is charge truly fundamental?

If you've ever been in a physics class, you probably know that like charges repel and opposite charges attract. But why? It's almost as if this thing known as 'charge' is a fundamental property of objects (in the same way mass is) - it sort of just exists. All of electromagnetism is powered by a single property - electric charge. Maxwell's equations, which govern electromagnetism, say nothing about what charge really is. 

The story begins with one of the fathers of quantum mechanics - Werner Heisenberg. At some point, Heisenberg turned his attention to the newly discovered neutron, suspicious to how similar it was to the proton, with the only difference between the two being their electric charge. Heisenberg wondered if the two particles were just in fact different states of a single particle which he dubbed the 'nucleon'. If protons and neutrons are just two states of the same particle, then maybe they're just differentiated by a quantum property analogous to spin. Heisenberg proposed this new property to be called 'isospin', with protons having an isospin of +1/2 and -1/2 for neutrons. For this new 'isospin' to truly do its job, it needed to explain the key difference between protons and neutrons: charge. Charge would have to depend on isospin, meaning that it is in fact not a fundamental property after all. 

Fast forward a few decades -- our particle colliders advance, leading to discoveries of lots of weird new particles. Some of these newly discovered particles have very similar masses, but totally different charges (like with our proton and neutron). Maybe the differences could be explained by groups of particles with a range of isospins? But what exactly is the link between isospin and electric charge? This mystery was solved by Kazuhiko Nishijima and Murray Gell-Mann; they noticed that there seemed to be a family of particles which were created only in pairs, similar to how the electron and positron do in order to conserve charge. But these newly discovered particles weren't doing this to conserve charge, nor isospin, nor any other known property at the time, indicating that an unknown quantity must be being conserved instead. Weird. This new quantity - given the name 'hypercharge' - seemed to obey the mathematics of electric charge rather than that of quantum spin. They went on to realise that electric charge, hypercharge, and isospin were intimately connected across all particles. The 3 quantities seemed to be linked via the relationship Q = I + Y/2 (Q is electric charge, I is isospin, Y is hypercharge).

The conservation of fundamental properties outline the interactions which are possible and those which are not. Murray Gell-Mann noticed, by plotting particles by their isospin and hypercharge, that peculiar geometric patterns arose. For example, groups of 8 particles formed hexagons and another group of 10 particles formed a triangle (with the bottom corner missing). He hypothesised that this was an undiscovered particle, which he called the 'omega baryon', with the correct isospin and hypercharge to fill that particular vertex of the triangle. The omega was eventually discovered by experimentalists, resulting in the main man winning the Nobel Prize. Gell-Mann went further to realise that these patterns were actually representations of a mathematical symmetry - SU(3). He proposed that the symmetries would make sense if nucleons themselves were not elementary particles, but instead were made up of smaller components known as 'quarks'. It was shown that isospin and hypercharge were just emergent properties that reflected the different types of quarks which make up these particles!

Starting with experiments at the Stanford Linear Accelerator Center in 1968, the reality of quarks quickly became conclusive. So after all this hard thinking, it turns out that isospin and hypercharge were as much mathematical abstractions as was electric charge. There must be something deeper which governs the differences between particle groups and electric charge itself. The answer lies with one of the forces of nature - the weak force. The weak force is for sure the most peculiar quantum force. For us to make sense of electric charge, we must think about the two strangest properties of the weak force. Firstly, the weak force can transform particles into other particles - something no other force can do. Secondly, it only works on left-handed particles. 

A consequence of quantum spin is this thing called 'chirality', which is essentially the projection of spin in the direction that a particle is moving. Particles can have right-haded chirality if their spin is clockwise relative to their momentum vector, or left-handed chirality for counter-clockwise. Only particles with left-handed chirality feel the weak force. For example, the electron has both a right-handed and left-handed component. Only the left component can emit one of the weak force carrier particles - the W boson - and in doing so transform into a neutrino. Remember when Heisenberg hypothesised that the difference between protons and neutrons were their isospin? Well we can play the same trick with the electron and the neutrino, and this new conserved quantity turns out to behave eerily similar to isospin. Let's call it 'weak isospin' (remember that only left-handed particles can have it); weak isospin is effectively the charge of the weak force carried by these W bosons. To fully explain weak interactions, we need a second charge carried by the Z boson. It acts more like electric charge, so we'll call it 'weak hypercharge'. Astonishingly, weak isospin and weak hypercharge are mixed in exactly the same way as Gell-Mann's versions of these quantities (i.e., Q = I' + Y'/2, where I' is weak isospin and Y' is weak hypercharge). We know that these weak versions of isospin and hypercharge must be fundamental because they're properties of elementary particles which cannot be broken into smaller pieces. It turns out that our old strong force versions of isospin and hypercharge emerge from the difference in quark content, but are ultimately driven by these more 'real' weak force quantities. In essence, the charges that drive electromagnetism are governed by the charges which drive the weak force.

What does this all mean? Is electric charge not really fundamental? Well, we need to question what being 'fundamental' actually means. We've learned that the electromagnetic and weak forces are deeply connected - or should I say - were deeply connected. These two forces were once united in what we call the electroweak force, whose charges were the same weak isospin and hypercharge we just discussed. Something happened to the electroweak force in the very early universe, meaning that these charges could only take on specific combinations of values, values which we now observe as electric charge. That event - the breaking of electroweak symmetry - created the weak and electromagnetic forces as we know them today. So electric charge is a sort of shadow of the ancient fields from the birth of the universe. Why the seperation actually happened is a topic for another day. In the process, the Higgs field was also created, granting mass to elementary particles (yet another supposedly 'fundamental' property). :)

published: 19/11/22 by kaan evcimen