Time, Equilibrium, and General Relativity

Abstract

Considered is "time as an interval” including time from the past and from the future, in contrast to time as a moment. Equilibrium as the basis for a description of changing properties in physics is understood to depend on the "mean velocity theorem”, while a "time” of equilibrium resembles a center of weight. This turns out to be a good method to derive properties for any function of time t including space coordinates q(t) and expressions for the time dependent Hamiltonian. Introduced are derivatives depending on time intervals instead of time moments and with these a new relation between the Lagrangian L and the Hamiltonian H. As an application introduced is a step by step method to integrate stationary state "local” time interval measurements to beyond "locality” in General Relativity. Because of limits on the resulting time interval measures, this allows for a probabilistic interpretation for quantities that have these intervals as time domain. Thus, these measures are interesting in both a GR as a QM sense. Another application of time interval is the discussion of the measurement of starlight radiation energy and QM wave packet collapse as an example of a time dependent Hamiltonian. Finally, a relation between starlight frequency, metric and space- and time intervals is discussed. The time intervals also question the time reversal symmetry of GR.