The duality of time

 Introduction to Relativity

‘What’s it all about, Albert?’

This Relativity thing, what is it, how does it work, and why do we need it?

There is a principle that I believe should be applied to what has arisen from Einstein’s theory of Special Relativity, and that is Occam’s Razor; which may be stated: “It may generally be taken that the simpler explanation is the better one.”

A Brief summary of Space and Time.

Let us begin by looking at what we mean without all the scientific gobbledygook that make it all so difficult for everyday folk.

Space is vast. It is a long, long way across, billions of light years. But, while it contains billions of huge galaxies, each with billions of stars, planets, comets, asteroids right down to microscopic Space dust, it is still 99.9999…% empty!

It is impossible to visualise just how big it is; nor with so much in it, just how empty it is.

Because it is virtually empty and has no structure, it is impossible to know when one is at rest in space. We know where we are and how we move relative to everything else in space. But how can one measure where one is and whether or how fast one is moving relative to empty space? 

Including Time along with the three dimensions we are so familiar with, Spacetime was created. The laws of science are the same everywhere and in every orientation in Spacetime.

Einstein’s famous theories rely on one more Physical Law and that is that the speed of light is constant. That it is the same wherever and however it is measured. It doesn’t matter how the light source is moving; nor how the destination is moving it will always travel the same distance in the same time.

Time; what is the nature of time? This is a question that scientists are still trying to answer. At its simplest, it is a measure of how long something takes.

Time can only be measured by comparison with the duration of a known process; such as the ticking of a clock; whether such a tick is the movement of its hands, the counting of a digital clock, the turning of the Earth. 

We use time in two different ways. Firstly to know what time it is, whether that be time of day, geological or cosmic time. Secondly we use time to measure durations or intervals. 

I liken these to modes of time to using a clock to tell the time of day, which may be considered  a subjective measure of time as it applies to us, the observers; and using a stop watch to time something specific, which could be considered objective time as it measures some other process.

When we specify a location in Spacetime we can use the coordinates of our three spatial dimensions to define exactly where it is, in the Frame of Reference we have defined.

Yet we cannot do that with time, for a moment in time happens at all locations.

We can specify a point on a line - a single coordinate; a point on a surface - two  coordinates; or a point within a volume of space - with three coordinates - the Cartesian axes we are so familiar with: width, height and depth; or Latitude, Longitude and Altitude; our old friends x,y and z.

But a moment in time is the same for more than just a single point in space. 

Fig. 1

Consider, a flash of light would travel at the speed of light in all directions. It would form an expanding sphere of light. The radius of that sphere, measured in light seconds would be the time it has been travelling in seconds. But that time will be the same for the whole sphere. So, whereas moving in space means changing location, moving in time means increasing the volume of the point in time.

Fig. 2

Subjective (background) time, the start of time was long long ago (around 13.8 billion years ago) which means that a moment in time today will be a sphere that encompasses the whole universe. That is one vast sphere, so vast that if we draw time as the vertical dimension in a spacetime diagram, the divisions will appear as horizontal lines. (Think how flat the surface of the Earth appears. Its radius is roughly 4,000 miles. Now imagine how flat it would appear if it were a billion times as big). Shown in green[Fig. 2] Objective (local) time, But when we time specific movements or processes, from the origin of our Frame of Reference, the centre of the sphere of time we are measuring will also be at the origin (0,0) of our Frame of Reference. Shown in red [Fig. 2]

It is this duality of time that has given rise to the concepts of Time Dilation, Length Contraction, time slowing slowing for a body travelling near the speed of light, the Relativity of Simultaneity, and the many paradoxes that have been envisaged.