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The fact that space and time are elastic, stretching and warping in synchrony with our passage, is weird, but inescapably true. The beams of particles at Cern, travelling within a mere fraction of light speed, arrive at their destination on time only when the subtleties of relativity are included in the accounting. GPS satellites locate you precisely, but have to include Einstein's arithmetic in the calculations. Some experiments at Cern agree with the predictions of relativity to better than one part in a trillion – that is like measuring the distance across the Atlantic Ocean to better than the width of a human hair – but only when relativity is taken into account.
For scientists certainly, and for many of us, perhaps surprisingly, Einstein's theory of relativity is needed to keep track of our daily affairs.
What has any of this to do with the speed of light?
Einstein's edifice is constructed on an experimental fact: that the velocity of light is independent of your own motion. Whether you are moving towards the source, or away from it, or are stationary, doesn't matter: speed of light is universal. This is counterintuitive. A fast racing car overtakes a slower one more gradually than it does the static spectators at trackside; however, a light beam passes everyone the same – spectators or Lewis Hamilton would measure the same speed. Counterintutitive certainly, but true, and it led to Einstein's world-view. And one of the basic consequences of Einstein's theory is that the speed of light – in a vacuum – is nature's speed limit. Nothing can travel through a vacuum faster than light.
Has Cern overthrown this paradigm? I doubt it. Light travels slower through water, glass, even air, than through a vacuum. Radio waves do, too. So light can be slowed down, but not sped up: the vacuum is nature's open road where light travels at the speed limit. We need to be careful when asking what exactly has the Cern experiment done, or, more pertinently, how did it do it?
Cern produces beams of neutrinos, ghostly particles that can travel through the earth as easily as a bullet through a bank of fog. A beam travels down through the surface of the Earth in a straight line, the Earth's surface curving upwards away from it initially, eventually bending downwards until, 730km later, at Gran Sasso, a laboratory near Rome, the neutrino beam re-emerges. This journey has taken about 1/500th of a second.