In Einstein's theroy of relativity how did he justify using the speed of light squared?

Answer 1

Einstein's insight was that mass holds an enormous amount of energy and that this mass can be, and is, emitting its energy slowly but surely. It explained how uranium could emit energy for thousands of years without losing mass. It also explained how the Sun could burn for billions of years.

For his famous equation, he needed a real huge number that is true everywhere, in all directions, in whatever physical condition. Only one was and is known to science : the speed of light.

As the speed of light is a natural constant and in itself a huge number, his insight was that the square of this number could be the missing link in the analogy between mass and energy.

Hetero, the formula became e = m * c^2

Answer 2

It was derived from basic principles of photon energy E = hf and momentum p = E/c. The math is quite solid. The physics, though, is being challenged by other theories (quantum physics and strings).

Unfortunately the derivations, there are several, do not copy and paste very well. I suggest you do what I did, search the web for "derivation of e = mc^2," you will find hundreds of hits and a number of them use elementary calculus (rather than tensors and such) to derive e = mc^2.

Answer 3

The simplest way I know of to get it intuitively is to think of Kinetic energy which is 1/2mv^2. Then at the speed of light you would get 1/2mc^2 - Of course you may then ask why does kinetic energy have the v^2 term in it? That derivation is a bit easier to follow than the relativity math.

Anyway, an easier link than given above is:

Answer 4

It is actually required by the equations that describe motion when the additional constraint that the speed of light (c) be constant in every inertial frame of reference. The actual derivation is easy to follow (if your algebra skills are up to snuff), and this site will walk you through it:

http://www.comcity.com/distance-time/3B.%20Distance-time%20theory%20part%20II.html

HTH

Charles

Answer 5

Since he didn't pick c² arbitrarily, he didn't have to justify it. It appeared as a direct consequence of E = hf and p = E/c as noted by eyeonthescreen.....