Research output: Contribution to journal › Article

**Dynamical locality and covariance : What makes a physical theory the same in all spacetimes?** / Fewster, Chris; Verch, Rainer.

Research output: Contribution to journal › Article

Fewster, C & Verch, R 2012, 'Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?', *Annales Henri Poincare*, vol. 13, no. 7, pp. 1613-1674. https://doi.org/10.1007/s00023-012-0165-0

Fewster, C., & Verch, R. (2012). Dynamical locality and covariance: What makes a physical theory the same in all spacetimes? *Annales Henri Poincare*, *13*(7), 1613-1674. https://doi.org/10.1007/s00023-012-0165-0

Fewster C, Verch R. Dynamical locality and covariance: What makes a physical theory the same in all spacetimes? Annales Henri Poincare. 2012 Nov;13(7):1613-1674. https://doi.org/10.1007/s00023-012-0165-0

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

abstract = "The question of what it means for a theory to describe the same physics onall spacetimes (SPASs) is discussed. As there may be many answers to thisquestion, we isolate a necessary condition, the SPASs property, that shouldbe satisfied by any reasonable notion of SPASs. This requires that if twotheories conform to a common notion of SPASs, with one a subtheory of theother, and are isomorphic in some particular spacetime, then they should beisomorphic in all globally hyperbolic spacetimes (of given dimension). TheSPASs property is formulated in a functorial setting broad enough todescribe general physical theories describing processes in spacetime,subject to very minimal assumptions. By explicit constructions, the fullclass of locally covariant theories is shown not to satisfy the SPASsproperty, establishing that there is no notion of SPASs encompassing allsuch theories. It is also shown that all locally covariant theories obeyingthe 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 Cauchyevolution). The covariance properties of relative Cauchy evolution and thekinematic and dynamical substructures are analyzed in detail. Calling localcovariant theories dynamically local if their kinematical and dynamicallocal substructures coincide, it is shown that the class of dynamicallylocal theories fulfills the SPASs property. As an application in quantumfield theory, we give a model independent proof of the impossibility ofmaking a covariant choice of preferred state in all spacetimes, for theoriesobeying dynamical locality together with typical assumptions.",

author = "Chris Fewster and Rainer Verch",

year = "2012",

month = "11",

doi = "10.1007/s00023-012-0165-0",

language = "English",

volume = "13",

pages = "1613--1674",

journal = "Annales Henri Poincare",

issn = "1424-0661",

publisher = "Birkhauser Verlag Basel",

number = "7",

}

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T2 - Annales Henri Poincare

AU - Fewster, Chris

AU - Verch, Rainer

PY - 2012/11

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N2 - The question of what it means for a theory to describe the same physics onall spacetimes (SPASs) is discussed. As there may be many answers to thisquestion, we isolate a necessary condition, the SPASs property, that shouldbe satisfied by any reasonable notion of SPASs. This requires that if twotheories conform to a common notion of SPASs, with one a subtheory of theother, and are isomorphic in some particular spacetime, then they should beisomorphic in all globally hyperbolic spacetimes (of given dimension). TheSPASs property is formulated in a functorial setting broad enough todescribe general physical theories describing processes in spacetime,subject to very minimal assumptions. By explicit constructions, the fullclass of locally covariant theories is shown not to satisfy the SPASsproperty, establishing that there is no notion of SPASs encompassing allsuch theories. It is also shown that all locally covariant theories obeyingthe 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 Cauchyevolution). The covariance properties of relative Cauchy evolution and thekinematic and dynamical substructures are analyzed in detail. Calling localcovariant theories dynamically local if their kinematical and dynamicallocal substructures coincide, it is shown that the class of dynamicallylocal theories fulfills the SPASs property. As an application in quantumfield theory, we give a model independent proof of the impossibility ofmaking a covariant choice of preferred state in all spacetimes, for theoriesobeying dynamical locality together with typical assumptions.

AB - The question of what it means for a theory to describe the same physics onall spacetimes (SPASs) is discussed. As there may be many answers to thisquestion, we isolate a necessary condition, the SPASs property, that shouldbe satisfied by any reasonable notion of SPASs. This requires that if twotheories conform to a common notion of SPASs, with one a subtheory of theother, and are isomorphic in some particular spacetime, then they should beisomorphic in all globally hyperbolic spacetimes (of given dimension). TheSPASs property is formulated in a functorial setting broad enough todescribe general physical theories describing processes in spacetime,subject to very minimal assumptions. By explicit constructions, the fullclass of locally covariant theories is shown not to satisfy the SPASsproperty, establishing that there is no notion of SPASs encompassing allsuch theories. It is also shown that all locally covariant theories obeyingthe 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 Cauchyevolution). The covariance properties of relative Cauchy evolution and thekinematic and dynamical substructures are analyzed in detail. Calling localcovariant theories dynamically local if their kinematical and dynamicallocal substructures coincide, it is shown that the class of dynamicallylocal theories fulfills the SPASs property. As an application in quantumfield theory, we give a model independent proof of the impossibility ofmaking a covariant choice of preferred state in all spacetimes, for theoriesobeying dynamical locality together with typical assumptions.

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