  The definition of invariant time is fundamental to relativistic symmetry.
Invariant time may be formulated as a degenerate orthogonal metric on a flat
phase space with time, position, energy and momentum degrees of freedom that is
also endowed with a symplectic metric $\omega =-d t\wedge d \varepsilon +\delta
_{i,j}d q^i\wedge d p^j$. For Einstein proper time, the degenerate orthogonal
metric is $d \tau^{o 2}=d t^2-\frac{1}{c^2}d q^2$ and, in the limit $c\to
\infty$, becomes Newtonian absolute time, $d t^2$. We show that the the
resulting symmetry group leaving $\omega$ and $d t^2$ invariant is the Jacobi
group that gives the expected transformations between noninertial states
defined by Hamilton's equations. The symmetry group for $\omega$ and $d \tau^{o
2}$ is the semidirect product of the Lorentz and an abelian group parameterized
by the time derivative of the energy-momentum tensor that characterizes
noninertial states in special relativity. This leads to the consideration of
invariant time based on a nondegenerate Born metric, $d \tau^2=d
t^2-\frac{1}{c^2}d q^2-\frac{1}{b^2}d p^2-\frac{1}{b^2c^2}d \varepsilon^2$. $b$
is a universal constant with dimensions of force that, with $c,\hbar$ define
the dimensional scales of phase space. We determine that the symmetry group for
transformations between noninertial states is essentially a noncompact unitary
group. It reduces to the noninertial symmetry group for Einstein proper time in
the $c\to \infty$ limit and to the noninertial symmetry group for Hamiltonian
mechanics in the $b,c\to \infty$ limit. The causal cones in phase space defined
by the null surfaces $d\tau^2=0$ bound the rate of change of momentum as well
as position. Furthermore, spacetime is no longer an invariant subspace of phase
space but depends on the noninertial state; there is neither an absolute rest
state nor an absolute inertial state that all observers agree on.
