Oct 21, 2026 03:58 PM
https://www.sciencealert.com/a-lost-schr...um-physics
EXCERPT: In his 1943 lecture, Whittaker had proposed a seemingly simple demonstration of why hidden variables couldn't exist [...] Enter Schrödinger. Or rather, stay in the wings, Schrödinger.
The physicist had been following the debate, and sometime after November 1944, he penned a response of his own, also titled "Collapse of Determinism" (there were several articles published as part of the debate that used the same title).
In it, he identified a significant flaw in Whittaker's argument. Whittaker assumed each photon carried a hidden variable with only two possible values, one determining whether it would pass through the polarizer and the other whether it would be reflected.
But Schrödinger pointed out that there was no reason to restrict the hidden variable to just two values. What if it could take any value between zero and one?
He then constructed a mathematical model in which the outcome depended on both the photon's hidden variable and the polarizer's angle. With the right rules, the model reproduced the probabilities quantum mechanics predicts, without requiring each individual interaction to be random.
There was a second part of the model that was also important. Schrödinger devised a deterministic rule for updating the hidden variable after a photon has passed through the polarizer – which meant his model could be used to reproduce the predictions for subsequent measurements.
Importantly, his aim was not to defend determinism because he necessarily believed in it. He was defending the possibility of determinism against specific claims that it was impossible.
"Experimental evidence + logical deduction can never prove that either the deterministic or the indeterministic view is impossible," he wrote. Schrödinger's response, however, never saw the light of day. Why he never published it remains a mystery, although Del Santo has a possible explanation.
In 1944, physicist Heinrich Pelzer published a similar hidden-variable model, showing that Whittaker's argument didn't hold up. Schrödinger may have learned of Pelzer's work and decided that the point had already been made. Yet Schrödinger's model went further, providing an explicit mathematical rule for how a photon's hidden variable would change after passing through a polarizer, allowing it to account for successive measurements.
Whatever his reasons, the manuscript remained unpublished, preserved in an Austrian archive until Del Santo brought it to light more than eight decades later. But there's another twist in the tale. Although Schrödinger is often portrayed as a champion of determinism, his own philosophical position was rather different.
As early as the 1920s, before modern quantum mechanics had even emerged, Schrödinger had argued that the laws of nature might be fundamentally statistical, rather than governed by an underlying clockwork of perfectly predictable events.
Influenced by physicist Franz Exner, he even described classical determinism as a "philosophic prejudice" and an "a priori belief". And his unpublished manuscript suggests that his position hadn't fundamentally changed by the 1940s – nor did it later. [...] His paper is available on preprint server arXiv... (MORE - missing details)
EXCERPT: In his 1943 lecture, Whittaker had proposed a seemingly simple demonstration of why hidden variables couldn't exist [...] Enter Schrödinger. Or rather, stay in the wings, Schrödinger.
The physicist had been following the debate, and sometime after November 1944, he penned a response of his own, also titled "Collapse of Determinism" (there were several articles published as part of the debate that used the same title).
In it, he identified a significant flaw in Whittaker's argument. Whittaker assumed each photon carried a hidden variable with only two possible values, one determining whether it would pass through the polarizer and the other whether it would be reflected.
But Schrödinger pointed out that there was no reason to restrict the hidden variable to just two values. What if it could take any value between zero and one?
He then constructed a mathematical model in which the outcome depended on both the photon's hidden variable and the polarizer's angle. With the right rules, the model reproduced the probabilities quantum mechanics predicts, without requiring each individual interaction to be random.
There was a second part of the model that was also important. Schrödinger devised a deterministic rule for updating the hidden variable after a photon has passed through the polarizer – which meant his model could be used to reproduce the predictions for subsequent measurements.
Importantly, his aim was not to defend determinism because he necessarily believed in it. He was defending the possibility of determinism against specific claims that it was impossible.
"Experimental evidence + logical deduction can never prove that either the deterministic or the indeterministic view is impossible," he wrote. Schrödinger's response, however, never saw the light of day. Why he never published it remains a mystery, although Del Santo has a possible explanation.
In 1944, physicist Heinrich Pelzer published a similar hidden-variable model, showing that Whittaker's argument didn't hold up. Schrödinger may have learned of Pelzer's work and decided that the point had already been made. Yet Schrödinger's model went further, providing an explicit mathematical rule for how a photon's hidden variable would change after passing through a polarizer, allowing it to account for successive measurements.
Whatever his reasons, the manuscript remained unpublished, preserved in an Austrian archive until Del Santo brought it to light more than eight decades later. But there's another twist in the tale. Although Schrödinger is often portrayed as a champion of determinism, his own philosophical position was rather different.
As early as the 1920s, before modern quantum mechanics had even emerged, Schrödinger had argued that the laws of nature might be fundamentally statistical, rather than governed by an underlying clockwork of perfectly predictable events.
Influenced by physicist Franz Exner, he even described classical determinism as a "philosophic prejudice" and an "a priori belief". And his unpublished manuscript suggests that his position hadn't fundamentally changed by the 1940s – nor did it later. [...] His paper is available on preprint server arXiv... (MORE - missing details)
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