Nothing travels faster than the speed of light, with the possible exception of bad news, which obeys its own special laws.
~Douglass Adams, Mostly Harmless

This is part 1 of a many-part series on faster-than-light travel. Before we can discuss how to travel faster than light, we need to understand why this is a problem in the first place. Why is the speed of light the universal speed limit? The answer starts with the invariance of the speed of light.

By this point, everyone knows that the speed of light is constant, but it is not at all obvious why this should be, or even what it means. Indeed, until the late 1800s, no one even considered the idea–people thought that light behaved like everything else.

The State of the Art at the Turn of the Century

In the old view of light, if the speed of light is meters per second, and I drive my car, headlights blazing, past you at 13 meters per second, then the light from my headlights should be travelling past you at meters per second. This is called Galilean relativity, and we now know it to be false.

When Galilean relativity was popular, we knew that light could be treated as a wave, and we knew a lot about waves. At the time, though, it was falsely believed that a wave needs a medium through which to travel. The archetypical example of a wave is the vibrating string. Ocean waves travel through water. Sound waves travel through… well, everything. There must be a medium through which light waves travel, or so we thought. This medium was called the luminiferous aether. People believed that the planets and stars were suspended in a sea of aether, and it was even thought that the aether might flow around the planets.

Measuring the Aether

If light travels through the aether, then it should be possible to measure the speed of the Earth with respect to the aether sea. In a series of experiments between 1881 and 1904, physicists tried to do just that. The most famous experiment was performed by Albert Abraham Michelson and Edward Morley. Michelson and Morley carefully bounced light from the same source down two perpendicular paths and back to an eyepiece. If the aether were not flowing with respect to the motion of the earth, then the light waves would return at the same time. If, on the other hand, the earth is moving with respect to the aether, light traveling down the arm parallel to the flow of the the aether will take longer to return to the eyepiece.

Of course, because light travels so quickly, it is impossible to measure the difference in travel time by hand. Fortunately, light can do the measurement for us through a phenomenon called interference. Imagine waves as wiggles on a very stretchy string. If I try and push up on the string (make a wiggle that goes up) and you try and push down on the string (make a wiggle that goes down) at the same time, neither of us ends up moving the string as much as we intended. This is called destructive interference. Similarly, if I push up on the string and you push up on the string, we’ll probably stretch it quite a lot. This is called constructive interference.

Michelson and Morley used this phenomenon to see how far away the returning light waves were from each other. If the waves are only partially offset from each other, the waves produce an interference pattern like the one below.

To account for the fact that the earth spins around the sun, and that their lab spins around the center of the earth, Michelson and Morley performed their experiment several times a day every day over the course of a year. The results showed absolutely no change. The light from each arm of the experimental apparatus always overlapped with the light from the other arm.

Fallout

We can draw one of three conclusions from Michelson and Morley’s results:

1. Michelson and Morley made a mistake. There should have been some change in time of flight for light in the two arms of the apparatus.
2. The aether is never moving with respect to the earth. Perhaps the earth drags the aether with it, forming eddies in the aether sea so that the Earth and the immediately surrounding aether always travel at the same speed.
3. There is no aether. The speed of light is constant for some other reason.

Michelson and Morley themselves thought they’d failed. The scientific community worked furiously to corroborate or overturn the results, but every subsequent experiment agreed with Michelson and Morley’s “failed” outcome. Some people tried to argue for the “aether dragging hypothesis,” however the theory was plagued with problems. Fortunately, James Clerk Maxwell had already unwittingly offered support for option 3: there is no aether.

 Maxwell’s Insight

The first indication that the aether view of light might be wrong actually came more than twenty years earlier, in 1864. It came from James Clerk Maxwell, a Scottish physicist and mathematician. Maxwell built on the triumphs of Carl Freidrich Gauss (the man had his fingers in everything), Andre-Marie Ampere, and Michael Faraday to produce a single, unified model of electromagnetism, described elegantly in four simple equations.

By Maxwell’s time, it was known that electricity and magnetism could be described by the interaction of electric and magnetic fields. An electric field is just an arrow at each point in space that tells me where a charged particle (say an electron) would move if I placed it in the area where the field was. Similarly, a magnetic field describes where a magnet would go. (Magnets are bit more complicated because there’s no such thing as “magnetic charge,” but the principle is the same.)

