Thermodynamic and kinematic origins of anisotropic relativity

Abstract

We recently developed the framework of anisotropic relativity through a perhaps surprising path - the new theory of thermodynamic relativity. Here we show that there is another, and in retrospect more obvious path, which is through asynchronous kinematics. We develop this framework through three progressive thought experiments: (1) Stationary observers that exchange a signal of particles and light beams in one-way opposite directions; (2) Nonstationary observers that exchange light signals; and (3) Nonstationary observers that exchange a signal of particles and light beams. Through these, we show the addition rule of one-way velocities, and that this is the same addition rule derived from thermodynamic relativity. We conclude that the broadest formalism of special relativity - the one derived from thermodynamic relativity that corresponds to linear Lorentz transformations, is actually connected with asynchronous kinematics and describes the asynchronous adaptation of Einstein's special relativity, or simply, the anisotropic relativity.

Keywords: Entropy; Space plasmas; Synchronization; Thermodynamics, relativity.

Fig. 1

Thermodynamic relativity provides a natural derivation of addition of velocities and the anisotropic adaptation of Einstein’s relativity. This paper shows a kinematic derivation of the addition of velocities.

Fig. 2

Thought Experiment 1: Two stationary observers exchange information through a signal made of a particle beam sent from A to B, and a light beam sent from B to A, once the particle beam is received. Kinematics is examined in the perspectives of observer’s A frame (a) and of observer’s B frame (b).

Fig. 3

Thought Experiment 2: Two nonstationary observers exchange information through a signal made of a light beam sent from A to B, and then, from B back to A. Similar to Fig. 2, kinematics is examined from the perspectives of observer’s A frame (a) and of observer’s B frame (b). Distance between A and B: L₀ at the time of emission from A, L_Re at the time B receives the signal, and L when A receives the signal from B; L₀ and L_Re not shown.

Fig. 4

Thought Experiment 3: Two nonstationary observers exchange information through a signal made of a particle beam sent from A to B, and then, a light beam sent from B to A. Similar to Figs. 2 and 3, kinematics is examined in the perspectives of observer’s A frame (a) and of observer’s B frame (b). Distances are defined in Fig. 3.