2 The Aristotelian Concept of Time

[208.3.1] The concepts of time and time evolution are fundamental for physics (and other sciences). [208.3.2]  Aristotle [22, Δ 11] defined time as α,⁢ρ⁢ι⁢θ⁢μ⁢o`⁢ς κ⁢ι⁢ν⁢η´⁢σ⁢ϵ⁢ω⁢ς (i.e. as the integer or rational number of motion<sup>b</sup> (This is a footnote:) <sup>b</sup> While Aristotle was perhaps counting heart beats, days, months, years, or time intervals determined with a κ⁢λ⁢ϵ⁢ψ⁢υ´⁢δ⁢ρ⁢α, the idea to count periods has persisted. [208.3.3] Today the unit of time corresponds to counting 9 192 631 770 periods of oscillation of a certain form of radiation emitted from 133Cs-atoms [23]. ), and formulates the idea, that past and future are separated by a mathematical point, that he calls τ⁢o` ν⁢υ~⁢ν (the Now). [208.3.4] Newton [24, p. 5] formulates and postulates ”Tempus absolutum verum et Mathematicum, in se et natura sua absque relatione ad externum quodvis, aequabiliter fluit, alioque nomine dicitur Duratio” ^c (This is a footnote:) ^c Transl.: ”Absolute, true and mathematical time flows uniformly, in itself, according to its own nature, and without relation to anything outside itself; it is also called by the name duration.”. [page 209, §0]    [209.0.1] The concept of time in modern physics is based on the ideas of Aristotle in their Newtonian formulation. [209.0.2] Time is viewed as a flux aequabilis (uniform flow) or succession of Aristotelian time instants.

[209.1.1] The theoretical and mathematical abstraction of this concept of time from general mathematical theories of physical phenomena has led to the fundamental principle of time translation invariance and energy conservation in modern physics. [209.1.2] All fundamental theories of contemporary physics postulate time translation invariance as a basic symmetry of nature.