PARENTS: RELATIVITY WORKSHOP WORKSHOPS ARCHIVE =============================================================================== Galilean and Extended Relativity. Galilean Relativity (GR) postulats that laws of Mechanics are rigorously identical in all Inertial Referentials (IR). GR #space may be considered as affine 4D #space encompassing: A)1D #time B)3D orthogonal, euclidian #space with metric signed by the Fundamental Euclidian Tensor del, known as Kroeckner Symbol: del(ij/)=1 for i=j del(ij/)=0 for i!=j or in matrix form: del(ij/)=[100,010,001]. GR Transformation between IR's is translation with additive speed composition (given B moving with V with respect to A, speed in B, vB, transforms into vA = vB + V). Einstein extended GR over electro-magnetic and optic laws saying that Physics is rigorously identical in all IR's. This Extended Relativity (ER) is usually referred to as Principle of Relativity. =============================================================================== Einstein considered his Special Relativity to be based upon the following axioms: A1.Principle of Relativity, or ER. A2.Einstein's Postulate (C in vacuum is constant and independent of source's- and observers referential). A3.#space of SR's MS is Minkowski #space. =============================================================================== Comment: This axiomatic is often called in the question as overdetermined. We shall quote some most interesting arguments, including the Theory of Aether, which stays outside of our axiomatic, but is important for its context and general understanding. =============================================================================== Aether All physicists in the period between 1873 (Maxwell's Equations) and 1887 (MM Experiment) believed that electromagnetic or light waves, like any waves, must move though a propagation medium, which they called Aether. There were two principal Aether hypothesis: 1) Aether is dragged by material referentials like air within a closed cabin and light behaves like sound. This hypothesis postulates Extended Relativity and Galilean Transformation, saying that light speed must satisfy the additive speed composition, that observing a rotating double star, we must measure light speed as faster when the star moves towards us, than otherwise. 2) Aether is a unique absolute referential and all other ones move relatively to it. This hypothesis drops the Relativity Principle with respect to Aether, and still requires the Galilean Transformation, i.e. the additive speed composition of light for referentials moving with steady speed with respect to Aether. =============================================================================== Field and SR Both Aether hypothesis have been refuted by MM experiment, which has shown that C is constant in all IR's. Up to this moment it has been believed that Maxwell Equations were purely mathematical constructs, which needed some physical support satisfying the current mechanistic principles. One of the greatest revolutions in science consisted in dropping the mechanistic attitude and postulating that: a) Maxwell Equations are not only abstract constructs of Mind, but describe the structure of an AUTONOMOUS physical concept called Field, which is directly available to experimentation without any intermediary agent. b) #space has the faculty of supporting and propagating Field without need of any intermediary agents. c) This #space supports a proper Transformation compatible with the constant C. d) Extended Relativity is supported by this #space and Transformation. Special Relativity founded in A1,A2,A3 is a concrete realization of these requirements. In particular, Minkowski #space supports in the most simple and natural way the proper Lorentz Transformation and, consequently the ER (details in chapter DERIVATION OF LORENTZ TRANSFORMATIONS). =============================================================================== Objection 1 A2. Einstein's Postulate of constant C is not an axiom, because it may be deduced from Maxwell's Equations and Extended Relativity. Arguments in favor of this objection will be stored in Depository under the present chapter on condition to be formulated in a way understandable to most participants. Against this objection it may be said that the postulate of non-constant speed of light was compatible with deductively consistent theories, such as Aether 1 and 2, that it was a well formed scientific physical hypothesis, experimentally verifiable, falsifiable and finally falsified. It appears symmetric and equally justified to elevate the opposed hypothesis of constant C, to the level of verifiable and falsifiable postulate. =============================================================================== Objection 2 A3 is not an axiom, because Minkowski #space may be deduced from A1,A2 as the unique possible support of ER. As above, arguments in favor of this objection will be stored under the present chapter. However, as long as they do not prove the uniqueness of Minkowski #space as support of SR, we will maintain A3 as an axiom =============================================================================== PARENTS: RELATIVITY WORKSHOP WORKSHOPS ARCHIVE