# Why the speed of light in the equation?

1. Jan 17, 2012

### jack616

Curious

Why does the equivalence of mass/energy involve the speed of light at all?
Is it because Einstein discovered that this was simply the correct multiplier
or was there some other reason to connect the speed of light to the relationship?

2. Jan 17, 2012

### elfmotat

To answer your question in a satisfying way I'd basically have to start from scratch and derive Special Relativity for you. Basically, the speed of light appears in nearly every equation in SR and the energy equation is no exception. Why it's there is a difficult thing to explain in words. All you really need to know is that it acts as a conversion factor between mass and energy.

3. Jan 17, 2012

### DaveC426913

You're looking at it backwards.

c is the fundamental speed limit of the universe.

The speed of light, being limited by nothing else, travels at the fastest possible speed of universe - which is c.

4. Jan 17, 2012

### jack616

Thanks - but
I ask the question because thats the question I'd like an answer to.
So perhaps someone else can explain the relationship ?
I realise it's tricky to explain some concepts.
And I'm not questioning that it IS the case.
I'm trying to understand why there is even a relationship there.
I've never heard it asked before but its puzzling me.

5. Jan 17, 2012

### jack616

sorry people I got mixed up replying to incoming answers - I'm not meaning to be combative here -

6. Jan 17, 2012

### jack616

Dave ok I can accept c is the universises speed limit
what I dont understand is why a speed limit is any part of
why mass=energy or vice versa.

If a mass is converted into energy why does the speed of light
have anything to do with calculating how much energy there is?

7. Jan 17, 2012

### elfmotat

Ok, let's try this: relativistic momentum is proportional to the Lorentz factor, and the Lorentz factor involves c. When you calculate the work done in bringing a particle from rest to some velocity (the kinetic energy) you integrate over the momentum. When you solve that integral it is easy to see that energy is proportional to c2.

8. Jan 17, 2012

### clem

It is just a matter of units. Minkowski showed that space and time are equivalent coordinates in relativistic 4D space-time. Historically, space and time had been given different units (meters and seconds). If they are expressed in the same units, then c does not appear in the equations of SR. That is the way in which most working relativists write their equation, without c appearing.

9. Jan 17, 2012

### DaveC426913

Yeah, clem's right. It's a unit conversion thing.

Don't quote me on this but, if you use a light-second as the distance, the formula ends up being simply e=m.

10. Jan 17, 2012

### maverick_starstrider

If you like, the original derivation was based on a thought experiment involving light reflecting off a mirror. However, everything about SR is far more general then the original thought experiment and has been pointed out it's a unit thing, if you take the unit of time to be a meter say (i.e. your unit of time is the time it takes light to go a meter) then E simply equals m.

11. Jan 17, 2012

### SHISHKABOB

the thought experiment about the light clock is what really makes you go "oh, the speed of light really IS important"

at least it did for me

12. Jan 17, 2012

### BF004

It stems from a derivation using Maxwell's equations. Long story short, you end up with:

c = 1/√[μ*ε]

Where μ and ε are the permeability and permittivity of free space, both of which are contants, thus c is constant as well. That is where c comes into play from a mathematical standpoin.

13. Jan 17, 2012

### maverick_starstrider

Um.. that comes from the derivation that an electromagnetic wave IS light. I don't know what that has to do with SR (well not directly)

14. Jan 19, 2012

### Necrostate

Conservation and mass, and conservation of energy, always appear separately in isolated systems. What Einstein did, was bringing the two laws of conservation together, and moreover, maybe re-define Mass and Energy, as two different names for the same thing (that's not quite accurate, but thinking of it this way is a good tool in order to understand harder equations/problems). Why c2 ? Well this is the constant of proportionality, you can derive the equation or look for the derivation, and see where did the c come from. Anyways, in natural units,and for convenience, c is replaced by a 1, which leaves us with a E=m, where E represents energy, and m represents mass (and not matter).