E=mc^2, but nothing can travel faster than light?

[Cosmic Philo]

I tried to find an answer to this here, but may have missed it.

There must be a flaw in my understanding here, since it seems to be contradictory. Mass times the speed of light squared = Energy, and yet (according to Einstein), nothing can travel faster than the speed of light?

I'm just curious also if anyone has a link handy, what is the equation that led to the famous e = mc^2 formula or are there a series of equations?

 

[jtbell]

There must be a flaw in my understanding here, since it seems to be contradictory. Mass times the speed of light squared = Energy, and yet (according to Einstein), nothing can travel faster than the speed of light?

Why do you think there is a contradiction?

 

[Cosmic Philo]

Of course the speed of light squared is much faster than the speed of light, and yet nothing can go the speed of light (much less that speed squared). If c^2 is impossible, what is the use of the famous equation?

But I must be misunderstading something (or everything! :-D).

 

[jtbell]

1. c^2 is not a speed. It has units of m^2 / sec^2, whereas speed has units of m/sec.

2. Even if it were a speed, simply because c^2 appears in an equation does not mean that anything is actually traveling at that speed.

 

[Cosmic Philo]

1. c^2 is not a speed. It has units of m^2 / sec^2, whereas speed has units of m/sec.

2. Even if it were a speed, simply because c^2 appears in an equation does not mean that anything is actually traveling at that speed.

That helps, thanks. I've beeen reading various books about physics and trying to grasp the main concepts. So somehow it works out that c^2 works in the formula as a static amount. I was under the impression that moving mass that fast would create energy (i.e., turn the mass into energy).

 

[russ_watters]

You're looking at an intermediate step in a calculation, not the input value. The input value is the speed of light, not the speed of light squared. You can also enter any actual speed into the equation and get the energy equivalent -- but entering 10 m/sec means your object is moving at 10 m/sec not 100 m/sec (or m^2/s^2).

 

[harrylin]

That helps, thanks. I've beeen reading various books about physics and trying to grasp the main concepts. So somehow it works out that c^2 works in the formula as a static amount. [..].

c (or c₀) is an electromagnetic vacuum constant, related to the impedance of free space; it just happens to correspond to the speed of light in vacuum. See for example:

http://en.wikipedia.org/wiki/Electromagnetic_wave_equation
http://en.wikipedia.org/wiki/Impedance_of_free_space

PS. the first (?) paper that precisely led to the mass-energy equation is rather complex, but even reading it diagonally may give you a feeling for how it was done:
http://www.fourmilab.ch/etexts/einstein/E_mc2/