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Degrees of Freedom

Degrees of Freedom

The boundless dimensions of math and physics

Being Mister Fantastic

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starchild Look at yourself in your bathroom mirror. Why, you look younger than your age!

And the farther you are from the mirror, the younger you look. If the mirror were really really far … remember the scene in “2001: A Space Odyssey” in which David Bowman sees himself as a fetus in the womb? Yup.

As you stand in your bathroom and you look down, the skin of your feet looks noticeably younger than that of your hands. Wait--bend forward and touch your feet. Do they still look younger?

Now walk to the kitchen and open the refrigerator. See that head of lettuce? The leaves are long—they reach halfway to the back of the shelf. The edges at the front look brown and wrinkly, but farther back the lettuce still look fresh green. If you stare at the lettuce long enough, you’ll see the wrinkles slowly move toward the back until they cover the entire thing.

It gets weirder. When you wave your arm straight out in front of you, it seems to drag in space, like sea grass bending in the waves. The hand eventually catches up, but with a delay.

http://www.youtube.com/watch?v=Z8cRD74MRsE

Next, you walk across the living room. When you get to the other side, you turn around and you look back. You notice that your feet didn’t move at all. It’s like they were stuck to the floor where you were standing before. Your entire body is stretched diagonally from here to other side of the room, as if you were pulling a trick worth of the Fantastic Four. Soon, your feet start moving, too, and eventually they catch up with you.

None of this is science fiction, Mister Fantastic. We see things because light travels from those things to our eyes. But light moves at a finite speed. The farther the object is, the longer it takes for light to reach you. So everything we see, we see with a delay. It is a very small delay—10 nanoseconds for something that’s ten feet away. For practical purposes, that’s too tiny for us to observe with the naked eye. But it’s just a matter of degrees.

If light happened to be a lot slower—for example if it took one second to cover one meter—the weirdness would become obvious. (An example, which I mentioned in my previous post about how space used to be red, is that if you were immersed in a medium that suddenly transitions from opaque to transparent--for example from ice to water--you would see a spherical wall surrounding you and expanding away from you in all directions, at the speed of light.)

To imagine a world with slow light does not require bending the laws of physics too much. Light already travels at different speeds in different media (water, air, glass), and in all those cases it goes slower in the medium than it does when it propagates through empty space. In certain very controlled situations, in fact, physicists can slow light down to the point that it becomes virtually still.

Empty space is also known as the vacuum. And Einstein's famous rule is this: nothing can travel faster than the speed of light in the vacuum. In principle, though, nothing prevents material things from moving faster in a medium than light moves in the same medium.

In practice, it’s rare for light to slow down so much or for matter to move so fast that matter can overtake light. But in some cases it does happen: this effect it is responsible for the blue glow of the cooling pools where nuclear waste is held. Thus, you could think of a medium that slows light so much that light becomes slower than your own motion.

So here's my tip for virtual reality geeks: develop an immersive system in which you can adjust the speed of light and see what happens to your body and the world around it. The results could be even trippier than "2001."

The Starchild image is a screenshot from a copyrighted film, and the copyright for it is most likely owned by Warner Brothers. The image is reproduced here as a web-resolution screenshot for critical commentary and discussion of the film; its use qualifies as fair use under United States copyright law.

The views expressed are those of the author and are not necessarily those of Scientific American.

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