In one of the letters written to the Infeld group in Warsaw Einstein wrote:
"A new manner of thinking is essential if humankind is to survive."

  
                        AXIOMS OF SPECIAL RELATIVITY

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Galilean and Extended Relativity.

Galilean Relativity (GalR) postulates that laws of Mechanics are rigorously 
identical in all Inertial Referentials (IR). GalR #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]. 
GalR 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 GalR 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.
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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.
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Aether

Aether theory was the context in which and against which Special Relativity was
conceived.

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.   
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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). 
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