Lost Schrödinger Manuscript Pokes a Hole in a Famous Quantum Argument

A three-page manuscript by Erwin Schrödinger, left unpublished in an Austrian library for more than 80 years, has resurfaced and adds a new chapter to the history of quantum physics. Physics historian Flavio Del Santo of the University of Geneva brought it to light, according to ScienceAlert.

The document shows Schrödinger taking apart an argument that quantum randomness cannot be explained by hidden factors. It also complicates his usual image as a physicist uneasy with quantum chance.

The debate Schrödinger stepped into

In classical physics, true randomness does not exist. Dice, computer random-number generators and coin flips all follow rules or physical forces that could, in theory, be predicted. That idea is called determinism.

At the quantum scale, ScienceAlert explained, the behavior of particles such as photons and electrons can be predicted only as probabilities. Physicists can calculate the likelihood of an outcome very precisely but cannot say what one particle will do. That leaves an open question: is the universe fundamentally random, or do unknown properties, called hidden variables, decide each outcome?

How the argument unfolded

• 1932: Mathematician John von Neumann published what many took to be a proof that hidden variables were impossible. ScienceAlert reported that research into such models largely stalled for more than a decade.
• 1935: Mathematician Grete Hermann found significant holes in von Neumann's reasoning, but her critique was mostly ignored.
• May 1943: Mathematician and physicist Edmund Taylor Whittaker gave a lecture arguing that quantum mechanics had overturned classical determinism and that quantum randomness was genuine.
• January 1944: Physicist Satyendra Nath Bose made a similar case in an address to the Indian Science Congress.
• July 1944: Mathematician Henry Piaggio reported on Bose's arguments in an article in Nature titled “Collapse of Determinism.” It drew a flurry of replies from physicists who doubted determinism was dead, and the argument continued in the journal for months.
• After November 1944: Schrödinger wrote his own response, also titled “Collapse of Determinism.” It was never published.

What the manuscript argues

Whittaker's example used photons passing through a polarizer, a device that filters light by its orientation. Quantum mechanics can predict what share of photons get through at a given angle. Whittaker argued that if each photon carried a hidden instruction saying whether to pass, changing the polarizer's angle while the photon was in flight would make that instruction useless. So, he concluded, outcomes could not be predetermined.

Schrödinger spotted a flaw, according to ScienceAlert. Whittaker had assumed the hidden variable could take only two values, one for passing and one for reflection. Schrödinger saw no reason for that limit and asked what would happen if it could take any value between zero and one.

He then built a mathematical model in which the outcome depended on both the photon's hidden variable and the polarizer's angle. With suitable rules, the model reproduced the probabilities that quantum mechanics predicts without making each individual interaction random.

Why it matters: a different picture of Schrödinger

The finding does not change what experiments show, and ScienceAlert did not describe it as new physics. Its significance is historical: it shows what one of the field's founders thought about reality and how he reasoned about a dispute that is still unresolved.

Schrödinger is often portrayed as uncomfortable with quantum randomness. The manuscript points the other way on one level. According to ScienceAlert, he believed some aspects of the universe could not be predicted, and he held that view even before quantum theory emerged in the 1920s. In the manuscript he wrote that “the strongest plea in favor of indeterminism is older than quantum mechanics.”

At the same time, his model showed that one prominent argument against hidden variables did not close the question. The manuscript does not settle whether the universe is fundamentally random. It does add a long-missing voice to a debate that Whittaker's and Bose's pronouncements had helped reopen in the mid-1940s.

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Around Prague, based on reporting by ScienceAlert