Relativity principle

Chubykalo and Smirnov-Rueda [2,56] have presented a renovated version of Hertz theory, that is in accordance with Einstein s relativity principle. For a single point-shaped charged particle moving at the velocity v, the displacement current in Maxwell s equation is modified into a convection displacement current ... 

Of course, in Eq. (6) the contraction form factor p is valid only in the arm that is parallel to the velocity vector. Equation (6) was interpreted by Lorentz and Fitz-Gerald as a real contraction [17]. It is important to see that in Eq. (6) the hidden parameter p is only one possible solution for the contradiction, but the result of the M-M experiment allows numerous other solutions based on the inner properties and features of the light. The M-M experiment destroyed the world picture of classical physics, and it required a new physical system of paradigms. Thus, for example, the applicability of Galilean relativity principle was rendered invalid. 

Figure 1. The frames of reference S and S in relative translational motion. In the frame of reference S, Lorentz transformation and special relativity principles are valid. In the frame of reference S, superluminal transformation and SLRT principles are valid.

In nonmathematical terms the relativity principle in physics is that there is not such thing as a neutral observer. Rather, any observer exists within a particular MST framework, and this framework affects his observations. 

It is possible to find in the history of science many vivid examples illustrating the relativity of the concept fundamental . For instance, the Planck postulate of energy quantization and the Bohr postulate on the quantization on angular momentum made a revolution in physics and were actually axioms at that time. At present from the formal viewpoint, they are only ordinary consequences of Schroedinger s equation [4], Another vivid example is provided by the four famous Maxwell electrodynamic equations which, as was found later, can be derived from Coulomb s law and Einstein s relativity principle [5]. 

Because of zero inertial acceleration (3.48), we can see from these general results (3.78)-(3.83), that the balances (3.70), (3.74)-(3.77) are valid in any inertial frame and not only in the one fixed with the distant stars. This assertion expresses the Galilean relativity principle about the impossibiUty of preference of any inertial frame. 

None of the two coordinate systems is privileged (relativity principle). 

This remarkable result also has implications for the measurement of spatial intervals. The measurement of a spatial interval requires the time coincidence of two points along a measuring rod. The relativity of simultaneity means that one cannot contend that an observer who traverses a distance X m per second in the train, traverses the same distance x m also with respect to the embankment in each second. In trying to include the law of propagation of light into a relativity principle, Einstein questioned the way in which measurements of space and time in different Galilean frames are compared. Place and time measurements in two... 

Transformations that preserve the relativity principle are called Lorentz transformations. The form of these looks complicated at first (see diagram). However, they arise from the simple requirement that there can be no experiment in dynamics or electromagnetism that will distinguish between two different Galilean frames of reference. 

Lorentz transformation (p. 100) velocity addition law (p. 103) relativity principle (p. 104)... 

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. 

In the last chapter the basic framework of classical nonrelativistic mechanics has been developed. This theory crucially relies on the Galilean principle of relativity (cf. section 2.1.2), which does not match experimental results for high velocities and therefore has to be replaced by the more general relativity principle of Einstein. It will directly lead to classical relativistic mechanics and electrodynamics, where again the term classical is used to distinguish this theory from the corresponding relativistic quantum theory to be presented in later chapters. 

As a prerequisite for the analysis of the implications of this new relativity principle we consider two events Ei and E2 connected by a light signal, e.g., the emission and subsequent absorption of a photon. An observer in IS will describe this process by the two events... 

The relativity principle of Einstein or, more precisely, the principle of constant speed of light led us to the definition of the four-dimensional distance Sj2 given by Eq. (3.4), which we recognized as an invariant quantity under Lorentz transformations relating different inertial frames of reference. It is therefore advisible to adopt a more suitable notation in order to reflect the... 

So far we have only exploited the principle of constant speed of light in all inertial frames, but not the (first part of the) relativity principle itself, cf. section 3.1.2. Due to the relativity principle the Lorentz back transformation from IS to IS must have the same form as given by Eq. (3.60) with v replaced by —v,... 

In section 3.1.2 we found the invariance under Lorentz transformations of the squared space-time interval s 2 between two events connected by a light signal being solely based on the relativity principle of Einstein, i.e., the constant speed of light in all inertial frames, cf. Eq. (3.5),... 

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... 

Continuous variables or coordinates are treated generally to work as expoint coordinates to envision higher order space pictures with which three- and four-dimensional lower bounds are remarkably dictated by the Kawaguchi-Hombu Theorem and its extension. Human concepts of nature from the most microscopic to more macroscopic phases have to be given in terms of three- and four-dimensional languages so as to provide the basis of the relativity principle, etc. Physical, psychological and even biological phenomena are characterized by conflicts and reconciliations between (3) and (4). ... 

---