According to special relativity, space and time are not completely independent entities but are interconnected in a four-dimensional framework called spacetime. This interconnection means that measurements of space and time are relative and can be influenced by the relative motion of observers.
In special relativity, the concept of simultaneity is relative, meaning that events that appear simultaneous to one observer may not be simultaneous to another observer in relative motion. This implies that measuring time with a ruler or space with a clock, as you suggested, would not be accurate or consistent across different observers.
In special relativity, distances in space and intervals of time are not absolute but depend on the relative motion between observers. This leads to effects such as time dilation and length contraction, where the measurement of time and space can be different for observers in relative motion.
To measure time accurately, one typically uses a clock, which is a device specifically designed to measure time intervals. Clocks can be based on various physical processes, such as the oscillations of a pendulum, the vibrations of an atom, or the decay of radioactive material. By comparing the readings of clocks at different locations, one can determine the differences in elapsed time between events.
Similarly, measuring space accurately is typically done using a ruler or some other measuring device that relies on the principles of geometry. The length of an object or the distance between two points can be determined by comparing it to a standardized unit of length.
However, it's important to note that the measurements of time and space in special relativity are observer-dependent. Different observers in relative motion may measure different time intervals and spatial distances due to the effects of time dilation and length contraction. The exact relationships between these measurements are given by the Lorentz transformations, which describe the transformations between different reference frames in special relativity.