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13040121

We

develop a theory for describing composite objects in physics. These can be

static objects, such as tables, or things that happen in spacetime (such as a

region of spacetime with fields on it regarded as being composed of smaller

such regions joined together). We propose certain fundamental axioms which, it

seems, should be satisfied in any theory of composition. A key axiom is the

order independence axiom which says we can describe the composition of a

composite object in any order. Then we provide a notation for describing

composite objects that naturally leads to these axioms being satisfied. In any

given physical context we are interested in the value of certain properties for

the objects (such as whether the object is possible, what probability it has,

how wide it is, and so on). We associate a generalized state with an object.

This can be used to calculate the value of those properties we are interested

in for for this object. We then propose a certain principle, the composition

principle, which says that we can determine the generalized state of a

composite object from the generalized states for the components by means of a

calculation having the same structure as the description of the generalized

state. The composition principle provides a link between description and

prediction.

©2012 Perimeter Institute for Theoretical Physics