The Message of Quantum Science by Philippe Blanchard & Jürg Fröhlich

Author:Philippe Blanchard & Jürg Fröhlich
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

where . Let us assume that p l  > 0 for at least two distinct values of l. The problem is that, in general, the assumption that does not imply that , for all for which p l  > 0; this is the phenomenon of “spontaneous symmetry breaking”. This means that the “sum rule” (7.84), Sect. 7.4.1, may be violated at the ith slot, for some 1 < i < n. Hence the family a 1, …, a n may not give rise to a family of consistent histories.

(2)In general, the centralizers are non-abelian algebras. If the centralizers are non-commutative algebras then identifying empirical properties of S observable at times ≥ t with elements of is subject to critique (ii), Sect. 7.4.3. Our task is then to find out which elements of may correspond to empirical properties of S. (The center of is denoted by . If were known to contain operators representing potential properties of S then these operators could be interpreted as empirical properties of S observed at some times ≥ t, and critique (ii) of Sect. 7.4.3 would not apply, anymore.)

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