Spacetime

A single entity, not space *and* time ...

Space includes three mutually perpendicular dimensions that we might think of as forward-back, left-right and up-down. For the sake of brevity I will call forward-back the x dimension, left-right the y dimension and up-down the z dimension. To locate an object in space we need to choose a reference point along each dimension from which to start our measurements. We will call that reference point zero. We get to choose the reference point because space is symmetrical with regard to location and orientation. If I move my apparatus to another lab table and turn it around to face a different way to repeat an experiment, I get the same results.

Next picture three real number lines, one along each spatial dimension, placed such that their zero points coincide. We will call the common intersection the origin. This arrangement allows us to identify any point in space by a set of three numbers, each representing the distance from the origin along a dimension. The three lines are called the x-axis, y-axis and z-axis each named according to the dimension it spans. The three numbers, written as (x, y, z), called coordinates, specify a point in space. The arrangement of three lines is called a reference frame. Each observer of events in spacetime may have her own reference frame. These frames may overlap, coincide or be in motion relative to one another. If a frame is not rotating and not accelerated, it is called inertial. In inertial frames free particles, not acted upon by an external force, move with constant velocity (speed and direction).

Points in space may be identified by (x, y, z) but events require additional specification. We must say not only where (location) but also when (time) in referring to events. Prior to the advent of Einsteinian Relativity, people thought of space and time as two independent aspects of nature. In ordinary human experience the unity of space and time is not obvious. In fact events, which are the things that really matter in understanding the universe and predicting the future, take place in a unified spacetime framework.

Now we need to include the t-axis in the discussion. The t-axis intersects the space axes with the chosen time zero at the origin. Since we can move along the t-axis without moving along any of the spatial axes, the t-axis must be perpendicular to all three spatial axes. We cannot visualize a fourth line perpendicular to three others but it surely is there.

With this unification, space and time are on an equal footing. That does not mean there is no difference between space and time but they may be treated in the same way and combined in mathematical expressions. One distinction between time and space is that time seems to have had a definite beginning whereas space has no natural limit in any direction. The second significant difference is that to use time in meaningful mathematical expressions in exactly the way that space is used; one must replace the time coordinate with the time coordinate multiplied by the square root of -1. No amount of mathematical finagling will get rid of the pesky minus sign that appears on squaring the time coordinate.

The location of an event is specified by (x, y, z, t) where t is the time coordinate of the event. Distances along the spatial axes are commonly reckoned in length (meters for example) while distances along the t-axis are commonly reckoned in units of time (seconds for example). In spacetime calculations it is often convenient to have common units on all axes. Fortunately Nature has provided us with the conversion factor between seconds and meters. One second is approximately 300,000,000 meters. We know this universal and constant conversion factor as the speed of light, 300,000,000 meters per second.