Rindler’s *Essential Relativity* is a well-written monograph that we can use to explore time and relativity. He describes the coordinate lattice of a single inertial frame of reference (section 2.5). Let us consider it with an eye toward the corresponding temporal coordinate lattice.

Start with the observer at the origin of an inertial frame, with a clock, and measure the distance to any particle by bouncing a light signal off it and multiplying the elapsed time by *c*/2 (where *c* is the speed of light). Angle measurements are made with a theodolite to derive 3-dimensional coordinates of the particle. Test particles at rest are placed at all the lattice points — integer multiples of a given length — each with a clock synchronized with the master clock at the origin by a single light signal emitted at time *t*_{0}; when this signal is received at any lattice clock, that clock is set to read *t*_{0} + *r/c*, where *r* is the predetermined distance from the origin.

This process is valid for a single inertial frame. With it the coordinates of all events can be read off locally, directly where the events occur, by suitable auxiliary observers. Rindler emphasizes that other types of signal could just as well have been used, for example cannon balls. I would add that probe vehicles on a street grid could also be used to set up such a lattice.

How does this read if we switch space and time? Let’s see.

Start with the observer at the *spacetime* origin of an inertial frame, with a *ruler*, and measure the *duration* to any particle by bouncing a light signal off it and *dividing* the *distance traveled* by 2*c* (where *c* is the speed of light). Angle measurements are made with a theodolite to derive 3-dimensional *temporal* coordinates of the particle. Test *events* at rest are placed at all the *temporal* lattice points — integer multiples of a given *time* — each with an *event* synchronized with the master *event* at the *spacetime* origin by a single light signal emitted at *point* *p*_{0}; when this signal is received at any lattice *event*, that *event* is set to read *p*_{0} + *ct*, where *t* is the predetermined *duration* from the origin *event*.

The result is a lattice built out of durations, not distances. As these are related to the distances via the factor *c*, it is equivalent to a lattice of distances. But conceptually it is different and the result is that distance or length is the independent variable and time is the dependent variable.