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Summary: Bell (1964) On the Einstein-Podolski-Rosen paradox

[Summary  by Søren Riis]
On Friday 8th April, we discussed the paper “On the Einstein-Podolski-Rosen paradox” Physics 1 (3), 195 (1964) by John Bell, where he introduced what later became known as Bell’s inequality.

One of the remarkable features of quantum physics is that a locally realistic theory cannot always describe measurements on spatially separated systems. Correlations that are allowed within the framework of a locally causal theory are usually referred to as classical.
The point is that quantum mechanics does not always result in “classical” correlations, and this can be quantified by the violation of Bell’s inequalities. These are constraints that have to be satisfied by any classical correlations.

In the meeting, we went over Bell’s paper. I was already familiar with Einstein Podolski Rosen’s 1935 paradox (the EPR paradox), and I have also tried to get my head round Bohr’s less known response (also from 1935) to the EPR paper. Also, I read various modern presentations of Bell’s inequality, but I never read Bell’s original paper.

I think John Bell’s interpretation of quantum physics is somewhat unclear. In Quantum Gravity 2, pp. 611 (1981) he wrote:
“When the ‘system’ in question is the whole world where is the ‘measurer’ to be found? Inside, rather than outside, presumably. What exactly qualifies some subsystems to play this role? Was the world wave function waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer for some highly qualified measurer — with a Ph.D.?”

Without going into the technical details a (simplified) way to think of the problem is that Alice and Bob are performing measurements of so-called entangled particles at two spatially separated places. The entanglement ensures that there is 100% correlation between Alice’s result of a measurement on her particle and the corresponding measurement on Bob’s particle, provided they measure the same quantity.

In the setup for Bell’s inequality, Alice can choose between 3 measurements A, B and C. and Bob also has a choice between three measurements A, B and C.
Expressed somewhat crudely (and stripping away further details), quantum physics predicts that we can have non-transitivity, so:

  1. the result of A is strongly correlated with the result of B, AND
  2. the result of B is strongly correlated with the result of C YET
  3. the result of A is uncorrelated with the result of C.

To dramatise the “essence” in the situation further, imagine that Alice and Bob repeatedly chose between 2 measurements among A, B and C. After 100s of repeated experiments they notice that

  1. if they measure A and B they always get the same result;
  2. if they measure B and C they always get the same result.

    But to their utter amazement, they notice that

  3. if they measure A and C they always get two different (opposite) results.

There have been various attempts to interpret quantum physics to make sense of such “impossible” correlations.
Within the last ten years, Bohr’s Copenhagen interpretation has lost its status as the primary interpretation, and an increasing number of physicists support wild interpretations like Everett’s many-worlds interpretation.

In my dramatised ERP thought experiment there is no reason to believe Alice and Bob would conclude that they split into different copies of themselves. The way I see the problem (which I think is the essence of the Copenhagen interpretation), it seems more natural that Alice and Bob find that the world as a whole follows some mathematical laws, so even their choice of measurements is a part of this mathematical pattern.
From this view, it is not just the two particles that are entangled. It seems that they would be forced to conclude that their choice of which measurement to perform would be similarly entangled in agreement with some underlying mathematical principles that are constraining the universe as a whole.


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