Special Relativity: Why Can’t You Go Faster Than Light?

Monday, November 28th, 2005

I like Daniel Hillis’s explanation of Special Relativity, in Why Can’t You Go Faster Than Light?:

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 is to 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). Another way of 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’s surprise, was that energy and mass are also just two different ways of measuring the same thing.

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