Richyy said:
The BBC said that if that proton at CERN was faster than light, that it would arrive at it's destination before it set off.
Can you post a link to the particular BBC article, and perhaps quote the wording of the statement you're referring to? A number of press articles have talked about the neutrino observations making time travel more feasible theoretically, but as far as I know none of them have said anything about the neutrinos actually traveling backwards in time.
The general rule in SR is not quite the way you stated it in the OP. The general rule is that if someone were to go faster than light, the time ordering of events they experienced would not be invariant--that is, it would not be the same for all observers. For example, suppose I have an "instantaneous teleporter" that can transport me from the Earth to the Moon in one second (the light travel time from Earth to Moon is about one and 3/4 seconds). And suppose that you are in a fast rocket ship that is flying past the Earth in the direction of the Moon. Consider the following scenario:
(1) I look at my watch as I step into the teleporter on Earth and see that it reads exactly noon and 0 seconds; I look again as I step out of the teleporter on the Moon and see that it reads noon and 1 second.
(2) A light beam is emitted from the Earth teleporter station directly at the Moon station at the instant I step in. I see it arrive at the Moon station 3/4 of a second after I step out of the teleporter there. So to me, I am still moving forward in time: I don't arrive at the Moon before I leave the Earth. But I do arrive at the Moon faster than light leaving Earth when I do can get there.
(3) You, in your rocket ship flying past Earth in the direction of the Moon, observe me departing the Earth and arriving at the Moon, by means of light emitted from those events. Light from my departure event arrives at your ship just as your clock reads noon and 0 seconds; you happen to be passing just over the Earth teleporter station at that instant, so the light takes virtually no time to get to you, and your clock is synchronized with my clock at that instant.
(4) You fly towards the Moon at such a speed that you will cover the distance from the Earth to the Moon in two seconds as seen by people on Earth (i.e., you are traveling at 7/8 of the speed of light relative to them). However, at that speed you will see the distance between the Earth and the Moon to be length contracted by a factor ofa about two, so it will only take about one second by your clock to cover the distance (the observers on Earth or the Moon will explain this by saying that your clock is running twice as slow as theirs, so it only ticks off half the time when covering the same distance).
(5) Even before you reach the Moon, however, you will see the light emitted from my arrival at the Moon. When you measure the time of arrival of that light, by your clock, and correct for the light travel time from the Moon to where you receive the light (remembering that the Moon is moving toward you as well), you will conclude that I must have arrived at the Moon before I left the Earth, according to your clock. So to you, I will seem to have gone backward in time.
As you can see from the above scenario, an observer has to be moving fairly fast, relative to someone who is moving faster than light, for it to look to them like the other is going backwards in time. The neutrinos that recently made the news, even if it turns out they *were* going faster than light, were only doing so by a few parts per million; so in order to see them going backwards in time, you would have to be moving, relative to the Earth, at least as close to the speed of light as a few parts per million. That's why I wondered about the exact wording of the BBC article; I doubt they were writing it on board a relativistic rocket.
Btw, the term "speed of light" in relativity is actually a bit misleading. There are really two separate ideas involved: first, that there is some "invariant speed" such that anything that moves at that speed from the viewpoint of anyone observer will move at that speed from the viewpoint of all observers. Second, that light moves at the invariant speed. But the second idea is logically distinct from the first; the first is a property of spacetime itself, while the second is just a property of light.
Oh, and welcome to Physics Forums!
