# Why light or C?

1. Nov 11, 2015

### halpmaine

Hello All.

Please forgive me if the answer to the following is found in PF but I didn't find it doing a search...

My question is this: what prompted Einstein to even consider light or better C as integral to E or, well, 'everything'? Was it mathematical such that he had the E and m but not the unknown variable (i.e. x = ?); was C the result of solving for x, if you will?

Thanks!

-Halp

2. Nov 11, 2015

### robphy

Einstein was motivated by electromagnetism (Maxwell's Equations).

3. Nov 11, 2015

### Staff: Mentor

My understanding is that the mass-energy equivalence was an implication that fell out of the math. But the motivation for the theory started with implications of a constant speed of light from Maxwell's equations and it's logical contradiction with the Galilean Principle of Relativity.

4. Nov 11, 2015

### PWiz

It all followed from the postulates of relativity. The Lorentz transformation can be derived from the postulates (and then we can get the velocity addition formula), and you can derive the relativistic expression for momentum from this. Once you have this expression, getting an expression for kinetic energy becomes a simple calculus exercise:
$$K.E.=\int F ds = \int v d(\gamma m_0 v)$$
Just use integration by parts and substitute the appropriate limits and you get $K.E.=(\gamma -1) m_0 c^2$. Some rearrangement shows that even if the kinetic energy of the object was decreased to 0, it would still possess some rest energy $E=m_0 c^2$, and this is what is required. ALL of relativity follows from the two postulates.

5. Nov 11, 2015

### Smattering

But historically that is not what happened. Several physicists were trying to find an invariant transformation for Maxwell's equations. And what they found was the Lorentz transformation. The postulates of relativity were added by Einstein a posteriori.

Here is a blog post on how Einstein derived $E = mc^2$:

https://terrytao.wordpress.com/2007/12/28/einsteins-derivation-of-emc2/

Not sure if that really accurate, but at least it sounds plausible.

6. Nov 11, 2015

### PWiz

I know, but the historical way is not always the most convenient/logical way to understand things. Also note that I originally said "can be derived" instead of "was derived".

7. Nov 13, 2015

### Mister T

The speed of light was an integral part of the formulation of his theory from the very beginning. It's the speed of propagation of electric and magnetic fields. It was his consideration of the relationship between electric and magnetic fields that led him to formulate his theory. The relationship between energy and mass was a part of that theory that followed from those considerations.