### 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.

### Margaret Thatcher's Legacy for Britain

The following is an adaptation of my thoughts at UCL's Conservative Society some months ago concerning the issue of the Conservative Parties vote of no confidence that lead to the resignation of Margaret Thatcher, her legacy for Britain and why she's so undeserving hated by the hard left.

When one enters parliament through members lobby there are four prime ministers commemorated and immortalized in statue form. The first of these figures, David Lloyd George seeded the beginnings of the welfare state, the second Winston Churchill served his tenure protecting us from physical annihilation during the Second World War, the third, Clement Attlee nationalized the health service and sought to drive Britain down the road of socialism and the fourth, the late Baroness Thatcher brought great economic revolution at the end of the Cold War.

It's been said of British politics that these last two figures though diametrically opposed were the only elections that ever really mattered. B…

### 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…

### 'Don't boo Labour, vote Conservative!' #ImWithHer

"My pitch is very simple, I'm Theresa May and I believe I'm the best person to be Prime Minister"

In an election one doesn't always get the option of voting for their primary candidate, for me that's been the case here. Originally I had supported Michael Gove and then Andrea Leadsom for leadership of the Conservative party but on June 8th we're expected to choose between Theresa May and Jeremy Corbyn. Whatever you think of the two personally, the choice of who offers better governance couldn't be clearer.

The most notable part of Jeremy Corbyn's "leadership" has been his support for the outrageous and policies of the far left. He supports the unilateral disarmament of British nuclear weapons, while supporting the right of Iran to have its own unrestricted nuclear program. He's had an industrial policy to nationalize the mining of coal but not to burn coal, and supports self-determination for the people of Palestine but not for the p…