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PLAN OF DB SPECIAL RELATIVITY
dba axioms of special relativity
dbb lorentz transformations
dbc length contraction and time dilation
dbd speed cumulation
dbe E=MC^2
dbf paradox of langevins traveller
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Site Plan
DBA.AXIOMS OF SPECIAL RELATIVITY
Galilean and Extended Relativity.
Galilean Relativity (GalR) postulates that laws of Mechanics
are covariant by GalR Transformation among 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 Euclidean 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 among 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 so extended Physics is covariant in all IR's by
particular SR Transformations known as "Lorentz
Transformations" (DBB.LORENTZ TRANSFORMATIONS).
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 invariant and
independent of source's- and observers referential).
A3.#Space of SR's AS (Abstract #Space)[G] is Minkowski
#Space.
Aether
Aether theory was the context in which and against which
Special Relativity was conceived.
All physicists in the period prior to 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 with 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 invariant among 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
Phenomenon 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 is subject of proper Transformations i
compatible with the invariance of 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 DBB.LORENTZ TRANSFORMATIONS)
