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Time/time direction/time reversal/Vollmer: the designation of a time direction is empirical and is made always only secondarily by additional assumptions - e.g. initial conditions in the mechanics and thermodynamics - rediance conditions in electrodynamics.
Time/logical form/Vollmer: temporal relationships can be expressed by real functions t(e1, e2) that are defined on event pairs. - Asymmetry: is then a formal property of this function to change the sign at reversal - this has nothing to do with reversibility of physical processes, also not with designation of one direction. - Time Reversal: only formal operation of changing the sign.
Invariant: is a formula that does not change under time reversal. - Time reversal invariance: So is a property of formulas or functions. - E.g. Newtonian equation of motion. - On the other hand: the question of whether natural processes are reversible, relates to the real world. - Problem. a T-invariant equation can describe both reversible and non-reversible processes. - If, then it does not yet contain complete information.
Definition Time Arrow/time direction/Vollmer: so we will call the fact that there are chains of events, whose part events never happen in reverse order - time direction is not a characteristic of the time, but of processes - that there are different classes of irreversible processes, there are different arrows of time: the expansion of the universe, the electrodynamic of spherical waves - that a process is irreversible, one cannot see that in looking at it. - It can also never be proven. - Causality/cause/effect/VollmerVsReichenbach: cannot define the arrow of time. - Reversed: these are not to defined without time arrow.
Irreversibility/Physics/time reversal/time arrow/Vollmer: We expect that the fundamental equations, equations of motion, laws of force, field equations are T-invariant, that is, that they change with time reversal.
Entropy/universe/Boltzmann/Vollmer: for him, the universe as a whole is in a thermodynamic equilibrium, so in the entropy maximum.
VollmerVsBoltzmann: the observations state the contrary. If we advance into more distant parts of the universe, we can always find low entropy. - If there were a region of space with decreasing entropy (increasing order), there would also be irreversible processes, but some time arrows would be reversed.
Die Natur der Erkenntnis Bd I Stuttgart 1988
Die Natur der Erkenntnis Bd II Stuttgart 1988