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on the results of that experiment. But what if the Standard Model is wrong? Couldn’t something totally different and unexpected happen? Maybe the Standard Model is not quite right and there is no Higgs particle. There is no arguing that these are genuine possibilities. Particle physicists are particularly excited because they know that the LHC must reveal something new. The possibility that the LHC will see nothing new is not an option at all because the Standard Model, stripped of the Higgs, just does not make sense at the energies that the LHC is capable of generating, and the predictions of the Standard Model simply fall apart. The LHC is the first machine to enter this uncharted area. More specifically, when two W particles collide at energies in excess of 1,000 times the proton’s mass energy, as they certainly will at the LHC, we lose the ability to calculate what is happening if we simply throw the Higgs parts of the master equation away. Adding the Higgs back in makes the calculations work out, but there are other ways to make the W scattering process work—and the Higgs is not the only option. Whichever way nature chooses, it is absolutely unavoidable that the LHC will measure something that necessarily contains physics we have never encountered before. It is not common for scientists to perform an experiment with such a guarantee that interesting things are going to reveal themselves, and this is what makes the LHC the most eagerly anticipated experiment in many years.

8

Warping Spacetime

Thus far we have thought of spacetime as fixed and unchanging—something akin to a four-dimensional stage or the arena within which “things happen.” We have also come to appreciate that spacetime has a geometry and that the geometry is most certainly not that of Euclid. We have seen how the idea of spacetime leads naturally to E = mc2 and how this simple equation and the physics it represents has become a foundation stone of both our modern theories of nature and the industrial world. Let us move toward the final twist in our story by asking one last curiosity-driven question: Is it possible that spacetime could be warped and curved differently from place to place in the universe?

The idea of curved space should not be new to us, of course. Euclidean space is flat and Minkowski space is curved. By which we mean that Pythagoras’ theorem doesn’t apply in Minkowski spacetime. Instead, the minus-sign version of the distance equation applies. We also know that the distance between two points in spacetime is analogous to the distance between different places on a map of the earth, in that the shortest distance between two points is not a straight line in the usual sense of the word. So Minkowski spacetime and the surface of the earth are examples of curved spaces. Having said that, the distance between two points in Minkowski spacetime does always satisfy s2 = (ct)2 - x2, and this means that it curves in the same way everywhere. The same can be said for the surface of the earth. Might it, however, make sense to speak of a surface that curves differently from place to place? What would spacetime look like if this were allowed, and what would the implications be for clocks, rulers, and the laws of physics? To explore this admittedly rather arcane-sounding possibility, we shall once again take a step down from the mind-bending four dimensions to the commonplace two dimensions and focus our attention on the surface of a sphere.

A smooth ball is curved the same way everywhere—that much is obvious. But a golf ball, with dimples in it, is not. Likewise, the earth’s surface is not a perfect sphere. As we zoom in, we see valleys and hills, mountains and oceans. The law for the distance between two points on the earth’s surface is only approximately the same everywhere. For a more precise answer we need to know how the earth’s undulating surface changes as we journey over the mountains and through the valleys between the start and finish of any journey. Could spacetime have dimples in it like a golf ball or mountains and valleys