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lorentz transformations

Theory of everything summary


INTRODUCTION

Theory of everything is a physical theory that is supposed to combine general relativity with quantum mechanics. Such theory falls under the category of quantum gravity. A lot of quantum gravity theories have been proposed but none has been fruitful. The removal of singularity like big bang, which Einstein's general relativity can not explain, compels physicists to unify quantum mechanics with general relativity. All of the attemps had gone in vain so far. String theory which compares elementary particles with tiny vibrating strings has not been experimentally verified yet. The theory is mathematically consistent though. Explanation of string theory will take a lot of time. I will briefly explain all the major theories and concepts of physics that have been discovered so far, with mathematical equations. So basic understanding of some advanced mathematics is necessary.


Classical physics of Newton and Einstein

Newton's physics Newton's physics describes motion and mechanics of massive bodies likes planets , stars and comets. The equations of motion are :
equations of motionequations of motion
These equations of motion plays a vital roles in dynamics both in classical and quantum physics (in a slight distorted way). The discovery of the universal law of gravitation of Newton was an interesting event.

equations of motion
The equation of the great law is very simple indeed

equations of gravitation
With the laws of mechanics Newton's physics can be wrapped up :

equations of mechanics

Einstein

But wait , Einstein who was a clever man did not like Newton's concepts of space , time and gravity . So he modified them in a radical way. Theory of relativity was dscovered , which says we can travel into our future , even in past too.

equations of relativity
So what does the picture above mean? it means a lot like these :

equations of relativity
t= time , x, y, z = space coordinates, c = light's speed , v = observer's velocity
The most revolutionary consequences as the mass and energy equivalence relation - using which atom bombs were developed..
equations of relativityequations of relativity
Einstein did not stop even after these remarkable discoveries. He shocked the world with the bold idea that our space and time are indeed curved. Spacetime is what we need to talk about to describe the universe. In mathematical language his ideas can be put in this beautiful form :
equations of general  relativity
The field equation simply tells "space tells matter how to move and matter tells space how to curve". This is the choreography of cosmic dance between space, time , matter and energy inside it. geodesics of particles

I forgot to speak of maxwell equations without which we can not speak with our cell phones, our eye could not see. Maxwell equations describes the propagation of light or electromagnetic waves. The mathematical elegance of the theory can be easily noticed while looking at the equations of Maxwell's :

Maxwell equations
Einstein made his field equation (described avove) consistent with Maxwell equations whereas Newton's law of gravitation was not.

Quantum physics

If you enter the world of quantum mechanics you will be shocked at least if you understand it. The laws of quantum mechanics governing electrons , neutrons, quarks are different than those of classical physics. Everything needs to be expressed in terms of probabilities. This is how it is done :

Schrodinger equations

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Reference materials:


Law of thermodynamics
A briefer history of time by S. Hawking
A brief history of time by S. Hawking
Quantum mechanics
Grand Design by Stephen Hawking
Higher Engineering Mathematics ( PDFDrive.com ).pdf
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