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schrodinger gets a lot of praise, and it is often left out that he was a predator to children.
separate the art from the artist?
Schrödinger also published a paper titled “On the Reversal of the Laws of Nature” where he proved that you can describe quantum systems in terms of a classical stochastic process. It is not well-known because he didn’t complete it himself, he only proved that the solution exists and is a solution to a scaling problem, but did not know how to solve the scaling problem, as the generic solution wouldn’t be discovered until many years later entirely independently of physics by a telephone engineer trying to forecast telephone traffic.
You do rarely see a paper discussing it and it’s usually referred to as “Schrödinger’s bridge,” as it allows you to take any two Born distributions and connect them through a stochastic trajectory. If you interpret these “bridges” as the actual “law” governing the system, then you can fit the entire system’s evolution to a stochastic trajectory, and the solution very generically works on any quantum system since it’s defined abstractly in terms of quantum information itself and not any specific physical model. For example, you can even apply it to qubits in a quantum computer, and treat them merely as bits with definite 0 or 1 values at all times that hop to new values stochastically at each logic gate.
In 1932, mathematician John von Neumann – one of the leading authorities on quantum theory’s foundational math – published what was widely interpreted as a mathematical proof that such hidden variables were impossible. His argument carried considerable weight, and for more than a decade, research into hidden-variable models largely stalled.
That argument was debunked by John Bell in his paper “On the Problem of Hidden Variables in Quantum Mechanics.” von Neumann employs a fallacy which would be repeated in Feynman’s later introduction to quantum mechanics with the double-slit, and again by Deutsch in his quadruple-slit experiment he introduces in the second chapter of his book “The Fabric of Reality.”
All three of them make the same fallacy of just adding the wrong statistics together from entirely different physical experiments.
For example, in Feynman’s double-slit argument, he computes the probability of where photons will land on the screen, P(x) ,by summing the probability of where photons land on the screen given they took the top path, P(x|top), and the bottom path, P(x|bottom), and concludes that a classical explanation should say P(x)=P(x|top)+P(x|bottom), and this sum fails in practice, so he concludes it is impossible to explain classically.
However, in order to measure P(x|top), you have to place a barrier to block the bottom path. If we call the bottom-barrier BB, then this is really P(x|top,BB). In order to measure P(x|bottom), you have to place a barrier to block the top path. If we call the top-barrier BT, then this is really P(x|bottom,BT). The sum then refers to the case where you have no barriers at all and get the double-slit pattern, and so P(x) is really P(x|¬BB,¬BT).
You can then see how Feynman was adding the wrong things.
He finds that:
- P(x|¬BB,¬BT)≠P(x|top,BB)+P(x|bottom,BT)
And concludes it cannot be explained classically. But, again, he is adding the wrong things.
He should be adding:
- P(x|¬BB,¬BT)=P(x|top,¬BB)+P(x|bottom,¬BT)
And that sum adds perfectly.
In Bohmian mechanics, the particles in the double-slit never cross the midline, and so P(x|top,¬BB) is exactly equal to the top half of the double-slit distribution, and P(x|bottom,¬BT) the bottom half, so of course they sum together to give you the full distribution.
This was the same conclusion Bell had when analyzing von Neumann’s paper who makes the same mistake of adding the wrong things from different experiments.
In my opinion, like Einstein, Schrödinger’s issue concern was less about determinism or indeterminism. It was more about realism. He wanted a coherent picture of objective reality, which quantum mechanics does not provide since it is only a theory about measurements and not about reality, and thus has to take measurements to be a fundamental postulate. In “‘Nature and the Greeks’ and ‘Science and Humanism’”, he laments that his wave mechanics did not achieve the goal he intended, which was to construct a picture of reality where things can be described as having a continuous existence independently of observation, because the continuous wavefunction still has to make an unnatural jump at the moment of measurement.
