Why Does E=mc2_ - Brian Cox [84]
Imagine you are blindfolded, holding a ping-pong ball by a thread. Jerk the string and you will conclude that something with not much mass is on the end of it. Now suppose that instead of bobbing freely, the ping-pong ball is immersed in thick maple syrup. This time if you jerk the thread you will encounter more resistance, and you might reasonably presume that the thing on the end of the thread is much heavier than a ping-pong ball. It is as if the ball is heavier because it gets dragged back by the syrup. Now imagine a sort of cosmic maple syrup that pervades the whole of space. Every nook and cranny is filled with it, and it is so pervasive that we do not even know it is there. In a sense, it provides the backdrop to everything that happens.
The syrup analogy only goes so far, of course. For one thing, it has to be selective syrup, holding back quarks and leptons but allowing photons to pass through it unimpeded. You might imagine pushing the analogy even further to accommodate that, but we think the point has been made and we ought not forget that it is an analogy, after all. The papers of Higgs et al. certainly never mention syrup.
What they do mention is what we now call the Higgs field. Just like the electron field, it has associated with it a particle: the Higgs particle. Just like the electron field, the Higgs field fluctuates, and where it is biggest the Higgs particle is more likely to be found. There is a big difference, though: The Higgs field is not zero even when no Higgs particles are around, and that is the sense in which it is like all-pervasive syrup. All of the particles in the Standard Model are moving around in the background of the Higgs field, and some of the particles are affected by it more than others. The last two lines of the master equation capture just this physics. The Higgs field is represented by the symbol φ and the portions of the third line that involve two instances of φ along with a B or a W (which in our compressed notation are tucked away inside the D symbol in the third line of the master equation) are the terms that generate masses for the W and Z particles. The theory is cleverly arranged so the photon remains massless (the piece of the photon that sits in B and the piece in W cancel out in the third line; again, that’s all hidden in the D symbol) and since the gluon field (G) never appeared, it too has no mass. That is all in accord with experiment. Adding the Higgs field has generated masses for the particles and it has done so without spoiling the gauge symmetry. The masses are instead generated as a result of an interaction with the background Higgs field. That is the magic of the whole idea—we can get masses for the particles without paying the price of losing gauge symmetry. The fourth line of the master equation is the place where the Higgs field generates the masses for the remaining matter particles of the Standard Model.
There is a snag to this fantastic picture. No experiment has ever seen a Higgs particle. Every other particle in the Standard Model has been produced in experiments, so the Higgs really is the missing piece in the entire jigsaw. If it does exists as predicted, then the Standard Model will have triumphed again, and it can add an explanation for the origin of mass to its impressive list of successes. Just like all the other particle interactions, the Standard Model specifies exactly how the Higgs particle should manifest itself in experiments. The only thing it doesn’t tell us is how heavy it is, although it does predict that the Higgs