In Erwin Schrödinger’s archive at the University of Vienna, under the reference number W33-781/9, lies an undated handwritten draft titled “Collapse of Determinism.” The author is Schrödinger himself. The text mentions the Nature correspondence up to and including a letter of November 25, 1944, so it was written later. It was never printed anywhere, ever: for eighty-two years the manuscript sat in an archive box, until Flavio Del Santo, a historian of physics at the University of Geneva, found it and published the first complete transcription with commentary in October 2026.
Its contents were worth waiting eighty-two years for. In the draft, one of the fathers of quantum mechanics builds a working hidden-variable model—an elegant mathematical counterexample to the era’s most famous argument for the fundamental impossibility of determinism. He constructs it carefully, gives a recalculation rule for every photon, tests it on two polarizers in succession. And never sends it to a journal. Meanwhile, the debate he did not answer winds down on its own—with the score “neither side proved”—and physics forgets about hidden variables for another decade, until David Bohm pulls them out of the drawer in 1952.
A headline flashed past in my feed, one of those “scientists are amazed” specials: Schrödinger’s lost manuscript supposedly overturns our understanding of quantum randomness. Out of habit, I braced for a retelling of a retelling, but went to the source—the Del Santo preprint on arXiv—and found a story far better than any sensation. It is not a story about physics, but about how scientific authority works: how one proof from 1932 froze the debate for fifteen years, how a critic who spotted its crack as early as 1935 went unheard, and how the man whose name would later label the determinists’ camp for twenty years was, at that very moment, writing a counterargument in their favor—and silently putting it away in a drawer.
Along the way, one detail emerged that makes the story thoroughly uncomfortable: eleven people took part in the journal debate, while Schrödinger was writing the twelfth reply. Eleven entered history. The twelfth entered the archive.
In 1932, John von Neumann published Mathematical Foundations of Quantum Mechanics—and in that book was a section read as a verdict: a supposedly rigorous proof that quantum mechanics could not be supplemented with hidden variables, and that randomness within it was therefore fundamental and irreducible. Arguing with von Neumann was difficult not so much on the merits as on status: one of the century’s greatest mathematicians had firmly shut down an entire line of inquiry.
The effect was such that physicists barely pursued hidden-variable models for fifteen years. The famous exception was the 1935 Einstein-Podolsky-Rosen paper, but it argued for the incompleteness of quantum mechanics without constructing any alternative model.
The critique of the proof itself appeared almost at once—and not from physicists.
Grete Hermann was a mathematician and philosopher from Bremen, Emmy Noether’s first doctoral student. Her 1926 dissertation on the termination of chains in the theory of polynomial ideals still survives inside computer algebra systems. In 1934, she came to Leipzig specifically to speak with Heisenberg and Weizsäcker about causality, and in 1935 published the philosophical work “ naturphilosophischen Grundlagen der Quantenmechanik,” which historians call one of the earliest and best philosophical analyses of the new mechanics.
Inside that work was a precise but devastating point: von Neumann’s proof demonstrates the impossibility of hidden variables only within the system of axioms that von Neumann himself had postulated. The circle is drawn in advance—within it, the prohibition holds, but it cannot sustain any claim to “fundamental impossibility.” Thirty years later, John Bell, unaware of Hermann’s work, would take apart the proof in exactly the same way—and that would become famous. But in 1935, her argument simply sank: as Del Santo’s preprint says, citing historians, she was “young, female, and an outsider” to the physicists’ debate. Hermann’s priority was restored only in 1974, when Max Jammer pointed to her in his history of quantum mechanics.
The irony is that Hermann was not defending hidden variables—she was defending Kantian causality and was convinced that quantum mechanics was compatible with it. But her point about the weakness of von Neumann’s proof was precisely the thing for which Bell would be patted on the back thirty years later.
While bombs fell over London, the mathematician Edmund Whittaker delivered a lecture to the Physical Society on May 18, 1943, titled “Randomness, Free Will and Necessity in the Scientific Conception of the World.” Its thesis: quantum mechanics had finally buried classical determinism, and von Neumann had proved it. On January 3, 1944, in Delhi, Satyendra Nath Bose—the Bose of Bose-Einstein statistics—gave a similar talk: “Fifty years ago belief in causality and determination was absolute. Today physicists have acquired knowledge, but lost faith.”
Both cited von Neumann, and the first warning sign was not the thesis itself but how easily it travelled: in July 1944, the mathematician Henry Piaggio published a Nature review titled “The Collapse of Determinism”—and the journal’s mail began to pour in. The peak came in October: Whittaker rolled out his favorite argument, simple and sharp. Malus’s law: a polarized photon passes through a polarizer with probability cos²φ, where φ is the angle between its polarization and the axis of the apparatus. Suppose each photon carries a hidden bit: 0 means “I’ll pass,” 1 means “I’ll be reflected.” Then, in an ensemble of N photons, exactly N·cos²φ must carry bit 0. But the polarizer can be rotated while the photons are in flight. You cannot rotate the photons’ bits—so the fraction that passes cannot depend on the angle. Yet according to Malus’s law, it does. Therefore, there are no hidden variables; the randomness is real.
