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.
Now I will discuss every dimension, starting from the zero dimension to the eleventh dimension.
0th Dimension (Zeroth Dimension)
There is no length, no breadth and no height of an object in the zeroth dimension. Example of zeroth dimension is a point.
Lets imagine someone is living in the zeroth dimension then he would neither have any body nor any shape. He can not move in any direction like forward, reverse, up or down. zeroth dimension is the basis of all the higher dimensions.
1st Dimension (First Dimension)
An object in first dimension has only one dimension i.e. length. A straight line is an example of first dimensional object. We can get straight line by joining two points.
A one Dimensional being can move only in a straight line. It cannot move in other dimensions like left, right and upward or downwards directions.
2nd Dimension (Second Dimension)
Second dimensional objects also known as two dimensional or 2D objects are flat shapes. Some common examples of two dimensional shapes are squares and triangles.
As the name denotes, two dimensional objects are made up of two dimensions length and breadth. 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.
3rd Dimension (Third Dimension)
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.
4th Dimension (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.
But if we consider the fourth dimension from the geometrical point of view then Hypercube is a 4 dimensional object. It is also called a Tesseract.
The relationship between a hypercube and a cube is same as that of cube and square. So in simple terms a hypercube or tesseract is four dimensional analog of the cube.
As a cube has 6 square faces, in the same way hypersurface of a tesseract consists of 8 cubical cells.
5th Dimension (Fifth Dimension)
A person living in 5th dimension can control time in different ways. A fifth dimensional being can move either in past or future as per his wish.
He would have all the powers that are possessed by a fourth dimensional being.
But he would also be able to be present at different locations at the same time. It would also be possible for him to do many jobs and have different hobbies simultaneously.
Actually Parallel universes exist in this dimension, therefore in the fifth dimension you can I have careers in different fields. In this case, you will have another versions of yourself in parallel universes who would be living their lives independently. They would have separate timelines for the parallel universes. Their lives in different parallel universes will be based on cause and effect. It means their lives will change as per the decisions made by your self versions in different universes.
But one limitation of fifth dimension is that you cannot meet your self version in directly using shortcuts to another timeline of parallel universe.
6th Dimension (Sixth Dimension)
A six dimensional being has all the powers that a person living in 5th dimension has along with some extra capabilities.
Parallel universes exist also in the 6th dimension. A six dimensional being can see all the presents, pasts and futures of all the parallel universes.
But one limitation of the sixth dimension is that all the parallel universes must have the same beginning (initial conditions) that is the Big Bang.
Like in the fifth dimension, in the sixth, dimension also you are free to choose multiple careers of your choice and your multiple versions can live their lives simultaneously in parallel universes.
As I already discussed, one problem with the fifth dimension was, you can not meet your self version in another parallel universe directly using shortcuts.
But the sixth dimension is free from this limitation. You can easily jump from the timeline of your universe to any point present on the timeline of any parallel universe.
7th Dimension (Seventh Dimension)
Seventh dimension can have infinite number of universes. A seventh dimensional being can have infinite forms of itself and can move from one universe to any other universe.
All the powers are possessed by a 7th dimensional being that a sixth dimensional being has.
The seventh dimension is free from the limitations of the sixth dimension.
The 7th dimensional universes may have originated from different start conditions.
And a person living in the seventh dimension can have infinite forms of itself which are able to move freely between all the infinite number of universes at his will. These infinite number of universes may have originated from different initial conditions not just the big bang.
8th Dimension (Eighth Dimension)
The eighth dimension has a plane of all the possible presents, pasts and futures for all the infinite number of parallel universes and all these infinite universes extend up to infinity.
String Theory says in the eighth dimension objects do not have any physical existence. You may think of it analogous to our digital world, where we can not touch the objects but only can see or hear them. They can change shapes, size and appear or disappear instantly. So it may be somewhat similar to the virtual reality.
9th Dimension (Ninth Dimension)
Infinite number of universes exist in the ninth dimension. It is possible for the universes in the ninth dimension to have their own laws of Physics and separate conditions and probabilities of their origin.
You will be surprised to know that in the ninth dimension many civilizations or aliens may live simultaneously at the same place. These coexisting civilizations may not see or feel the presence of each other.
The ninth dimensional being would have mind boggling super powers. That being would be capable of going to any point in time- past, present or future of any infinite number of universes.
He would have no physical form and would be able to move freely in space and time in any of the universes.
10th Dimension (Tenth dimension)
The 10th dimensional being would have infinite powers. He would be able to do the things that are beyond your imagination.
He would be able to control even the spacetime and everything present in all the infinite number of universes.
So what would you call that 10th dimensional being who is infinitely powerful.
I think we can call him The God!!!
Some researches also suggest that God lives in the 10th dimension.
11th Dimension (Eleventh Dimension)
Many unanswered questions were arised when the superstring theory was introduced. Therefore to answer these questions, eleventh dimension was proposed by the researchers.
We can observe only three dimensions of space and One dimension of time. It is not possible for us to observe higher dimensions as higher dimensions are Compactified or curled up.
According to superstring theory, everything in the universe is made up of one dimensional and infinitely small vibrating loops called strings.
Even the subatomic particles are made up of Strings and unique characteristic of each subatomic particle is because of the manner in which the strings vibrate.
It is interesting to note that, frequency of vibration of the string is responsible for the mass of the particle.
But the string theory does not answer two important questions related to strings, what these tiny strings are made of and where they come from.
Size of the strings is of the order of 10^(-33) cm. This size is unimaginably small. This is many times smaller than the diameter of the nucleus.
10^-33 cm is actually millionth of a billionth of a billionth of a billionth of a centimeter.
I know Without giving an analogy our brains can not understand, how small this number is.
If we increase the size of an atom up to the size of the observable universe, then the size of the string would be just equal to a tree.
My dear friends this was all about 11 dimensions. I hope I could answer most of your questions regarding dimensions.
