An analogy one could use is length and width. What is the height of a rod? This may sound like a simple question, but imagine that there is no gravity and we are in an inertial frame of reference. There are two people, one sitting standing straight up and the other is tilted at an angle of 30º. Each person will think that they are the one which is standing straight and it is the other person who is tilted. Therefore, height for one person is a mixture of height and width/tilt for the other person. Thus, each person will see the rod to be a different height. The following diagram will help explain the concept.
Total distance is same for all the observers where D2 = H2 + W2 and D2 = H’2 + W’2.
Time-Space experiences the exact same thing. Space of one observer is a mixture of space and time for another observer. The same concept is applied to time.
As observed with height and width, the
distance is always the same. This
also applies to space-time where the space-time distance is always the same.
Δs2 = cΔt2 + (Δx2 +
Δy2 + Δz2).
The idea of directional space and time leads us to one conclusion, space-time is 4 dimensional, i.e., time, height, length, and width where the latter 3 constitute space.