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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.

Comments

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

    ReplyDelete
    Replies
    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.

      Delete

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