Schrödinger's unpublished hidden-variable model in the 1944-45 debate over the "Collapse of Determinism"

For most of human history, the universe was imagined as a giant, perfect clockwork. If you knew the exact position and speed of every gear and spring, you could predict the future with absolute certainty. This idea, known as determinism, suggested that randomness was a sign that we simply lacked enough information. If we could see every tiny detail of a coin toss—the force of the thumb, the air resistance, the spin—we would know exactly whether it would land on heads or tails. The coin itself would be following a strict, unbreakable rule.

This comfortable view of reality was shattered in the early twentieth century by the discovery of quantum mechanics, the physics of the very small. In this strange new world, nature seemed to operate on pure chance. When a scientist measures a particle, the theory only predicts the odds of different outcomes, not the result itself. For decades, many physicists believed this randomness was fundamental, meaning the universe itself was not a clockwork machine but a place where events truly happen without a cause. However, a few thinkers wondered if this randomness was just like the coin toss: a sign that the theory was incomplete and that hidden, unseen factors were actually guiding the particles. A famous mathematician once claimed to prove that such hidden factors were impossible, silencing the debate for a time. But in the mid-1940s, the question suddenly roared back to life, leading to a forgotten chapter in the history of science where one of the field's founders quietly proved that the door to determinism was never truly locked.

In the middle of the 1940s, a lively debate erupted in the pages of the scientific journal Nature. Two prominent speakers had recently argued that quantum mechanics had finally disproven the old idea of a predictable universe. They claimed that the strange behavior of light and atoms could not be explained by any hidden rules or secret variables. One of these speakers, a British physicist named Edmund Taylor Whittaker, offered a specific challenge. He argued that if you tried to explain why light passes through a filter at certain angles using hidden variables, the math simply would not work. He suggested that a particle could not carry enough information to decide its fate in every possible situation. This argument, which relied on a simple logic about how light behaves, convinced many that the search for a hidden, deterministic explanation was over.

Enter Erwin Schrödinger, one of the founding fathers of quantum mechanics. While the public debate raged on, Schrödinger was quietly working on a response. He drafted a handwritten manuscript, which has remained unpublished and unknown until now, in which he directly addressed Whittaker's challenge. In this document, Schrödinger did something remarkable: he built a working model that showed hidden variables were indeed possible. He demonstrated that if you imagine a photon carrying a continuous stream of hidden information, rather than just a simple yes-or-no switch, you can perfectly reproduce the strange statistical patterns of quantum mechanics. He showed that the argument against hidden variables was flawed because it assumed the hidden information was too simple to handle the complexity of the experiment.

Schrödinger's model was a clever construction. He imagined that every photon carried a hidden number, like a secret code, that determined whether it would pass through a filter or be blocked. Crucially, this number was not just a binary choice but a value that could change smoothly. When a photon passed through a filter, Schrödinger showed that this hidden number would update itself in a specific, rule-based way, ensuring that the next time the photon encountered a filter, it would behave exactly as quantum mechanics predicted. By doing this, he proved that you could explain the "random" behavior of light using strict, deterministic rules. The apparent randomness was not a feature of the universe itself, but a result of our inability to see these hidden numbers.

However, the most surprising part of Schrödinger's discovery is not the model itself, but what it meant for his own beliefs. One might assume that by building a deterministic model, Schrödinger was trying to save the idea of a clockwork universe. The paper reveals that this was not the case at all. Schrödinger had long been a critic of determinism, believing that nature was fundamentally statistical and unpredictable. He viewed his new model not as a confession of faith in a predictable universe, but as a "proof of principle." He was essentially saying to his critics: "You claim it is logically impossible to explain quantum mechanics with hidden variables. I have just shown you that it is possible. Therefore, your claim of impossibility is wrong." He was not arguing that the universe is deterministic, only that it could be, and that no mathematical proof had successfully ruled it out.

The manuscript also highlights a broader lesson about how science handles ideas of impossibility. Schrödinger noted that even the most rigorous mathematical arguments, like the one that had silenced the debate for a decade, could be limited by the way the problem was framed. He argued that experimental evidence and logic could never definitively prove that a deterministic view was impossible; they could only show that it was inconvenient or required extra assumptions. His work served as a reminder that in science, declaring something impossible is a very high bar to clear.

This forgotten debate eventually faded away, partly because Schrödinger never published his findings. He may have realized that another physicist had already published a similar, though less detailed, solution, or perhaps he felt his philosophical point had been made without needing a formal publication. It would take several more years and the work of other scientists before the idea of hidden variables would return to the mainstream with full force. Today, we know that while local hidden variables cannot explain all quantum phenomena, the story of Schrödinger's 1944–45 manuscript remains a fascinating glimpse into a moment when the giants of physics were still wrestling with the very nature of reality. It shows that even the most skeptical minds were willing to test the boundaries of what was thought to be impossible, not to change their minds, but to ensure that the rules of the game were truly understood.