow definite trajectories guided by a quantum potential. The work demonstrates that this model reproduces all standard quantum predictions while restoring determinism and continuity, offering a foundational alternative to the Copenhagen interpretation and foreshadowing Bohm's later concepts of active information and the implicate order.

ABSTRACT

The aim of this article is reproduce and analyze an original article of David Bohm sent to Louis de Broglie in 1951. This article is the older document of David Bohm about his well known hidden variable theory based on the pilot wave interpretation of Louis de Broglie. We analyse the chronology and the history of this fascinating document.

Motivation & Objective

• To recover and analyze David Bohm's original 1951 manuscript on a causal and continuous interpretation of quantum theory, previously unpublished and overlooked.
• To clarify the historical chronology of Bohm's development of the pilot-wave theory, particularly its evolution from this 1951 draft to his 1952 publications.
• To demonstrate that the 1951 manuscript already contains the core ideas of Bohmian mechanics, including the quantum potential and guidance equation, in a form that predates and anticipates his later work.
• To highlight the significance of this manuscript as a foundational step toward Bohm’s later ontological frameworks, such as the implicate order and active information.
• To contextualize Bohm’s approach within the broader philosophical and physical debates of the time, especially in response to criticisms from Pauli, Einstein, and others regarding determinism in quantum theory.

Proposed method

• Reproduction and critical analysis of the undated 1951 manuscript 'A Causal and Continuous Interpretation of the Quantum Theory' (ACCIQT) from the Louis de Broglie archives at the French Academy of Sciences.
• Use of the standard pilot-wave formalism: particles with definite trajectories guided by a complex wave function Ψ satisfying Schrödinger’s equation.
• Derivation of the quantum potential U = −(ℏ²/2m)(∇²|Ψ|)/|Ψ|, which governs particle dynamics via the equation of motion m d²x/dt² = −∇(U + V), where V is the classical potential.
• Application of the guidance condition p = ∇S, where Ψ = R e^{iS/ℏ}, ensuring consistency of momentum with the phase of the wave function.
• Analysis of the statistical ensemble assumption P = |Ψ|², showing its dynamical stability under the equations of motion, analogous to classical statistical mechanics.
• Comparison of the 1951 manuscript with Bohm’s 1952 Physical Review papers and his later works (e.g., The Undivided Universe) to trace conceptual evolution and continuity.

Experimental results

Research questions

• RQ1 What were the core physical and conceptual ideas in Bohm’s 1951 manuscript on a causal quantum theory, and how do they compare to his later published work?
• RQ2 Why was this 1951 manuscript never published, and what was its intended submission venue, given historical evidence of a rejected submission to Nature?
• RQ3 How does the 1951 manuscript anticipate Bohm’s later ontological concepts such as active information and the implicate order?
• RQ4 To what extent did the manuscript already contain the essential elements of Bohmian mechanics, including the quantum potential and guidance condition?
• RQ5 What does the existence of this manuscript reveal about Bohm’s philosophical stance toward determinism and the nature of quantum reality in the early 1950s?

Key findings

• The 1951 manuscript 'A Causal and Continuous Interpretation of the Quantum Theory' is a foundational, previously unpublished precursor to Bohm’s 1952 pilot-wave theory, containing the core equations of motion and the quantum potential.
• The manuscript establishes that particle trajectories are deterministic and continuous, guided by the wave function via the quantum potential U = −(ℏ²/2m)(∇²|Ψ|)/|Ψ|, which reproduces all standard quantum effects.
• The guidance condition p = ∇S ensures consistency of momentum with the phase of the wave function, and the probability density P = |Ψ|² is preserved over time due to the dynamics.
• The statistical ensemble assumption arises naturally from the chaotic, diffusive nature of particle motion under the quantum potential, mirroring classical statistical mechanics.
• The manuscript demonstrates that a causal, continuous, and deterministic interpretation of quantum mechanics is not only logically consistent but also empirically viable, countering the Copenhagen interpretation’s claim of incompatibility.
• The manuscript predates and anticipates Bohm’s later ontological developments, such as active information and the implicate order, suggesting a deep continuity in his foundational thinking from 1951 onward.