Shadows

October 19, 2004 9:15 AM

A shadow can go faster than light, but apparantly this does not break any physical laws as a shadow cannot communicate information. What happens if I tell someone that I will make a large shadow on the moon, visible from Earth, and that if the shadow does not move, then they should phone me. However, if it does move (at a speed faster than light), they shouldn't phone me. Hasn't information been transmitted?
posted by Orange Goblin to Science & Nature (12 answers total)

Blatently stolen from another website:

Recent experimental evidence shows that it is possible for the group velocity of light to exceed c. One experiment made the group velocity of laser beams travel for extremely short distances through caesium atoms at 300 times . However, it is not possible to use this technique to transfer information faster than ; the product of the group velocity and the velocity of information transfer is equal to the square of the normal speed of light in the material.

Exceeding the group velocity of light in this manner is comparable to exceeding the speed of sound by arranging people in a distantly spaced line of people, and asking them all to shout "I'm here!", one after another with short intervals, each one timing it by looking at their own wristwatch so they don't have to wait until they hear the last person shouting.

See also: superluminal shadows. Basically, yes you can transmit information, but you're still stuck using slower-than-light techniques.
posted by Civil_Disobedient at 9:38 AM on October 19, 2004

How would they be able to see the movement of the shadow faster than light?
posted by kenko at 9:42 AM on October 19, 2004

The shadow can move along the moon's surface at a speed faster than light. The image of the shadow on the moon can not move toward the earth at faster than the speed of light.

Both you (making the shadow) and the person on the earth (observing) will see the shadow move along the moon's surface at faster than light, but the observer on the earth will observe the shadow after you.
posted by mfbridges at 9:43 AM on October 19, 2004

From an information-theoretic point of view, you have not encoded any information on the shadow itself; you have encoded information on its state. And you determine the shadow's state by using light. So, really, nothing is moving faster than light in your scenario.
posted by stratis at 10:03 AM on October 19, 2004

They're sitting on the moon, looking at the shadow of your finger in your very bright flashlight. You move your finger. The light that your finger was blocking moves towards the moon at the speed of, well, light. When that light arrives at the moon, they then see the shadow start to move. The information was transmitted at the speed of light.
posted by ook at 10:08 AM on October 19, 2004

(The error here is in thinking of the shadow as a thing that is moving. Really all that moves is the imaginary point on which the shadow is being cast -- which isn't a thing at all.

Think of the example of the laser beam flicking from one site of the moon to the other: the light is moving at the speed of light towards point X. You turn the laser to aim at point Y: the first photon that's emitted from the laser now travels to point Y at the speed of light. All the photons that were emitted while you moved the laser also each travel at the speed of light towards various points between X and Y. The dot of light that moves from point X to point Y will appear to move faster than light could travel from point X to point Y -- but that's because that dot isn't a thing that's moving, it's just a series of different photons impacting at different points.

The fact that we perceive that dot as a moving thing can lead to the misconception that information is being transmitted from point X to point Y faster than light. What's really happening is that information is being transmitted from point Z -- you with the laser -- to both points X and Y at exactly the speed of light. (The signals in this case being: light stops being transmitted to point X, and light starts being transmitted to point Y. There's no direct communication from point X to point Y.)

The shadow example is exactly the same, just inverted.

Relativity isn't even involved in this "paradox" -- you can do the same thing with water squirted from a garden hose and it'll still work out exactly the same at a slower scale: the 'wet spot' where the water lands as you move the hose moves faster than the speed of the water, but any individual bit of water doesn't change speed.)
posted by ook at 10:27 AM on October 19, 2004

a shadow can communicate information, as your example shows. what it can't do is communicate information faster than the speed of light - your example doesn't show that.

if i am in tucson and want to communicate with you in new your (say), i can flash a shadow on the moon, and make it move very fast. but the time between me turning on my huge shadow-making spotlight and you knowing that something has happened is still controlled by the speed of light - the light from my laser goes to the moon (in places), "creating" the shadow, and then back to your eye, where you "see" the shadow.

so whether the shado moves faster than light, or flashes on and off, or whatever, doesn't alter how fast the message gets from me to you.

does that make sense?
posted by andrew cooke at 10:34 AM on October 19, 2004

Actually, b1tr0t, I dont think thats whats being discussed here. A better analogy is this:

If I send a signal down a wire and then split it into ten different signals and send each of those signals to, say, ten different TV screens, then I will have an image that is being broadcast simultaneously. Kind of like when you see lots of television sets at a store all tuned to the same channel.

Now, I add latency to each of the 10 outgoing wires at staggered intervals. If I do this, I can make the image seem to "move" across TV screens. I can make the image move across at *any* speed I want, even faster than the speed of light, even infinitely fast (i.e. simultaneously, which is how they were set up to begin with)

Of course, nothing is actually moving faster than the speed of light.
posted by vacapinta at 12:44 PM on October 19, 2004

O--A-----X
 \       |
  \      |
   B     |
    \    |
     \   |
      \  |
       \ |
        \|
         Y

Light source at O, shining on surface XY. If you place your hand at A, a shadow appears at point X sometime after that. The time between inserting your hand at A and its shadow appearing at X is limited by the speed of light. The shadow moves from A to X at the speed of light.

Here's the tricky bit. Now, move your hand quickly from A to B. The shadow moves from X to Y. The shadow's "motion" from X to Y may appear to be faster than the speed of light. However, the time at which the shadow starts moving from X to Y is not instantaneous with the time you start moving your hand from A to B. There's a delay between when you start moving your hand, and when the shadow starts to move. That delay is limited by the speed of light and the distance between A and X. Similarly, the arrival of the shadow at Y is delayed, limited by the speed of light, from the time your hand arrives at B.

The shadow's apparent motion from X to Y is not limited by the speed of light. The shadow's motion from A to X, as well as from B to Y, is limited by the speed of light. There is no supraluminal transmission of information here, as what you are doing is not transmitting information from X to Y, but transmitting information from A to X, and from B to Y. Someone at X has no way of taking advantage of the apparent supraluminal motion of the shadow to transmit information to Y.

What happens if I tell someone that I will make a large shadow on the moon, visible from Earth, and that if the shadow does not move, then they should phone me. However, if it does move (at a speed faster than light), they shouldn't phone me. Hasn't information been transmitted?

Information has been transmitted, just not faster than light. Although the motion of the shadow across the moon's surface is not limited by the speed of light, the delay between the time the object casting the shadow starts moving and the time the shadow itself starts moving is limited by the speed of light.
posted by DevilsAdvocate at 1:16 PM on October 19, 2004

You guys just blew my mind.
posted by LimePi at 2:51 PM on October 19, 2004

There's a fun book by a guy named nick herbert called "superluminal loopholes", that looks at these kinds of thought experiments.
posted by mdn at 8:51 PM on October 19, 2004

You could do the same thing with bullets.

Mount hypothetical super-fast machine gun on a swivel. The gun will spray thousands of bullets during the 1/100th of a second sweep that covers the moon from edge to edge.

On arrival at the moon, the first and last bullet will be separated by 3500km, but will arrive only fraction of a second apart. The hail of bullets will sweep across the moon at mindbreaking speed (350 000km/sec = 1 260 000 000 kmh) but it'd be lunacy to suggest the bullets themselves are moving that fast.

Replace bullets by shadow and you get the same situation.
posted by five fresh fish at 9:11 AM on October 20, 2004