What's the purpose of the speed of light in $E = mc^2$?

Is $E=mc^2$ not just $E=m$. What does the speed of light have to do with this other than to give it a really big number so it looks cool? What spectrum of light is used? How can we test the speed of light with out a stationary point to test it from?

The speed of light is there for much more than to look cool, and in fact there are a number of derivations of mass-energy equivalence that shows why $c$ is present; I will say that one basic reason is that the units of mass and energy are different, so we require at least some sort of constant factor to make the units work. I'll also say that we often use units where $c = 1$, making $E = m$ true; this is, however, separate from the question you're asking.

The spectrum of light is irrelevant, as all light moves at the same speed $c$, as can be shown from Maxwell's equations. Furthermore, $c$ can be calculated from two fundamental constants: the vacuum permittivity constant $\epsilon_0$ and the vacuum permeability constant $\mu_0$. These constants are the the same in every reference frame, and so the speed of light must be the same in every reference frame, as per the postulates of the theory of relativity. Changing reference frames only changes the apparent frequency of light, that is to say, its location in the spectrum. This is what we call red/blueshifting.

• c is never one meter per second, thats simply wrong. We often use units where c =1, dimensionless one, then E=m is true. It basically means that within these units time and length carry the same dimension (1/Energy). – Noldig Apr 16 '14 at 11:37
• @Noldig Ah, sorry, you're right. I'll fix that now, thank you! – EtaZetaTheta Apr 16 '14 at 21:27

The speed of light in a vacuum is invariant: it is the same no matter what point you pick as "stationary". So if I'm on a train, and you're on the ground, and we both measure $c$, we'll get exactly the same number.

The speed of light does not depend on the wavelength. Gamma rays travel at the same speed $c$ as radio waves. The frequency $f$ and wavelength $\lambda$ change according to $c = \lambda f$.

The fact that the speed of light is invariant leads to a long chain of implications - along the way comes $E = mc^2$. The presence of $c$ is not just for making it look cool, but actually a necessary consequence of special relativity.

• So to measure the speed of light we take two fixed points a and b and time how long it takes light to go from a to b. Since the speed of light is fixed if points a and b are moving in the same direction as the light and let's say at 1/10 the speed of light would this not give false measurements and also give us red shift and blue shift depending on which position a and be are in? – Neo1979 Apr 16 '14 at 4:18
• @neo1979 no. That is the crux of "relativity". The speed of light is constant regardless of what inertial frame of reference you are in when you measure it. This leads to time dilation (clocks change), Lorentz contraction, ... – Floris Apr 16 '14 at 4:24
• Red shift will be observed when the source is moving relative to the destination, or vice-versa (which is equivalent). In your scenario, the observer at point b will observe no redshift. It's important to realize that that statement isn't a derivation of any sort (although it can be tested empirically). It's the founding axiom of relativity: in any inertial (0-acceleration) reference frame, the laws of physics (and $c$) are the same. From that stems many interesting consequences, like Lorentz contraction (which you've almost re-discovered). – Scott Lawrence Apr 16 '14 at 4:24
• So I may be lost here but let's say that I am on a ship traveling at near the speed of light and I do a speed of light test on board said ship I would get the same speed of light as if I did the same test on earth and this is due to time dilation. – Neo1979 Apr 16 '14 at 4:39
• @Neo1979 Yes, you've definitely got it, but I would like to nitpick and say that the invariance of the speed of light (that is, the reason the speed of light is always measured as $c$) isn't really caused by time dilation. Time dilation is an effect of the invariance of the speed of light. – EtaZetaTheta Apr 16 '14 at 5:54

One shoul think as c as a kind of space-time conversion constat, massless energy travel at this speed. Light and gravity are kinds of massless energy. The idea of E=mc^2 is that mass converts to energy like this.