Why Does E=mc2?
139
a phenomenon that traveled at the special universal speed limit—electromagnetic waves. This played a key role in Einstein’s thinking, and perhaps without this coincidence, Einstein would not have discovered relativity. We shall never know. “Coincidence” may be the right word because, as we shall see in Chapter , there is no fundamental reason in particle physics that guarantees that the photon should be massless. Moreover, there is a mechanism known as the Higgs mechanism that could, in a different universe, perhaps, have given it a nonzero mass. The c in E = mc 2 should therefore be seen more correctly as the speed of massless particles, which are absolutely forced to fly around the universe at this speed. From the spacetime perspective, c was introduced so we could define how to compute distances in the time direction. As such, it is ingrained into the very fabric of spacetime. It may not have escaped your attention that the energy associated with a certain mass carries with it a factor of the speed of light squared. Since the speed of light is so great compared to everyday, run-of-the-mill speeds (the v in 21 mv 2) it ought to come as no surprise that the energy locked away inside even quite small masses is mind-bogglingly large. We are not yet claiming to have proven that this energy can be accessed directly. But if we could get at it, then how huge an energy supply could we be, quite literally, sitting on? We can even put a number on it because we have the relevant formulas on hand. We know that the kinetic energy of a particle of mass m moving with a speed v is approximately equal to 21 mv 2 and the energy stored up inside the mass is equal to mc 2 (we shall assume that v is small compared to c ; otherwise, we would need to use the more