Amir D. Aczel (amirdaczel.com) writes about mathematics and physics and has published 18 books, numerous newspaper and magazine articles, as well as professional research papers.
A Higgs candidate event from the ATLAS detector of the LHC.
Courtesy of CERN
What made me fall in love with theoretical physics many years ago (in 1972, when I first met Werner Heisenberg) was its stunningly powerful relationship—far beyond any reasonable expectation—with pure mathematics. Many great minds have pondered this mysteriously deep connection between something as abstract as mathematics, based on theorems and proofs that seem to have little to do with anything “real,” and the physical universe around us. In addition to Heisenberg, who brilliantly applied abstract matrix theory to quantum physics, Roger Penrose has explored the deep relation between the two fields—and also, to a degree, between them and the human mind—in his book The Road to Reality.
And in 1960, the renowned quantum physicist and Nobel Laureate Eugene Wigner of Princeton wrote a fascinating article that tried to address the mysterious nature of this surprising relationship. Wigner marveled at the sheer mystery of why mathematics works so well in situations where there seems to be no obvious reason why it does. And yet, it works.
Amir D. Aczel has been closely associated with CERN and particle physics for a number of years and often consults on statistical issues relating to physics. He is also the author of 18 popular books on mathematics and science, and has been awarded both Guggenheim Foundation and Sloan Foundation fellowships. Many thanks to Steven Weinberg of the University of Texas at Austin and to Barton Zwiebach of MIT for their helpful comments.
Readers of this blog have probably heard the standard fare about how the Higgs boson “gives mass” to everything in the universe, probably with some kind of analogy, like the one about a famous person walking through a crowded room, pulled every which way by admiring crowds, and that these connections “make the person massive“—as the Higgs field does with particles. Now that we finally seemed to have pinned down the elusive particle, I want to explain where the Higgs came from and what it does. While our understanding of the particle comes from some complicated math, the formulas actually tell a fascinating story, which I’ll recount in this post. All you need to keep in mind is that in the modern understanding of physics, categories aren’t as starkly separate as you might think: particles can be represented as waves or fields, and a force can also be viewed as a particle or a field.
So, a fraction of a second after the Big Bang, the universe had four kinds of “photons” floating around—the usual photon of light, and three other massless particles that “look” and act just like the photon. We label them: W+, W-, and Z. They are bosons, meaning carriers of force, as is the usual photon.
At the Big Bang, the universe also had one, unified, mighty force called the Superforce ruling it. But a tiny fraction of a second before the era I am talking about, the Superforce began to break down, successively “shedding off” part of itself to make the force of gravity, and another part of itself to make the strong nuclear force, which later would be active inside the nuclei of all matter, holding quarks inside protons and neutrons once these composite particles came into being. The two forces, gravity and the strong force—important as they are—do not enter our main story today.
The remnant we have of the Superforce at the time we are talking about, a tiny fraction of a second after the Big Bang, has three forces of nature held together inside it: electricity, magnetism, and something called the weak nuclear force, which later would be responsible for beta decay, a form of radioactivity. You may remember from a physics course that “electromagnetism” unifies electricity and magnetism, as Maxwell taught us over a century ago. But, during the era I am talking about, there are really three linked forces: electro-magnetic-weak; all three are held together as the electroweak force that remained from the Superforce after it had shed off gravity and the strong force.*