3 The Physical Elements of the Special Theory of Relativity
15
We can also formulate this effect of time dilatation leaning towards the formulation
of the length contraction and in foresight of our upcoming discussion on mechanics
as follows. The unit of measure for time measurement is a certain period of oscillation
which has the value T o for the static clocks. For the time T that the moving clock U v
needs to move from U o to U 1 , we measure using the static clocks T = t T o . In other
words, t is the coefficient of measure of time T referred to the unit of measure T o ; t is
the number of oscillations. The moving clock oscillates slower. Its unit of measure, the
oscillation period T
, is in comparison with T o according to T
= T o /
(1 − v 2 /c
2
L
longer, and it is stretched. This is the reason for the term ‘time dilatation’. For the
time T that the moving clock U v needs to move from U o to U 1 , we measure using the
moving clock U v itself T = t
T
. Here, t
= t
1 − v 2 /c
2
L is the above coefficient of
measure of time T referred to the unit of measure T
; t
is the number of oscillations
of the moving clock U v .
3
It is noticeable that all these formulas, even those used for mechanically built
measuring-rods and clocks do in fact include the speed of light. What is even more
striking is that it is not possible to build any clocks or measuring-rods without it.
In Chap. 11, we will have to return to this point. We will observe in the examined
phenomena that the above described the behaviour of measuring-rods and clocks
is characteristic of a ‘participation of an ether’. In the light of this, we will try to
understand Einstein’s [12, 13] statement ‘Only we must be on our guard against
ascribing a state of motion to the ether’. This means that the physical properties of
our measuring-rods and clocks are in respect to the ether of such a kind that they are
not able to respond to the ether.
An important fact has yet to be mentioned. The question ‘why’ concerning time
dilatation and length contraction is not specifically asked in the Special Theory of
Relativity. It is only shown that if we measure one and the same velocity for light,
then we have to conclude that in principle all measuring-rods and clocks show this
behaviour. This does not mean, however, that the question ‘why’ about these effects is
forbidden by the Special Theory of Relativity. However, it is just that all traditional
attempts of explanation are excluded by the particular axiomatic structure of this
theory. In Einstein’s axiomatic approach, all problems of SRT can be reduced to the
universal constancy of the speed of light. This is the axiomatic base of the theory. A
more simple explanation than the reduction to the axioms does not exist. This is the
problem. Is there any point in trying to discover a ‘mechanism’ that could clearly
explain these changes for moving measuring-rods and clocks? We will come back
to this question if we succeeded in finding out a real existing physical model, our
‘miniatur version’ of SRT.
The first direct observation of time dilatation of a ‘clock’ was achieved in 1938/39,
as described in the papers of H. J. Ives [44, 45] and G. J. Stillvell and G. Otting’s
3 Here, we will inform you of our notation which we will carry on throughout this book. All
statements about space and time described using moving measuring-rods and clocks are represented
by primed symbols. If measuring-rods and clocks of different velocities are involved, then tildes or
roofs are used; see Chap. 17.
15
We can also formulate this effect of time dilatation leaning towards the formulation
of the length contraction and in foresight of our upcoming discussion on mechanics
as follows. The unit of measure for time measurement is a certain period of oscillation
which has the value T o for the static clocks. For the time T that the moving clock U v
needs to move from U o to U 1 , we measure using the static clocks T = t T o . In other
words, t is the coefficient of measure of time T referred to the unit of measure T o ; t is
the number of oscillations. The moving clock oscillates slower. Its unit of measure, the
oscillation period T
, is in comparison with T o according to T
= T o /
(1 − v 2 /c
2
L
longer, and it is stretched. This is the reason for the term ‘time dilatation’. For the
time T that the moving clock U v needs to move from U o to U 1 , we measure using the
moving clock U v itself T = t
T
. Here, t
= t
1 − v 2 /c
2
L is the above coefficient of
measure of time T referred to the unit of measure T
; t
is the number of oscillations
of the moving clock U v .
3
It is noticeable that all these formulas, even those used for mechanically built
measuring-rods and clocks do in fact include the speed of light. What is even more
striking is that it is not possible to build any clocks or measuring-rods without it.
In Chap. 11, we will have to return to this point. We will observe in the examined
phenomena that the above described the behaviour of measuring-rods and clocks
is characteristic of a ‘participation of an ether’. In the light of this, we will try to
understand Einstein’s [12, 13] statement ‘Only we must be on our guard against
ascribing a state of motion to the ether’. This means that the physical properties of
our measuring-rods and clocks are in respect to the ether of such a kind that they are
not able to respond to the ether.
An important fact has yet to be mentioned. The question ‘why’ concerning time
dilatation and length contraction is not specifically asked in the Special Theory of
Relativity. It is only shown that if we measure one and the same velocity for light,
then we have to conclude that in principle all measuring-rods and clocks show this
behaviour. This does not mean, however, that the question ‘why’ about these effects is
forbidden by the Special Theory of Relativity. However, it is just that all traditional
attempts of explanation are excluded by the particular axiomatic structure of this
theory. In Einstein’s axiomatic approach, all problems of SRT can be reduced to the
universal constancy of the speed of light. This is the axiomatic base of the theory. A
more simple explanation than the reduction to the axioms does not exist. This is the
problem. Is there any point in trying to discover a ‘mechanism’ that could clearly
explain these changes for moving measuring-rods and clocks? We will come back
to this question if we succeeded in finding out a real existing physical model, our
‘miniatur version’ of SRT.
The first direct observation of time dilatation of a ‘clock’ was achieved in 1938/39,
as described in the papers of H. J. Ives [44, 45] and G. J. Stillvell and G. Otting’s
3 Here, we will inform you of our notation which we will carry on throughout this book. All
statements about space and time described using moving measuring-rods and clocks are represented
by primed symbols. If measuring-rods and clocks of different velocities are involved, then tildes or
roofs are used; see Chap. 17.