by Tim James
Sadly, because Noether was Jewish, she was hounded out of Germany during the rise of Nazism and subsequently fled to America. But on the plus side she was received by a loving community of scientists who saw her as their undisputed queen. She earned her long-overdue recognition and her obituary in the New York Times, penned by Einstein, described her as ‘the most significant mathematical genius thus far produced since the higher education of women began’.3
BE CALM, LITTLE ONE
One of the conserved quantities that emerge from Noether’s theorem is called the lepton number. No rocket science needed to figure that one out: the number of leptons in the universe stays the same. It is a symmetrical law but irritatingly it looks too symmetrical on paper, because there is one known process where the symmetry is broken.
It is called beta decay, discovered by Madame Curie (the other queen of physics). It happens when a proton in the core of an unstable nucleus turns itself into a neutron, seemingly at random. As it does so, it spits out an electron, which darts away from the atom, detected by us as radioactivity.
In terms of a Noether law this makes sense because charge has to be conserved. If a neutral neutron turns into a positive proton it has to generate a negative electron too. But if lepton number has to be conserved alongside it, have we not just broken that law by generating an electron where there was none previously?
The explanation posed by Wolfgang Pauli (the guy who shot down de Broglie’s pilot wave) was that there had to be another particle generated. Some sort of anti-lepton that possessed no charge.
Enrico Fermi called this hypothetical particle a neutrino, meaning ‘little neutral one’, and for twenty-five years we hunted them to try and prove Noether right. Unfortunately, neutrinos are the most inconspicuous and non-interacting particles known to physics so this was no simple feat.
Consider the neutrinos made in the core of our Sun where protons and neutrons change into each other all the time. A photon takes about ten thousand years to bounce its way to the solar surface from the centre, being absorbed and re-emitted by every particle it encounters along the way. A neutrino makes that same journey in twenty-three seconds.
Earth is constantly bombarded by solar-produced neutrinos and almost all of them shoot through the planet without blinking. Roughly sixty-five billion neutrinos passed through the tip of your little finger as you read this sentence.
It is not easy building a detector for something utterly uninterested in being detected. The world’s biggest neutrino detector is the Super-Kamiokande (Super-K) near Hida, Japan, located 1 kilometre below the surface of a mountain (to filter out cosmic rays).
The Super-K houses a tank of 50,000 tonnes of ultra-pure water and trillions of neutrinos pass through it every second, most of them doing nothing. But every once in a while they strike an electron from its atom, which we can detect as a faint glow.
Neutrinos turned out to be real particles and thus lepton number is conserved. It took a quarter of a century to find them but they are elegant proof that Noether’s theorem is correct. Oh, and of course neutrinos come in three generations called the electron-neutrino, muon-neutrino and tauon-neutrino.
A SIGN OF WEAKNESS
The reason for the scarce interactions of neutrinos is that they have very few properties and do not couple to the fields with which we are familiar. They do not have colour, so will not talk to the gluon field, and they do not have charge, so will not talk to the electromagnetic/photon field either.
But neutrinos will occasionally interact with electrons. Plus, we know quarks emit them when changing identity from up to down, so there must be some field they are interacting with in order to do so. Something a lot weaker. It was named the weak field. Seriously.
Take an up quark with its +⅔ charge. When it turns into a down quark it becomes −⅓, meaning it loses +1 charge somehow. We have always thought charge stays put but the weak field might be violating that assumption.
The weak field could be carrying positive charge away from a quark in the form of a virtual positively charged ‘weak particle’. Virtual particles never last, however, so this particle will decay soon afterwards, transferring energy into the positron and neutrino fields to conserve charge and lepton number. We can explain an up quark turning into a down quark like this:
Read from bottom to top, we begin with an up quark. It couples to the weak field and generates a positive weak particle (W+), turning into a down quark itself.
This positively charged weak quantum then decays, making a regular neutrino (represented by that wonky V symbol) and a positron to conserve the positive charge (shown as an electron with a little bar above it). The reverse process also happens, except with a W− particle.
You are probably thinking that the weak-field particle must have some awesome name to go with photon and gluon but I’m afraid by this point everyone seems to have got bored, so they tragically called them W particles. W+ if carrying positive and W− if carrying negative.
The property a particle needs to couple with the weak field and emit W particles is called ‘weak isospin’ and comes in two varieties, +½ and −½. Quarks, leptons and neutrinos have weak isospin but its coupling constant is very low, so we rarely see its influence.
But what in the name of Erwin Schrödinger’s cat-munching ghost happens when neutrinos meet? They both have weak isospin, which means they should create virtual particles between them. This cannot happen through W+ or W− interaction because neutrinos are chargeless. There has to be a third weak particle available, one with no charge. Sheldon Glashow named it the Z particle, because it stands for zero charge, I guess?
The Z and W particles were observed in 1973 and 1983 respectively at the Gargamelle detector in Switzerland (named after the giant from the François Rabelais novel The Life of Gargantua and of Pantagruel, not the incompetent bad guy from The Smurfs).
