So, you’re driving a car at half the speed of light. (Both hands on the wheel, please.) You turn on the headlights. How fast would you see this light traveling? What about a person standing by the road? Would they see the light beam moving at 1.5 times the speed of light? But that’s impossible, right? Nothing is faster than light.
Yes, it seems tricky. The problem is, our ideas about the world are based on our experiences, and we don’t have much experience going that fast. I mean, the speed of light is 3 x 108 meters per second, a number we represent with the letter c. That’s 670 million miles per hour, friend, and things start to get weird at extreme speeds.
It turns out that both the driver and the person on the road would measure the light as traveling at the same speed, c. The motion of the light source (the car) and the relative motion of the observers make no difference. Albert Einstein predicted this in 1905, and it’s one of the two main postulates behind his theory of special relativity.
Oh, it doesn’t sound so “special” to you? Well, what he then showed is that if the speed of light is a universal constant, then time is relative. The faster you move through space, the slower you move through time. The clock on a hyper-speed spaceship would literally tick slower, and if you were in that ship, you would age more slowly than your friends back home. That’s called time dilation.
A Commonsense Example
The idea that everyone sees light traveling at the same speed seems like common sense. But let’s look at a more familiar situation, and you’ll see that it’s not how things usually work. Say you’re driving at 10 meters per second, and someone in the car takes a tennis ball and throws it forward with a speed of 20 m/s. A bystander who happens to have a radar gun measures the speed of the ball. What reading do they get ?
Nope, NOT 20 m/s. To them the ball is moving at 30 m/s (i.e., 10 + 20). So much for common sense. The difference arises from the fact that they are measuring from different “reference frames,” one moving, the other stationary.
It’s all good, though; everyone agrees on the outcome. If the ball hits the person, the miscreants and the bystander would calculate the same time of impact. Yes, the people in the car see the ball moving at a slower speed, but they also see the bystander moving toward them (from their perspective), so it works out the same in the end.
This is the other main postulate of special relativity: The physics are the same for all reference frames—or to be specific, for all “inertial,” or non-accelerating, frames. Observers can be moving at different velocities, but those velocities have to be constant.
Anyway, now maybe you can see why it’s actually quite bizarre that the speed of light is the same for all observers, regardless of their motion.
Waves in an Empty Sea
How did Einstein get this crazy idea ? I’m going to show you two reasons. The first is that light is an electromagnetic wave. Physicists had long known that light behaved like a wave. But waves need a medium to “wave” in. Ocean waves require water; sound waves require air. Remove the medium and there is no wave.
But then, what medium was sunlight passing through as it traveled through space? In the 1800s, many physicists believed there must be a medium in space, and they called it the luminiferous aether because that’s fun to say.
In 1887, Albert Michelson and Edward Morley devised a clever experiment to detect this aether. They built a device called an interferometer, which split a beam of light in half and sent the halves along two paths of equal length, bouncing off mirrors, and merging again at a detector, like this:
Obviously they didn’t have a laser, but they had a similar light source. Now, if the Earth was moving through an aether as it circled the sun, that aether would change the speed of light, depending on whether the light was moving in the direction of Earth’s motion or at a right angle to that motion.
And here’s the genius part: They didn’t have to actually measure the speed of light, they only had to see if the two beams arrived at the detector at the same time. If there was any change in speed, the beams would be out of sync and would cancel each other when recombined. That interference would show up as a dark spot on the detector. If they moved at exactly the same speed, the sinusoidal waves would align and you’d see a bright spot.
They ran this experiment at all different times of year to get different angles with respect to the sun, but the result was always the same. There was no change in speed—which meant, sadly, that people had to stop saying “luminiferous aether.” Evidently, light waves could travel through a vacuum!
Maxwell’s Equations and Reference Frames
The reason for this, as proven by Heinrich Hertz, is that light is an electromagnetic wave—an oscillation of electric and magnetic fields perpendicular to each other. The changing electric field creates a magnetic field, and the changing magnetic field creates an electric field, and this endless cycle makes light self-propagating. It can travel through empty space because it's two waves in one.
Now for the rough part (mathematically). We know the relationship between the electric and magnetic fields—it’s described in Maxwell's famous four equations. If you use some math stuff (full details here), it's possible to write the following equations for the electric field (E) and the magnetic field (B). (If all these Greek symbols are Greek to you, just skip over this.)
All you need to know is that, together, these equations describe an electromagnetic wave. But wait! That's not all. If we plug in the values of μ0 and ε0—the fundamental magnetic and electric constants, respectively—you get a wave speed (v for velocity) that is exactly the speed of light:
Einstein used this to postulate that the speed of light was the same for all observers. How? Well, since we accepted that any one inertial reference frame is as valid as another, Maxwell's equations must work in both. That means the speed of light is the same in both reference frames—even if they’re in motion relative to one another. UNLIKE the tennis ball scenario above!
Time Dilation
Finally, imagine we build a clock to measure time. Not one of your grandfather’s clocks with a swinging pendulum, which would be a problem in zero gravity. Our clock is cooler than that. Basically we get two parallel mirrors and bounce a pulse of light back and forth between them.
If we know the distance between the mirrors (s) and the speed of the light (we do, it's c), then we can calculate the time for one tick.
Now assume our clock is in a spaceship with a big window, like in the movies. This spaceship is moving with a constant velocity that is half the speed of light (c/2) with respect to some nearby planet. Someone on that planet uses a telescope to look through the spaceship window and peek at the light clock. Here's what that planet person would see:
Notice that since the spaceship is moving, the light has to travel at an angle in order to hit the other spot on the opposite mirror. If we continued this, it would be a series of zigzags. Take a minute to think about that.
It’s like if you were riding in a bus and tossed a ball straight up and then caught it without moving your hand. In your reference frame, the ball just moves straight up and down. But to that guy on the street, the ball would trace out an arc, moving up and down but also forward.
In our light clock, since the light has to travel at an angle to hit the correct spot, it travels a farther distance. Oh, but that light still travels at the speed of light, so it takes more time to reach the other mirror. And if the spaceship is moving at a speed of c/2, that would be a lot more time. Result? As seen from the person on the planet, the spaceship clock ticks slower. There you have it: time dilation.
Does this mean that time goes slower for the people on the spaceship? Nope. In their reference frame the light just bounces up and down and time is normal.
Yes, it seems very weird, but it's not. It only seems weird because we never travel anywhere near the speed of light. In fact, time slows down in any moving vehicle—even when you get in your car and drive to work—but at normal speeds the effect is so tiny that it’s imperceptible.
