154
16 Two Axiomatic Systems for Special Relativity
The observer in
would thus determine, according to (164) that the (light) signal
in
moves in the x
-direction with the velocity c L − v. However, as we already
know, Michelson’s experiments proved exactly this to be false.
Having in mind the analysis of Poincaré, at first we have to observe that the
axiomatics of Special Relativity in any case decomposes into two different statements:
(A) A definition of simultaneity.
(B) An axiomatic statement about certain physical facts.
Then, we need to distinguish between two fundamentally different approaches to the
axiomatic formulation of Special Relativity:
I. We ask for a general principle of symmetry that governs the objects of our
physical search in all inertial systems.
II. We primarily ask: How do our measuring-rods and clocks behave in a single
and therefore preferred inertial frame?
I. This is the Einsteinian, the royal path to the Special Theory of Relativity. Its
explicit axiomatic fundamental is the Einsteinian principle of relativity that we quoted
in Chap. 2, (and at the beginning of the last chapter). In order to arrive, following
this path, together with Einstein at Special Relativity, we demand that Maxwell’s
equations for the description of electromagnetic processes have to be identical for
all inertial systems. This would have the consequence that all physical parameters
of this theory, here the speed of light c L , would have one and the same numerical
value in all inertial systems. This important conclusion from the application of his
principle of relativity on the Maxwell theory was especially formulated by Einstein
as the universal constancy of the speed of light (quotation in Chap. 2, p.7).
With the help of the universal constancy of the speed of light, Einstein introduced
a synchronisation of clocks in an arbitrary inertial system and deduced the relativity
of simultaneity, Lorentz contraction, time dilatation, the Lorentz transformation, the
dependence on velocity of inertial masses, as well as the inertia of energy. These
effects would also function identically in every inertial system.
Constructing Special Relativity with the help of Maxwell’s electrodynamics does
not mean that electromagnetic phenomena have a dominant meaning for the whole
of physics. Any other theory could be taken up this position, e.g. the theory of weak
interactions or simply mechanics. Electrodynamics was just the historical cardinal
point for the discovery of Special Relativity—not more, not less. The basis of theoretical physics is the Special Theory of Relativity.
We do not intend to illustrate Einstein’s path and therefore refer the reader to his
original papers Einstein [14, 16] (cf. the English translation in Einstein [15]). The
simple synchronisation procedure according to Einstein is described in Chap. 3. After
that a synchronisation of clocks in any physical textbook was explained along these
lines (except Liebscher’s [57] approach, see below), so that the unprepared reader
could get the impression this procedure would be physically compelling. Though H.
16 Two Axiomatic Systems for Special Relativity
The observer in
would thus determine, according to (164) that the (light) signal
in
moves in the x
-direction with the velocity c L − v. However, as we already
know, Michelson’s experiments proved exactly this to be false.
Having in mind the analysis of Poincaré, at first we have to observe that the
axiomatics of Special Relativity in any case decomposes into two different statements:
(A) A definition of simultaneity.
(B) An axiomatic statement about certain physical facts.
Then, we need to distinguish between two fundamentally different approaches to the
axiomatic formulation of Special Relativity:
I. We ask for a general principle of symmetry that governs the objects of our
physical search in all inertial systems.
II. We primarily ask: How do our measuring-rods and clocks behave in a single
and therefore preferred inertial frame?
I. This is the Einsteinian, the royal path to the Special Theory of Relativity. Its
explicit axiomatic fundamental is the Einsteinian principle of relativity that we quoted
in Chap. 2, (and at the beginning of the last chapter). In order to arrive, following
this path, together with Einstein at Special Relativity, we demand that Maxwell’s
equations for the description of electromagnetic processes have to be identical for
all inertial systems. This would have the consequence that all physical parameters
of this theory, here the speed of light c L , would have one and the same numerical
value in all inertial systems. This important conclusion from the application of his
principle of relativity on the Maxwell theory was especially formulated by Einstein
as the universal constancy of the speed of light (quotation in Chap. 2, p.7).
With the help of the universal constancy of the speed of light, Einstein introduced
a synchronisation of clocks in an arbitrary inertial system and deduced the relativity
of simultaneity, Lorentz contraction, time dilatation, the Lorentz transformation, the
dependence on velocity of inertial masses, as well as the inertia of energy. These
effects would also function identically in every inertial system.
Constructing Special Relativity with the help of Maxwell’s electrodynamics does
not mean that electromagnetic phenomena have a dominant meaning for the whole
of physics. Any other theory could be taken up this position, e.g. the theory of weak
interactions or simply mechanics. Electrodynamics was just the historical cardinal
point for the discovery of Special Relativity—not more, not less. The basis of theoretical physics is the Special Theory of Relativity.
We do not intend to illustrate Einstein’s path and therefore refer the reader to his
original papers Einstein [14, 16] (cf. the English translation in Einstein [15]). The
simple synchronisation procedure according to Einstein is described in Chap. 3. After
that a synchronisation of clocks in any physical textbook was explained along these
lines (except Liebscher’s [57] approach, see below), so that the unprepared reader
could get the impression this procedure would be physically compelling. Though H.