I want to discuss one further argument against local realism from Lucien Hardy in another well known set of publications, that were submitted in 1992 and 1993. In two papers titled "Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories" and "Nonlocality for two particles without inequalities for almost all entangled states". These papers present what is more commonly known as "Hardy's paradox".

These must be the nail in the coffin for any reasonable person who wants to still defend local realism. The experiment shows that the predictions of quantum mechanics differ from that of any local realist and local hidden variable theory.

The experiment involves using a stream of positions and electrons both sent through separate beam splitters on the left and the right. The wave function of each particle "splits" along the w path and the v path. These are then rejoined at the second beam splitter in phase so that if there's no interaction between the electrons and the positrons then an interference pattern is detected at c (constructive interference).

However if you set up the experiment so that the elections on the right interfere with the positrons on the left, the electrons and positrons will annihilate producing photons

So that only particles in the v path reach the second beam splitter. These waves are not coherent with anything so they meet at detectors c and d with equal probability. We can therefore assume that any detection at either d detector means that there was an anihilation event between the two beams at point P. Whenever a detection is made at d the corresponding particle is at u so that

However if we analyse this experiment from the perspective of a local hidden variable theory, wherein particles are independent there can be no detection at d because they would have to travel though the u path where here is an annihilation event. Local hidden variables have a problem then, because these experiments have been performed and there is a detection at d with a Pr(d) =1/16.

There's a Pr(e+) and Pr(e-) entering both w beams of 1/2 each, so 1/4 and then a further 1/4 probability of each reaching either d detector. So both taken together give a probability of 1/16.

Some more context is probably necessary, if one thinks of quantum theory as being local and as maintaining realism then there is a frame of reference in which a detection can be made at the d detector for the positron, while the corresponding particle in the electron beam has not reached the beam splitter. Similarly you can can have a frame of reference in the opposite direction in which the reverse is also true, where the electron has reached the detector but the positron has not yet reached the beam splitter. Both of these claims cannot be correct, if you compare both frames of reference the particles must have come through either w path and anihilated. So we've arrived at Hardy's paradox.

One possibility is that the particles detection at d is not independent of the second particle in u and there was some influence that occurred faster-than-light or another is that perhaps the measuring device does not register a property the particle had before detection and so there was no definite measurement outcome. The experiment appears to confirm the long held belief that any realist or hidden variable theory must deny locality in order to be consistent with the predictions of quantum mechanics.

### 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…