Causation and Its Basis in Fundamental Physics

ions or fuzzings or coarse-grainings of the object, which are all derivative.) Alternatively, if fundamental reality is something more esoteric like an entangled quantum field or an eleven-dimensional arena inhabited by strings, then there maywell be no parts of fundamental reality that count as an instance of the object, in which case the object is unambiguously derivative. Empirical Analysis and the Metaphysics of Causation  Insofar as discussion in this volume will be concerned, it will suffice for us to adopt a single sufficient condition for an existent being derivative. I will specify this sufficient condition in terms of the ontological status of quantities, but it holds of existents generally. A quantity is derivative if its magnitude requires some specification beyond the totality of fundamental reality (and beyond any specification required to locate the quantity in fundamental reality). For example, themass of any corpuscle at any time in the simple theory of classicalmechanics is a quantity that has a determinatemagnitude once we have specified the spatio-temporal location of the corpuscle whosemasswe are considering. By contrast, the kinetic energy of any corpuscle (at any time) is derivative. A corpuscle’s kinetic energy is equal to one-half its mass times its speed squared, mv. In the simple theory of classical mechanics, no fundamental structures suffice for a given corpuscle’s absolute speed; there are only corpuscle speeds relative to other corpuscles. However, if we select an appropriate frame of reference to serve as a universal standard for being at rest, we can say that a corpuscle’s speed is its speed relative to this rest frame. Then, because we have associated a determinate speed with each corpuscle, there will be a well-defined value for each corpuscle’s kinetic energy. The kinetic energy of a corpuscle is an example of a derivative quantity because there is nothing in fundamental reality that corresponds to a unique correct value for the kinetic energy (at the corpuscle’s spatio-temporal location) unless we augment the model with a parameter that doesn’t correspond to anything in fundamental reality, namely this stipulation of what counts as being at rest. Whenever a parameter used for describing reality does not have a unique correct assignment given how fundamental reality is structured, let us say that it is fundamentally arbitrary. A choice of rest is one example of a fundamentally arbitrary parameter. More generally, coordinate systems and so-called gauge degrees of freedom are fundamentally arbitrary. Fundamental reality might make some coordinate systems more convenient than others for characterizing the distribution of matter, but fundamental reality itself is independent of our conventions for assigning labels to points of space-time. Any quantity that is coordinatedependent is derivative. By convention, we can adopt the policy that the fundamentally arbitrary specification needed to locate a region in space-time (orwhatever space is the container of fundamental material stuff) does not by itself make the contents of that region derivative. The locating information should instead be interpreted as merely defining the component of fundamental reality under consideration. Imagine two solid blocks in an otherwise empty portion of space, each composed of massive corpuscles bound together by short-range forces. Fig. . provides two different characterizations of the very same fundamental arrangement of corpuscles that constitute the two blocks. By choosing a rest frame, one bestows on each corpuscle a well-defined (non-relational) velocity. The total kinetic  Causation and Its Basis in Fundamental Physics