The objections came in waves. The experimentalist Gilbert West wrote a sentence in October that deserves to be framed: “many, knowing how easily assumptions conceal themselves in analytical arguments, refuse to be overawed by mathematics.” In January 1945, he delivered the main blow: Whittaker had shown only that causality limps if all parameters are hidden inside the photon itself. But the polarizing crystal is an honest physical object with parameters of its own; account for the lattice, and the argument falls apart. All the while, the experimental people were entertaining themselves separately: the meteorologist Ernest Gold argued about coins, while Jerzy Chrzanowski sent Nature a report on a real experiment—a mechanical device with fixed tossing conditions produced almost always the same outcome. The classical “randomness” of a coin turned out, as it should, to be cryptodeterminism.
In March 1945, Piaggio summed up the eleven publications, ending with a quotation from Russell in 1936: there are no conclusive arguments for complete determinism—but none against it either. A truce. No one in that debate knew that a twelfth letter existed.
In the manuscript, Schrödinger begins with an admission: “I too was puzzled by this conclusion. For the absurdity is clearly produced by the simplifying assumption of only two discrete values of the parameter.” And he builds a correction.
Each photon has a hidden variable λ, a real number from 0 to 1, uniformly distributed. The transmission rule is this: a photon passes a polarizer at angle φ if and only if λ ≥ sin²φ. The fraction that passes is exactly cos²φ; Malus’s law is reproduced, while every outcome is predetermined in advance. No bits—a real number sufficient for any angle.
The subtle point is the second polarizer. After the first one, only photons with λ ≥ sin²φ survive in the ensemble; the distribution is no longer uniform. Schrödinger provides a solution for that as well: every transmitted photon recalculates its variable according to λ′ = (λ − sin²φ)/cos²φ—the survivors once again uniformly fill the interval from 0 to 1. Then the second polarizer, at angle φ′, transmits a fraction cos²(φ′ − φ)—exactly what quantum mechanics predicts. For reflected photons, he writes down an analogous rule, adding: “I see no contradiction in allowing such changes.”
Look closely at what happened here. The outcome for each photon is a function not only of its hidden variable, but also of the apparatus setting. That—the dependence of the parameter on context—is exactly what Whittaker did not allow, and exactly where his argument died. Del Santo separately emphasizes a detail missed by everyone in the debate, Schrödinger included: there is nothing specifically quantum here. If you can move the floor beneath a coin while it is in the air, one bit will not be enough either. The real lesson of Whittaker’s example is “do not skimp on hidden variables,” not “hidden variables do not exist.”
Del Santo’s most plausible reconstruction is that Schrödinger learned of Heinrich Pelzer’s work. Pelzer was an Austrian physicist whose paper proposing a hidden-variable model for Whittaker’s example was accepted on January 21, 1944, and published on May 1 of that year in the Proceedings of the Physical Society. For a single polarizer, his model is mathematically equivalent to Schrödinger’s—it can be obtained simply by renaming the variable. Pelzer was cited directly in the Nature debate, in West’s January letter. It makes perfect sense that, seeing this, Schrödinger decided the point had already been made: there was nothing left to answer, and no reason to answer it. His draft, meanwhile, was broader and more ambitious—a model plus an examination of the limits of “proofs of impossibility” themselves.
There also remains a philosophical postscript without which the whole manuscript cannot be read. “Experience plus logic can never prove the impossibility of either a deterministic or an indeterministic view. At best, the body of evidence will show that one of the pictures... is extremely inconvenient, because it requires unjustified hypotheses.” And then—a blow against his own camp: “The strongest argument for indeterminism is older than quantum mechanics.” From the early 1920s onward, under the influence of Franz Exner, Schrödinger regarded the laws of nature as deeply statistical, and determinism as a “fundamental dogma of classical physics” and a “philosophical prejudice.” For him, the hidden-variable model was not a renunciation but a proof by contradiction: determinism may not be necessary, but it cannot be outlawed by decree.
Here the central image of Del Santo’s paper comes into focus. Einstein, Schrödinger, and Bohm—the three men whom popular culture has long appointed standard-bearers of determinism—all constructed hidden-variable models at different times. And none of the three was a determinist in the careful sense: Einstein regarded proposals for a deterministic completion of quantum mechanics with explicit unease; Bohm wrote openly and extensively against mechanical determinism (there is even a collection titled Why Bohm Was Never a Bohmian); and Schrödinger was a committed indeterminist long before quantum mechanics and remained one for the rest of his life. They built models as demonstrations of principle—against a prohibition, not for a creed. The story in which the “classics” of quantum randomness defended determinism was written after the fact.
Von Neumann’s proof hung on the throne for more than thirty years—until Bell—not because it was correct, but because it was signed. West’s line about “refusing to be overawed by mathematics” is worth keeping close whenever someone else’s rigor looks beyond challenge: in 2018, Mermin and Schack published an analysis with the telling title “Homer nodded”—until recently, even historians believed that von Neumann had simply made a surprising oversight.
The second lesson is about Hermann. The distance between her 1935 analysis and Bell’s in 1966 is thirty-one years and one social detail: who is speaking, and from where. Her argument did not lose a gram of force over those years; it lost itself, in a place indecent for physics—in a discipline foreign to it.
And Schrödinger’s manuscript is beautiful precisely because he chose not to publish it. Not every draft has to become a paper; sometimes the most important thing about a letter is that you understood the answer before you had time to send it, and calmly put the paper away in a drawer. For eighty-two years, it waited to say one thing: even the man who formulated the wave equation did not consider the ban on hidden variables rigorous. He simply had something more interesting to do—write letters to an editor who had already made up his mind.