What is space-time ?

You may have heard the word “space-time” form your friends, books etc. We use the word “space-time” all the time in “Special theory of relativity” and “General theory of relativity”. In fact all the calculations of these revolutionary theories are based on “spacetime”. So what is it actually? And how do we imagine this? Why is it so useful in explaining the universe? Is time a fourth dimension? Bla bla bla…. Lots of questions.  Now let’s try to find the answers to these questions.

The concept of “space-time” was first defined by Hermann Minkowski in 1904. He was the first to understand the usefulness and importance of “space-time”. So, it is often called “Minkowski spacetime”.

Suppose you are sitting on a chair in a garden with a clock in your hand. Now make a 3D coordinate system (take yourself as the origin and choose  x axis, y axis and z axis ). So, everything around you is a part of your system and you can calculate the exact positions of each object (from their coordinates). Set the clock to zero and then start. At time t = 0s, a cat is at point A(Consider the diagram, you are at O(0,0,0)).

At a particular moment , you can think that the world is slowed down to standstill. Everything around you is frozen and so the cat. Now you can calculate the position of the cat (Note that everything around you is frozen, not you). The cat is at (5,0,0). Suppose that the cat does not move as time passes. After a certain time, say, at time t = 5s, the cat is at the same position i.e. at (5,0,0). The cat and you are at rest in your coordinate system. But there is something that is running .It is the time. Time is passing. At every instant you measure the positions of the objects. It is like that you have taken photos of your surroundings every second. All the images are identical(for the sake of simplicity let us assume that everything around you is at rest). The cat is at rest in every image. But there are 5 copies of the same image( 5 photos in 5 seconds). Similarly, you and your whole coordinate system are moving along the time axis and there are five copies of the same coordinate system. You have moved from time t = 0s to time t = 5s. It may be confusing and you may not get the point. Think carefully. Consider the below diagram for help.

Note that the whole coordinate system with you is moving along the time axis. The direction of the z axis seems to be the same as the direction of the time axis. But they are not, as I said, the whole coordinate system is moving along the time axis. Think it carefully. You are at rest in your coordinate system .But you can see that your clock is running which means that the time is passing. It means that besides your three dimensional coordinate system there is  another axis along which we are moving. It is the time axis. Obviously we can’t see it. But we can feel the time passing. If the cat moves then its position also changes with time (which is shown in the diagram below).

So the 3 Dimensional space and the time axis together makes a 4 dimensional “space-time” where time is the fourth dimension. It is impossible to imagine all the four dimensions together. So, we usually omit one or two of the three special dimensions and make a spacetime diagram. We use spacetime diagrams to describe motions of particles and it is extremely popular in theories like “Special theory of relativity”. It becomes easier to understand the results of these theories if we use spacetime diagrams. Some important aspects of these theories are totally based on the spacetime. If the cat is moving only in the x direction then the diagram below shows the spacetime diagram of the motion of the cat.