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Georges Metanomski An Introduction to Relativistic Dialectics
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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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DBA 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, Euclidean #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 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 AS is Minkowski #Space.
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Aether
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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 #Space
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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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First Newton's Paradox
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Pre-relativistic Physics was founded in Noumenalistic dogmas of absolute time
and #Space, the latter supposed to have the mechanistic fabric of "billiard
balls". The only admitted action involved a "ball" hitting another, which could
propagate as a chain of hits. Thus, action was considered as basically local.
Mechanistic physicists overlooked a contradiction: Only Continuum may admit
local action. Granular mechanistic fabric implies action at distance equal to
the size of the elementary granule. Now, we don't know anything about the
elementary "balls", neither their size, nor their internal structure and
behaviour. Nobody ever observed them, as they are pure metaphysical concepts.
Nevertheless, admitting for arguments sake the mechanistic "locality" principle,
Newton's gravity attraction between remote masses appeared in the mechanistic
context as "action at distance", contradicting the "locality" principle.
This contradiction is known as the First Newton's Paradox.
Questioned about it he answered with his famous: "hypotheses non fingo", meaning
that science observes, structures, predicts and verifies, but does not deal with
metaphysical dogma. An ill-founded Theory may only be a recipe of formulas void
of physical sense. Closer to us Dirac expressed more boldly the same idea
subscribing to the null interpretation of ill-founded Quantum Mechanics with his
famous dictum "Shut up and calculate!".
Actually, Newton implicitly discoverd the concept of Field. Gravity Force
exerted on a unit mass detector at distance r from mass M: F = -GM/r^2
may be expressed as gradient of potential Field P(r)=GM/r. However, he did not
dare to call into question the dogmatic foundations of science of his time and
considered his Theory as recipe of mathematical formulas refusing to interpret
them.
We had to wait for Einstein's Relativity to confer on Field the status of
autonomous Phenomenon, founding henceforth physics in replacement of
metaphysical dogmas. This new foundation solves the First Newton's Paradox.
Indeed, Field as a Continuum admits on the one hand the genuine locality and,
on the other hand, interprets the apparent action at distance as propagation of
local impulse along continuous trajectory. Einstein rated the solution of
Newton's Paradoxes as his topmost achievement, because he admired Newton and
considered him as his Master.
In the meantime, in spite of "hypotheses non fingo", the mechanistic phantasms
kept on haunting physics culminating in the Aether Theory which caused perhaps
the greatest waste of time, resources and ingenuity in the history of science.
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