Unreality at the Local

Quantum entanglement

Correlating Reading and Understanding
Chapter three of On Physics and Philosophy was a pretty frustrating read.

D’Espagnat seems to be drawing several threads slowly towards a core conclusion, but it often feels like an extremely meandering trail.

Working from the top down, here are some of the points he seems to be making.

The Basic Theme
Bell’s theorem makes predictions about how observations of two particles relate to each other.

Bell’s inequalities predict certain correlations at a distance when you assume locality and a belief in free experimental choice.

The locality condition (more or less) states that influences can’t travel faster than the speed of light.

The belief in free experimental choice lets the experimenter decide what to test, otherwise it’s hard to do empirical science.

If your results don’t match Bell’s inequalities at least one assumption (locality or free choice) is wrong.

A pair of photons created by the same atom will be entangled. We can measure a photon and and its distant partner.

Do that with enough photons and we get a pattern to compare with Bell’s inequalities.

Experiments by Aspect and others show that Bell’s inequalities are violated at the microscopic level.

Since we want to believe in experimenters’ free will, locality must be discarded.

Supplementary Points
A “supplementary theorem” devised by four scientists states that if there are faster-than-light influences between the photons in the pair, these influences cannot convey matter, energy, or usable signal.

If one rejects objectivist realism then locality or nonlocality is a meaningless distinction. But nonseparability remains in play.

If you try to add hidden local variables to specify the particles’ polarizations in advance (right at the source) then you get the wrong predictions.

Even More Points to Ponder
The violation of Bell’s inequalities is often assumed to imply the falsity of all hidden variable theories.

In fact the experimental data only disprove the falsity of local hidden variable theories.

Non-local hidden variable theories such as de Broglie’s or Bohm’s match the predictions of standard quantum mechanics (at least non-relativistically). A pilot wave controlling localized particles must still travel through both slits of a double-slit experiment.

By extension, the disproving of locality shows the limitations of Descartes’ “divisibility by thought.”

You cannot spatially divide the photon pair’s wave function and still get the predictions of quantum mechanics that Bell’s theorem and the Aspect-type experiments say you should.

Last revised 18 June 2010

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