The “traditional” beauty of theoretical physics is its equations. If we want to describe something, or the way something behaves, we can write down a relation between some properties we think that thing will obey.

The simplicity and symmetry of these equations – to someone who understands them – is amazingly beautiful.

Given the mass of a ball, the height, angle, and strength with which it is thrown, physics will tell you the path the ball with take through the air, how long it will be in the air for, and how far away and how hard it will hit the ground.

Physics can fully describe this system with just a few simple properties.

But what if you want to describe the ball itself? We could say it’s red, but what does that really mean? To describe colour you need to consider the light being reflected from the ball.

You could say the ball’s made of plastic, but you need to describe the molecules, then the atoms they’re made of, then the subatomic particles they’re made of, and so on …

What theoretical physics strives towards is a description of everything, all in one place. The ultimate goal would be a “Theory of Everything” or a “Grand Unified Theory” but, as far as we can tell so far, gravity doesn’t behave in a way that would fit such a theory.

For everything in the entire universe besides gravity, we have the “Standard Model of Particle Physics”, which describes every particle we know about and how these particles interact together via the remaining forces:

- Electromagnetism (responsible for light, electricity, magnets).
- The strong nuclear force (responsible for holding everything together).
- The weak nuclear force (responsible for radioactivity).

As far as the basic building blocks of matter go, we have two categories in the Standard Model: fermions and bosons.

All of the matter that makes up your body consists of just three fermions: two quarks and an electron.

There are six types of quarks in the Standard Model – given the names “up”, “down”, “strange”, “charm”, “bottom” and “top”, in order of increasing mass – but of these only the two lightest (up and down) are used to make protons and neutrons.

Put some protons and neutrons together with some electrons and you have atoms. Put some atoms together and you have matter.

Bosons help other particles “communicate”, and this communication is what we call a force.

When two electrons repel each other, they exchange photons – the particles responsible for light – and we call this exchange the electromagnetic force.

Because photons are massless, they can travel a long way from the particle that emitted them.

There are similar bosons that particles use to communicate the other forces – the exchange of heavy W and Z bosons is what we call the weak force (given that the W and Z are “heavy”, the range of the weak force is small), and the exchange of massless gluons is what we call the strong force.

Confused yet? It won’t help that the W bosons have an electric charge, so they *also* communicate with photons. Stranger still, the gluons have another charge called “colour” which means they can communicate with themselves.

So now we have all we need to construct matter: some fermions and some bosons. We just need to write an equation that describes everything written above in a simple, symmetrical way.

And here it is:

Makes sense, right?

Just as we can calculate the path of a ball through the air with a few pieces of information, the parameters in the above equation ensure the dynamics of theoretical particles match what we see in the real world.

To theoretical physicists, the above equation is beautiful, elegant, compact, and exhibits lots of the symmetries we expect to see in nature. So what’s wrong with it?

It’s not that it has a lot of terms – it needs to describe how each of the particles interacts with all the others. It’s that it needs more information.

There’s a mathematician’s quote about having too many parameters in a model:

“With four parameters I can fit an elephant, and with five I can make him wiggle his trunk”.

The Standard Model has 19 parameters which we fit to experiments: most of the fermion masses, and factors that determine the way certain groups interact.

Having so many parameters takes away some of the beauty of the Standard Model – a full theory shouldn’t need additional information.

One set of parameters that the Standard Model doesn’t require is the mass of neutrinos (fermions) as it predicts they are massless.

Experimentally, this is not true and, moreover, the fact they can change type of neutrino (which they have been shown to do) isn’t allowed if they are massless.

Neutrinos have other properties, too, and one of these is the way that they behave, which we call “left-handed” and “right-handed”.

Experimentally, the W bosons only interact with left-handed neutrinos, while the Standard Model predicts this interaction should be symmetric – in other words, the poor right-handed neutrinos shouldn’t miss out.

But the most controversial issue is that, although every other particle in the Standard Model has been detected, the elusive Higgs boson has not (or, if is has, has not been identified correctly).

In the Standard Model, the Higgs boson is responsible for explaining the masses of the heavy fermions and bosons.

Experiments at the Large Hadron Collider are searching for the Higgs, but if we don’t see it where we expect it to be, it may be the final nail in the coffin of the Standard Model.

There are also some features that physicists consider to be missing from the Standard Model (apart from gravity). The biggest of these is the lack of room for dark matter particles.

Such shortcomings lead some people to call the Standard Model a “Theory of Almost Everything”.

So What’s the Next Option?

“Beyond the Standard Model” physics covers options such as supersymmetry – in which there are copies of all the particles but where fermions and bosons are swapped – and string theory – an attempt to reconcile quantum mechanics and general relativity.

These go some way towards rectifying some issues that the Standard Model faces, but, at present, tend to introduce further inconsistencies.

For now, it’s probably best to trust that nature has a remarkable way of keeping track of what’s going on at the tiniest scales, and be happy that it’s easy to understand how bigger objects – such as red balls – behave.

Author: Jonathan Carroll, Post Doctoral Research Associate, Centre for the Subatomic Structure of Matter

This article was originally published on The Conversation.