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Max Born introduced the Born Rule in a paper from 1926. But was this really the first time that a connection between quantum mechanics and randomness was noticed?

Today, quantum mechanics and randomness seem to be so closely connected that it's hard to imagine that 21 years should have past between Einstein's 1905 paper on the photoelectric effect, and the realization that randomness might be involved if "energy is exchanged only in discrete amounts".

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  • $\begingroup$ There is no randomness in quantum mechanics. What is there is called "uncertainty". The difference between the two is enormous: it's one imaginary unit in the equations of motion, which changes absolutely everything. For starters, there wouldn't be a universe without it... one can't build a non-empty universe on "randomness". $\endgroup$ – CuriousOne Sep 11 '14 at 0:07
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    $\begingroup$ @CuriousOne - what are you talking about? In quantum mechanics, the value of a measured quantity does not have a cause, it's a random variable distributed according to the Born rule. If your physical theory has a causal explanation for the actual outcome of the measurement, then your theory is something other than quantum mechanics. $\endgroup$ – Mitchell Porter Sep 11 '14 at 1:32
  • $\begingroup$ As for the remarks about i and the existence of the universe, I can only guess at what you have in mind. $\endgroup$ – Mitchell Porter Sep 11 '14 at 1:32
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    $\begingroup$ @CuriousOne: you write "[quantum systems] are perfectly causal...", but then "the outcome of an individual measurement... is not fully determined". The last part is where randomness enters, according to quantum theory. $\endgroup$ – Mitchell Porter Sep 16 '14 at 5:47
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    $\begingroup$ @CuriousOne - orthodox QM for more than 80 years has been, the wavefunction evolves deterministically according to Schrodinger's equation, until an observation is made, at which point the wavefunction jumps RANDOMLY to some eigenstate of the observable, with a probability equal to ... blah blah, I'm sure you know this. $\endgroup$ – Mitchell Porter Sep 16 '14 at 6:27
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Certainly not. I was already known for a long time that certain microscopic phenomena were best described by probabilistic theories, the prime example being radioactivity. Even on the classical level, statistical mechanics (canonical example: Brownian motion) had prepared some physicists to relax their classical conceptions of reality.

However, it was of course not clear how exactly quantum phenomena and 'randomness' are connected until the advent of quantum mechanics and Born's interpretation of $|\Psi(x,t)|^2$. The small book 'Uncertainty' is largely dedicated to the development of these concepts in the late 19th/early 20th century, and is a nice read even though it does not really get down to the nitty gritty of the technical details.

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