Science Fiction and the Cosmic Speed Limit

One of the enduring themes of science fiction is the galactic empire:  thousands of star systems tied together by gleaming spaceships hurtling through the cosmos.  And why not?  Civilization on Earth progressed from hunter-gatherers eking out a bare existence to planet-spanning empires over the course of a few thousand years.  Surely our next step will be to colonize the Galaxy.  Unfortunately, a galactic empire of this sort would be doomed, not by alien adversaries, nor by internal dissension, but by the discoveries of a German physicist more than a century ago.  Albert Einstein may have been one of the greatest physicists of all time, but he did more to crush the childhood dreams of aspiring interstellar explorers than anyone who ever lived.  Einstein posted a cosmic speed limit back in 1905, and it’s still in force.

No matter how much energy you pump into a spaceship, no matter how hard you push it, it can never move faster than the speed of light.  Needless to say, this throws a wet blanket on science fictional dreams of space travel.  The stars in the Galaxy are typically about 10 light years apart, while cities in the United States are about 100 miles apart.  So exploring our galaxy in a spaceship moving at nearly the speed of light would be like driving around the country on a tractor plodding forward at the dizzying speed of six feet per hour!  Imagine a band of explorers fanning out over North American on a fleet of these tractors, and you have some idea of the difficulty of exploring and colonizing our galaxy.  Even visiting another city, much less holding a civilization together, would be impossible if we were limited to such a slow speed.

But why is there a cosmic speed limit?  Like many new ideas in physics, it grew out of an apparent contradiction between two different fields -- in this case, classical mechanics, which describes the motion of matter through space, and electromagnetism. 

Let’s begin with a mundane example.  Imagine that you are cruising down the highway in the left lane at 70 miles an hour.  Ahead of you in the right lane is a car moving at 60 miles an hour.  Obviously, you’ll pass this car quickly, but how quickly?  From your point of view, it looks like you are moving at 70-60 = 10 miles an hour relative to the slower car.

So far, so good.  We have an intuitive sense that we can add and subtract speeds like this.  But here’s the problem.  When scientists were codifying the laws that explained electricity and magnetism, a bonus popped out of the equations:  they predicted that we ought to see some sort of radiation travelling at about 186,000 miles a second.  And of course, scientists had already seen this radiation:  it was called light!  But there seemed to be no way to get light to travel at any other speed.  The equations gave the same speed for light, without providing any hint that the speed would be different if you were moving toward or away from the motion of the light.

Most scientists thought that there was some sort of problem with our understanding of the way that light propagates.  After all, the theory that predicted the existence of light was only a few decades old, so maybe there was something missing from it.  But Einstein took a much more radical position.  He suggested that our laws for adding and subtracting speeds, which physicists had taken for granted for hundreds of years, must be wrong.  In fact, he postulated that the speed of light had to be the same no matter how fast you moved toward or away from the light!

This is a truly bizarre idea.  Let’s go back to your car travelling at 70 miles an hour down the highway.  If you threw a baseball out the front of the car at 10 miles an hour, a friend standing on the side of the road would see the ball moving forward at 70+10 = 80 miles an hour.  But now suppose you turned on your headlights.  Would the light travel down the road at 186,000 miles per second + 70 miles an hour?  No!  Your friend standing by the road would measure the light moving at 186,000 miles per second, and so would you.

Similarly, you can never “catch up” with a beam of light.  If you had a spaceship that could move at half the speed of light, and you tried to overtake a ray of light, you would still see it escaping from you at 186,000 miles a second.  Even if you could speed up to 99.999% of the speed of light, you would see the light moving away from you at exactly the same speed.  Light is the proverbial gingerbread man – run as fast as you can, but you’ll never catch it.  You won’t even get close.

In fact, the laws for adding and subtracting speeds have to conspire to keep the speed of the light the same no matter how fast or in what direction an observer is moving.  The only way to make this happen is for space and time to expand or contact as objects move.   Before Einstein, scientists believed that space and time were rigid and unchanging.  Rulers always had a fixed length, and time passed at the same rate everywhere.  But Einstein’s theory predicted that space and time were malleable.  As objects moved closer and closer to the speed of light, they would shrink in their direction of motion, and time would slow down for them.  And all of this would ensure that the speed of light was unchanging.

For instance, if a spaceship whizzed past you at 90% of the speed of light, you would see it shrink to only half its size.  And if you could peek through the spaceship window and watch a clock inside the ship, it would appear to be running only half as fast. (This is called “time dilation”).   You might think that the passengers in the space ship would then see you stretched to twice your length, with your clock running twice as fast, but in fact the opposite is true.  From the point of view of the spaceship passengers, they are at rest, and you are flying by them in the opposite direction at 90% of the speed of light.  So they would see your clocks running slow and your body compressed to half its width.  Isn’t this a contradiction?  Who is correct?

           

You both are.  One of Einstein’s postulates is that the laws of physics are same for any person moving at a constant speed and direction (this is technically called an “inertial reference frame”).  So each of you is entitled to consider yourself at rest, with the other person moving at nearly the speed of light.  And each of you sees the other person’s clock running slow.  (And yes, this is as weird as it sounds).

But now we can set a trap for Dr. Einstein.  What happens when the spaceship lands and you compare clocks with the spaceship passengers?  Whose clock was really running slow?  The problem is that you’ve now violated one of Einstein’s rules.  His prediction only applies if you keep moving at a constant speed and direction.  (Since this is a very special set of circumstances, this theory is called the special theory of relativity, or special relativity for short.).  When the space ship slowed down and returned to Earth, it had to change both its speed and direction -- it had to accelerate.  At that point the equivalence between you and the spaceship is broken, and time really does run slower on the spaceship (and faster for you).

One other prediction of special relativity is that the speed of light is an absolute limit.  And that's where the problem for science fiction comes in.  How has science fiction tried to evade this limit, or to live within its boundaries?  That's what I want to talk about in my next post.