Proving special relativity: episode 3

One of the most nonintuitive consequences of Einstein’s theory of special relativity is the idea that different people will experience time at different rates. This has no analog in classical theory, and yet it is easy to observe at laboratories such as Fermilab and CERN.

“Time waits for no man” goes the saying, and it appears to be true. Inexorably the moments of our lives tick away until we have none left and slip away into the darkness. However, as painful as that truth is, we have some comfort in the fact that time marches on equally for all of us — pauper and prince. Time plays no favorites.

Einstein turned this comforting truism on its head in 1905 when he published his theory of special relativity. In one of the most nonintuitive consequences of his theory, time does not march at the same pace for us all — it depends on a person’s velocity. Slow-moving objects age more quickly than their speedy brethren.

That just didn’t seem even possible.

Luckily, at particle accelerator laboratories, it is pretty easy to increase the velocity of subatomic particles and put Einstein’s idea to a strict test. Let me immediately get to the punch line: As bizarre as it seems, Einstein is right.

There are a ton of examples I can give from every particle accelerator laboratory on the planet, and they all confirm the theory of special relativity beyond a shadow of a doubt. Let’s use one to illustrate the point: the Fermilab MINOS beamline, which shoots neutrinos in the direction of Minnesota.

Fermilab makes neutrinos by slamming high-energy protons into a target, creating a spray of particles. The most common are pions, which then decay into muons and neutrinos. Since the pions come flying out of the collision, they move while they are decaying.

To see the effect of relativity, we need to see just how long of a tunnel is needed to let them decay. To do that, we need to know the pions’ velocity and how long they live. In the same way that you can combine the speed of a car and the time it travels to determine the distance of its trip, you can figure out how far a pion will travel before it can decay.

We know very well how long stationary pions live. Because pion decay is essentially a form of radioactive decay, individual pions don’t have a fixed lifetime any more than people do — some live longer and some shorter. But we can certainly say 95 percent of pions decay in 80 billionths of a second.

Let’s say the pions have an energy of 14 GeV, traveling at 99.995 percent the speed of light (186,000 miles per second). Combining velocity and time, we would predict that the NuMI/MINOS decay tunnel would need to be about 76 feet long to contain all of the pion’s decay. Yet the actual tunnel is 2,320 feet long — almost half a mile. You know that Fermilab wouldn’t dig a much-longer-than-needed tunnel just for fun. There had to be a reason for its length, and that reason is Einstein’s theory of special relativity.

One of the predictions of relativity is that moving clocks tick more slowly than stationary ones. There are many forms of clocks, from an old-style grandfather clock to the beat of a human heart. The steady decay of particles such as pions forms its own clock, and because of the effects of relativity, the moving-pion clock is slower than the stationary-pion clock, which means Fermilab scientists had to design the NuMI/MINOS tunnel to be long enough to accommodate the longer lifetime of the moving, decaying pion.

Using the velocities and lifetimes described here, classical physics says that every pion would have decayed in the 2,320-foot-long tunnel — after all, it really only needed 76 feet anyway. Yet Fermilab physicists know that only about 40 percent of the pions will decay before they smash into the end of the tunnel about half a mile away. This is exactly what is predicted by relativity.

While the fact that clocks tick more slowly if they are moving is not at all intuitive, every time we shoot a beam of neutrinos at Minnesota, we conclusively prove that the universe can be nonintuitive. Relativity works.

—Don Lincoln

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