Abstract
The concept of time is examined using the second law of thermodynamics that was recently formulated as an equation of motion. According to the statistical notion of increasing entropy, flows of energy diminish differences between energy densities that form space. The flow of energy is identified with the flow of time. The non-Euclidean energy landscape, i.e. the curved space–time, is in evolution when energy is flowing down along gradients and levelling the density differences. The flows along the steepest descents, i.e. geodesics are obtained from the principle of least action for mechanics, electrodynamics and quantum mechanics. The arrow of time, associated with the expansion of the Universe, identifies with grand dispersal of energy when high-energy densities transform by various mechanisms to lower densities in energy and eventually to ever-diluting electromagnetic radiation. Likewise, time in a quantum system takes an increment forwards in the detection-associated dissipative transformation when the stationary-state system begins to evolve pictured as the wave function collapse. The energy dispersal is understood to underlie causality so that an energy gradient is a cause and the resulting energy flow is an effect. The account on causality by the concepts of physics does not imply determinism; on the contrary, evolution of space–time as a causal chain of events is non-deterministic.
Highlights
Where does the arrow of time come from? Is the question that phrases succinctly (Eddington 1928) the puzzle about the origin of irreversibility
Based on the above-mentioned common characteristics of evolutionary processes, we propose that the flow of time is the flow of energy
Causal relationships are embedded in the properties of time-oriented Lorentzian manifold (Weyl 1949) whose evolution is given by the second law and the principle of least action
Summary
Where does the arrow of time come from? Is the question that phrases succinctly (Eddington 1928) the puzzle about the origin of irreversibility. Time in its many manifestations would deserve a through inspection (Savitt 1995; Zeh 2007) but the present study is limited to examining the basic question, What is time?, using the second law given as a recently derived equation of motion (Sharma & Annila 2007). It connects the principle of increasing entropy to the decreasing free energy explicitly. Various energy gradients are equalized by diverse transport and transformation processes, e.g. diffusion, heat flows, electric currents, chemical reactions (Kondepudi & Prigogine 1998). Thereafter, we use the second law and the principle of least action to analyse how the flow of time manifests itself in the basic physical processes
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