A recently analyzed unpublished manuscript by Erwin Schrödinger has provided new insights into the historical debate over quantum determinism. The document, which remained in the archives of the University of Vienna, offers a mathematical counterexample to the long-held belief that hidden information cannot account for the seemingly random outcomes of quantum measurements. This discovery adds a significant layer of complexity to the historical narrative of Schrödinger's philosophical position on the nature of reality.
The manuscript, titled "Collapse of Determinism," was drafted during the mid-1940s, a period of intense debate regarding whether quantum mechanics fundamentally ended the possibility of a predictable universe. Physicist Flavio Del Santo, who conducted the transcription and analysis, notes that Schrödinger’s work was not intended to propose a definitive theory of how nature operates. Instead, it served as a sophisticated rebuttal to specific arguments made by other physicists, demonstrating that ruling out one specific explanation does not automatically invalidate all deterministic models.
At the heart of the dispute was the concept of "hidden variables"—the idea that particles might carry underlying information that determines their behavior, even if that information is inaccessible to observers. While the 1932 work of John von Neumann was widely interpreted as ruling out such variables, the Schrödinger manuscript challenges this by providing a deterministic model for polarized light. By assigning each photon a value between zero and one, Schrödinger showed that the statistical results of Malus’ law could be reproduced by a deterministic rule, even if the individual outcomes appeared random to the observer.
Furthermore, Schrödinger addressed the technical hurdle of how these hidden values would persist through successive measurements. He proposed a mathematical rule to redistribute the values after each interaction, ensuring the distribution remained consistent with quantum predictions. This demonstrated that a deterministic framework could, in theory, mimic the probabilistic nature of quantum mechanics in specific experimental setups.
The manuscript likely remained unpublished because a similar model by Heinrich Pelzer was published in 1944. However, Del Santo highlights that Schrödinger’s draft was significantly more ambitious, combining a concrete mathematical model with deep philosophical reflections on the limits of impossibility proofs. The discovery underscores the complexity of Schrödinger's thought: he was capable of constructing a deterministic universe while simultaneously maintaining a belief in the fundamental randomness of the natural world.