Why can't things go faster than the speed of light? And how do we know that the speed of light is the universal speed limit?

You probably know Albert Einstein's most famous equation \( E = m c^2 \). It tells us how much energy we would get if we could turn a certain amount of matter into energy, as we do in nuclear reactors.

That equation tells us how much energy is in mass at rest. It takes energy to get that mass moving, and we can get that energy back when we put on the brakes. To account for this energy of motion, there is an extra factor added to Einstein's equation. This factor is called gamma, and is represented in the formula by the Greek letter \( \gamma \) (gamma):

$$ E = \gamma m c^2 $$

Gamma itself, of course, is a function of velocity. Specifically, it is this function:

$$ \gamma = { 1 \over { \sqrt { 1 - { v^2 \over c^2 } } } } $$

When dealing with very high speeds like the speed of light, the arithmetic gets tedious if we choose a speed like miles per second, or meters per second. But if we choose to measure speed in light years per year, the arithmetic just goes away, because the speed of light \( c \) becomes 1.

Einstein's equation becomes:

$$ E = \gamma m $$

All speeds are now expressed as a percentage of the speed of light.

At speeds we normally encounter, gamma is extremely close to 1. But as velocity approaches 1, think about what happens to gamma. It gets bigger.

Gamma determines what we call relativistic effects. One such effect is the Fitzgerald Contraction, which says that if we see something passing by at high speed, the length of that object appears to be shorter than if it were at rest. Likewise, the mass of the object appears to be larger than when it was at rest. And time passes more slowly to passengers in a fast moving spaceship than it does for the people left back at home. They all change by a factor of gamma.

A graph makes this easy to see:

The more massive an object is, the harder it is to get it moving. It takes more energy to get a car going 60 miles per hour than it takes to get a baseball going 60 miles per hour.

Notice that the faster our spaceship goes, the more gamma increases its mass. As gamma approaches infinity, so does the mass we are trying to accelerate. It takes an infinite amount of energy to accelerate an infinite mass.

That's why nothing that has mass can be made to go as fast as light.

It is a limit. Limits are not just mathematical ideas. They are real things.