Do you know how to derive the General Theory of Relativity?

[FoxCommander]

I am trying to get the coeficient gamma=1/squareroot(1-(v/c)²)

I am trying to do this by my own knowledge starting from scratch.

Can someone give me the first step? I want to see if i can get there but i just need a hint i am not sure on where to start

Thankyou very much,
Fox

 

[Born2bwire]

I think you mean special relativity, I think that would be a much more doable venture than General Relativity. Well, just off the top of my head, I guess you start with the same mental exercises that Einstein did. Some of the basic principles is that light always travels at c in every reference frame and that observers must agree on the same physics in every reference frame. He did a lot of examples in terms of what happens to clocks as a result. You can think of a clock as a ray of light bouncing back and forth between two sets of mirrors that are separated by a predefined distance.

So what happens when the clock is observed by an observer in its rest frame? What happens if there is a second observer that is moving relative to the clock and his motion is along the direction of the light's path? What if his motion is perpendicular to the light's path? In this way you should be able to get an idea on how to derive time dilation.

Einstein published a small book on special and general relativity that works his way through all of these gedanken experiments to derive the basics of relativity. It is an excellent read for any physics student and provides a very feasible framework for someone to derive the basics of special relativity on their own.

 

[jtbell]

I am trying to do this by my own knowledge starting from scratch.

Even Einstein didn't start completely from scratch. He started from some assumptions about how the universe works. What are your assumptions?

 

[Fredrik]

Imagine a rocket going from left to right. (Draw a picture). Imagine a laser attached to the side of the rocket that's "up" in the picture, aimed in the "down" direction, so that it hits the opposite wall. Draw this laser beam as it appears to an observer on the rocket, and to an outside observer relative to whom the rocket is moving with speed v. The former sees the light going straight down, and the latter sees it going diagonally. Draw both of these lines in the same picture, and complete the triangle with a line representing the movement of the rocket as seen by the external observer. This is a right triangle, so the pythagorean theorem applies. Use it, and you'll find gamma.

You have to assume that both observers see the light move at speed c, and you have to make sure not to assume that they agree about how much time it took.

 

[John232]

(ct')^2+(vt)^2=(ct)^2

Simple pythagreon therom given the projectile of light.