Department of Philosophy, University of Pittsburgh

A fundamental question of interest for philosophers of science in
general, and philosophers of physics in particular, is: *"Are relativity
and quantum nonlocality consistent?"* Some philosophers have ignored or
made light of the fact that, at least on a purely formal level, the answer
to this question has long been known: Yes, there is a mathematically
consistent theory -- viz., algebraic relativistic quantum field theory
(AQFT) -- that combines in a rigorous manner the fundamental assumptions
of both quantum theory and the special theory of relativity. In fact, it
appears that not only are relativity and quantum nonlocality consistently
combined in AQFT; relativistic causality actually enforces quantum
nonlocality in this context.

One sharp example of this phenomenon is the so-called Reeh-Schlieder (RS)
theorem. In this presentation, I will show explicitly how the RS theorem
uses the assumption of relativistic causality to derive a highly nonlocal
conclusion. In particular, I will focus my discussion around explicating
two claims that have been made about the RS theorem: (1) Simon Saunders
claims that the RS theorem is a "purely relativistic result." I will show
that while in one mathematically precise sense, Saunders' claim is true --
viz., the RS theorem fails when we pass to the non-relativistic limit (c
-> infinity) -- in the strictest sense it is false, since a modified
version of the RS theorem continues to hold in nonrelativistic,
Galilei-invariant quantum field theory. (2) According to Irving Segal,
the RS theorem (*if* its premises were true) would entail that, "the
entire state vector space of the field could be obtained from measurements
in an arbitrarily small region of space-time!" I will show the precise
sense in which Segal's claim is true, and I will argue that the resulting
nonlocality is not -- as Segal supposes -- "at variance with the spirit of
relativistic causality."

SSPB 1208, 3 pm

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