The Z and W discoveries verified the behaviour of neutrinos, confirmed the existence of the weak field and once again proved Noether’s symmetry laws correct. But as you probably know by now, quantum physics is like an infernal Rubik’s Cube. As soon as we solve one part we muddle up something else.
A TOTALLY USELESS IDEA
All quantum field theories involve two types of object: matter particles (quarks, electrons, neutrinos) and interacting force-field particles (photons, gluons and W/Zs).
Matter particles are collectively called fermions and have properties such as occupying space, whereas force-carrying particles are collectively called bosons and are able to overlap.
Your body is made of fermions (electrons and quarks), which is why you take up a volume. A beam of light, on the other hand, is made from bosons (photons specifically), which is why torch beams pass through each other rather than banging together like lightsabres. In that respect, bosons are a disappointment.
When a particle interacts with the weak field it often involves a change in charge, so the weak and electromagnetic fields are obviously coupled. The early quantum field theory for the weak field was called ‘quantum flavour-dynamics’ (QFD) but since the weak and electromagnetic fields talk to each other the full theory, which includes all photon and weak interactions, is called ‘electroweak theory’ and won a Nobel Prize for Steven Weinberg, Abdus Salam and Sheldon Glashow. I would have called it quantum electroweak-dynamics myself because it would give us the acronym: QEWD.
It is a very symmetric theory but this elegance is also its biggest flaw since the photon and weak fields are drastically different.
Ws and Zs are short range but photons travel forever. The weak force requires three different particles while the electromagnetic force works with only one. Then there is the biggest broken symmetry of all: W and Z particles have mass and photons do not. That is not something we expect for force-carrying bosons that overlap, so something was breaking symmetry between the photon field and the weak one.
In the mid-1960s three people independently hit on the same solution. Robert Brout, François Englert
and Peter Higgs suggested you could preserve electroweak symmetry the same way Pauli solved the lepton symmetry problem – add a new field/particle.
At the start of the universe, they argued, in the initial flickering moments of creation, the electromagnetic and weak fields were identical. But there was a third field lurking in the background and when this field ‘switched on’ everything changed.
This field is not like the others because its resting value is not zero; it is an actual number everywhere. Because of such an unusual property this new field had the ability to create different particles out of itself rather than one. These quanta are called Goldstone bosons, after physicist Jeffrey Goldstone, and they couple to the weak field majorly.
Prior to this field sticking its nose in, particles of the weak field were massless and infinite ranging, just like photons, but when the Goldstone bosons mixed with them, their character changed and they became the W+, W– and Z.
I like to imagine the weak field laid carefully on top of this eccentric new field like wallpaper placed on a wall. The wall has three kinds of bump on its surface (Goldstone bosons) and they push through the weak wallpaper, making it look like three kinds of weak particle to any casual observer.
Since the photon field does not couple to this additional field its particles are left untouched, becoming the photons we are used to. Boom. Symmetry successfully broken… assuming you could detect this freaky field. Which, no surprise, you cannot.
The idea of a non-zero field ‘switching on’ at the dawn of time and having three types of particle was not only exotic, it was untestable since Goldstone bosons are hidden within weak particles, making them invisible.
The journals to which Brout, Englert and Higgs submitted their idea all refused the idea, with one even replying that it was ‘of no obvious relevance to physics’.4 It was neat mathematically, but you could not test it, which prompted Higgs to grumble to a member of his research team, ‘this Summer I have found something that is totally useless’.5
BROKEN MIRRORS
We know the story has a happy ending though, so we should look at this new field closer. In some of the literature you see references to the weak-field particles ‘eating’ Goldstone bosons. How does this happen? The answer is to do with a particle property we have ignored until now because it, too, looks totally useless.
Charge, colour, spin, weak isospin, etc. determine how particles interact with various fields but Dirac’s quantum field theory predicts another property called chirality, from the Greek word for ‘handedness’. It is a property particles have and it does absolutely nothing.
Chirality can be described mathematically but has no obvious physical meaning. We just know that each particle/field seems to oscillate from one chirality to another, back and forth like the tick-tock of a clock, and we call the two chiralities left- and right-handed. It does not mean particles are waving alternating little hands into the air like some dad-disco move, although they might as well be. We have no idea.
For most of quantum history, chirality sat there in the equations hopping from left to right doing plum nothing. Particles flip their chirality to one handedness, then flip back. Then they flip again. And then back. Until you introduce the weak field.
In 1956 Chien-Shiung Wu and her team were conducting experiments on cobalt atoms to test how symmetric the weak force was. The strong and electromagnetic forces work the same whichever way a particle is facing but Wu discovered that the weak force breaks symmetry. Radioactive decay particles are only emitted from an atom whose chirality is in the left-hand state.
Although a particle like a quark has weak isospin (the weak field property) all the time, its ability to interact with the weak field is only present in its left-hand chirality. We say that a left-handed particle has a ‘weak hypercharge of +1’ and a right-handed particle has a ‘weak hypercharge of 0’, i.e. it will couple to the weak field or not.
