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Mental Introduction to General Relativity

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General theory of relativity
Artificial Satellite Orbiting Earth,From the perspective of General Theory of Relativity

We know about special relativity. Hope you knows ūüėÄ


So lets get to know about the general one now. The general theory as the name suggests is the generalized form of the special theory. In fact, Einstein found a small disability for his special theory,which forced him to solve it. Finally he understood that special theory was only the scratch on the tree, while the tree is still to be unexplored.

You have to know what is an inertial frame before reading from now on. You will have to take time and refer books for that. For my easiness I will just tell you that ,“an inertial frame is where inertia works. Where the newton’s laws are completely valid”.


If you are too lazy to read about inertia and Inertial frame,don’t neglect the advice¬†“you won’t understand a bit” ūüėÄ


Special theory is only considering the inertial frames or it is invalid out of it.


But what remains out of it?

It’s the¬†Acceleration.


Special relativity is invalid in any accelerating frame. Einstein too did what everyone would do. Looked for a solution.

His thoughts were about the effects of acceleration,and not acceleration itself. It took nearly 10 years for him to find an answer. The answer was later called as general relativity.


The core statement is the principle of equivalence;which says that an observer who is inside a laboratory,which is closed can never distinguish between the effects produced by a gravitational field and Acceleration.


Consider yourself locked inside a container. You don’t know what’s going on outside. The only thing you know is,you are inside a container. Lets assume the container was kept in a rocket and was ejected into the sky. The speed is increasing and increasing,that is¬†the rocket is accelerating. You,inside the container doesn’t know about this,but may feel some stiffness or some extraordinary feelings,like one which you feel inside your stomach¬†when you are using a Lift.


Now consider a second case,where the container,containing you is passing beside the sun,or any planet,or any gravitationally attracting body,or any gravitational source,you will feel the same thing,the same feeling you felt,while you was inside the rocket.

why is it like this? Einstein too was puzzled.

Why the acceleration was making us feel like gravity? What could be the possible reason?

Acceleration is gravity!

  • What? How could that ever be possible?
  • Are we gravitating,while we accelerate in our car?
  • Is my ball gravitating while it is falling?
  • Is moon accelerated towards earth?
  • Is earth accelerating towards moon?

I could say it easily,but to convince you,i need to explain about its mathematics,which is quite complex.


The basic needs of general theory of relativity is expertise in Riemann Geometry and Tensor Algebra. Instead of that,let us start with something that we know.


The usual three dimensional world we have studied using the algebra,coordinate geometry and other mathematical usual high school terms,all belong to Euclidean space.

What is this Euclidean Space anyway? 

The space between my finger? any two objects? or the space we always refers to the outer world above stratosphere?

No!

It is a mathematical concept,a region we consider,where our set of ordinary mathematics works efficiently well.

But is there any space other than that? well, there are!


One of the major and central property of Euclidean space is that,the ‘shortest distance’ between any two points is a ‘straight line’ connecting them. Which we usually finds by taking the coordinates and finding their root mean square relationship.

But Einstein wasn’t satisfied with these, He adopted the mathematical space created by Minkowski,which got its name after its creator itself :¬†The Minkowski Space.


In Minkowski Space,there are 4 mutually perpendicular axis. For a point to be located,we need four independent coordinates. The fourth one is time,precisely ict. Well,we no more call the location in Minkowski space a point,but an event. Event is the analogous to a point in Euclidean Space.


However we are not very well equipped to visualize these ideas with our common thoughts,right now. Hope we can,in our future time.


But why i have to mention that here?

Because Einstein adopted this to his relativity theory. Why?


He found that,the Lorrentz transformations,which are the basic principle of Special relativity,can be illustrated as just the axial rotation in Minkowski space.

Which means, 

Rotating an axis in Minkowski space is equivalent to transforming a coordinate using Lorrentz transformation.

So he could easily rotate the axis here,rather than transforming using some unknown weird equation. This thought arised a new thought in him.

It must be the Minkowski space,where the complete relativity lies,where the entire cosmos have been build!

2 COMMENTS

  1. Going past a massive body while inside a container; case of moon revolving earth and earth revolving sum; these are no accelerating frames. These are free falls and Free fall is considered to be an inertial motion. What is equivalent to a container in a space ship that is accelerating through space, is a container that is resting on earths surface or in rest in any gravitational field.

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