Time keeping is a human invention as old as human culture, the universal master clock being the movement of the celestial bodies. Nowadays, the master clock is a physical instrument located in a designated laboratory. The time indicated by a particular clock is called its proper time. By general agreement, the proper time of the master clock is our standard time. Every other clock located somewhere, has its own proper time, different for every point in space. A global time is defined through the expedient of the synchronization of local clocks.
This concerns, in particular, the fundamental laws of physics that describe how things change in time. From Newton’s equations of motion (1672) to the Standard Model of particle physics (1973-74), the whole of physics, and science in general, is about change with respect to a global time variable, traditionally denoted by the symbol . Without such a variable, basic formula in physics like to define speed, would not make any sense. But how then does this physical time relate to the multitude of proper times of local clocks?
It is the great achievement of Albert Einstein in 1905 that he was able to answer this fundamental question by analyzing what precisely it means to synchronize stationary clocks located at different points in space. Any synchronization scheme should fulfill at least three consistency requirements:
- Homogeneity: if a clock (at position) B is synchronized with a clock A at a certain time, then clock B stays synchronized, verifiable by the same procedure (i.e., it is meaningful to say that clock B is synchronized with clock A).
- Symmetry: if clock A is synchronized with clock B, then clock B is synchronized with clock A (i.e., it is meaningful to say that the two clocks are synchronized).
- Transitivity: if clocks A and B are synchronized and clocks B and C are synchronized then clocks A and C are synchronized.
In his paper of 1905 Einstein proposes a synchronization procedure based on a radical new definition of physical time, now known as Einstein time,
- Einstein time is restricted to reference frames that are inertial, that is, in which the equations of Newtonian mechanics hold good (at low velocity) and clocks are stationary with respect to each other.
- Einstein assumed that his definition of 'time' meets the above consistency requirements. The necessary proof was later provided by Hermann Weyl in 1923.