Lost Schrödinger manuscript reveals his true view of quantum randomness

A Forgotten Manuscript Sheds Light on Schrödinger’s View of Quantum Randomness

Erwin Schrödinger is best known for the wave equation that bears his name and for the famous thought experiment that illustrates quantum superposition. Less widely recognized is his participation in the early 20th‑century debate over whether the probabilistic nature of quantum mechanics reflects genuine indeterminism or merely hidden variables that are inaccessible to measurement. A recently uncovered, three‑page handwritten manuscript—now transcribed and analyzed by physicist Flavio Del Santo—reveals that Schrödinger briefly constructed his own hidden‑variable model, not as a declaration of belief in a deterministic universe, but as a proof‑of‑principle that such models could not be ruled out outright.

---

The Historical Context: From Classical Certainty to Quantum Uncertainty

In classical physics, apparent randomness—such as the outcome of a coin toss—arises from incomplete knowledge of initial conditions. Early quantum pioneers wondered whether a similar “hidden‑variable” explanation might underlie the statistical predictions of quantum mechanics. The debate intensified after John von Neumann’s 1932 theorem, which many interpreted as a definitive proof against hidden variables, and later resurfaced with arguments from figures like Edmund Taylor Whittaker (1943) and Satyendra Nath Bose (1944). Their thought experiments involved polarised light passing through rotating filters, suggesting that if photons carried fixed instructions, rotating the filter after emission could not alter transmission probabilities, contrary to quantum predictions.

Schrödinger’s Unpublished Response

Contrary to the common portrayal of Schrödinger as a staunch determinist, the manuscript shows him taking a more nuanced stance. In his handwritten notes, he proposes a hidden‑variable scheme where each photon possesses a continuous property—rather than a simple binary instruction—governing its interaction with polarizers. Del Santo’s reconstruction demonstrates that Schrödinger’s model reproduces the quantum‑mechanical transmission rates for a single polarizer and, crucially, remains consistent when light traverses multiple polarizers in succession. This addresses a shortcoming identified by Heinrich Pelzer, who argued that earlier hidden‑variable proposals failed under sequential measurements.

Why the Manuscript Remained Hidden

The document, dated to the period after November 1944, appears to have been set aside by Schrödinger, likely after learning of Pelzer’s counter‑arguments. It was stored in the Schrödinger archive at the University of Vienna and escaped scholarly notice until Del Santo’s recent archival work. By transcribing the manuscript and comparing its calculations with contemporary publications, Del Santo places Schrödinger’s effort squarely within the broader 1940s debate over the “collapse of determinism.”

---

Rethinking Schrödinger’s Legacy

The manuscript does not overturn Schrödinger’s reputation as a champion of wave mechanics, but it does nuance our understanding of his philosophical position. Even before quantum theory took shape, Schrödinger entertained the possibility that nature might be fundamentally statistical. His hidden‑variable construction was intended as a logical exercise: to show that deterministic explanations could, in principle, mimic quantum statistics, even if they offered no deeper insight into the underlying reality. As Del Santo concludes, the work serves as a proof of concept rather than evidence of Schrödinger’s personal commitment to a fully predetermined universe.

---

What This Means for Modern Foundations Research

The rediscovered manuscript underscores the historical richness of the quantum foundations debate and reminds contemporary physicists that the line between determinism and indeterminism has long been contested. While modern experiments—such as Bell‑test violations—have placed stringent constraints on local hidden‑variable theories, non‑local or contextual models remain an active area of inquiry. Schrödinger’s brief foray into hidden variables illustrates that even the era’s leading theorists were willing to entertain a spectrum of possibilities, reinforcing the importance of keeping an open mind when probing the deepest layers of quantum reality.

---

In short, the newly transcribed Schrödinger manuscript provides a rare glimpse into his analytical approach to the determinism debate, revealing a hidden‑variable model that matches quantum predictions for polarised light while emphasizing his view that neither deterministic nor indeterministic explanations can be definitively proven or disproven by experiment alone.