Can something move faster than the speed of light?

Question

Imagine you have a bird, flying directly north. The sun is shining directly east (from the west). There is a wall to the east of the bird which runs at 45 degree angle so that as the bird flies forward it's perpendicular distance from the wall increases (e.g. running south-west to north east). So, as the bird flies north, it's shadow moves up the wall, going north at exactly the same speed. But because the wall is at an angle, the shadow is actually moving a greater distance than the bird in a set amount of time. So, the shadow is moving faster than the bird by a certain ratio. Now imagine that (somehow) this bird could travel at the speed of light. The shadow would therefore be travelling faster than the speed of light.

Answer 1

No, and it has to do with the fact that there is a time delay between when the bird is moving north and when the shadow starts moving, and that is dependent on how far the bird is from the wall, which increases as the bird keeps moving north. In your example, you're assuming that the bird and the shadow move at the same time. That's how you can get V(shadow) always = sqrt(2) V(bird), but this equation assumes c = infinite.

So if we now calculate V(s) but set the speed of light to C:

V(b) = x/t, where x is the distance the bird moves northward and t is the amount of time elapsed.

V(s) = sqrt(2)x/(t+t'), where t' is the time it takes light to travel from the bird to the wall. Note that the total time used to calculate V(s) is (t+t'), because we need to wait for the light from the bird to reach the wall.

t' = x/C, since the wall is at a 45 degree angle thus the light will travel the same distance x as the bird.

Hence, V(s) = sqrt(2)x / [(x/V(b)+(x/C)], factor and cancel out x

V(s) = sqrt(2)V(b) / [1+(V(b)/C)]

This is the correct equation for V(shadow) as a function of V(bird), and you can see that in the limit that C => infinity, V(s) = sqrt(2)V(b), but if C is finite and V(b) = C, we do NOT get V(s)=sqrt(2)C, faster than light! Instead, we get something much more sensible:

V(s) = C/sqrt(2), less than the speed of light!!!

Answer 2

No, and it has to do with the fact that there is a time delay between when the bird is moving north and when the shadow starts moving, and that is dependent on how far the bird is from the wall, which increases as the bird keeps moving north. In your example, you're assuming that the bird and the shadow move at the same time. That's how you can get V(shadow) always = sqrt(2) V(bird), but this equation assumes c = infinite.

So if we now calculate V(s) but set the speed of light to C:

V(b) = x/t, where x is the distance the bird moves northward and t is the amount of time elapsed.

V(s) = sqrt(2)x/(t+t'), where t' is the time it takes light to travel from the bird to the wall. Note that the total time used to calculate V(s) is (t+t'), because we need to wait for the light from the bird to reach the wall.

t' = x/C, since the wall is at a 45 degree angle thus the light will travel the same distance x as the bird.

Hence, V(s) = sqrt(2)x / [(x/V(b)+(x/C)], factor and cancel out x

V(s) = sqrt(2)V(b) / [1+(V(b)/C)]

This is the correct equation for V(shadow) as a function of V(bird), and you can see that in the limit that C => infinity, V(s) = sqrt(2)V(b), but if C is finite and V(b) = C, we do NOT get V(s)=sqrt(2)C, faster than light! Instead, we get something much more sensible:

V(s) = C/sqrt(2), less than the speed of light!!!

Answer 3

Your example is a very clever argument, and you're absolutely CORRECT that a shadow CAN move faster than light. Let me simplify things and explain how 'something' (like a shadow) can move faster than light.

Suppose I have a very powerful laser and I shine it at the moon. The moon is only 0.0000771 steradians in the sky and on the order of 3.5e3 km in diameter(I just googled this number), so even sweeping my laser angle fairly slowly will result in the dot on the moon moving faster than light.

No, I'm not a crazy person - this result doesn't contradict relativity. The spot on the moon isn't a "thing" in the sense of cars and electrons and the like. It's nothing more than a location, marked by some photons hitting it. The spot can't carry energy or information, so there is no problem with it moving faster than light. The same would be the case for a shadow.

Answer 4

I share some of your questions. The big bang is an enigma, no? If all the mass in the universe was contained in a singularity, it must have been the ultimate black hole, and it is very difficult to see how or why it could become unstable. The expansion of the early universe, if the same physical laws that we know applied then, must have been slower than the velocity of light. And in the early universe, if all of the matter was contained in such a small volume of space, why did it not act as a black hole and draw everything back into itself? Further, there is some speculation that the rate of expansion of the universe is actually increasing. If that is so, then what is the cause or mechanism for such a phenomenon? Alternatively, the entire universe, as we know it, must be the ultimate black hole, but it doesn't act like one. The maximum acceleration as matter approaches the event horizon of a black hole is the speed of light. If you were standing at the event horizon of a black hole, the light waves would be so bent by the gravity there that you should be able to see the back of your own head one circumference away!

Answer 5

Saying that the bird's shadow at the speed of light would move faster isn't correct, Just the same as a jet moving at the speed of sound doesn't make it's sound speed up.

Answer 6

I've always wondered about that... but there are other examples of things that seem to be able to move faster than the speed of light.

Consider spinning a string (with a weight attached) around your head. Now consider the point half way from your head to the weight and suppose it is traveling at the speed of light. Then, the weight is moving faster than the speed of light, right? probably not!

Answer 7

We can only imagine the scissors effect. Where 2 light vectors approach a point in space, their closing speed would be the same as if you were closing a pair of scissors. The vertex moves faster than the individual scissor arms.

Answer 8

Your proposition is correct. Since a shadow is caused by the absence of light energy, Einstine's formula is correct. And it proves that NOTHING does go faster than the speed of light. LOL!

Answer 9

Sounds like question that won't get you into heaven. If you didn't see joke look around it might still be around.
Last couple of months team of scientist got sound to move faster than light article in Scientific American. They did it sending through stuff that had me wondering, but they may have used your angle pun intended to make their claim.

Answer 10

u cannot imagine.

there has been nothing recorded till now to even reach the speed of light. according to the einstiens theory of special relativity nothing can travel at speed of light.

in this theory also speeds consodered are somewhat like 0.99 or 0.98 or something like this times the value of c.