Special Relativity: Why Can't You Go Faster Than Light

An Essay by W. Daniel Hillis



You've probably heard that nothing can go faster than the speed of light, but have you ever wondered how this rule gets enforced? What happens when you're cruising along in your spaceship and you go faster and faster and faster until you hit the light barrier? Do the dilithium crystals that power your engine suddenly melt down? Do you vanish from the known universe? Do you go backward in time? The correct answer is none of the above. Don't feel bad if you don't know it; no one in the world knew it until Albert Einstein worked it out. The easiest way to understand Einstein's explanation understand the simple equation that you have probably seen before: e = mc2. In order to understand this equation, let's consider a similar equation, one for converting between square inches and square feet. If i is the number of square inches and f is the number of square feet, then we can write the equation: I =144 f . The 144 comes from squaring the number of inches per foot (122 = 144). writing the same equation would be i = c2f, where c in this case is equal to 12 inches per foot. Depending on what units we use, this equation can be used to convert any measure of area to any other measure of area; just the constant c will be different. For example, the same equation can be used for converting square yards to square meters, where c is 0.9144, the number of yards per meter. The c2 is just the conversion constant. The reason why these area equations work is that square feet and square inches are different ways of measuring the same thing, namely area. What Einstein realized, to everyone one's surprise, was that energy and mass are also just two different ways of measuring the same thing. It turns out that just a little bit of mass is equal to a whole lot of energy, so in the equation, the conversion constant is very large. For example, if we measure mass in kilograms and energy in joules, the equation can be written like this: e = 90,000,000,000,000,000 m. This means, for example, that a charged-up battery (which contains about one million joules of energy) weighs about 0.0000000001 grams more than a battery that has been discharged. If we work with different units, the conversion constant will be different. For instance, if we measure mass in tons, and energy in BTUs, then c will be 93,856,000,000,000,000. (It happens to work out that the conversion constant in a particular set of units is always the speed of light in those units, but that is another story.) If we measure both energy and mass in what physicists call "the natural units" (in which c = 1), we would write the equation: e = m, which makes it easier to understand; it just means that energy and mass are the same thing.