Space-time is thought to curve and ripple. Is a kind of metatime required in or during which such events take place?
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Space-time is thought to curve and ripple.
Space-time, i.e. the set of all events under consideration (specificly: coincidence events), together with all relations between these events (primarily: by listing who, among all principal identifiable participants, took part any one coincident event), is thought to be not necessarily homogenous and/or isotropic by definition, but (possibly) to consist of distinct regions which (may) differ in terms of suitable measures, such as curvature.
Is a kind of metatime required in or during which such [differences and distinctions] take place?
No: at least some measures of (possible) differences are defined intrinsically, appealing only to participants and the coincidence events in which they took part. Some examples are sketched
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This is an open problem, the problem of Time in General Relativity and Quantum Gravity (e.g here and here).
The solution would require a (radical) synthesis of General Relativiy, Quantum Field Theory and especially Thermodynamics (the 2nd Law).
Many people, due to the treatment of time parameter in general relativity (general covariance principle), take a stance that (flow of) time is an illusion (sth this author does not agree with).
Another approach is to interpret the time parameter in General (and Special) Relativity as duration time and not as event instant time, this provides a workaround for many cases.
Furthermore work by Prigogine and others has shown that in non-linear systems one can define a unique Liouville-type operator which is not-time symmetric and which can define a (new) unique time-parameter for the dynamic evolution of the system (Prigogine's lecture on the Nobel prize).
The problem of time in physics and chemistry is closely related to the formulation of the second law of thermodynamics. Therefore another possible title of this lecture could have been: “the macroscopic and microscopic aspects of the second law of thermodynamics”. It is a remarkable fact that the second law of thermodynamics has played in the history of science a fundamental role far beyond its original scope.
Suffice it to mention Boltzmann’s work on kinetic theory, Planck’s discovery of quantum theory or Einstein’s theory of spontaneous emission, which were all based on the second law of thermodynamics.
