DIMENSION

First of all let's understand what we mean by dimensions? Dimension is defined as the minimum number of coordinates that are needed to specify that point in it. Example, to specify a sheet of paper we need two coordinates only; length and breadth. Therefore it is a two dimensional object. But to specify a cube in space 3 coordinates are needed these are- length breadth and height. Therefore we call it a three dimensional object.

According to classical physics there are 3 dimensions of space; length, breadth and height and one dimension is of time. String theory requires 10 dimensions but as per M theory total no. of dimensions are 11. In Bosonic string theory spacetime is 26 dimensional. But now the Question arises, if there are so many dimensions in existence then why we are not able to perceive them? Why we cannot feel the presence of higher dimensions? Actually We might be living in higher dimensions without being aware of it. But because of the limitations of our brain and senses we may not be able to perceive them.

According to some researches extra dimensions may be curled up at extremely small scales. This scale is so small that we can not see them with our experiments based on current technologies. As we live in a three dimensional world, it's very hard for our 3 dimensional brain to visualize higher dimensions. There is a process known as compactification, where higher dimensions are curled in on themselves. On changing our reference frame and going into microscopic level we will find higher dimensions. Suppose we are looking at a rope from some distance which is tied between two rocks. From this distance we will see only one dimension of the rope i.e. length.

Now Imagine that an ant is crawling onto the rope. So from the frame of reference of ant, the rope is at least 2 dimensional as it can see it's breadth and thickness also along with its length. The ant can also feel the grooves and roughness of the rope. If we go to microscopic level and see from the reference frame of atoms then we will see a whole new world of 3 dimensional atoms having solid nucleus and electrons revolving around it in 3 dimensional space. On going further into the microscopic level of strings inside the atom, we will see that strings are vibrating in 11 dimensions. Everything in this universe is made up of tiny vibrating loops known as strings according to string theory. So now you can understand how we can find higher dimensions at the microscopic level.

There is no third dimension of height or depth, therefore, these objects are flat figures having non zero area but zero volume. If someone is living in two dimensions, then he would be able to move only on a surface without being able to move in up or down directions. He will not have any idea of the third dimension which is height. Can you imagine what will happen when a 3 dimensional object enters into the world of two dimensional being? Let's understand it with an interesting example. Suppose a two dimensional being present in his two dimensional space is watching a three-dimensional apple entering into his flatland world on a vertical axis perpendicular to the plane of the flatlander.

But as we know a two dimensional being cannot see a three dimensional object. So how would that 3 dimensional apple look like from the frame of reference of that flatlander? He can not see the Apple until it touches his 2 dimensional plane as it's above his flatland and he cannot see anything which is above or below his 2 dimensional plane world. but as the Apple just touches the plane, he will see a dot which is nothing but the point of contact of the Apple to the plane. Now as the Apple goes below his plane world, he sees a circle growing in size on his plane and the size of the circle is maximum when half of the Apple is Above and half is below the plane and then the circle size becomes smaller and smaller and then a point and finally it disappears for him. It means the 2 dimensional being sees only the cross sectional view of the Apple that is cut by his 2 dimensional plane at that moment.

So for a person living in a particular dimension, objects of higher dimensions suddenly may appear from nowhere, may change shapes and size and then disappear into space. It may appear supernatural or kind of magic for a lower dimensional being but for that higher dimensional object it's nothing special. It just moves in dimensions that are not perceived by him. Third dimension (3D) On adding one more dimension to 2 dimensional objects we enter into the world of three dimensions. This third dimension is of height. Therefore to represent three dimensional or 3D objects we need three coordinates length, breadth and height.

As we have Already discussed that two dimensional objects are plane figures therefore have zero volume. But three dimensional objects are solid objects and therefore have non zero volume. Some common daily life examples of three dimensional things are balls, chair, car and we humans. We live in a three dimensional world. This is the reason we can move in forward, reverse, up and down directions easily. as we have full control over the three dimensions of space.

Fourth dimension Time is considered the fourth dimension. A four Dimensional being can move freely in time dimension. It would have full control over time. He would be able to move in any desired direction in time; past or future. Suppose you are living in a four dimensional world then you would be able to go to a certain point in time in past and change your decisions. But we humans are 3 dimensional beings, therefore have full control over the three dimensions of space but we are forced to move only in one direction in time- the forward direction, as we are three dimensional beings.