### Consistent Histories

Consistent Histories is an interpretation of quantum mechanics that started in 1984 with a statistical physicist Robert Griffiths, who discovered a set of criteria designed to assign conditional probabilities based on classical rules of probability. The interpretation was picked up by Roland Omnes in 1988 who gave the theory a formal logical systemisation and later by James Hartle and Murray Gell-Mann, who emphasise the role of decoherence in replacing collapse of the wave function in 1990.

The interpretation starts with with subspaces of the Hilbert space and applies to closed systems by treating them as a sequence of events or "histories". An event specificies the properties of a system as a projection operator on the Hilbert space, where:

A "homogenous history" is taken as a series of such operators. The evolution of these histories from event-to-event is stochastic and evolves according to the Schrodinger equation in Griffiths' original formulation. Only histories which satisfy a set of consistency conditions are assigned probabilities and given an interpretation in the theory. These histories do not represent real features of reality but are a useful frame work for discussing time sequences of possibilities, they behave as classical histories only to the extent that they are non-interfering. The weight of a history is given by

E represents the event or its operator. If two histories have weights which are orthogonal such that interference is negligible

Then their weights can be added together. This may be extended to include so called "families" which is a space to include all non-interfering histories. For such families we can consider a generalised coordinate description of any classical field that is considered fundamental to physics, like the gravitational field, if the projection operators up to n include all the possible field variables, Hartle and Gell-Mann call this set exhaustive.

We can then go on to define "alternative histories" as an exhaustive set of histories containing an alternative range. The extreme case is to give a complete set of operators at all times, a completely fine-grained history. However it is essential to the Histories approach that fine grained histories cannot be assigned probabilities.

A consistent account of probability will involve a suitable set of coarse grainned histories. The Hartle Gell-Mann approach further specifies specific conditions which apply to the early universe for projection operators. Not only must they commute but their product must be equal to zero. We can later abandon this restrictive condition for later times for an alternative set of histories. It is not necessary to apply Consitent Histories to the entire universe but if one does then the wave function is treated as pre-probability but plays no role in the ontology of the interpretation.

When one integrates the projection operators

You obtain a decoherence function

Once decoherence is introduced the two projection operators will diverge and represent possible histories of the system. Griffiths and Omnes began considering small levels of decoherence whereas Hartle and Gell-Mann are interested in strong decoherence. In either case decoherence replaces measurement of the system and the interpretation retains locality. The decoherence function depends on both the density matrix and Hamiltonian of the early universe, Hartle and Gell-Mann follow the time evolution of the operator back to the early universe, which is intended to solve the preferred basis problem.

What history actually occurs? According the formalism, histories are treated similar to the wave function when calculating the path of a particle, a central tendency is located along classical trajectories when the projection operator is coarse grained and the wave function very slowly spreads out. Only histories which are sufficiently coarse grained and therefore close to the classical path will have a high probability of occurring.

In order for a quasi-classical realm to correspond to the set of histories however, one must avoid a completely fine grained description but mustn't have a description which is grained too coarse such that no classically unambiguous description is any longer available.

### William Lane Craig and 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 and a working class radical would never lead the Conservative party, Thatcher was both and her launch into power was almost 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…

### Creation Of Universes from Nothing

The above paper "Creation of Universes from Nothing" was published in 1982, which was subsequently followed up in 1984 by a paper titled "Quantum Creation of Universes". I decided it would be a good idea to talk about these proposals, since last time I talked about the Hartle-Hawking model which was, as it turns out, inspired by the above work.
Alexander Vilenkin also explains in a non-technical way the essential idea in his book; Many World's in One – one of the best books I've ever read – it mostly covers cosmic inflationary theory but the 17th chapter covers how inflation may have begun. In fact Vilenkin is one of the main preponderant who helped develop inflation along with Steinhardt, Guth, Hawking, Starobinsky, Linde and others.
Although I won't talk about it here, Vilenkin also discovered a way of doing cosmology by using something called "topological defects" and he has been known for work he's done on cosmic strings, too.
In ex…