Chapter 10
Measuring-Rods and Clocks in Motion
Measuring-rods and clocks have to be able to be moved. One likes to have a ruler
and a stopwatch at hand when one rushes off to the position where a motion is to
be recorded. However, how does one measure the length of an object that flies by,
how do we measure its time of flight from position A to position B? Do we have to
jump on to the object and position our ruler and start our stopwatch at position A
and stop it at position B? It would be far more comfortable and practical to stay in
one position and just let the object fly by. We mark on our ruler the simultaneous
positions of both end points of the object. This should represent its length. In order
to measure the time of flight between A and B, we would just simply compare the
readings of the stopwatches as the object arrives there. Does it make a difference
how we arrange and use our instruments of measurement? Is not it just a matter
of taste and competitiveness if the observer jumps on to the object or just remains
seated and watches it fly by? Well, in both cases, we have to move the instruments
of measurement even if only to distribute the stopwatches along the course that we
started simultaneously at the starting position, as in the second case.
The process of synchronising clocks positioned at different locations without
moving them was described in Chap. 2. In order to do this, we need to have a signal
at hand, and we need to know its exact velocity. In our equations for the linear chain
(31), we tacitly agreed that at the positions x i =
L
N
i of all N masses one and the
same time t would be measured. It was this fact that allowed us to formulate the
solution (32). We thus assumed that we have introduced a synchronised time for the
whole linear chain. The question of clock synchronisation was never put forward in
Newtonian mechanics. It was mutually accepted that one could transport an already
ticking clock to any position where it could be used to synchronise another clock.
It was left to A. Einstein to ask this question: Can we really be certain that moving
clocks do not change their pace? How can we be sure that the oscillation period
of a moving clock does not change? As strange as this question may seem to the
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_10
91
Measuring-Rods and Clocks in Motion
Measuring-rods and clocks have to be able to be moved. One likes to have a ruler
and a stopwatch at hand when one rushes off to the position where a motion is to
be recorded. However, how does one measure the length of an object that flies by,
how do we measure its time of flight from position A to position B? Do we have to
jump on to the object and position our ruler and start our stopwatch at position A
and stop it at position B? It would be far more comfortable and practical to stay in
one position and just let the object fly by. We mark on our ruler the simultaneous
positions of both end points of the object. This should represent its length. In order
to measure the time of flight between A and B, we would just simply compare the
readings of the stopwatches as the object arrives there. Does it make a difference
how we arrange and use our instruments of measurement? Is not it just a matter
of taste and competitiveness if the observer jumps on to the object or just remains
seated and watches it fly by? Well, in both cases, we have to move the instruments
of measurement even if only to distribute the stopwatches along the course that we
started simultaneously at the starting position, as in the second case.
The process of synchronising clocks positioned at different locations without
moving them was described in Chap. 2. In order to do this, we need to have a signal
at hand, and we need to know its exact velocity. In our equations for the linear chain
(31), we tacitly agreed that at the positions x i =
L
N
i of all N masses one and the
same time t would be measured. It was this fact that allowed us to formulate the
solution (32). We thus assumed that we have introduced a synchronised time for the
whole linear chain. The question of clock synchronisation was never put forward in
Newtonian mechanics. It was mutually accepted that one could transport an already
ticking clock to any position where it could be used to synchronise another clock.
It was left to A. Einstein to ask this question: Can we really be certain that moving
clocks do not change their pace? How can we be sure that the oscillation period
of a moving clock does not change? As strange as this question may seem to the
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_10
91