In Episode Eight, Carl Sagan takes us into the impossibly weird world of Einstein’s relativity. Special relativity is one of the most beautiful ideas I’ve ever encountered. Unlike most deep theories, the math is straightforward, at least at its most basic level. It is something that everyone can grasp, and once you understand it, you’ll never forget it again. Ready?

Special relativity comes from a simple idea. If you jump on an interstellar spaceship and go to use your electric toothbrush, it still works. Why? Because there is no difference in traveling at 99% the speed of light and standing perfectly stock still. No difference at all. The laws of nature are exactly the same.

If I throw a baseball to you in our interstellar spaceship, it obeys the same laws of motion as it would were the spaceship lazily drifting through the solar system at some pedestrian speed well below the speed of light. The same, Einstein realized, must be true for all other physical phenomena.

Electric toothbrushes use electric motors, and electric motors work because of the way moving electrons affect other moving electrons. How do they do that? By sending out light of very long wavelengths. That long wavelength light (that’s what makes your AM radio buzz when you hold your electric toothbrush near – try it!) is still light – even though we can’t see it, we can pick up this invisible light perfectly well on our instruments (like AM radios).

That invisible light coming from your electric toothbrush moves at (you guessed it!) the speed of light; if it didn’t, your electric toothbrush wouldn’t work. If it works here on Earth, Einstein said, then it must also work in your interstellar spacecraft. And if it works in an interstellar spacecraft, then even when traveling at 99% the speed of light, your electric toothbrush makes light that travels at – the speed of light!

Einstein said that for the world to be consistent, for motion and non-motion to really be equivalent, the speed of light has to be the same for you no matter how fast you’re moving. The speed of light is the same for all observers. And electric toothbrushes remain on the list of approved devices for interstellar flights.

But here’s the thing. Moving light can be used for lots of different things, including creating clocks. Suppose we create two clocks – call them light clocks. They use a single piece of light and two mirrors. The light bounces up and down inside the clocks.

If both the clocks remain still relative to each other, then they stay perfectly in sync. When one piece of light bounces off the top mirror, so does the other. But what if we put one of these clocks on the interstellar spacecraft. To you, riding along with the clock, the clock behaves just as it had back on Earth, the light going up and down, up and down. But to someone watching back on Earth, the light in the moving clock takes a diagonal path from mirror to mirror.

But (as every student of Pythagoras knows) that diagonal path has to be longer than the straight line path taken by the clock still back on Earth. Since the piece of light always moves at the same speed, and it’s traveling a longer distance, it must take a longer time to move from mirror to mirror.

But time is exactly what the clock is measuring! So to you back on Earth, the moving clock seems to run slow. In fact, if the spacecraft reaches its destination, circles back, and splashes down on Earth, you’ll find that the astronauts on board have experienced less time passing than you have. Aboard the moving spacecraft, time itself slows down! In essence, those aboard the spacecraft live in a different time than those back on Earth. By moving near the speed of light, they’ve remade their universe.

All this from such a simple observation: the speed of light is always the same. Einstein’s ideas changed our view of reality forever. And the best part is this: *you* can take this same journey, riding along on a light clock, discovering for yourself how an electric toothbrush on a speeding spacecraft remakes your own personal universe.

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February 5, 2009 at 2:01 am

Why Does the Pythagorean Theorem Work? « Turtle Universe[…] something else. If you made it through my light clock blog entry, you know that Special Relativity comes right out of the Pythagorean Theorem. The light […]

February 5, 2009 at 10:02 pm

I. J. KennedyBut wouldn’t the clock on the Earth, by the same Pythagorean argument, appear to be running slow to the space travelers?

February 6, 2009 at 2:33 am

stephenwhittHi I.J.,

Yes, and that’s what physicists really mean when they say the twin paradox. Why, since there are no priveledged frames of reference, has one twin aged more than the other when they come back together? I’ve asked this question myself, and the answer is that it matters who turns around. In the act of turning around and coming back to the Earth, the space travelers return to that particular flow of time, and they find the ones they left behind much older.

February 10, 2009 at 8:09 pm

A.J.Steve-

Check out this article. I think you will find it very interesting.

http://www.newscientist.com/article/mg20126941.900-super-clocks-more-accurate-than-time-itself.html

February 10, 2009 at 9:42 pm

stephenwhittThanks AJ. So the mathematics behind general relativity (as opposed to special relativity) are far more complex than anything I can easily approach. Is that because the effects are so tiny?

Here’s what I mean: Nature does what she does and doesn’t seem to care if the mathematics behind her actions are utterly complex (turbulence, etc) or relatively straightforward (F=ma). Did we sort of intuitively design our mathematics to describe the world, and so that’s the “easy” math, but when we apply this “easy” math to events outside our experience, the math gets complicated? If we lived in a world where general and special relativity effects, quantum effects, etc., were everyday, would our “easy” math reflect that?

Or, does our existence hinge on the fact that the world is well-behaved on the macro and slow scale? Perhaps if the speed of light were much less or Planck’s constant much larger, we couldn’t survive at all?