U. Ben-Ya'acov, "Internal-time and dilatations in classical relativity", J. of Phys.: Conf. Ser. 66 (2007) 012009

The proper-time of any classical (non-quantum) relativistic system, derived from its centre-of-mass (CM) coordinate, is defined and identified as an observable – the system's internal time observable, measuring its aging and internal evolution. This is a Lorentz-invariant observable, and its de¯nition requires that the system be symmetric not only under Lorentz- Poincarµe transformations but also under uniform scaling, with the associated existence of a dilatation function D. These dilatation functions are required to be varying – not conserved – quantities, due to the existence of masses, and they exist at least for a very large family of systems. They split into a CM-part and an internal part, which is in general non-vanishing. The proper-time is expressed, as an observable, as a combination of the global dilatation function D and the internal dilatation function Dint, where D brings into it the generic time-like variation while Dint brings in the time-like variation that involves the details of the internal evolution of the system.

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