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Kinematics, Dynamics, and the Structure of Physical Theory

Every physical theory has (at least) two different forms ofmathematical equations to represent its target systems: the dynamical

(equations of motion) and the kinematical (kinematical constraints).

Kinematical constraints are differentiated from equations of motion by

the fact that their particular form is fixed once and for all,

irrespective of the interactions the system enters into. By contrast,

the particular form of a system's equations of motion depends

essentially on the particular interaction the system enters into. All

contemporary accounts of the structure and semantics of physical

theory assume that the equations of motion, i.e., the dynamics, is the

most important feature of a theory. I argue to the contrary that it

is the kinematical constraints that determine the structure and

empirical content of a physical theory in the most important ways:

they function as necessary preconditions for the appropriate

application of the theory; they differentiate types of physical

systems; they are necessary for the equations of motion to be well

posed or even just cogent; and they guide the experimentalist in

design of tools for measurement and observation. It is thus

satisfaction of the kinematical constraints that renders meaning to

those terms representing a system's physical quantities in the first

place, even before one can ask whether or not the system satisfies the

theory's equations of motion.

Author Information:

Erik Curiel

Munich Center for Mathematical Philosophy (LMU Munich)