An unpublished, undated manuscript belonging to Erwin Schrödinger lies in the Austrian Central Library for Physics at the University of Vienna. Physicist Flavio Del Santo at the University of Geneva retrieved it and analyzed its contents to establish a likely date it was written and also what the famous physicist thought about random outcomes in quantum physics.
The draft is titled ‘Collapse of Determinism’ and addresses one of the major problems in quantum physics – randomness of events. Quantum theory is usually used to predict the probabilities of measurement but never specific outcomes. Physicists have wondered whether this is a result of incomplete knowledge of the domain.
For instance, the outcome of a coin toss seems random at first. However, if one has information about how hard the coin was tossed and the speed of the wind in the area of the toss, then there is reliable information to predict the outcome too. In the quantum realm, much remains uncertain. However, if particles carry information that determines their behavior, would they become more predictable or deterministic?
What famous physicists thought
The debate between determinism and indeterminism in quantum mechanics has split the physicists into two groups that stand strongly by their views. While Einstein, David Bohm, and Schrödinger are often seen as champions of determinism in scientific history, Santo argues that there stance was more nuanced and less polarised than many think. Schrödinger’s unpublished manuscript is a case in point.
Quantum particles carrying information that could determine their behavior is termed hidden variables, since this information might not be accessible for scientists to observe it. In 1932, mathematician John von Neumann published a result that suggested that hidden variables should not be added to quantum mechanics,
During World War II, Taylor Whittaker, a British physicist and mathematician, questioned determinism, invoking Neurman’s work and citing an example of polarized light passing through a polarizer. In this setup, the angle between the polarized light and the polarizer determines how much light can pass through the latter.
Quantum mechanics expresses the outcome as a probability. However, Whittaker used two values for hidden variables in this hypothesis and argued that these could not reproduce the changes that were created when the polarizer was turned. Schrondinger’s manuscript is a response to this assumption.
What Schrödinger wrote
In his three-page manuscript, Schrondinger questions the restriction built into Whittaker’s reasoning and wonders why hidden variables had only two possible values. Instead, he suggested an alternative where each photon was assigned a value between zero and one.
The numbers were distributed evenly across the incoming beam, and whether the photon passed the polarizer depended on its number and the polarizer’s angle.
Across photons, the setup reproduced the expected transmission rate, which can be predicted using Malus’ law, but each individual outcome depended on the apparatus setting and the proposed number of the photon.
Schrodinger’s manuscript also solves the problem that arises after the first measurement, where the distribution changes. So, he created a mathematical rule that changes the photon’s number after it is transmitted or reflected and restores the distribution as per Malus’ law.
The question then remains is why did Schrödinger not publish this? According to Del Santo, this was likely because Heinrich Pelzer, an Austrian physicist, challenged Whittaker in a published paper. Although Pelzer’s approach was different, it still made the same point.
Del Santo warns that the manuscript must not be used to claim that Schrondinger sided with a deterministic view of nature. This unpublished work could be a test of an argument rather than endorse the model, Del Santo wrote in a analysis paper.
This paper can be found on the preprint server arXiv.