12 The Measurement of the Critical Velocity
129
The traditional method of deriving Special Relativity with its a priori postulated
universal constancy of critical velocity for all observers moving towards each other
with a uniform velocity has been turned upside down. In fact, we have done nothing
more than to consequently continue developing the FitzGerald–Lorentz contraction
hypothesis (cf. FitzGerald [20], Lorentz [61, 62], Einstein [15]) as well as applying
Poincaré’s ideas for synchronising clocks, until we received the complete Special
Theory of Relativity. We have thus proved that this contraction hypothesis does not
stand in contradiction to Special Relativity as is sometimes believed, e.g. in the
textbook of R. Pathria [72] on relativity we read, ‘Although the Lorentz–FitzGerald
hypothesis explains the null result of Michelson- Morley experiments reasonably
well, its ad hoc nature and hypothetical character prevent it from being convincing
enough. In fact, we shall find that in the theory of relativity there is no place at
all for such a hypothesis; the explanation of the null results of Michelson- Morley
experiments is actually contained in the postulate on the ‘constancy of the speed of
light for all inertial observers’. S. P. Puri [79] writes ‘This result
5 differs from the
contraction hypothesis postulated by Lorentz and FitzGerald to explain the negative
results of Michelson- Morley experiment, since Eqs. (1–36) gives a symmetrical
relation between two measuring sticks in relative motion, whilst hypothesis required
a change in length for a single rod depending on its actual velocity through a real fixed
aether’. Even in R. Becker’s [1] traditional standard textbook on electrodynamics
incorporating Special Relativity, the FitzGerald–Lorentz hypothesis is commented
on in the following way: ‘Although the contradiction hypothesis is to be regarded
as an immediate forerunner of the Theory of Relativity, it should be emphasized
that the concept, when standing by itself, contradicts the fundamental Principle of
Relativity. Thus, if the moving observer compares the scale moving with him with
a scale at rest, he can obviously confirm, that his own scale is actually shortened.
In principle, then, we should have available a means of experimentally determining
the state of absolute rest simply by observing which of various more or less rapidly
moving unit-length scales possessed the greatest length’.
Where is the mistake in this argumentation? The author fails to see that the observer
sitting on the moving measuring rod, thus the observer in
is not in the position to
measure a length being at rest in o , in reference to him a moving length, if he did not
synchronise his clocks according to a well-defined set of regulations. This length is
in fact, according to definition, nothing more than the difference of the simultaneous
coordinates of its end points in
. However, due to the fact that H. A. Lorentz’s
moving observer does not have a set of regulations for the synchronisation of clocks,
neither the timed order of events, nor the length of a moving ruler is defined in
. It
is however correct, that FitzGerald and Lorentz believed at that time in an ether that
defined an absolute reference system and that all moving lengths were contracted
with respect to this reference system. Such behaviour has been shown by our kinks
moving relative to the crystal lattice as discussed in Chap. 10. However, we now
know that this ether falls out of the theory if we consequently continue using this
hypothesis. In order to achieve this, the contraction of the measuring-rod has to be
supplemented with the dilatation of time of a moving clock. Here, it is also taken for
5 “This result” is Puri’s formula (1–36), which is identical with our contraction formula (112).
129
The traditional method of deriving Special Relativity with its a priori postulated
universal constancy of critical velocity for all observers moving towards each other
with a uniform velocity has been turned upside down. In fact, we have done nothing
more than to consequently continue developing the FitzGerald–Lorentz contraction
hypothesis (cf. FitzGerald [20], Lorentz [61, 62], Einstein [15]) as well as applying
Poincaré’s ideas for synchronising clocks, until we received the complete Special
Theory of Relativity. We have thus proved that this contraction hypothesis does not
stand in contradiction to Special Relativity as is sometimes believed, e.g. in the
textbook of R. Pathria [72] on relativity we read, ‘Although the Lorentz–FitzGerald
hypothesis explains the null result of Michelson- Morley experiments reasonably
well, its ad hoc nature and hypothetical character prevent it from being convincing
enough. In fact, we shall find that in the theory of relativity there is no place at
all for such a hypothesis; the explanation of the null results of Michelson- Morley
experiments is actually contained in the postulate on the ‘constancy of the speed of
light for all inertial observers’. S. P. Puri [79] writes ‘This result
5 differs from the
contraction hypothesis postulated by Lorentz and FitzGerald to explain the negative
results of Michelson- Morley experiment, since Eqs. (1–36) gives a symmetrical
relation between two measuring sticks in relative motion, whilst hypothesis required
a change in length for a single rod depending on its actual velocity through a real fixed
aether’. Even in R. Becker’s [1] traditional standard textbook on electrodynamics
incorporating Special Relativity, the FitzGerald–Lorentz hypothesis is commented
on in the following way: ‘Although the contradiction hypothesis is to be regarded
as an immediate forerunner of the Theory of Relativity, it should be emphasized
that the concept, when standing by itself, contradicts the fundamental Principle of
Relativity. Thus, if the moving observer compares the scale moving with him with
a scale at rest, he can obviously confirm, that his own scale is actually shortened.
In principle, then, we should have available a means of experimentally determining
the state of absolute rest simply by observing which of various more or less rapidly
moving unit-length scales possessed the greatest length’.
Where is the mistake in this argumentation? The author fails to see that the observer
sitting on the moving measuring rod, thus the observer in
is not in the position to
measure a length being at rest in o , in reference to him a moving length, if he did not
synchronise his clocks according to a well-defined set of regulations. This length is
in fact, according to definition, nothing more than the difference of the simultaneous
coordinates of its end points in
. However, due to the fact that H. A. Lorentz’s
moving observer does not have a set of regulations for the synchronisation of clocks,
neither the timed order of events, nor the length of a moving ruler is defined in
. It
is however correct, that FitzGerald and Lorentz believed at that time in an ether that
defined an absolute reference system and that all moving lengths were contracted
with respect to this reference system. Such behaviour has been shown by our kinks
moving relative to the crystal lattice as discussed in Chap. 10. However, we now
know that this ether falls out of the theory if we consequently continue using this
hypothesis. In order to achieve this, the contraction of the measuring-rod has to be
supplemented with the dilatation of time of a moving clock. Here, it is also taken for
5 “This result” is Puri’s formula (1–36), which is identical with our contraction formula (112).