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

Understand

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.