Saturday, 26 February 2011
Classes of models
For the introduction to this blog, see my topic ‘Challenging Bell with a local realistic simulation of EPR-Bohm’
One should probably differentiate between models that leave out a part of the measurements for some plausible reason (class A), or those who use the full dataset for the calculation of the Bell inequality (class B). The Bell inequality is based on getting a fair sample of the measurements, but in real experiments using present technology one can’t be sure about that.
The de Raedt model (see first blog) is such a class A simulation, because it excludes the counting of hits that exceeds a certain time window between the particles. A second model in this class might be that of Ashwanden (1), who corrects for the intensity of a photon at the polarizer, and gets results that are more compatible with the real experiment as the quantum expectation. It looks somewhat cleaner, because it seems to correct the individual particles at the polarizer’s, and not- like in the de Raeth simulation - as a correction on the combined time-delay properties when counting the results (and thereby using both polarizer angles in this calculation).
With the class A simulations one always runs the risk that it will be invalidated at some moment by better experiments, because somehow a loophole in the experiment is exploited. The only model that I know that is (probably) of class B is that of Joy Christian, but because of the quite complicated Clifford calculations it still has to prove itself in an event by event simulation (I could surely use some help here;). It is worth mentioning that recent publications seem also to suggest a close relationship between QM and Clifford algebra (2, 3, and 4).
It might be that in the end class B simulations turns out to be impossible (and the theorem of Bell is valid) but that the results of real experiments are caused by some hidden variables that corresponds to elements of reality, as the time window of de Raedt, the intensity of Ashwanden or possibly the 2d spin of Sanctuary (see first blog), so that Bell is not applicable to the EPR-Bohm experiment.
1) Dr. Manuel Aschwanden, A classical view of quantum entanglement , http://www.iis.ee.ethz.ch/~schenk/theses/aschwanden.pdf
2) Algebraic Quantum Mechanics, Algebraic Spinors and Hilbert Space, B. J. Hiley, http://www.bbk.ac.uk/tpru/BasilHiley...chanic%205.pdf
3) The Clifford Algebra Approach to Quantum Mechanics B: The Dirac Particle and its relation to the Bohm Approach, B. J. Hiley and R. E. Callaghan, http://arxiv.org/PS_cache/arxiv/pdf/...011.4033v1.pdf
4) The Clifford Algebra approach to Quantum Mechanics A: The Schroedinger and Pauli Particles, B. J. Hiley and R. E. Callaghan, http://arxiv.org/PS_cache/arxiv/pdf/...011.4031v1.pdf