(August 24, 2018 at 3:31 am)vulcanlogician Wrote: So this is a perplexing thought experiment I found online.
The sun is approximately eight "light minutes" away. This means that if the sun were suddenly to go dark, we on Earth would not become aware of it until eight minutes after the fact. Most of us are familiar with this aspect of the speed of light.
Now here's the weird thing: the speed of light is also the speed of causality. And the implications of this are semi-paradoxal (at least to me). In any case, it seems to defy my intuitions about how time and causality work.
This thought experiment demonstrates the part that I consider paradoxal:
Let's say there is a light switch, floating beside the sun, that can turn the sun on and off. If somebody flips the sun off, it would take us eight minutes to realize on Earth that the sun had been turned off (just as I said in the beginning of the post). Now, suppose you had a stick that stretched all the way from the Earth to the sun and you used the stick to hit the switch and turn off the sun. From the moment you thrusted the stick to flip the switch, how long would it take for you (on Earth) to see the sun go out?
The answer is: approximately 16 minutes. Why? Because, the speed of light is the speed of causality. It takes eight minutes for a cause on Earth to become an effect on the light switch that is floating beside the sun. So it would take 8 minutes for the other end of the stick to be affected by your thrust from earth, then it would take 8 more minutes for you to realize the sun had actually gone out.
Doesn't this seem counterintuitive? It seems like it should only take eight minutes to see the sun go out because the other end of the stick would only have to travel a few centimeters. But that is not the case.
What happens when you 'use the stick to turn off the sun'? You push on it. That produces a compression wave that travels down the stick at the speed of sound in that stick. This is much, much slower than the speed of light. So, in fact, it would take much longer than 8 minutes for the compression wave from your push to get to the sun. Once it does, and the sun goes out, the effects of that move outward at the speed of light.
The point is that in relativity, there are no 'solids' that instantaneously transmit information from one end to the other. Such transmission happens as a compression wave along the solid which travels at much less than the speed of light.
