Relativity Principle of Einstein

For the reasons discussed above we have to abandon the Galilean principle of relativity and accept that Newton s laws cannot be fundamental laws of Nature. We thus consider Maxwell s equations for electromagnetic fields to be valid in all inertial frames of reference and consequently obtain the relativity 

Maxwell s equations have the same form in all inertial frames. 

The reader should compare this formulation with its nonrelativistic counterpart given in section 2.1.2. As a direct consequence of the covariance, i.e., invariance in form, of Maxwell s equations we obtain the desired result that the speed of light c is the same in all inertial frames of reference, cf. Eq (3.1). This immediately implies that the coordinate transformations relating the description of events in different inertial frames can no longer be the Galilei transformations but have to be replaced by more suitable coordinate transformations. 

The explicit form of these so-called Lorentz transformations will be derived in the next section. 

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 

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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. 

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... 

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),... 

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