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Showing posts from January, 2018

### Movie Review: Darkest Hour

Before Churchill was ever appointed as Prime Minister, by 1938 Chamberlain had gone to Munich to negotiate the German annexation of the Sudetenland. He thought he had Hitler sign off on any further territorial claims over land in Europe, but Hitler reneges on his promise, invades Czechoslovakia and occupies Prague. Poland under increasing pressure to give up the free-city of Danzig, (carved out of east Prussia by the treaty of Versailles), Chamberlain reverses his policy of appeasement and rises to support Poland against any action that threatens its independence.

If ever there was a midnight hour for Europe, it was still to come with the Molotov-Ribbentrop pact, signed on August 24th 1939. The Nazis and the Soviet Union's non-aggression treaty, that delineated spheres of interest over Europe and the joint-invasion of Poland. That invasion fell on September 1st, three days later Chamberlain announces a state of war between Hitler and Great Britain. All of this occurs before the s…

### Set Theory

This post is a very brief introduction to some of the basic concepts of set theory. Set theory is a branch of mathematical-logic, that has wide applications across disciplines. Its not just used in the obvious way of studying the foundations of mathematics by mathematicians but also in physics, social science, and even by philosophers as a theory of semantics for predicate logic (although you can do propositional logic without set theory).

A set is a collection of elements, or members; the notation for a set is specified by listing its components. So the set of even numbers can be represented a
$E: \left \{ 2,4,6,8 ... \right \}$$E: \left \{ x: x > 0 \wedge even\right \}$ Either of these notations is valid. Further, elements of a set can only be in that set, once. So   $E: \left \{ 2,2,2,4,4,6,8 ... \right \} = E: \left \{ 2,4,6,8 ... \right \}$ The notation used to indicate that something is an element of a set, is using the Greek symbol "epsilon". That is: $4 \epsilon S$…

### Consistent Histories and the PBR theorem

Several years ago now a much discussed theorem in the foundations of physics was discovered by three physicists, Matthew F. Pusey, Jonathan Barrett andTerry Rudolph. I had meant to discuss their paper some time ago, and realized I couldn't find anywhere, where anyone was talking about the theorem in the context of the Consistent Histories approach. So I've decided now to correct that.

The theorem states that under certain conditions a model which affirms both that (a) there are underlying ontological states of a system and (b) the wave function is given an epistemic interpretation, cannot be consistent with quantum theory, and so must be discarded.

Right off the bat, we know the Consistent Histories approach affirms (b), so the most straight forward response could be to reject (a) and some Consistent Historians are perfectly willing to do that, e.g. Lubos Motl and Roland Omnes. As for (b) in the CH approach, the wave function is treated as "pre-probability" in the sen…