Historical Debates over the Physical Reality of the Wave Function

This paper provides a detailed historical account of early debates over wave-function realism, the modern term for the view that the wave function of quantum theory is physically real. As this paper will show, the idea of physical waves associated with particles had its roots in work by Einstein and de Broglie, who both originally thought of these waves as propagating in three-dimensional physical space. De Broglie quickly turned this wave-particle duality into an early pilot-wave theory, on which a particle’s associated phase wave piloted or guided the particle along its trajectory. Schrödinger built on de Broglie’s phase-wave hypothesis to provide a comprehensive account of the nascent quantum theory. However, Schrödinger’s new undulatory mechanics came at the cost of replacing de Broglie’s phase waves propagating in physical space with a wave function propagating in a system’s abstract configuration space. The present work will argue that this move from three-dimensional physical space to a many-dimensional configuration space was a key reason why the founders of quantum theory uniformly abandoned the physical reality of the wave function. This paper will further clarify that de Broglie introduced two distinct pilot-wave theories, and will then argue that it was Bohm’s rediscovery of the second of these two pilot-wave theories over two decades later, as well as Bohm’s vociferous defense of wave-function realism, that were responsible for resurrecting the idea of an ontological wave function. This idea ended up playing a central role in Everett’s development of the many-worlds interpretation.

💡 Research Summary

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The paper offers a comprehensive historical reconstruction of the debate over wave‑function realism—the view that the quantum wave function corresponds to a physically real entity. It begins by distinguishing between the abstract quantum state (a vector in Hilbert space) and the configuration‑space wave function Ψ(q), emphasizing that the latter is the focus of the analysis.

The narrative traces the origins of the idea that particles are accompanied by real waves back to Einstein’s 1905 light‑quantum hypothesis and, more concretely, to de Broglie’s 1923‑24 phase‑wave concept. De Broglie introduced a “phase‑harmony” condition that required the associated wave to have a super‑luminal phase velocity, which he labeled fictitious but nevertheless used to guide particle trajectories. In his early work he already employed guiding‑language, suggesting that the wave’s rays correspond to possible particle paths.

Schrödinger’s 1926‑27 development of wave mechanics shifted the wave from three‑dimensional physical space to the abstract, high‑dimensional configuration space of a many‑particle system. This move, together with Born’s statistical interpretation (|Ψ|² as a probability density), led the founders of quantum theory to treat the wave function as a calculational tool rather than a material field. Schrödinger himself initially defended a realist reading but, by 1928, publicly abandoned the idea that his configuration‑space wave had ontological status.

The author then distinguishes two distinct pilot‑wave programs proposed by de Broglie. The first, the “double‑solution” theory (1927), posits two kinds of waves satisfying the same wave equation: a singular, solitonic wave identified with the particle, and a regular wave that implements Born’s statistics. The mathematical complexity of this scheme caused de Broglie to set it aside. The second program, presented in his 1930 book, employs only a single wave—Schrödinger’s configuration‑space Ψ—as a guiding field for particles moving in three‑dimensional space. Even here de Broglie regarded Ψ as an abstract, non‑ontic entity when the configuration space became many‑dimensional.

In 1951, David Bohm contacted de Broglie, learned of the second pilot‑wave model, and independently reconstructed it in 1952. Bohm’s papers introduced a precise guiding equation, incorporated decoherence to address the measurement problem, and—crucially—asserted that the wave function, despite residing in configuration space, should be taken as physically real. Bohm’s explicit defense of wave‑function realism revived the ontological status of Ψ and provided a conceptual bridge to Hugh Everett’s many‑worlds interpretation, where the universal wave function is the sole ontology.

The paper also documents the uniform opposition to wave‑function realism among the early quantum pioneers—Einstein, Born, Bohr, Heisenberg, Dirac, Pauli, and Schrödinger—who all treated the wave function as a mathematical or statistical device. This consensus, rooted in the transition to configuration‑space formalism and Born’s probability rule, explains why wave‑function realism fell out of favor for decades.

Finally, the author argues that the historical trajectory shows wave‑function realism is not a recent fashionable stance but a revival of ideas that were present, albeit suppressed, in the early 20th‑century debates. Bohm’s contributions—especially his early use of decoherence—have been under‑appreciated, yet they were pivotal in reshaping the philosophical landscape of quantum theory. The paper concludes that a renewed, historically informed discussion of wave‑function realism is essential for clarifying the relationship between abstract configuration‑space entities and physical reality in contemporary quantum foundations.