Proposition: Construction of a Light Clock

In any inertial reference frame \(\mathcal I\), it is (theoretically) possible to construct a light clock by placing two mirrors in a vacuum at a fixed distance \(d\) and letting a light particle "bounce" between them. The "tick duration" of such a light clock is then given by the formula

\[\operatorname{tick duration}:=\frac dc\]

where \(s\) denotes the time unit of one second, and where \(c\) denotes the (constant) speed of light in a vacuum:

\[c=299.792.458 \frac{\operatorname{m}}{\operatorname{s}}\]

The following figure demonstrates a model of a light clock:


In particular, if \(d=1m\), the tick duration of this clock in \(\mathcal I\) is

\[\frac dc=\frac {1m}c=\frac {1m}{299\,792\,458\frac ms}=\frac {1}{299\,792\,458}s.\]

For \(d=299\,792.458\,m\) the tick duration would be

\[\frac dc\approx\frac {299.8\,km}c=\frac {1}{1000}s=1\,ns.\]

Proofs: 1

Definitions: 1
Proofs: 2

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  1. Weingärtner, Andreas: "Spezielle Relativitätstheorie - ganz einfach", Books On Demand, 2016