### GHZ Experiment vs Local Realism

Today I want talk about a famous paper titled "Bell's theorem, quantum theory and the conception of the Universe" which contains a thought experiment by Greenberger, Horne and Zeilinger that creates real problems for anyone who understands fundamental physics in terms of local realism, assuming it could even survive the difficulty captured in Bell's inequality theorem. The GHZ argument is not so reminiscently, simple at least as far as fundamental physics goes. I first came across the argument listening to an online lecture by the physicist Sidney Coleman but the argument against local realism here is unique in that it does not involve the derivation of any inequality over a statistical series of measurements like Bell's theorem does.

Most physicists believe the GHZ experiment is problematic for realist and hidden variable theories, the only way to make these compatible with the experiment is to appeal to exotic non-localities. The experimental set up involves three entangled particles whose spin can be measured in the x or y directions using a Stern-Gerlach device. We can set up a quantum mechanical experiment so that
• All measurements must yeild a value for spin that is either +1 or -1
• Measure all three particle's spins in the horizontal direction and the product of their spins is -1
• Measure one particle in the horizontal direction and two in the vertical direction and the product of their spin is +1
Suppose these particles have spin independent of any measurement, the horizontal component of particle a, b and c would be

Their vertical component is given by

If we obtain a measurement of the horizontal component of particle a then the product of this measurement with the vertical component of particle b and c obtains a value of +1 (from one of the bullet points earlier). The same is true of measuring the horizontal component of particle b with the vertical component of particle a and c and also the horizontal component of particle c with the vertical component of particle a and b. So that

This can be derived from local realism but it contradicts one of the predictions of quantum mechanics that three measurements of spin for three entangled particles in our set up in the horizontal direction will yeild a value of -1 therefore we can affirm that local realism is incompatible with the predictions of quantum mechanics. Local realism makes an assumption somewhere that is invalid. We can set up the experiment so that the product of the vertical component of particle a and the horizontal component of particle b is -1 this would require that the vertical component of particle c is also -1 so that

Suppose that in the experiment the horizontal component of particle a is measured with the veritcal component of particle b and these yeild a product of +1 then in this case the vertical component of particle c must also be +1 so that

The value particle c's spin has changed in accordance with the measurement context, this property is called "contextuality" and makes sense of the experiment without violating special relativities rule on super luminal signalling.

1. "No sub luminal to super luminal signalling" not ever ? ;D

1. Unfortunately not. SR tells us it would take an infinite amount of energy to accelerate an object of mass to the speed of light.

### 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, 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…