The miracle of gravity(shattering newton's dream )

To all the reader,s out there, i have a simple, yet difficult question , what is gravity?, and you might answer, yeah, newton,s idea was that gravity is a force which has no apparent cause, but you see, everything has a cause, and in the case of gravity, it is so shocking that you might fall out of your chair reading this, gravity is NOT A FORCE. What? , did your highschool teachers lie to you about the 500 year old belief

that gravity is a force, or did they not know enough material to teach gravity more concisely, the second one stands out , well, the idea of gravity is so subtle , yet so beautiful that general relativity, is widely acknowledged as the greatest ever creation of the human mind

So, what is it? Imagine you are jumping up and down on a trampoline, and a spectator throws a ball on it, now notice the ball's path the instant you land, and the instant you fly, does the ball move in a curve, why? Why does that not go straight, gravity!!!!!!!, it is gravity., you curve the path of the trampoline and it curves the motion of the ball!

Now we are finished, arent we, no, i have yet to explain to you the mathematical terms of it, here we go

The equations that describe gravity are known as Einstein field equations or

Guv-guv=8g/c4tuv

Simple, right? Wrong

It looks simple but actually is hell complicated let's break it down, before explaining all this, i would like to give you all a basic intuition about tensors, you might know what vectors are, quantities having magnitude and direction, or in a mathematical sense

2i+j+k

Which says, move 2 units to the left of the x axis, i unit down to the y axis and i up

So those are lines giving directions, just as you saw in the above image, the grid, it has two vectors u and v, on which the whole idea of gravity revolves, let's see tensors

A tensor is a extra addition on a vector space(a structure called manifold) which changes the shape or properties of the structure,a manifold is a 3 dimensional surface , let,s see it,s mathematical form

manifold

So the thing you see is called a manifold, it has a kind of cosine shape, whatever now let's see some examples of tensors.

Kronecker delta

As mentioned vectors are denoted by i, j,k , tensors have the same notation

delta=ij

Where i and j are the x and y axis respectively

Rij=dxij/dpij

It is just specifying the direction in which the rate of change of the quantity will occu

These are tensors, the black lines you see,

So they can also be written as a matrix, for example

pij=[pik pil pij pjk p]

In the case above this is a stress tensor which measures the impact of various forces on a body consider a rubber ball, you squeeze it, the rate of change of all it,s points will be determined by a tensor

kij=du/dx u is the displacement in the i direction and x is the rate of change at x means it is changing in te x direction

Anyway let,s get back to our work

Ruv-1/2Rguv=8g/c4tuv

Deriving this is beyond the scope of our topic, will cover some other time but here

Ruv is called the ricci tensor which measures the curvature of space

guv is the metric tensor which specifies the directions in which space is being curved

Tuv is the stress energy momentum tensor determining the total energy of the universe, thus causing mass to move,

More depth

y= 1/2 gik (dgi/drik-drik/del)

Here g is th collection of vectors u and v, namely uv, vu and the dot products of all those ……

The rate of change of christoffel symbols gives the ricci tensor stating the rat of change of those vectors u and v

The metric tensor also describes the curvature of space and is represented in the form ofa matrix, namely curvature at different points

And the strress tensor determines the momentum, energy flux of all particles within the gravitational field

That,s it, we are done……

(Note i am using y as the christoffel symbol since i don’t have the letter )