"The Degeneracy of Time: Proper Time and Becoming in Einstein-Minkowski Spacetime" In the transition to Einstein-Minkowski physics, certain concepts that had previously been thought to be univocal or absolute properties of systems turn out to be degenerate. For instance, mass bifurcates into the relativistically invariant proper mass m, and the relative mass, or mass in an inertial frame in which it is moving at a speed v = (beta)c, whose quantity is a factor (gamma) = (1 - beta-squared)^-1/2 times the proper mass. The concept of time is likewise degenerate: there is the time co-ordinate t, whose quantity varies (like relative mass) according to the inertial frame chosen, and there is the proper time tau, which is frame-invariant but path-dependent, and calculated by an integration along the path taken. In this paper I argue that the significance of this degeneracy has been insufficiently appreciated by many philosophers and physicists, who assume that the time co-ordinate carries the same ontic load as in classical physics. They then argue that the relativity of simultaneity, in making the class of events simultaneous with the "now" depend upon the reference frame chosen, is thereby incompatible with the notion of an objective becoming. This would be true if the time co-ordinate in E-M spacetime--i.e. the time in a given inertial frame-- measured the rate of becoming of a process. I argue, however, that if that were so, the twins in the twin paradox could not have aged differently. On the contrary, a sufficently general resolution of that paradox applicable to curved paths requires recognition that the rate of becoming of a process is path-dependent, objective, and measured by the proper time.