Solving Ball's Shadow: Theoretical Analysis

[The Rev]

Suppose you drop a ball alongside an exponential curve. On the other side of the ball is a continuous light source that is always shining perpendicular to the ball's path, such as in view 1.

As the ball drops, the edge of the balls shadow on the curve moves, while the curve is still vertical, at the speed of the ball, but as the shadow's edge moves further and further along the curve, it rapidly speeds up, as in view 2.

When the shadow's edge approaches the part of the curve that is horizontal, it's speed should approach infinity, as in view 3. However, can it?

$$\infty$$

The Rev

 

[JesseM]

Yes, a shadow is not a physical object, nor can the faster-than-light speed of the shadow allow us to transmit any information faster than light, so there's no contradiction with relativity here. Similarly, if you shine a laser beam at the moon and change the angle of the beam, the spot on the moon can travel faster than light (even though no individual photon does so)--see here. Also see the superluminal scissors.

 

[The Rev]

That's pretty cool.

$$C$$

The Rev