  Trace Dynamics is a classical dynamical theory of noncommuting matrices in
which cyclic permutation inside a trace is used to define the derivative with
respect to an operator. We use the methods of Trace Dynamics to construct a
noncommutative special relativity. We define a line-element using the Trace
over spacetime coordinates which are assumed to be operators. The line-element
is shown to be invariant under standard Lorentz transformations, and is used to
construct a noncommutative relativistic dynamics. The eventual motivation for
constructing such a noncommutative relativity is to relate the statistical
thermodynamics of this classical theory to quantum mechanics.
