Shadows cannot “go” anywhere at any speed of their own initiative; they have no mass, and no energy. They are hitchhikers riding in the empty boxcars of light trains.
True: shadows have no mass or energy, so they're not subject to the restrictions of relativity. Thats the whole point. Nonetheless we cognize them as coherent structures maintaining integrity over vast distances. And as coherent structures they DO 'travel' faster than light.
Intriguing! And beautifully explained. It left me wondering: Could this capacity of shadows be used in some way to communicate? To transmit information faster than electromagnetic radiation could carry it? What do you think, Margaret?
Sadly no it can't. The essence of this is that it can't be used to transmit information, which is why it doesn't violate relativity. If it could be used to transmit info then some kind of energy would be transferred faster than light and that would be a violation of special relativity. Its intersting to think through why you can't use this for sending info - it was an exercise we were set in physics class when i studied SR at university.
That's very hard to wrap my non-mathematical head around. I mean, if I perceive a shadow, then I know I've seen something. I now possess knowledge that I saw something which was not there before. Which is information. Does SR demand that the faster-than-light shadows by imperceptible?
David - this is a non-trivial exercise in relativistic thinking, but here goes. The thing is that if you are very far out in space the shadow can pass by you at faster than the speed of light - that's the simple geometry of what happens as a circle gets bigger the father away you go from its source. But you can't *transmit* information faster than the speed of light using the *edge* of the shadow because the light *from* the source of the transmission to you (far out in space) still has to travel at the speed of light. So although the *edge* of the shadow will in fact be percieved to travel faster than light where you are (out in space) - the sender can't *affect* that edge faster than light-speed. So while you will perceive something (the edge of the shadow) that is traveling faster than light, no informatic *change* can be conveyed faster than light. Its' a subtle yet brilliant phenomenon.
This is really intriguing to think about. I guess what I envisioned (using my senses and experience that evolved for the non-relativistic world) is a message-in-a-bottle kind of deal, where the sender affects the shadow at Point A (before sending it anywhere) but I see, from your lucid explanation, that controlling the effect (so that the message is preserved) requires that something travel "with" the shadow. And that "something" can't go faster than light.
Something tells me there is a SF story to be written in which a character drives themselves nuts trying to make FTL shadow-messaging work. Thanks for posting about this!
Yes, It's very sci-fi. I've ended up in arguments with multiple people at dinner parties (always guys, often with engineering or computer training) who insist the shadows-faster-than-light isn't possible. I explain I studied it in a university course on relativity and they still don't believe it. Its so intersting how deeply Einstein's injunction is embedded in our cultural DNA ... but nature is ever capable of confounding us... Glad you enjoyed this all.
Shadows cannot “go” anywhere at any speed of their own initiative; they have no mass, and no energy. They are hitchhikers riding in the empty boxcars of light trains.
True: shadows have no mass or energy, so they're not subject to the restrictions of relativity. Thats the whole point. Nonetheless we cognize them as coherent structures maintaining integrity over vast distances. And as coherent structures they DO 'travel' faster than light.
Intriguing! And beautifully explained. It left me wondering: Could this capacity of shadows be used in some way to communicate? To transmit information faster than electromagnetic radiation could carry it? What do you think, Margaret?
Sadly no it can't. The essence of this is that it can't be used to transmit information, which is why it doesn't violate relativity. If it could be used to transmit info then some kind of energy would be transferred faster than light and that would be a violation of special relativity. Its intersting to think through why you can't use this for sending info - it was an exercise we were set in physics class when i studied SR at university.
That's very hard to wrap my non-mathematical head around. I mean, if I perceive a shadow, then I know I've seen something. I now possess knowledge that I saw something which was not there before. Which is information. Does SR demand that the faster-than-light shadows by imperceptible?
David - this is a non-trivial exercise in relativistic thinking, but here goes. The thing is that if you are very far out in space the shadow can pass by you at faster than the speed of light - that's the simple geometry of what happens as a circle gets bigger the father away you go from its source. But you can't *transmit* information faster than the speed of light using the *edge* of the shadow because the light *from* the source of the transmission to you (far out in space) still has to travel at the speed of light. So although the *edge* of the shadow will in fact be percieved to travel faster than light where you are (out in space) - the sender can't *affect* that edge faster than light-speed. So while you will perceive something (the edge of the shadow) that is traveling faster than light, no informatic *change* can be conveyed faster than light. Its' a subtle yet brilliant phenomenon.
This is really intriguing to think about. I guess what I envisioned (using my senses and experience that evolved for the non-relativistic world) is a message-in-a-bottle kind of deal, where the sender affects the shadow at Point A (before sending it anywhere) but I see, from your lucid explanation, that controlling the effect (so that the message is preserved) requires that something travel "with" the shadow. And that "something" can't go faster than light.
Something tells me there is a SF story to be written in which a character drives themselves nuts trying to make FTL shadow-messaging work. Thanks for posting about this!
Yes, It's very sci-fi. I've ended up in arguments with multiple people at dinner parties (always guys, often with engineering or computer training) who insist the shadows-faster-than-light isn't possible. I explain I studied it in a university course on relativity and they still don't believe it. Its so intersting how deeply Einstein's injunction is embedded in our cultural DNA ... but nature is ever capable of confounding us... Glad you enjoyed this all.