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Penrose-Hawking Singularity Theorems

Between 1965 and 1970, Penrose and Hawking proved a set of six singularity theorems together, all of which make varied assumptions and have different starting points. ** Though, when a cosmologist refers to the "Penrose-Hawking Singularity theorem" they're probably referring to the sixth theorem, which was proven in 1969 in a famous paper titled "The singularities of gravitational collapse and cosmology". This is the most powerful formulation of the Penrose-Hawking theorem, and it's the one I'll talk about here.

Of course, this all begs the question, what is a 'singularity?' In some text books you may find that a singularity appears in a model when the null or timelike geodesics cannot be extended indefinitely; that is to say, if the paths of photons or particles with mass terminate at some finite time into the past. That tells us when a singularity appears but not what it really, actually is. This turns out to be a difficult task but in The La…
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No Deal is Better than a Bad Deal

With the consent of both houses of parliament, Theresa May moved to trigger Article 50 back in March, making it the expressed will of not just one Prime Minister, but of the people and of their elected representatives. If the reality hasn't set in by now, it should have: we are leaving the European Union.

The only question that remains is whether we leave on favorable terms with an agreement in place that covers, not least of all trade or in keeping with the Prime Minister's oft-repeated phrase "no deal is better than a bad deal", we leave without a trade deal, and make the necessary arrangements to keep our economy competitive.

This latter option which involves tariffs, is how most countries conduct their trade with the European Union, we would in affect, be left with a "US-style" or "Chinese-style" relationship to the EU. One conducted on WTO terms, instead of a more favorable bilateral basis.

The possibility of leaving without a deal is hardly…

Brexit Transition Worries

In recent headlines, a lot of the debate over Brexit has now shifted to a debate over the transition period Theresa May proposed in her Florence speech. Overall, the speech she made was well-judged and statesmen like, and for whatever it's worth I think Theresa May is a competent politician of sound mind. I hope she stays on as Prime Minister.

There's nothing wrong in principle with an implementation period after the time limit of Article 50 has expired. As one MEP put it "Brexit is a process not an event" it's going to involve the gradual repatriation of powers back to the United Kingdom, rather running off a cliff edge and imposing multiple changes on businesses all at once, but there is a serious worry about the terms of implementation.

If under the transition phase we remain a member of the single market, the custom's union, and under the jurisdiction of the European Court of Justice, come March 2019, we will in fact have not left the European union. We&…

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…

Theresa May is No Liberal but She's Still Better than Jeremy Corbyn

It's a lonely time to be a classical liberal; none of the main parties are offering a truly liberal-Brexit.

All the main parties in Britain support regulations on pay, fixing prices (typically on energy or alcohol), telling businesses who they can place on corporate boards, all are supporting increased spending and further borrowing, (most noticeably on projects like HS2, foreign aid, pensions, winter fuel, defense or health care). All have industrial strategies.

Theresa May has at least some redeeming qualities, her one-in-two-out rule on regulation, her promise for flatter, simpler taxes and her commitment to free trade, to name a few. Jeremy Corbyn is far worse, proposing a dramatic change in how we accept goods and services, erecting barriers to trade and commerce around the world, he's offering full socialism. Nationalisation, tax hikes, sequestration of assets and a currency collapse that could lead to exchange controls.

Classical liberalism has never been cultivated in…