# The speed of a shadow?

1. Dec 5, 2009

### EsPhi

My friend was explaining to me once how the only faster then light is shadow. It was very odd. He said that if we have a star being orbited by a planet with a period of one days and surronding this system is a "wall", upon which to cast a shadow, 1 light year away. So, if the planet circles the sun in a year, then so must its shadow. So if the radius of the circle is 1lty, the the circumference is Pi lty! Meaning the shadow is going ~3.1415x faster then the speed of light? This doesn"t seem to make sense to me... In the same way a person running around a light bulb in a circular room will have a shadow going faster the them.

To the same degree a moon orbiting a planet in a circular "room" which has light emitting walls will have a shadow going slower then it, because it will cover less distance in the same time. This seems illogical to me! There must be some kind of contradiction... obviously the time it takes for the light to reach the wall will make the shadow lag behind the planet to an observer infinite metres away, who can somehow see this... but that won't make the shadow any slower... I'm trumped. Anyone have anything to add?

2. Dec 5, 2009

### Thermodave

A shadow is just your perception of an area with fewer photons bouncing off of it. It doesn't have a true speed because it's not a real thing but rather a lack of something. Nothing about a shadow travels faster than the speed of light because there is nothing to move.

3. Dec 5, 2009

### EsPhi

But the nothing is moving faster then light. I mean.. thats not even a good answer haha. We accept gravity, time, energy, and force yet these are very abstract things. How can the lack of light be faster then light itself?

4. Dec 5, 2009

### ideasrule

Why can't it? Your friend's reasoning proves that it's possible.

5. Dec 5, 2009

### Thermodave

My point was that nothing in this situation is moving besides an idea. There is nothing violating relativity. All of the things you named (forces, energy, time, distance...) relate to work or the ability to do work. They aren't all that abstract. A shadow has no mass or energy so if you are saying that it has a speed then that is indeed a very abstract concept.

6. Dec 5, 2009

### kote

A shadow is not a physical thing, but an image in your perception. Stare at the sun for a bit until you start seeing spots (hypothetically - don't actually). Close your eyes. See the spots on the back of your eyelids? Now open your eyes. See the spots back up on the sun again?

You just transported those spots instantly from your eyelids to the sun. Magic. Or were they just in your eyes and brain the whole time?

Or you can just think of reflecting light as something that an object does. A shadow "moving" is a series of discrete (or independent/individual) objects stopping their reflection of light one after another. There is no thing that is actually traveling.

If you and some of your friends do "the wave" like they do in crowds at sports games, "the wave" might "move" at a rate of... I don't know, 10m/s. Now spread yourself and your friends out over a distance of one light year. Do the wave again, over a period of 5 seconds. Your wave just "moved" at 6307200 times the speed of light. Really nothing moved. It was just a few independent things doing something that looks physically connected but really isn't.

Last edited: Dec 5, 2009
7. Dec 5, 2009

### deviant937

Instead of a light source and a body to create a shadow, lets use a laser. If we had a room which was circular, with a radius of 1 light year, we can all agree that it takes 1 year for the light of the laser to reach the edge of the room. Now lets say the laser is rotating at 1 rps. This means that the dot from our laser is moving around the outer wall at a speed of pi * lighyear / second. This appears to be moving faster than the speed of light.

The key is that the dot is not comprised of the same photons. This would be similar to if we made a FedEx Package gun able to shoot packages at .9999999c, and shot out a consistent "beam" of packages. The velocity of the wave of packages would be traveling faster than the speed of light, however each individual package would still only be traveling at .9999999c.

8. Dec 5, 2009

### deviant937

To do the wave 1 of 2 things must happen.

A) Each person acts as a function. When I see the person before me "activate" I should activate. This is limited by the speed of light. If X is the distance between nodes, D is the delay from when a node sees the node before it activate to when it activates and c=3.0*10^8 we can calculate the wave speed as

Wave Speed= X/(D + X/c).
As D -> 0 WaveSpeed -> C

B) Each person is programmed with a time at which to activate. In this case, there is not a wave, but rather a series of independent events, which if timed properly, appear to be related, but are not.

9. Dec 5, 2009

### DaveC426913

OK, deviant has the right idea, I just find it a bit confusing.

Think of a lighthouse sweeping in a circle. The spot of light shines on the Moon then the Sun, then Jupiter, all in a fraction of a second.

The way to resolve the paradox is to think of the beam of light as individual photons, analagous to the stream of bullets from a machine gun. No matter how fast I sweep the gun in circles, the photons/bullets are never travelling faster than the muzzle velocity.

10. Dec 5, 2009

### EsPhi

I guess this helps. Thanks!