Einstein synchronization

Einstein synchronisation (or Poincaré–Einstein synchronisation) is a convention for synchronising clocks at different places by means of signal exchanges. This synchronisation method was used already by telegraphers in the middle 19th century, but was popularized by Henri Poincaré and Albert Einstein who applied it to light signals and recognized its fundamental role in relativity theory. Its principal value is for clocks within a single inertial frame.

According to Albert Einstein's prescription from 1905, a light signal is sent at time ${\displaystyle \tau _{1}}$ from clock 1 to clock 2 and immediately back, e.g. by means of a mirror. Its arrival time back at clock 1 is ${\displaystyle \tau _{2}}$. This synchronisation convention sets clock 2 so that the time ${\displaystyle \tau _{3}}$ of signal reflection is defined to be

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