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Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?

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JournalAnnales Henri Poincare
DateE-pub ahead of print - 24 Mar 2012
DatePublished (current) - Nov 2012
Issue number7
Volume13
Number of pages62
Pages (from-to)1613-1674
Early online date24/03/12
Original languageEnglish

Abstract

The question of what it means for a theory to describe the same physics on
all spacetimes (SPASs) is discussed. As there may be many answers to this
question, we isolate a necessary condition, the SPASs property, that should
be satisfied by any reasonable notion of SPASs. This requires that if two
theories conform to a common notion of SPASs, with one a subtheory of the
other, and are isomorphic in some particular spacetime, then they should be
isomorphic in all globally hyperbolic spacetimes (of given dimension). The
SPASs property is formulated in a functorial setting broad enough to
describe general physical theories describing processes in spacetime,
subject to very minimal assumptions. By explicit constructions, the full
class of locally covariant theories is shown not to satisfy the SPASs
property, establishing that there is no notion of SPASs encompassing all
such theories. It is also shown that all locally covariant theories obeying
the time-slice property possess two local substructures, one kinematical
(obtained directly from the functorial structure) and the other dynamical
(obtained from a natural form of dynamics, termed relative Cauchy
evolution). The covariance properties of relative Cauchy evolution and the
kinematic and dynamical substructures are analyzed in detail. Calling local
covariant theories dynamically local if their kinematical and dynamical
local substructures coincide, it is shown that the class of dynamically
local theories fulfills the SPASs property. As an application in quantum
field theory, we give a model independent proof of the impossibility of
making a covariant choice of preferred state in all spacetimes, for theories
obeying dynamical locality together with typical assumptions.

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