Finding ordinary objects in the world of quantum mechanics

“Configuration space” is normally introduced as a name for some sort of mathematical abstraction. There are various candidates: when the application we have in mind is that of formulating the laws of a classical mechanics of point-particles living in Newtonian absolute space, one especially natural candidate is the set of all functions from particles to points of space. This set is naturally regarded as a “space” in its own right, since there are natural extensions of geometrical notions like betweenness and distance from the points of space to the members of this set.1 The history of the universe can then be exhaustively represented as a function from times to points of configuration space—in the Langrangian formalism for classical mechanics, the basic dynamical laws are expressed as constraints on this sort of function. The claim that a given function h accurately represents the history of the universe can be analysed, straightforwardly, as the claim that at each 1The definition of betweenness is straightforward: f1 is between f2 and f3 iff for each particle p, f1(p) is between f2(p) and f3(p). The standard definition of distance is more complicated: the distance between f1 and f2 is √ ΣpMass(p)| f1(p) f2(p)|. The naturalness of this particular definition only becomes apparent once one starts to think about how to use configuration space in formulating the laws of classical mechanics.