Wednesday, 7 October 2015

A bit more on Bell

Some readers of the last post on Bell  may claim that I have missed the point. What my last account fails to do they would say is take into account the effect of the polarisation settings and the fact that they can be changed during the time of flight. So that as the usual story goes if the polarisation of the left detector is changed then the polarisation of the photon (or electron) will change in accordance with that polarisation but because the other photon must have opposite spin then it will change its polarisation accordingly.

I think from a statistical point of view this is misguided. A polariser acts as a filter and for a given polarisation angle only a fraction of the particles in the beam will be able to pass the polariser in a accordance with Malus's Law the probability of passing through the filter being proportional to the square of the cosine of the angle between the polariser setting and the photons polarisation angle. On emergence the photons that pass through the filter will have the polarisation of the polariser.

However some photons will not pass through. The polariser has destroyed any correlation there might have been with an EPR pair. Similarly at the other end a different number  of  photons will also pass through. The number of photons that pass through both ends being dependent on the polariser settings All this can be calculated from the basic laws of quantum physics. But given that polarisers will destroy any prior correlation. I can't see why it is inconsistent with the idea that before 1 or both of the photons hit the polarisers they were emitted from the source with perfect anti-correlation.

Clearly if one thinks the Bell State applies to single pairs alone then one would have to invoke some spooky action at a distance, But from a statistical point of view all we have is the probability of the photons electrons or whatever emerging through the polarisers.  One has to imagine the pairs being randomly emitted from the source with all sorts of polarisation angles, each pair being anti-correlated especially as the Bell state is rotationally invariant. However it is not clear, if one is just concerned with the overall transmission probability of photons through the polarisers which is all one can measure, that the photon that passes through the left polariser is one that is paired with the photon that passes through the right hand polariser. Because the polariser obviously destroys any correlation. Imagine if for example there was only 1 polariser say the left side then clearly the polarisation of the other photon would not change.

Given that in order to verify the statistics many events have to occur then there is no way of ever detecting a single pair of photons.

On that basis then I still feel justified in denying the need for any form of super-luminal signalling between a single pair of photons.

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