Research output: Contribution to journal › Article

Journal | Annales Henri Poincare |
---|---|

Date | E-pub ahead of print - 24 Mar 2012 |

Date | Published (current) - Nov 2012 |

Issue number | 7 |

Volume | 13 |

Number of pages | 62 |

Pages (from-to) | 1613-1674 |

Early online date | 24/03/12 |

Original language | English |

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.

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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