The Science Corner: Bell’s Inequality

At the end of my last article (printed in the old Hashmark) I signed off saying that I had embraced relativism. I was swayed by the soothing words of Keats: “beauty is truth, truth beauty – that is all ye know on Earth, and all ye need to know”. So you may be wondering what became of my venture in the land of relativism; well, all I’ve got to say is that it’s nice for a holiday but I wouldn’t want live there. For example, banks do not accept that the fact that I am overdrawn is only a relative truth and must be put in the cultural context of a nation on the verge of a spending-lull-induced episode of deflation. The sad fact is that I went over my limit (and am consequently in line for a fine) and that relativism is rubbish at solving inequalities.

Bell’s Inequality pops up in many places, including quantum theory, but where does it come from? Here is a simple proof using the set theory:

Three sets: A, B, C

Prove that: (the number of elements in set A but not in set B) plus (the number of elements in set B but not in C) is greater to or equal to (the number of elements in set A but not set C).

Define:

The number of elements in A, not B, not C = a

The number of elements in B, not A, not C = b

The number of elements in C, not B, not A = c

The number of elements in both A and B but not in C = d

The number of elements in both A and C but not in B = e

The number of elements in both B and C but not in A = f

The number of elements in both A and B and C = g

Visual aid:

Everything inside the circle is an element of A;sans-titre.JPG

Everything inside the rectangle is an element of B;

Everything inside the triangle is an element of C.

Therefore, the number of elements in set A but not in set B = a + e, in set B but not in set C = b + d, and in set A but not set C = a + d

So,
Bell’s inequality can be written as:

(a + e) + (b + d) >/= a + d

All original Robbie Tea work.

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2 Comments

Filed under Hashmark Science, Maths, Science, The Science Corner

2 responses to “The Science Corner: Bell’s Inequality

  1. Jimineybob

    Nice work

  2. Alan

    The return of the science corner, yeah my favourite part

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