Skip to main content

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.


Post a Comment

Popular posts from this blog

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…