Basic Particle Theory: Higgs 101

There’s a beyond masterful explanation of symmetry and super-symmetry in a post titled “Higgs 101” over on the blog Cosmic Variance (a blog run by a number of cutting edge cosmologists). I can only wish I could explain the origins of the Standard Model as well as they have.

After a quick explanation of the history of early 20th century particle physics the explanation of symmetry begins:

“I believe that the greatest (and I mean THE greatest) discovery of the 20th century was to recognize that every symmetry in nature coresponds to some conserved physical quantity. It is a great sorrow that Emmy Noether did not win the Nobel Prize for this profound work. Symmetries are all around us – some are very simple, and some not so simple. For example, consider symmetry in time. The laws of physics are (we presume) the same now as they are at the time you finish reading this sentence, and will be the same 100 years from now. If you move (translate) in time, the rules stay the same. This symmetry in fact leads to conservation of energy. Likewise, if you move in space, the laws of physics are the same. This leads to conservation of momentum. If you rewrite the laws of physics in a frame of reference rotated 42.6 degrees from the one where you are writing them now, they are the same…conservation of angular momentum! Wow!

But it gets much better. We know, since the beginning of the last century, that you need to obey the rules of relativity. Fine. Also quantum mechanics. Okay…how? We write down wavefunctions that obey all the rules. Then we make them also obey all the symmetries we know about.

It turns out that wavefunctions are represented by complex numbers, which have real and imaginary parts. (By imaginary, we mean multiples of the square root of -1, not ‘eleventy-forty seven’ which is perhaps another imaginary number.) Complex numbers are rich and fascinating, and the calculus of complex functions of complex numbers is great fun and beautiful. Most remarkably, this calculus describes the world perfectly when combined with quantum mechanics and relativity!

‘Describes the world perfectly.’? Okay, well, it describes a broad swath of phenomena at the subatomic particle level really well…freakily well. We call it the Standard Model. I give it capital letters here because it has become so deeply established, and has such predictive power over such a broad range of phenomena that you have to give it a proper name. And I and most of my friends live for the day when we can destroy it and return it to lower case letters, the formerly standard model.

It’s only a model, after all. To build the Standard Model we assume that our wavefunctions obey certain peculiar symmetries, called gauge symmetries. The simplest to understand is called U(1). With complex wavefunctions, the probability for finding a particle at a certain place/time is calculated by finding modulus of the wavefunction, sort of its absolute value or magnitude. You square it, basically, in the complex space in which it lives. It turns out, though, that you get exactly the same answer for this probability if you square the wavefunction, or the wavefunction multiplied by a complex number of modulus 1 (e to the something imaginary). This something imaginary can in fact be a function of position in spacetime. It is, in fact, the same as a rotation of the wavefunciton in the complex plane…and that’s U(1) symmetry.

Here comes the miracle: if you impose upon our relativistic, complex, quantum-mechanical wavefunctions the requirement that they be invariant under these U(1) transformations, then you get electromagnetism. Conservation of electric charge. A massless photon. QED – quantum electrodynamics, in all its 12-digit precision glory. Electromagnetism is a simple consequence of the U(1) symmetry of any wavefunction.”

From here, after a quick tour of quark and gluon symmetries, the author then moves on from this point to explain the sorts of predictions being made by looking at other observed symmetries – and their attendant conservation principles.

The Higgs particle comes as a result of the changes needed to make the theory explain the weak field and the electric field.

Which it does – in spades. The problem is that in spite a great deal of effort, no one has ever found the Higgs particle. Which brings into question the whole wonderful edifice.

So the question is, are we looking in the wrong place, or do we need to figure out the error in the theoretical underpinnings…

Read the rest here: Higgs 101 | Cosmic Variance

Author: Nick Knisely

Episcopal bishop, dad, astronomer, erstwhile dancer...

2 thoughts on “Basic Particle Theory: Higgs 101”

Comments are closed.