Radar Coordinates

One has to understand clearly what the spatial coordinates
and the temporal duration of events mean in physics.
Albert Einstein, 1949

Axiomatic relativity takes the homogeneity and isotropy of the inertial spacetime coordinates ${t, x, y, z}$ as a given. However, to give meaning to these coordinates, one has to understand what duration and distance mean in physics. In later lectures and publications, Einstein elaborates on his view that the physical interpretation of these coordinates, in a given inertial system, must involve the results of certain measurements of spatial and temporal intervals.

In relativity theory, the coordinates ${t, x, y, z}$ find their empirical basis in the 'imaginary physical experiments', as Einstein described them in 1905, that are today’s practice. In an inertial frame, a stationary observer using light (radar) signals, see (3.1), (3.2):

Defines an event A on his worldline to be simultaneous with the distant event B that happens at time $t_{B} = ({\bar{t}}_{A} + t_{A}) / 2;$
Assigns a spatial distance $\bar{A B} = c ({\bar{t}}_{A} - t_{A}) / 2$ to the separation of B from A; here $t_{A}$ and ${\bar{t}}_{A}$ are the times of sending and receiving the signal by A, respectively.

By defining simultaneity and distance in this way, a non-accelerating observer can, in principle, set up a coordinate system to label each event by its radar distance from his own location, and the time at which it happens, according to the radar definition of simultaneity. These labels are the inertial coordinates of special relativity.

One speaks of Einstein synchronization, but in fact, the above prescription entails a specific measurement procedure for the construction of a physical coordinate chart, that is, a one-to-one mapping of spacetime onto R⁴, for an inertial frame to which the chart is said to be adapted. One refers to this type of chart as a Lorentz chart.

A Lorentz chart combines Cartesian coordinates and Einstein time. The geometric structure of Minkowski space rest on the invariance properties of these Lorentz charts, with the unique feature that time and space are Minkowski orthogonal.
By construction, the radar coordinates of spacetime respect the homogeneity and isotropy of spacetime, or stated differently, they reflect the symmetry properties of the physical laws.