At this point you start to feel like the whole of quantum physics is a loopy bunch of properties assigned at random during the big bang with no rhyme or reason. But if you want the laws of physics to be a little more orderly I am afraid you need to find another universe. I recommend the one where I am Batman. Unless you are already in that one, in which case stay put.
CHEW YOUR BOSONS WITH YOUR MOUTH CLOSED
Let us go back to the Z boson, a particle with no colour or charge. It is essentially a photon with two differences: it has mass and it couples to the weak field when in its left-handed chiral state.
Because the Z boson is alternating between coupling to the weak field and not, its weak hypercharge is going back and forth from +1 to 0 over and over. But look out, who is that coming over the hill towards us? Why, it’s Emmy Noether!
‘Guess what?’ she says. ‘Weak hypercharge is a conserved property too.’ And with that she drifts away, smiling contentedly to herself at the damage she hath wrought.
According to Noether’s theorem, if the Z boson is switching its weak hypercharge on and off, that property must be going to and coming from somewhere. It is a conserved property so it cannot vanish or appear. There must be a field that can absorb and donate weak hypercharge from/to the Z boson. And this is what the Brout–Englert–Higgs field does.
Each time the Z boson becomes left-handed it sucks up weak hypercharge from the field (absorbs a Goldstone boson) and when it flips back to right-handed chirality it returns weak hypercharge to the field (releases a Goldstone boson).
I imagine a Z particle as being like one of those chattering-teeth toys that are constantly opening and closing, accepting and spitting out weak hypercharge as they move.
In a Feynman diagram this means a Z particle is mixing and un-mixing with the Brout–Englert–Higgs field constantly, so when we discovered a Z particle we were discovering the Goldstone boson ‘in its mouth’ as well.
This Feynman diagram shows a Z particle zigzagging its way up the page, hopping chirality from left to right. It starts off in the L state and then flips to the R, releasing a Goldstone boson in the process, which carries away the weak hypercharge (shown as a dashed line). It travels in the R state for a moment but then flips back to the L state, absorbing a Goldstone boson and regaining weak hypercharge. Forever and ever and ever.
WHO CARES?
When two particles interact, their fields couple. But if a particle is changing its identity constantly the coupling can be lost.
It is as if a Z particle changes mood every few seconds, switching from jokey and cheerful to sombre and serious. If you want to tell the Z particle a joke you have to be quick because it will flip to deadpan momentarily and your interaction will be lost. Or if you want to tell the Z particle about the death of your pet horse you need to be equally quick because in a moment it’s going to start cracking dead-horse puns in your face.
As the Z particle flips its personality, it becomes harder to interact with, and a particle which is hard to interact with is not easily influenced. Z particles will barrel through the fields around them like a bullet through fog, but a particle that does not change personality is easier to affect.
In other words, rapid chirality-flipping makes a particle hold its trajectory whereas slow chirality-flipping makes a particle easier to deflect. We have just described the difference between something being heavy and something being light.
A photon can be bounced around because it is massless, but a Z particle is not easy to grip onto and holds its momentum, making it very heavy. Chirality-flipping turns out to be where mass itself comes from so the Brout–Englert–Higgs field allows the Z particle to have mass and the photon to be massless!
It is not just the Z particle either. Something like a muon is flipping its chirality at a faster rate than an electron, meaning it would be even harder to slow down and thus would present as a heavier particle. Which of course, it does.
In fact, the W+, W–, electrons, muons, tauons and all the quarks are flipping their chirality constantly, which means their hypercharge needs to be
conserved through the Brout–Englert–Higgs field. Each particle couples to this field via a mechanism called Yukawa coupling and turns out to be the very reason particles are able to have mass in the first place. Not so useless now, eh?
HOLY MASS-CONSERVING SYMMETRY-BREAKING FIELD, BATMAN!
As we have already seen, there is no way of detecting the Brout–Englert–Higgs field. The Goldstone bosons which allow particles to chiral-flip (gain mass) are mixed in with the particles themselves and we cannot get them on their own.
In fact, the Nobel laureate Leon Lederman wrote a whole book about this frustration. Originally he wanted to call it The God-damn Particle because Goldstone bosons are so god-damn hard to find, but his publishers were not happy with that so he shortened it to The God Particle. Far less controversial.6
So, how do you detect a field whose particles are always mixed in with others? This is where Peter Higgs went further than Brout and Englert, and why people started referring to the whole thing as the Higgs field (probably also because it is easier to say).
Since this field is different to the others, Higgs believed it could do something novel: carry shockwaves. The other fields have zero value at every point in space but the Higgs is non-zero and if you gave it enough of a whack you can send a momentary compression through it, detectable as a momentary quantum in the Higgs field. A Higgs boson.
Technically the Higgs boson does not do anything interesting, it just proves the Higgs field is there, which is why physicists had difficulty explaining it in 2012. The Large Hadron Collider has a circumference of 27 kilometres, came at a price tag of $9 billion and costs a further $1 billion a year to run, drawing 1.3 terawatts of electrical power. If a journalist asked the very fair question, ‘What does the Higgs boson do?’ it would be pretty unwise to answer by saying, ‘Oh, it does nothing.’