Can I communicate faster than light?
Great site! I am a recent college grad from UC Berkeley, and I double-majored in Math and Economics. However, I do enjoy doing a lot of outside reading on topics of science, so I found myself here.
In any case, my question is in response to the answer for the question entitled "How can the Universe expand faster than the speed of light during inflation?" The answer was written by Kristine Spekkens, and in it, she stated that information cannot be propagated at faster than light speeds. I'm not quite sure what exactly is meant by information, but I have a thought experiment which I cannot reconcile with this assertion about propagating information faster than light.
Suppose I live on Earth and have a friend who lives on Pluto. If I want to send him a message, I could do so by radio, but the information would not arrive to him faster than light, and would take several minutes to reach Pluto. However, suppose instead that I had a really, really long stick that stretched all the way from Earth to Pluto. If I wanted to send a message to my friend, I can do it nearly instantly simply by tapping out a message in Morse Code onto the surface of Pluto, using my stick. In this manner I have transmitted information at a speed much greater than light.
Is there something wrong with this experiment? How do you reconcile this?
Your idea of communicating with your friend by tapping a stick won't let you do this faster than the speed of light, unfortunately. When you tap a stick, the "tap" is the result of a wave travelling through the stick from your end to the other end. To see this, try the following experiment: get a friend, and stand a few feet apart with a string between you and your eyes closed. Get your friend to shake one end of the string, and your job is to tell him when you feel the shake. When you're a few feet apart, you'll know "instantaneously", since the speed of the wave your friend is sending along the string travels much faster than a few feet in a second. Now try the same thing, but on opposite sides of a football field. Now, the wave will take a few seconds to get to you, so there will be a delay between your friend's shake and your reaction. Now, if you take a string and make it more dense and rigid, you've got the stick in your example: the physics is the same. So, it will take a finite amount of time for your tap to get from the Earth to Jupiter. What is the maximum speed that a wave can travel through your stick? The speed of light, of course!
We could try to be even more devious in trying to communicate faster than the speed of light: suppose that your friend on Pluto had a very sensitive detector that picks up small changes in the gravitational force on Pluto caused by the Earth. In order to communicate with him, you develop a technology that lets you change the separation between the two planets. Your friend detects this on his meter, all the way at Pluto, and you proceed to "wiggle" the Earth into a morse code of sorts. That's instantaneous, right?
It turns out that again here, the answer is no: gravity travels at the speed of light too! Even though they have not yet been directly detected, the waves that carry information about the gravitational field around an object (gravity waves) were proven to travel at the speed of light just last October, in an experiment involving the bending of a quasar's light around Jupiter (this result is still somewhat controversial, however, check out this posted answer for details).
For reasons that people haven't yet worked out, the speed of light appears to be the fundamental limit in every branch of physics, from the materials in your tapping stick to gravity waves, even when light is not being used for communication. That's why I used the term "information" in my previous answer, since there are more ways to send information then by simply sending light signals.
And, there is no harm in making something move faster than the speed of light, as long as you're not sending information along with it. As a final example, imagine that you're in a football stadium packed with people, and they're doing the "wave". This works because you stand up just as you see the person next to you standing up, so that a wave propagates around and around the stadium. If you do the wave in this way, the fastest it can ever travel around the stadium is the speed of light, because you have to take your cue to stand (or to push a button, say, if standing takes too long) from the person next to you, and that can only travel at the speed of light. Suppose, however, that the stadium manager wanted to make a really spectacular show, and gave everybody in the audience a piece of paper with the exact time at which to stand. Then in principle, you could make the wave go arbitrarily fast, since you can tell people to get up at arbitrary times. So with some careful coordination of times, you could make a wave go faster than the speed of light. Does this defy the most fundamental law of physics? NO, because the orchestrated wave made by giving everyone a piece of paper carries no information in it: you gave them the information (when to stand up) beforehand, on the papers. In the extreme, you could tell everyone to stand at exactly the same time on their papers: again, since you gave them the information of when to stand beforehand, the "infinitely" fast wave doesn't violate physics at all. In the "real" wave, when you take your cue from the person next to you, the information of when to stand can only go at the speed of light.
Suppose the same "stick" (between the Earth and Pluto) was pushed and pulled (in Morse code) instead of tapped...being solid, wouldn't the entire "stick" move at the same time? Obviously the stick would not be moving at the speed of light but (it seems to me), the information being sent/received would be.
Unfortunately, your idea doesn't stump the finite speed of light either! The next time you're in a pool (or near some water), stand a foot or two from the edge and "push" the water with your hands; the "push" doesn't reach the wall right away, but takes some time to get there. Essentially, your "push" initiates a wave in the water, that carries the push to the edge. The exact same thing happens in solid objects; although you don't notice it, a "push" gets to the other side of a stick via a wave similar to that in water, and the more "solid" you make the stick the faster that wave goes. However, to the best of our knowledge, the maximum speed of a wave in a solid is the speed of light. So, even if you push and pull the stick instead of tapping it, you are still limited to transmitting information at the speed of light.
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