# Faster than the speed of light is relatively fast

As expected, it appears that the report of faster-than-light neutrinos was a consequence of an error, in this case a loose cable. A short post on website of the journal Science explains:

According to sources familiar with the experiment, the 60 nanoseconds discrepancy appears to come from a bad connection between a fiber optic cable that connects to the GPS receiver used to correct the timing of the neutrinos' flight and an electronic card in a computer. After tightening the connection and then measuring the time it takes data to travel the length of the fiber, researchers found that the data arrive 60 nanoseconds earlier than assumed. Since this time is subtracted from the overall time of flight, it appears to explain the early arrival of the neutrinos. New data, however, will be needed to confirm this hypothesis.

(I applaud the scientific caution in the last sentence.)

By the way, you often see it asserted that Einstein's special theory of relativity rules out faster-than-light travel but usually without explanation. Sometimes it's pointed out that it would take infinite energy to accelerate anything with mass to the speed of light, which is true, but the problem is more fundamental than that. (Photons can move at the speed of light because they don't have "rest mass," which in modern relativity is called "invariant mass" or just "mass.")

Special relativity is based on two well-supported assumptions: first, that the laws of physics are the same from the viewpoint of all observers not experiencing acceleration, and second that the speed of light is the same relative to (and as measured by) all such observers, even if they're moving with respect to each other. The first principle actually comes from Galileo's conception of relativity. The second seems counterintuitive, but it's implied by the first together with Maxwell's equations governing of electricity and magnetism and borne out by experiments carried out for over a hundred years.

So why does special relativity rule out speeds faster than light?

Start by imagining that you're floating somewhere between the galaxies when three spaceships in a row zip past you, all moving at the same speed but coasting with their engines off. Suppose that the middle spaceship is halfway between the other two, and just as it passes you, you see simultaneous flashes of light from the other spaceships. You reason, "Even at the speed of light, it took a little time for those flashes to reach me, so if I'm seeing them at the same time now, they must have been emitted a little while ago, when the first spaceship was closer to me than the third one. So since the flash from the third spaceship had to travel farther to reach me, that flash must have been emitted first."

On the other hand (or tentacle, or whatever), an occupant of the middle spaceship would reason, "I'm at rest relative to those two spaceships and they're the same distance from me, so if I see the flashes at the same time, they must have been emitted at the same time."

Obviously, you and the occupant of the middle spaceship disagree about whether the flashes happened simultaneously, but that's cool. In fact, if another unpowered spaceship happened to be zipping past you at the same instant in the opposite direction, someone in that spacecraft would agree with you that the flashes occurred at different times but would disagree about which flashed first!

This is known in relativity circles as the breakdown of simultaneity. In general, if two events -- call them A and B -- are happen in different places but from the standpoint of one unaccelerated observer happen at the same time, then it's always possible for there to be another observer who concludes that A happened before B and a third who concludes that B happened before A. As long as none of them can prove the others wrong, there's no violation of the laws of physics, and the observers just have to agree to disagree.

But suppose Event A is the sending of a message (anything from a subspace radio transmission to an hand-delivered letter) and Event B is the receipt of that message. For observers who think A happened before B this seems fine, but for those who think B happened first, the message was received before it was sent. And that's time travel.

So special relativity doesn't entirely rule out faster-than-light travel or communications; it just means that if it exists, so does time travel, with all its paradoxes.

I should add, by the way, that on larger scales involving the expansion of the universe general relativity comes into play, and it does allow faster-than-light motion. In fact, we actually observe distant galaxies with red shifts high enough to indicate that they're zooming away from us faster than light owing to the expansion of space. But causality still seems to be constrained by the speed of light.

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