Part 4 of my review of the book: “The Big Picture: On the Origins of Life, Meaning and the Universe Itself,” by Sean M. Carroll. Part 3 is found here.
Carroll devotes a few chapters to assessing how well we understand the world. He introduces us to Rev. Thomas Bayes who, in the latter part of his life, studied probability. He was published posthumously on the subject. His work has become widely used in mathematics, principally statistics, and also in physics. The subject has become to be known as Bayesian inference or Bayesian probability.
Bayes’ main idea involves how to treat the probability of a proposal being correct in the light of new evidence becoming available. In physics we rely on what we already know, or what we think we have established as foundational and we build upon that. When we get new information that could change our view we need to update what we believe is the probability of the hypothesis being correct in light of that new information. That probability is what is called a credence, or the degree of belief that we hold that we are correct.
So Bayesian inference attempts to apply a quantitative value to what we might infer from our attempts to explain the physical world. It is the basis of scientific investigation. In terms of experimental discoveries it is easy to see how this might apply. We can never prove any hypothesis or theory correct. All we can hope to do is update our credence, meaning to increase the probability of a theory being correct. In physics a threshold is established of 5σ (5 sigma) above which it is said that a discovery has been made. Statistically that is like saying there is only 1 in a 3.5 million chance that the signal isn’t real and thus the theory is wrong. That is a very low probability indeed. But some discoveries have been made at the level of 3σ or less.1 I know of one hypothesis that had a 6σ probability yet it turned out to be wrong.2
But things don’t always work out to be correct, even with a statistical probability above 5σ. Any hypothesis may be refuted but it can never be proven. Do you remember the claim of faster than light neutrinos in 2011? The OPERA team’s experimental results indicated a 6σ level of confidence, which is much higher than the 5σ usually required for new particle discoveries. But in the following year, as many expected (because we don’t expect any particle to break the speed of light limit), an error was found in the experimental analysis resulting from a loose fibre optic cable, and that meant those neutrinos obeyed the universal speed limit. When the new information came in the Bayesian credence could be updated to nearly zero.