Galileo relativity principle

The inadequacy of the mechanical model of light first became apparent when the electromagnetic equation of motion was seen to violate Galileo s principle of relative motion. As derived by Maxwell, electromagnetic motion is described by a wave equation ... 

The identification of relations between statics and dynamics became a constituting part in the explanation of unity of the laws of mechanics in (Lagrange, 1788). Deriving the equations of trajectories from the equation of state (1) turned out to be possible owing to the assumptions made about observance of the relativity principle of Galileo and the third law of Newton and, hence, about representability of any trajectory in the form of a continuous sequence of equilibrium states. From the representability, in turn, follow the most important properties of the Lagrange motion curves existence of the functions of states (independent of attainability path) at each point possibility to describe the curves by autonomous differential equations that have the form x = f x) dependence of the optimal configuration of any part of the curve upon its initial point only. These properties correspond to the extreme principles of the optimal control theory. 

Based on Newtonian mechanics, Galileo introduced a relativity principle, stating that all laws of physics must be the same in all inertial reference systems. In other words, the coordinates x and x in two different reference systems, moving with a relative velocity v, are related as... 

The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is characterized by the mathematical methods invented by Newton, Galileo (the principle of relativity [4]), among others. Numerous books contain introductory synopses of the basic principles of the Newtonian mechanics, see for example the books by Arnold [4], Ferziger and Kaper [39] and Cercignani et al. [14],... 

The mechanical principle of relativity, coupled with the suggestion of uniformity of time flow in all inertial reference systems, is referred to as Galileo s principle of relativity. 

Einstein has generalized Galileo s principle of relativity. According to Einstein s principle of relativity, it is impossible by either mechanical or by physical experiment (in particular, electrical, magnetic or optical) conducted in an inertial system, to distinguish if this system is at rest or in rectilinear uniform motion. This statement is the basis of the special relativistic theory (see Section 1.6). 

Obviously, all relativistic expressions transform into classic ones at speeds that are small in comparison with the speed of light in vacuum. Therefore the principles presented by Einstein do not contradict the general statements of the Galileo relativity. Chemists only meet the relativistic approach occasionally, e.g., energy of inner electrons of heavy atoms, some details of physical methods of investigations and some others. 

For physical objects and reference frames moving with speeds ixc or u< , Einstein s theory led to the results of classical nonrelativistic theory Lorentz transformations changed into Galileo s transforms and the Einstein relativity principle into Galileo s relativity principle. 

Such an attitude to equilibrium thermodynamics - the science which revealed irreversibility of the evolution of isolated systems and asymmetry of natural processes with respect to time - is related to some circumstances that require a thorough analysis. Here we will emphasize only one of them which is the most important for imderstanding further text. It lies in the fact that the most important notion of thermodynamics, i.e. equilibrium, became interpreted exclusively as the state of rest (absence of any forces and flows in the thermodynamic system) and equilibrium processes - as those identical to reversible ones. These one-sided interpretations ignored the Galileo principle of relativity, the third law of Newton and the Boltzmann probabilistic interpretations of entropy that allow dynamic interpretations of equilibria and irreversible interpretations of equilibrium processes. 

---