Historian of physics Flavio Del Santo of the University of Geneva discovered an unpublished manuscript by Erwin Schrödinger that had been kept in an Austrian library for more than 80 years. In the three-page text, one of the founders of quantum mechanics challenged the claim that quantum physics rules out determinism—the view that events have causes that make it possible, in principle, to determine their outcome in advance. The study of the find was published as a preprint on the arXiv server.

Can quantum randomness be explained by hidden variables?

The manuscript was likely written after November 1944, when physicists were actively debating whether the development of quantum mechanics meant a definitive rejection of determinism.

According to a widespread interpretation of quantum theory, the results of measurements of individual particles are described by probabilities. This gave rise to the question: is nature truly fundamentally random, or could the observed outcomes be determined in advance by unknown physical quantities?

Such hypothetical quantities are called hidden variables. If they exist, quantum probabilities could potentially be explained by the incompleteness of our knowledge of the system, rather than by nature’s intrinsic randomness.

In the discovered manuscript, Schrödinger argued against the claim that such an explanation is impossible in principle. He wrote that “the strongest argument in favor of indeterminism predates quantum mechanics itself,” thereby indicating that the debate over randomness did not arise solely with the emergence of the new physical theory.

What Schrödinger objected to in mathematician Whittaker’s argument

One target of his criticism was a claim made in 1943 by the British mathematician Edmund Whittaker. Whittaker considered photon polarization and concluded that it was incompatible with a certain type of hidden-variable explanation.

Specifically, he assumed that such a parameter could take only two values. Schrödinger proposed an alternative model in which the hidden quantity could take any value from zero to one.

According to Del Santo’s description, the model made it possible to reproduce quantum probabilities. In addition, Schrödinger provided a rule for updating the hidden parameter after each measurement. Thanks to this, the model described not only a single experiment but also a sequence of measurements.

The point of the argument was not that Schrödinger proved the existence of hidden variables or established the deterministic nature of the universe. He showed that the claim of the fundamental impossibility of a deterministic explanation could not be considered proven on the basis of Whittaker’s arguments.

Why the work remained unpublished

Why Schrödinger did not publish the manuscript is unknown. Del Santo suggests that the physicist may have abandoned the idea after learning of a similar model proposed by Heinrich Peltzer in 1944.

In the historian’s view, such works are important not necessarily as final solutions to fundamental problems. They can demonstrate that a certain possibility is not ruled out, contrary to widespread beliefs or claims of its impossibility.

The discovery refocuses attention on the long-standing debate over what randomness in quantum mechanics actually means. At the same time, it does not overturn the results of later hidden-variable research or prove that the world is deterministic.

The manuscript shows something else: even one of the creators of quantum mechanics did not consider the question of the nature of randomness settled and was prepared to challenge overly categorical conclusions about the limits of possible physical explanation.