S14. Space-time

"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." - Hermann Minkowski

In this note and few more, I’ll be discussing about the concept of spacetime. Here, we’ll start by giving an introduction of the spacetime.

In conventional Newtonian Mechanics, Euclidean Geometry plays an important role. Cartesian coordinates seemed most naturally adapted, and straight lines could be conveniently accommodated. Time was viewed independent of space—as a separate, one-dimensional continuum, completely homogeneous along its infinite extent. Any “now” in time could be regarded as an origin from which to take duration past or future to any other time instant. Within a separately conceived space and time, from the possible states of motion one could not find an absolute state of rest. Uniformly moving spatial coordinate systems attached to uniform time continua represented all unaccelerated motions, the special class of so-called inertial reference frames. Thus initially, even though space time could have been fabricated to describe events we could only imply that space and time was something very fundamental and remained unchanged. Therefore there was no need for further generalization.

However, with the discovery of special relativity, our notion of space and time was changed and therefore we have to understand space and time as some kind of  a union to preserve independent reality. “In physics, spacetime (also space–time, space time or space–time continuum) is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as existing in three dimensions and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions. From a Euclidean space perspective, the universe has three dimensions of space and one of time. By combining space and time into a single manifold, physicists have significantly simplified a large number of physical theories, as well as described in a more uniform way the workings of the universe at both the super galactic and subatomic levels.” –wikipedia

Here’s a diagram of the space vs space time

         

What's the difference?

At first it may seem like there may not be any difference, but there is a vast difference. Firstly, the first diagram is a mathematical model of the dimension we perceive in two dimensions in universe. The point $(x,y)$ represents physical point in the space. Whereas, the second diagram is a mathematical model of the two dimensional event perceived in one dimensional space dimension. The points $(x,t)$ represents the events in the spacetime. Secondly, these two diagram obeys different set of rules.

To understand what I mean, Prof. Susskind has a very good explanation for it. I recommend you to go through it.