Irreversibility of time in general relativity

Abstract

Background and Objectives: The equations of classical dynamics of particles and waves admit solutions with the reverse flow of time. Therefore, it is generally assumed that classical dynamics does not reflect the irreversibility of time. On the other hand, the increase in the entropy in thermodynamics, also the collapse of wave functions in quantum mechanics shows that the irreversibility of time is manifested in these disciplines of physics. However, arguments can be made that the classical equations of continuous motion do not allow motion in all parameters of physical states. This article considers the inverse of time flow in dynamic equations of gravitation fields and in dynamic equations of particles in gravitation fields. Methods: Synchronous coordinate system was used to analyze time dependences of dynamic variables in the space warped by matter. The invariant transformations of dynamic equations including the time flow inversion were seen to conclude about time irreversibility in general relativity. Conclusion: Transformations with reversed time have been seen in general equations of gravitation fields and in general equations of particle motion in gravitation fields. Also the gravitation plane wave and the isotropic cosmological model have been considered. These transformations show that only inversion of time flow without another inversion is impossible. Thus we can draw the arrow of time in dynamic equations as well as in thermodynamics or quantum mechanics. 

Keywords

• reversibility and irreversibility of motion
• irreversibility of time in general relativity
• arrow of time