- Schrödinger's manuscript explores the issue of randomness in quantum physics.
- Physicists are engaged in a heated debate over determinism and indeterminism.
- Schrödinger questions Whitaker's hidden variable hypothesis and proposes an alternative.
- The manuscript may have remained unpublished due to its similarity to the views of Peres.
An unpublished, undated manuscript belonging to Austrian physicist Erwin Schrödinger is held at the Austrian Central Physical Library at the University of Vienna. Physicist Flavio Del Santo from the University of Geneva has retrieved and analyzed the manuscript to determine its possible date of writing and the renowned physicist's views on the randomness of results in quantum physics. This draft, titled "The Collapse of Determinism," addresses a major issue in quantum physics—the randomness of events. Quantum theory is typically used to predict the probabilities of measurements but never predicts specific outcomes.
Physicists have long pondered whether this is due to an incomplete understanding of the field. For example, the outcome of a coin toss may seem random at first glance. However, if one knows the force with which the coin is tossed and the wind speed at the time of the toss, the outcome can be reliably predicted. In the quantum realm, many things remain uncertain. However, if particles carry information that determines their behavior, would this make them more predictable or deterministic?
The Debate Between Determinism and Indeterminism
Views of renowned physicists The debate between determinism and indeterminism in quantum mechanics has divided physicists into two camps, with both sides firmly entrenched in their views. Einstein, David Bohm, and Schrödinger are typically seen as advocates of determinism in the history of science, but Del Santo argues that their positions are more nuanced and less oppositional than many imagine. Schrödinger's unpublished manuscript serves as an example. Quantum particles carrying information that may determine their behavior are referred to as hidden variables, as this information may not be observable by scientists. In 1932, mathematician John von Neumann published a result suggesting that hidden variables should not be added to quantum mechanics.
During World War II, British physicist and mathematician T. W. Whitaker questioned determinism, citing von Neumann's work and illustrating the case 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, Whitaker used two values for hidden variables in this assumption and argued that these could not reproduce the changes produced when the polarizer is rotated. Schrödinger's manuscript is a response to this hypothesis.
Schrödinger's Alternative
In his three-page manuscript, Schrödinger questions the inherent limitations of Whitaker's reasoning and wonders why hidden variables have only two possible values. Instead, he proposes an alternative that assigns each photon a value between zero and one. These numbers are evenly distributed within the incoming beam, and whether a photon passes through the polarizer depends on its number and the angle of the polarizer. Through the photons, this setup reproduces the expected transmission rate, which can be predicted using Malus's law, but each individual outcome depends on the device settings and the proposed numbers of the photons.
Schrödinger's manuscript also addresses the issue that arises after the first measurement, where the distribution changes. Thus, he creates a mathematical rule that alters the numbers after the photons are transmitted or reflected, restoring the distribution according to Malus's law. The question then arises: why did Schrödinger not publish it? According to Del Santo, this may be because Austrian physicist Heinrich Peres challenged Whitaker in a published paper. Although Peres's approach was different, it expressed the same viewpoint. Del Santo cautions that this manuscript should not be used to claim that Schrödinger supported a deterministic view of nature.
This unpublished work may be a test of an argument rather than a support for the model, Del Santo writes in an analysis paper. This paper is available on the preprint server arXiv.
Impact of Schrödinger's Manuscript on Quantum Theory
Schrödinger's unpublished manuscript provides a new perspective on the issue of randomness in quantum mechanics, challenging the traditional hidden variable hypothesis. The manuscript reveals Schrödinger's profound contemplation of quantum particle behavior, particularly his views on hidden variables, which may provoke a reevaluation of the nature of quantum theory. Although the manuscript remains unpublished, its content continues to inspire current research in quantum physics and may facilitate further exploration of the debate between determinism and indeterminism.