### A Simple Mathematical argument against Everett

Any question that we can formulate using quantum mechanics, like the expectation value of an electron's spin in two different states simultaneously, can be given an answer. Simply we can state it as being

$Prob =\left \langle \psi |P| \psi \right \rangle$

P is the projection operator, so that it is a product of two other projection operators on the state of an electrons spin. Such that

$P = P_{A} \cdot P_{B}$

These are both projection operators but on a subspace. So that the expectation value of the electron in state "up" corresponding to the first projection operator and expectation value of the electron in the state "down" corresponding to the second projection operator, are both one if the projection operator P is one. So that we have

We should see that

$P = P_{A}\cdot P_{B} = 0$

We then have an answer for the probability of finding the electron in both states simultaneously

The probability of finding the electron in both the spin up and the spin down state is zero. By contrast the Everett or Many Worlds Interpretation imagines that both states of the electron are equally real in parallel branches of the wave function which would surely correspond to a value of one not zero. We then see that the error in the Everett interpretation is that they misidentify the logical conjunction as something other than binary multiplication. The principles of quantum mechanics as it is standard to formulate them and the Everett Interpretation are two proposals that should then be taken as incompatible.

### Three Things William Lane Craig Gets Wrong About the Hartle-Hawking No Boundary Proposal

Classical standard hot Big Bang cosmology represents the universe as beginning from a singular dense point, with no prior description or explanation of classical spacetime. Quantum cosmology is different in that it replaces the initial singularity with a description in accord with some law the "quantum mechanical wave function of the universe", different approaches to quantum cosmology differ in their appeal either to describe the origin of the material content of the universe e.g., Tyron 1973, Linde 1983a, Krauss 2012 or the origin of spacetime itself e.g., Vilenkin 1982, Linde 1983b, Hartle-Hawking 1983, Vilenkin 1984.

These last few proposals by Vilenkin, Hartle-Hawking and others are solutions to the Wheeler-DeWitt equation and exist in a category of proposals called "quantum gravity cosmologies" which make cosmic applications of an approach to quantum gravity called "closed dynamic triangulation" or CDT (also known as Euclidean quantum gravity). I&#…

### How Should Thatcherites Remember the '80s?

Every now and again, when I talk to people about the '80s I'm told that it was a time of unhinged selfishness, that somehow or other we learned the price of everything but the value of nothing. I can just remember that infamous line from Billy Elliot; 'Merry Christmas Maggie Thatcher. We all celebrate today because its one day closer to your death'. If it reflected the general mood of the time, one might wonder how it is she won, not one but three elections.

In an era when a woman couldn't be Prime Minister, her launch into power was accidental owing in part to Manchester liberals and the Winter of Discontent. Yet I'm convinced her election victory in '79 was the only one that ever truly mattered. Simply consider the calamity of what preceded it, the 1970s was a decade of double-digit inflation, power cuts, mass strikes, price and income controls, and the three day week. Britain was sick, it needed fundamental restructuring but no one seemed to quite under…

### Can inflation be eternal into the past?

Back in 2003 a paper appeared on the arXiv titled "Inflationary spacetimes are not past complete" that was published by Arvind Borde, Alan Guth and Alexander Vilenkin which has had considerable amounts of attention online. The theorem is rather uninteresting but simple and doesn't require a very complicated understanding of math. So I thought I'd explain the result here.

It's purpose is to demonstrate that inflationary models are geodesically incomplete into the past which they take as "synonymous to a beginning" but Vilenkin stresses that the theorem can be extended to non inflationary models so long as the condition of the theorem that the average rate of expansion is never below zero is met. These models too then are incomplete into the past. Consider the metric for an FRW universe with an exponential expansion

Where the scale factor is

Since the eternal inflation model is a "steady state cosmology" the mass density and the Hubble paramet…