(If this doesn’t belong in GQ move it accordingly. Thanks).
I am researching for an article I intend to write, and I got lost in the thickets of hypothetical concepts.
I have been reading about the speed of dark, or the fact that things like a cast shadow (or a laser pointer’s point) can move across the face of a distant enough object at speeds greater than the speed of light, since it’s not a particle or information moving. It’s my understanding a shadow has limitless speeds.
The example showed a spotlight being shot from the earth onto the face of the moon, and a guy waving his finger around in front of it, causing the shadow on the face of the moon to move at speeds faster than light.
My questions are:
Theoretically, if one had such a set up, they could cast instant “night” up the far-object, which could be used as a form of information? A code system of blinks of darkness could relay messages (or information) at ultralightspeeds. Like black-out morse code. Is my concept flawed? Since the movement of a laser’s point works in the same infinite speed way, it seems to me a kind of coded information could easily be sent unfathomably quickly.
Can an object theoretically have a shadow cast on it from so far away that the observer initiating the shadow would view the shadow’s movement on a delay?
or is the movement of a visible shadow, no matter how theoretically far away, always visibly move instantaneously?
1: The moving finger is on Earth, and that’s the source of the information. The information moves from the finger to the Moon at merely the speed of light. The shadow can move across the Moon arbitrarily quickly, but that doesn’t matter, because the finger isn’t on the Moon.
2: The shadow moves very quickly, but that doesn’t mean you see it instantly. If you sweep your finger across the spotlight on Earth, you won’t see the shadow moving across the Moon until a couple of seconds later. In fact, the initiator of the shadow will always see the shadow moving on a delay-- It’s just that, for typical human distances, the delay is too short to be noticeable.
Another way to think of it is that the point of light is moving from spot A to spot B on the Moon faster than light could move from that point. But nothing at point A affects the point of light seen at point B in any fashion, so no information can be conveyed to point B from point A by this method (at any speed).
Information could be conveyed from the Earth to point A and point B by the light, but that information is traveling with the light at the speed of light. So from Earth you can get the same message to point B faster than you could send it to point A and have them send it to point B. But that’s no violation of relativity because the distance from Earth to point B is less than the distance from Earth to point A then point B.
A simple way to answer these questions yourself is simply to work out a way to put it into practice.
For example, you want to use a shadow Morse Code. But how exactly would that work? If I wanted to let someone on the moon know that a battle had been lost on Earth, how would I transmit that information using shadow Morse Code? If someone on one side of the moon wanted to let someone on the other side that a battle had been lost, how would they transmit that information using shadow Morse Code?
When you stop to think about this, you will see that there isn’t any way to transmit information using shadows.
If someone wants to transmit a message to the moon using shadows, it will arrive at exactly the same time as the same message being carried by light since both are being carried by the same medium: visible light. The shadow is just an absence of information. While that absence can *be *information, it can only be propagated at the same speed as the light that it is carried on.
If someone wants to transmit information from one side of the moon to the other, they can’t. The shadow is being cast from Earth. To transmit the information using the shadow, they would need to first transmit the information to Earth, then the person on Earth could create the shadow, which would travel back to the moon at the speed of light regardless of how fast the shadow travels once it starts moving.
Because the speed of the shadow is relative to the angle and distance between the light source and the object it strikes, it’s always going to be faster to transmit the information directly than to transmit it back to earth to be relayed back. In simple terms, you signal has to first traverse the two long sides of a triangle (moon-earth and earth-moon) before it can make a fast shadow that will move at FTL speeds across the third short side (the face of the moon).
It can never be faster to traverse the two long sides of a triangle than to move directly across the short side. Ergo your information will never travel FTL. Even if the shadow the information produces moves at a thousand times light speed, if first has to complete a moon-earth round trip and that will always be slower than transmitting a radio signal directly across the moon.
Your shadow can’t even begin to move until information has first traveled from moon to earth and back again.
A shadow is just the absence of light. Light streams from one place to another at C. Think of it like a train. The end of the train isn’t travelling any faster than the head. The absence of train does not appear down the tracks any faster than the head of the train.
If you cast a shadow on the moon with your finger, the edge of the shadow is just the edge of the train of light travelling to the moon.
You can imagine a beam of light shone on the moon like squirting a hosepipe of water. You can wiggle the end of the hose and the stream of water changes direction. Point the hose at a wall. Watch the point where the water hits the wall. Wiggle the hose fast enough and the point on the wall where the hose points gets ahead of the actual point where the water hits the wall. Wiggle it really fast and you can see snaking shapes in the water on their way to the wall, and the point where the water hits the wall can be a few cycles later than the hose wiggles. Light is no different.
Yes, as above. The shadow is delayed exactly the same as the light.
Morse code with shadows would be simply changing the code so that you signalled the gaps between the dots and dashes with light.
Oh, and another thing. If the shadow travels faster than light, what happens if you put your hand in front of the light source before the light beam has made it to the moon?
This is similar to the “scissor paradox” or “wave paradox” where the point of contact of the blades of a pair of scissors can ‘move’ along the edge faster than light or the point at which a wave strikes the shore can do the same if they are almost parallel.
so i suppose the conclusion is a form of shadow Morse code couldn’t work any more efficiently than, say, a signal light, since the light being blocked has to travel at the speed of light anyway?