Hidden Variables Revisited

Atul Singh Arora, Kishor Bharti, Arvind

Jagdish Mehra

R.F. Streater

Richard David Gill

Pearle (1970) gave an example of a local hidden variables model which exactly reproduced the singlet correlations of quantum theory, through the device of data-rejection: particles can fail to be detected in a way which depends on the hidden variables carried by the particles and on the measurement settings. If the experimenter computes correlations between measurement outcomes of particle pairs for which both particles are detected, he or she is actually looking at a subsample of particle pairs, determined by interaction involving both measurement settings and the hidden variables carried in the particles. We correct a mistake in Pearle's formulas (a normalization error) and more importantly show that the model is simpler than first appears. We illustrate with visualizations of the model and with a small simulation experiment, with code in the statistical programming language R included in the paper. Open problems are discussed.

Jonathan P. Dowling

Now that we have a few more concepts under our belts, I would like to go back and revisit in some more detail just what John Bell proved in 1964 about entangled states. He considered a simple quantum situation like the entangled ions in Alice and Bob’s pocket watches and then set about to compare the predictions of quantum theory for such a setup to the predictions of a classical hidden variable theory that had all of Einstein’s constraints: reality, locality, and certainty. Remember-there was already the Bohm hidden variable theory, well known in 1964, which did predict the same outcome as quantum theory, but this Bohm theory doesn’t count because it violates Einstein’s locality condition. (Einstein thumbs his nose at the Bohmians.) Bell’s goal was to see if he could construct a local classical hidden variable theory that would agree with all the predictions of quantum theory and satisfy Einstein’s three conditions. If such a hidden variable theory could be found, then it would be tempting to just replace quantum theory with that hidden variable theory and all the spookiness would just disappear. But in order for this project to succeed, the classical hidden variable theory had to obey all three of Einstein’s reality, locality, and certainty conditions and reproduce all the predictions of quantum theory. at was just too tall of an order to ask of any local hidden variable theory, Bell discovered. Something, somewhere, had to give.

Detlef Dürr, Dustin Lazarovici