# Isn’t Bell’s probability density for hidden variables too restrictive?

1. May 22, 2007

### nekkert llup

J.S. Bell (Physics Vol.1, No. 3, 1964) excludes from consideration any distribution $$\rho$$ of the hidden variable $$\lambda$$ that formally depends on the vectors $$a$$ and $$b$$, except if $$\rho ( \lambda ,a,b) = \rho ' ( \lambda ,a) \rho ' ( \lambda ,b)$$ i.e. if the distribution can be factored in a part depending on $$a$$ and not on $$b$$ and another part depending on $$b$$ and not on $$a$$. Otherwise he could not derive (22). On precisely which grounds did Bell introduce this restriction? For example, does the locality requirement lead to this restriction? How?Are other principles involved?

Edit: I made an unforgivable error: According to Bell, neither $$\lambda$$ itself nor its density distribution $$\rho ( \lambda )$$ may depend on $$a$$ and $$b$$. The question is still the same: why not?

Last edited: May 23, 2007