Lost Schrödinger Manuscript Shows He Built a Hidden-Variable Model Without Believing in It
A Geneva physicist transcribed three handwritten pages sitting unpublished in Vienna for 80 years and found Schrödinger's model matched quantum predictions even through several light filters.
Quantum mechanics usually cannot say what will happen in a single event. It predicts only the probabilities of different outcomes. Erwin Schrödinger, one of the theory's pioneers, was deeply involved in the argument over what that randomness means, yet part of his contribution has stayed hidden for more than 80 years. In a new study posted on the arXiv preprint server, Flavio Del Santo of the University of Geneva analyzes an unpublished Schrödinger manuscript and what it says about his thinking.
The puzzle is old. In a coin toss, the result only looks random because no one can measure every force acting on the coin. Since the early days of quantum theory, some physicists have wondered whether quantum randomness works the same way. In so-called hidden-variable theories, particles carry unobserved properties that secretly decide the outcome of each measurement. In 1932, mathematician John von Neumann published what many took as proof that such properties could not exist, and the idea was largely abandoned.
The question came back in the 1940s. In 1943, Edmund Taylor Whittaker argued that quantum mechanics had destroyed the classical idea of a predictable universe. He imagined particles of light passing through a polarizer, a filter whose orientation determines how much light gets through. If each particle carried a hidden pass-or-block instruction, he reasoned, turning the filter after the light had set off could not change those instructions. Quantum mechanics, by contrast, predicts that the fraction passing through should change.
Satyendra Nath Bose made a similar case in 1944, and the exchange became a lively debate in the journal Nature. Heinrich Pelzer answered with a model showing that Whittaker's argument did not hold up. Schrödinger, often portrayed as a champion of determinism, joined in with a three-page handwritten response in which he built his own hidden-variable model, simply to show that such explanations could not be ruled out.
That response never reached print. It has sat largely unnoticed in the Schrödinger archive at the University of Vienna. Del Santo transcribed it for the first time and used it to reconstruct the debate from other publications of the period. Rather than the simple yes-or-no instruction Whittaker assumed, Schrödinger gave each particle of light a hidden property with a whole range of possible values. Del Santo's calculations confirmed that the model matches the predictions of quantum mechanics. Going a step beyond Pelzer, it also still works when the same light passes through several filters in a row.
The analysis dates the manuscript to sometime after November 1944 and suggests Schrödinger may have shelved it after learning of Pelzer's work. More important, it complicates the picture of the man. Building a working hidden-variable model did not mean he believed in a fully predetermined universe. As he put it, experiments and logic could never prove either view impossible, and since the 1920s, before quantum mechanics had even taken shape, he had suspected that nature's laws might be fundamentally statistical.
Del Santo concludes that the model was a proof of principle rather than evidence of Schrödinger's commitment to determinism. The work is a preprint, so it has not yet been through peer review. It is posted on arXiv as Schrödinger's unpublished hidden-variable model in the 1944-45 debate over the "Collapse of Determinism."
