Q:

E=mc^2 looks like an F=ma equation where a=c^2. Does this mean that if you were to convert a mass to energy, it would be the amount required to accelerate an equal mass to the speed of light? If so, how does this reconcile with the fact that the object cannot actually attain the speed of light? If not, how fast WOULD it accelerate to?

- Scott Harris (age 49)

Kansas City, MO, USA

- Scott Harris (age 49)

Kansas City, MO, USA

A:

Interesting thought, but there's no reason to expect that the *E* in *E* = *mc*^{2} would have some special significance in Newton's second law (*F* = *ma*). Newton and his laws didn't know about relativity or the constant speed of light. *F* = *ma *is an approximation that works at low speeds, and it isn't valid when we start thinking about speeds near *c*. If I do try to use Newtonian physics to predict the velocity of an object with kinetic energy equal to *mc*^{2}, I find that the answer is about 1.41 times the speed of light, which we know isn't correct.

There are relativistic equations that are valid at any speed that can tell us what happens when Newton's laws fail. That's how we should calculate the actual velocity of the object. You can check the calculation yourself using a reference like —write down the expression for kinetic energy, and solve for velocity. Here's a plot of my result, showing how the object's velocity as a fraction of the speed of light depends on its kinetic energy. Notice that to reach the speed of light (*v*/*c* = 1) the object would need to have infinite kinetic energy. When the kinetic energy is equal to *mc*^{2}, the object's velocity will be about 87% of the speed of light.

Rebecca Holmes

*(published on 08/16/2014)*