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

  1. May 22, 2007 #1
    J.S. Bell (Physics Vol.1, No. 3, 1964) excludes from consideration any distribution [tex] \rho [/tex] of the hidden variable [tex] \lambda [/tex] that formally depends on the vectors [tex] a [/tex] and [tex] b [/tex], except if [tex] \rho ( \lambda ,a,b) = \rho ' ( \lambda ,a) \rho ' ( \lambda ,b)[/tex] i.e. if the distribution can be factored in a part depending on [tex] a [/tex] and not on [tex] b [/tex] and another part depending on [tex] b [/tex] and not on [tex] a [/tex]. 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 [tex] \lambda [/tex] itself nor its density distribution [tex] \rho ( \lambda ) [/tex] may depend on [tex] a [/tex] and [tex] b [/tex]. The question is still the same: why not?
     
    Last edited: May 23, 2007
  2. jcsd
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