U. Ben-Ya'acov, "Internal-time Observable of Classical Relativistic Systems", J. Phys. A: Math. Gen. 39 (2006) 667-683

U. Ben-Ya'acov, "Internal-time Observable of Classical Relativistic Systems", J. Phys. A: Math. Gen. 39 (2006) 667-683. http://stacks.iop.org/JPhysA/39/667
The relativistic framework with its symmetries offers a natural definition for the internal time of classical (non-quantum) physical systems as a Lorentz-invariant observable. The internal time observable, measuring the system's aging or internal evolution, is identified with the proper-time of the system derived from its centre-of-mass (CM) coordinate. For its definition as an observable it is required that the system be symmetric not only under Lorentz-Poincare transformations but also under uniform scaling, with the associated existence of a dilatation function D, and yet that D be a varying – not conserved – quantity. Two alternative definitions are discussed, and it is found that in order to maintain simultaneity of the CM time with the events that define it it is necessary to split the dilatation function into a CM-part and an internal part.

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