Dr. Scarani opened the talk by noting a paper he placed on arxiv.org about Aquinas and the sense that the universe would not be perfect without randomness.
He moved on to discuss randomness in two senses: Process Randomness, which implies that there is an observer unable to predict the output of the process; and Product Randomness, the lack of structure of a product, which turns out to equate with the need for a very long algorithm to replicate the product. Products are tested for randomness by a battery of statistical tests. He gave an equation embodying a mathematical definition of [product] randomness. Not being an information theorist, I had not seen it before.
He went on to note the difference between the randomness of classical physics, which is always about a lack of complete information about a system. If one had that information, the system under the classical assumption would be perfectly defined, and as we have noted a number of times, Einstein among others desperately wanted to get back to that deterministic paradigm. "The Old One doesn't throw dice."
The core of the talk was what Scarani called a "high school level" presentation of Bell's theorem. I would like to meet the high school student who could follow it at the speed at which he gave the talk, but probably could have unpacked it given a couple of hours to do so even at that age. Bell's theorem is one of those cunning little mathematical gems that seems to prove the unprovable, namely, to make a prediction about something going on in a process one by definition cannot see into. Bell sets up a statistic that, if there are hidden rules governing physics below the scale at which the uncertainty principle lets us see, must nevertheless in real experiments end up being less than 2. Since the 1980s a series of ever more careful experiments have been done, and the answers in the papers Scarani reviewed had answers between 2.4 and 2.7; the answer is never below 2. According to Bell's theorem, this means that there is a really random process going on down there, and not just random products.
At the end, as we discuss in the audio, Scarani ran down the list of remaining possibilities for understanding the quantum foundations of the universe:
- There is real randomness.
- "Superdeterminism." This depends on breaking an assumption of the Bell theorem, which is that the quantum process is being fed input that itself is not really random from the perspective of that process, which would seem to imply some sort of physics puppet master controlling the experimenter.
- The many worlds hypothesis, again something we have mentioned a number of times. I am still not buying that stock.
- The only allowable sort of hidden variables (the name Bohm is attached to the most commonly discussed of these) would require particles communicating with each other at infinite speed, "deliberately" trying to wreck the experiment, and with the interaction hidden in a way workers in the field have called "conspiratorially hidden." I.e., we would be living in a universe run by a sort of Cartesian evil deity.
On that theme, note that I blundered off into talking in a sort of Cartesian dualist fashion about the relationship between soul and body there after the 14 or 15 minute mark.