II 51
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.
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Initial conditions.
II 234
Time/logical form/Vollmer: temporal relationships can be expressed by real functions t(e1, e2) that are defined on event pairs.
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Events.
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.
>Asymmetry, >Symmetries.
Time Reversal: Time Reversal is only a formal operation of changing the sign.
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Equations, >Time reversal, cf. >Time travel, >Past, >Present,
>Future.
II 325
Invariant: a formula is invariant that does not change under time reversal.
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Invariants.
Time reversal invariance: So is a property of formulas or functions. - E.g. Newtonian equation of motion.
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Formulas.
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.
II 236
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.
>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.
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Causality, >
Cause, >
Effect.
II 238
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.
II 252
Entropy/universe/Boltzmann/Vollmer: for him, the universe as a whole is in a thermodynamic equilibrium, so in the entropy maximum.
II 253
VollmerVsBoltzmann: the observations state the contrary. If we advance into more distant parts of the universe, we can always find low entropy.
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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.