In simple terms, Maxwell’s equations say the following:

• Gauss’ Law: The total strength of a divergent electric field that passes through a closed surface is proportional to the sum of the total charge enclosed by that surface. This proportionality constant is a function of the material the field is contained in and it is the permitivity of the medium, denoted . In vacuum, this is the permitivity of free space, denoted . Electric charge always produces a divergent field.
• There are no magnetic monopoles: It is impossible to produce a divergent magnetic field, and there is no “magnetic charge.”
• Ampere’s Law: The strength of a magnetic field loop is proportional to the sum of the change in an electric field passing through the loop and the electric current passing through the loop. The proportionality constant is a function of the material the field is contained in, and it is the permeability of the medium, denoted . In vacuum, this is the permeability of free space, denoted . It is impossible to produce a magnetic field that does not form a loop.
• Faraday’s Law: The strength of an electric field loop is proportional to the rate of change of a magnetic field passing through the loop.

It’s possible to define a wave as any phenomenon governed by a special type of equation, called the wave equation. Maxwell discovered that, if he combined the four laws of electrodynamics that he’d unified, he could make a wave equation, and that this equation described light. In Maxwell’s beautiful theory, a changing electric field induces a changing magnetic field (by Ampere’s law), which in turn reproduces the electric field (by Faraday’s law).

Because the changing electric and magnetic fields induce each other, Maxwell’s electromagnetic radiation doesn’t need a medium to propagate in. Because the strength of the magnetic field is proportional to the rate of change of the electric field, it shouldn’t be terribly surprising that the the speed of light in a medium turns out to be a function of the proportionality constants, the permitivity and permeability of free space:

   

where is the speed of light in a medium. This means that the speed of light in a vacuum is a function of physical constants only–it doesn’t depend on the speed of the observer at all:

   

where and are the permeability and permitivity of free space respectively.

But this is staggering! That means that if you shine a flashlight down the road, and I speed past you, headlights blazing, the photons from your flashlight and my headlights are going the same speed, despite the speed my photons should be getting from my car. (I’m ignoring that the speed of light in air is slower than the speed of light in a vacuum. The results turn out to be the same.) It is this result that explains Michelson and Morley’s “failed” experiment, and it is this result that leads Einstein to formulate special relativity, setting light as the speed limit of the universe. I’ll talk about that more next time.

Hidden Assumptions

There’s a hidden assumption in my argument. I’m assuming that the laws of physics are invariant no matter how fast you go. This idea seems obvious, but it’s not. The idea was first posited by the interestingly named uniformitarians. Uniformitarianism was one side of a debate in geology in the late 1700s and early 1800s, the other side being Catastrophism. Uniformitarians argued that the modern Earth formed slowly as the result of many long-term natural processes. Catastrophists argued that the modern Earth was formed in a few cataclysmic events. Creationists favored catastrophism, because it could easily be tied to biblical history.

In modern times, we know that the earth was shaped by both long-term forces and short-term cataclysms. However, one of the founding ideas of uniformitarianism became one of the founding ideas of science. The uniformity of natural law (source):

The laws of nature are constant across space and time.

It doesn’t sound like a big idea, but it is. We couldn’t do science without it. If natural law changed, then, as David Hume pointed out, empiricism is pointless. All laws we believe in today may not be true tomorrow, and no model has truly predictive power. The sun may simply fail to rise tomorrow. No explanation needed. It is for this reason that Einstein’s theory of relativity is sometimes called a theory of invariance–It is founded on the belief that the laws of nature are not relative.

Further Reading

There are many wonderful places to learn about this particular era in the history of science, and especially on special relativity. Here are some of my favorites.

• Walter Isaacson’s biography on Albert Einstein contains a surprisingly accessible and accurate picture of special relativity. Einstein’s life also makes a very good story.
• Modern Physics for Scientists and Engineers, by Taylor, Zapharatus, and Dubson offers a fairly accessible description of special relativity.
• Conrad Ranzan gives a nice, if extremely terse, history of the luminiferous aether on his site.
• Andrew D. Iraci’s site gives a nice history of the ideas of “aether” in physics and scientific thought. It has many nice diagrams too.

Questions? Comments? Hatemail?

Next week (Probably Saturday. I apologize for getting this article out two days late, and I’ll work to figure out a more consistent schedule.) I’ll discuss how Albert Einstein took the invariance of the speed of light seriously, how this resulted in special relativity, and how special relativity enforces a speed limit for the universe. In the meantime, I’d love to know what you all think? Is there anything you’d like to know more about? Is there anything you do know more about you’d like to share? Is there anything I got wrong? Let us all know in the comments.