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4 Irreversibility

[123.7.1] On the more theoretical side the presentation in Perpignan has discussed the irreversibility paradox. [123.7.2] More specifically, it was shown, how the theory of fractional dynamics suggests to turn the irreversibility problem upside down. [123.7.3] The so called “reverse irreversibility problem”, was first formulated in [21], and it has been solved quantitatively. [123.7.4] The normal irreversibility problem is:

Definition 1 (Normal irreversibility problem).

Assume, that time is reversible. Explain how and why time irreversible equations arise in physics.

[123.7.5] The assumption that time is reversible is made in all fundamental theories of modern physics. [123.7.6] The explanation of macroscopically irreversible behaviour for macroscopic nonequilibrium states of subsystems is due to Boltzmann. [123.7.7] It is based on the applicability of statistical mechanics and thermodynamics, the large separation of scales, the importance of low entropy initial conditions, and probabilistic reasoning [23, 29]. [123.7.8] The reversed irreversibility problem is:

Definition 2 (Reversed irreversibility problem).

Assume, that time is irreversible. Explain how and why time reversible equations arise in physics.

[123.7.9] The impossibility of performing experiments in the past is fundamental and evident. [123.7.10] Therefore, as emphasized in [21], it must be postulated, that time is fundamentally irreversible. [123.7.11] While the starting assumption of the normal irreversibility problem contradicts experiment, the starting assumption of the reversed problem agrees with experiment.