All About Dimensions

Defination: Quantities that allow us to specify the position of a particle or visualize it.

In string theory, spacetime is 26-dimensional or 10-dimensional (As per bosonic string theory and superstring theory respectively) and in M-theory it is 11-dimensional.

Zeroth  dimension ,a point, a single dot with no practical measures.

Many points come in a specific straight configuration to form a line, the 1st dimension.

Many lines come in a specific straight configuration to form a plane, the 2nd dimension.

Same with the 3rd dimension, many planes come together to form a object.

Now, many planes come together to form a world line, the 4th dimension, Time.

Say, there is a world line(commonly called the time line), its just like a 1d line on a plane, so what’s the space of the rest of the plane, possibilities. There are infinite number of points orthogonal or at any angle to the world line, so are possibilities. This is the 5th dimension. I will like to elaborate this dimension. In the 5th dimension, there are 2 most accepted theories, the MWI(Many Worlds Interpretation) and the Copenhagen Theory.

When Quantum Mechanics was developed, the Mathematics was developed at the base. Now, the equations yielded wierd results.

To understanding the implications, and to cover them in form of a physical theory, quantum physicists split into two groups which had different ideologies.

One of them was the Scientist Group which worked at the Copenhagen University.

I just checked at Wikipedia: Neils Bohr and Werner Heisenberg were the key people in this group, and they were associated with Copenhagen University at the time. So this method of interpreting different aspects of Quantum Mechanics is called the Copenhagen Interpretation

In the Copenhagen Interpretation, the quantum properties are all covered in a mathematical form called the Wave function.

For example, consider the Quantum Superposition.

In our example, let's take an electron which is in a Superposition of two spin states: +½ and -½

This can be represented by a wave function.

Now, according to Copenhagen Interpretation, when the electron is observed, a wave function collapse occurs, and the electron comes into one of the two states in reality.

In Many Worlds Interpretation, when the electron is observed, the Universe splits into two. In one universe, the electron collapses into +½ and in the other universe, it collapses into -½.

In this way, there are all the universes with all the different possibilities

This was the basic difference between the two ideologies. The Copenhagen Interpretation assumes a random collapse, while the MWI assumes both types of collapses in different universes .

Now, if we can change our version of the universe we would be 6^th dimensional beings. The presence of different versions of the universes is  like planes in a infinite space. There are a total of approximately 10⁵⁰⁰ universes currently. This is the 6^th dimension.

The 1^st dimension is like the 4^nd dimension, a simple line and a world line. The 2^nd dimension is like the 5th  dimension a simple plane and a plane of possibilities. The 3^rd  dimension is like the 6^th dimension, a simple solid and a solid of all the possibilities and different version of the universe.

                                                              

 I can explain only till the 6^th dimension as for the next for dimensions, either I have a blurred idea or don’t know much about to explain it. So, I stop the description of dimensions here.

 Now, the best part, about us. We are 4 dimensional beings but have the privileges to control only the first 3 dimensions.

I think beings can control `n-1` dimensions when they are allowed to `n` number of dimensions. They can feel the last dimension flowing or just feel(or see) its presence there but cannot control it. It is different purely by nature.

As for humans, the 4 dimensional beings, we can control the first 3 dimensions and feel the flow of time, the 4th dimension, in a particular direction (from past to future). Similarly, the flatlands creatures or the 3 dimensional beings can move only in the two dimensions but can see the 3^rd dimension. It's a bit confusing as it means that time is not flowing in the beings having lower space dimensions than us as they don't have the 4^th dimension. Even, imagine a two dimensional animal living on a one-dimensional Earth would have to climb over each other in order to get past each other. If a two dimensional creature ate something it could not digest completely, it would have to bring up the remains the same way it swallowed them, because if there were a passage through its body, it would divide the creature into two separate parts. Our two–dimensional being would fall apart. Similarly, it is difficult to see how there could be any circulation of the blood in a two dimensional creature. So I conclude that the universe can have a minimum of 4 dimensions for the development of intelligent beings like us  (We are very lucky though to be on the edge).

I would like to say about the higher dimensions though as there very interesting and open up a  borders view for imagination. Let's see the 5^th dimensional beings first, the view there would be like this: People can move back (in past) or front (in future) in time. They will have the extra freedom (in the sense of 4 dimensional beings like us). They can see or feel the presence of their existence in different universes or they can predict the possibilities of their present existence. In a broad sense, they can look and understand their future light cone and past light cone (also referred to as time cone. I will sure assume that you all know the term and will not elaborate it further as it will even go a bit off topic). Their extra freedom will be changing into some other present. There would also be problems with more than three space dimensions.

The gravitational force between two bodies would decrease more rapidly with distance than it does in three dimensions. The significance of this is that the orbits of planets, like the Earth, around the sun would be unstable. The least disturbance from a circular orbit, such as would be caused by the gravitational attraction of other planets, would cause the Earth to spiral away from or into the sun. We would either freeze or be burned up. In fact, the same behavior of gravity with distance would mean that the sun would also be unstable. It would either fall apart or it would collapse to form a black hole. In either case, it would not be much use as a source of heat and light for life on Earth. On a smaller scale, the electrical forces that cause the electrons to orbit around the nucleus in an atom would behave in the same way as the gravitational forces. Thus, the electrons would either escape from the atom altogether or it would spiral into the nucleus. In either case, one could not have atoms as we know It seems clear that life, at least as we know it, can exist only in regions of space-time in which three space and one time dimension are not curled up small.

Ok, now some interesting aspects of dimensions.

It is accepted that There may well be other regions of the universe, or other universes (whatever that may mean) in which all the dimensions are curled up small, or in which more than four dimensions are nearly flat. But there would be no intelligent beings in such regions to observe the different number of effective dimensions.

A Cube is a basic 3D object whereas a tresseract is a basic 4D object (Refer Gif Below). Similarly, a penteract is a 5^th dimensional object and so on.

Now suppose that there is a doughnut shaped object in space. You want to get to the opposite side of your initial position A. See this it's like you want to go from point A to point B. First let’s see for a 2 dimensional being. He will travel using the path P1 and next a 3 dimensional being will travel using the path P2(As he can cut directly through space using his 3^rd dimensional privilages which the 2 dimensional being will call his extra freedom). Now supposing the speed of both the objects to be equal, we can say that the 3 dimensional being traveled much faster than the 2 dimensional being. So, from this example I can conclude that we can travel faster using higher dimensions.(Indeed, this is exactly what is use is used in Sci-fi movies to travel between Galaxy or for covering very long distances quickly. Although, it's a shame that most people watching or producing the shows don't exactly know the amazing idea that they are dealing with!!)