See the basic setup   The math derived here.

      ————– distance = X nanoseconds light velocity ————–     

Imagine you and a friend agree to go to separate locations and flip a coin and record on a clip board what you get.   Imagine afterward you get together and compare notes and see that the entire list is identical ? 

That is what essentially what happens when two entangled photons separate and they go through polarizers at the end of their paths. 

Video:  Bell's Inequality and Photon Entanglement Video

Interesting points of note in the video

  • pop bottle bottom glasses on 70's guy!
  • Eigenvalues of a quantum mechanical solution are what you can observe.  You never observe solutions that are combinations of eigenvalues.
  • StarTrek looking test apparatus mock up.  Scotty would have felt at home fixing this bugger!
  • Einstein did not like ghostly action at a distance.  EPR
  • Assume quantum theory is incomplete: Look for a hidden variable. Photon pairs are emitted with a shared equal hidden parameter.
  • Theories using hidden variables have been created that preserve locality and realism
  • Experiments that only test perfect correlations do not force us to choose between quantum explanation and hidden variable method
  • John Bell was the first person to show how to bring the two theories into conflict so they could be tested
  • Testing perfect correlations are tantamount to looking at one sock and seeing it is blue and concluding the sock on the other foot is blue
  • Imperfect correlations: set the target polarizers at unequal angles.
  • Alain Aspect and company tested Bell's Theorem
  • Tunable lasers were required for this test setup

 

Notes regarding entanglement for purposes of understand the math / mechanics

 

Bell's Theorem: The Quantum Venn Diagram Paradox

The following video gives a good simple explanation

Alain Aspect Video Presentation

 

 


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