16 Two Axiomatic Systems for Special Relativity
165
extended’. This arises from the different definitions of simultaneity. If we consider a
definition of simultaneity which does not fulfil the elementary principle of relativity
with Reichenbach, it is important to differentiate between Lorentz contraction and
Einstein contraction.
In the context of our Lorentzian way II. to Special Relativity, we understand
Reichenbach’s argumentation in this way. We demand Lorentz contraction as a fundamental physical law for a primary preferred frame o . Einstein contraction is a
property of the inertial frames
moving with respect to o . It depends on the
definition of simultaneity. Here, we have to point at that. There is a definition of
simultaneity so that all inertial frames have equal rights. Especially, the primary preferred frame o is an arbitrary inertial frame and so Lorentz contraction becomes
identical with Einstein contraction.
From the Lorentzian way II. to Special Relativity, the following conclusion should
be emphasised:
The FitzGerald- Lorentz contraction hypothesis does not contradict the basic principle
of relativity.
The negative assessment of the Lorentz hypothesis, which is sometimes still
shared today, cf. our discussion in Chap. 12, p.129, corresponds with a misunderstanding of Reichenbach’s thesis. Here, we wish to state that H. Minkowski did not
encourage this error. Starting out from Einstein’s principle of relativity, Minkowski
shows in Lorentz [60], ‘that the Lorentzian hypothesis is completely equivalent to the
new conception of space and time, which, indeed, makes the hypothesis much more
intelligible’. This passage from Minkowski’s famous paper was obviously forgotten.
This could have had something to do with the fact that Reichenbach [83] himself, who
explicitly discussed Minkowski’s work and ideas, to our knowledge, did not explicitly mention this Minkowski’s statement. And Einstein himself? He writes, discussing
the Michelson experiment, cf. Einstein [17], Chap. XVII, ‘Lorentz and FitzGerald
rescued the theory from this difficulty by assuming that the motion of the body relative to the ether produces a contraction of the body in the direction of motion, the
amount of contraction being just sufficient to compensate for the difference in time
mentioned above. Comparison with the discussion in Section XII shows that also
from the standpoint of the theory of relativity this solution of the difficulty was the
rigth one’.
If we replace the velocity of light c L with the critical velocity c o of sine-Gordon
equation, all considerations concerning Special Relativity can be illustrated directly
using solids. This applies to the explanation of the relativistic effects as to the solution
of the well-known relativistic paradoxa and thus leaves no room for interpretation.
165
extended’. This arises from the different definitions of simultaneity. If we consider a
definition of simultaneity which does not fulfil the elementary principle of relativity
with Reichenbach, it is important to differentiate between Lorentz contraction and
Einstein contraction.
In the context of our Lorentzian way II. to Special Relativity, we understand
Reichenbach’s argumentation in this way. We demand Lorentz contraction as a fundamental physical law for a primary preferred frame o . Einstein contraction is a
property of the inertial frames
moving with respect to o . It depends on the
definition of simultaneity. Here, we have to point at that. There is a definition of
simultaneity so that all inertial frames have equal rights. Especially, the primary preferred frame o is an arbitrary inertial frame and so Lorentz contraction becomes
identical with Einstein contraction.
From the Lorentzian way II. to Special Relativity, the following conclusion should
be emphasised:
The FitzGerald- Lorentz contraction hypothesis does not contradict the basic principle
of relativity.
The negative assessment of the Lorentz hypothesis, which is sometimes still
shared today, cf. our discussion in Chap. 12, p.129, corresponds with a misunderstanding of Reichenbach’s thesis. Here, we wish to state that H. Minkowski did not
encourage this error. Starting out from Einstein’s principle of relativity, Minkowski
shows in Lorentz [60], ‘that the Lorentzian hypothesis is completely equivalent to the
new conception of space and time, which, indeed, makes the hypothesis much more
intelligible’. This passage from Minkowski’s famous paper was obviously forgotten.
This could have had something to do with the fact that Reichenbach [83] himself, who
explicitly discussed Minkowski’s work and ideas, to our knowledge, did not explicitly mention this Minkowski’s statement. And Einstein himself? He writes, discussing
the Michelson experiment, cf. Einstein [17], Chap. XVII, ‘Lorentz and FitzGerald
rescued the theory from this difficulty by assuming that the motion of the body relative to the ether produces a contraction of the body in the direction of motion, the
amount of contraction being just sufficient to compensate for the difference in time
mentioned above. Comparison with the discussion in Section XII shows that also
from the standpoint of the theory of relativity this solution of the difficulty was the
rigth one’.
If we replace the velocity of light c L with the critical velocity c o of sine-Gordon
equation, all considerations concerning Special Relativity can be illustrated directly
using solids. This applies to the explanation of the relativistic effects as to the solution
of the well-known relativistic paradoxa and thus leaves no room for interpretation.