Σάββατο 6 Απριλίου 2024

The geometry of the fourth dimension and the space-time

Ιn Physics, a dimension can be defined as the magnitude of something in a particular direction. Everything that surrounds us is made up of three dimensions.
These are known as three-dimensional or 3D objects. Before we look into the fourth dimension, first we need to understand the first three dimensions.
The zero dimension
For example, let’s take a sheet of paper. Place a dot on the paper. A dot does not have a direction or a magnitude. So, we can say that this dot does not have any dimensions. Let’s call this a zero dimension (0D).
0D, 1D, 2D, and 3D.
The first dimension
Next, from this dot, let’s draw a straight line along the x-axis. Now, we can measure the length of this line. So, we can say that this line has only one dimension. This is called a one-dimensional object or 1D.

The second dimension
Next, from this line, draw lines on both ends along the y-axis and convert this into a square. Now, for this square, we can measure both its length and width. As we are able to measure both it’s length and width, now we can say that this square has two dimensions. These are called two-dimensional or 2D objects.

The third dimension
Next, from this square, draw lines along the z-axis and convert this into a cube. Now, we can measure not only its length and width but also its height. As we can measure its length, width, and height, now we can say that this cube has three dimensions. These are called three-dimensional or 3D objects.
3D objects
Similarly, objects that we see around us have length, width, and height making them three-dimensional.

The fourth dimension and the space-time continuum
In 1905, Albert Einstein published his Special theory of relativity which considers time as the fourth dimension.

Let’s take a look at the cube again. As long as the cube is stationery, we can pinpoint its position along x,y and z-axis.

But, what if this cube starts moving? How can we pinpoint its exact position?

In order to say the position of this moving object, Einstein introduced a dimension called “Time” into this 3D space.

You may wonder how can “Time” be a dimension? For something to be a dimension, it must have a direction and a magnitude. Similarly, time can be measured (ex: seconds).

And, time always flows in the forward direction. So, Einstein considered time as the fourth dimension. Now, with the help of time, we can pinpoint the exact location of this moving cube.
Time as the fourth dimension.
For example, we can say that at 8:00 am this cube was at a particular downward position (x,y,z) and at 9:00 am it was at an upward location (x,y,z) with the help of time.

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