Time: Its Structure and Role in Physical Theories

I. Physical time and the problem of its structure.- I.1 Introduction.- I.2 The order structure of time.- I.2.1 Partial and total order relations.- I.2.2 Newtonian case: total temporal order.- I.2.3 Einsteinian case: partial temporal order.- I.2.4 Cosmic time functions.- I.2.5 Causal theories of time.- I.3 The topological structure of time.- I.3.1 Time and the topology of spacetime.- I.3.2 Discrete versus continuous time.- I.3.3 Temporal orientability.- I.4 The metrical structure of time.- I.4.1 Clocks in Newtonian and Einsteinian physics.- I.4.2 A geometrical interpretation of the twin paradox.- I.4.3 The Unity of Time.- I.5 Conclusion.- Notes.- II. The geometrical nature of physical time: parameter time and coordinate time.- II.1 Introduction.- II.2 Parameter and coordinate.- II.3 Parameter and coordinate time in Newtonian physics.- II.3.1 Newtonian space and time: absolute time as parameter.- II.3.2 Newtonian spacetime: absolute time as parameter and coordinate.- II.4 Parameter and coordinate time in Einsteinian physics.- II.4.1 Relativistic space and time: proper time as parameter.- II.4.2 Relativistic spacetime: proper time and coordinate time.- II.4.3 Parameter and coordinate time in the general theory of relativity.- II.5 The geometrical nature of time in quantum mechanics.- II.6 Translation of the space and time into the spacetime formalism and vice versa.- II.7 The geometrical nature of time and dynamics.- II.8 Parameter versus coordinate time in the study of time; some philosophical issues.- Notes.- III. Time asymmetry.- III.1 Arrow of time: time asymmetry and time flow.- III.2 Time asymmetry.- III.2.1 A probabilistic conception of time asymmetry.- III.2.2 Discussion of probabilistic time asymmetry.- III.3 (Ir)reversibility and the time reversal operator T*.- III.3.1 Time reversal.- III.3.2 (Ir)reversibility and time reversal invariant laws.- III.3.3 The time reversal operator T*.- III.3.4 (Ir)reversibility arrl levels of description.- III.3.5 T*-violation in elementary particle physics.- III.4 Time asymmetry and temporal orientability.- Notes.- IV. Thermodynamical time asymmetry and the second law of phenomenological thermodynamics.- IV. 1 Introduction.- IV. 1.1 Different kinds of time asymmetry.- IV. 1.2 The origin of thermodynamic time asymmetry.- IV. 2 The mechanical program.- IV.2.1 Boltzmann’s deterministic H-theorem and the reversibility objections.- IV.2.2 The time symmetrical statistical H-theorem.- IV.2.3 Thermodynamic time asymmetry and human observation.- IV.2.4 Thermodynamic time asymmetry and open systems.- IV. 3 The thermodynamical program.- IV.3.1 Mechanics as a special case of thermodynamics.- IV.3.2 Complementarity between mechanics and thermodynamics.- IV. 4 Discussion.- Notes.- Epilogue.- Name index.