How does symmetry shape nature's laws?

All of our modern theories in physics are based on mathematical ideas of symmetry, including Einstein's famous ideas of relativity and the Standard Model! But how and why is this the case? James Farr dragged Graihagh Jackson out of the office with a tennis ball to explain...

James - Einstein's theories completely revolutionised the way we think about gravity and they were all sparked off by a simple fact which Einstein noticed about the speed of light which we're going to think about now.

Graihagh - Okay, so what's this got to do with a tennis ball though?

James - Well, the normal way we think about speeds is they add up in a very simple way. To demonstrate this, if you can now go and stand about 10 meters or so away from me Graihagh...

Graihagh - Okay, about 10 meters.

James - If you can now throw the ball to me, not too hard of course.

Graihagh - Okay, I'm going to do an underarm throw. Ready?

James - Here we go. That took about a second to get to me. So, we can say it was traveling 10 meters per second. We both agree on that, right?

Graihagh - I'd say so, yeah.

James - So, if we do this again, this time, you're going to be running towards me as you throw the ball.

Graihagh - Okay, I'll give you my best cricketers throw. Okay, ready?

James - Go for it. That was much faster that time.

Graihagh - I'm sorry, James.

James - That's quite alright.

So, the ball was much faster because you were running as you threw the ball.

So, you can add the speed you are running at maybe 5 meters a second onto the speed you threw the ball at because you threw it just as hard as you did before.

So, we had 5 plus 10 to get about 15 meters a second. That's the overall speed of the ball relative to me. How did the speed of ball look relative to you?

Graihagh - Well, it didn't feel or look any different to me.

James - You threw the ball exactly as hard as you did before. So, it should be the same speed.

So here, we've got a demonstration of two different observers - me and you, Graihagh - observing the same ball but thinking that it's going at two different speeds.

Graihagh - Okay, so the movement of that ball is relative to us, you could say?

James - Exactly and that's what's so different about light. If you were firing a beam of light rather than throwing a ball, the little photons which make up the beam of light would all seem to be moving at exactly the same speed, both from my perspective and from yours even though you're moving relative to me.

Graihagh - Good to know, just in case I go throwing balls of light any time soon.

James - Balls of light aside. This idea that light must always appear to travel at the same speed no matter how fast and what direction we're traveling was Einstein's stroke of genius.

He realised this by looking at the symmetries in the equations that describe light as Daniel Bowman from the University of Cambridge explained...

Daniel - One way of noticing that there's something symmetric going on is to notice that there's something that's not changing.

If we look at the symmetric objects from different point of view they look the same, that's how we identify that an object symmetrical rather than arbitrary. And so here, there was also a hint that there was something that didn't change.

Two different observers moving relative to each other would agree on the speed of light. And so, underlying this, there's a hint that there's a symmetry that enforces this. And so, that symmetry is what's called Lorentz symmetry or Lorentz invariance.

James - These so-called Lorentz symmetries aren't actually too complicated. If you can imagine trying to measure the distance between two points on a piece of paper then no matter how much you rotate your piece of paper, that measurement will always stay the same, right?

It's sort of the same for light, in that the speed of light must always be the same for every observer which means that there must be some kind of underlying symmetry. But how do we know that this is true?

Daniel - To a theorist, you know it's true because it's too beautiful not to be in some sense. I think even Einstein once said, if an experiment came out that would disagree with his theory of relativity, both special and general, it's too bad for the experiment. There must be something wrong with the experiment because the theory itself is too beautiful to fail.

But of course, at a practical level, we do have now plenty of experiments that just show us that this is really what's happening.

James - How has this had an effect on physics?

Daniel - One way, especially for theorists, I think, it has demonstrated the power of pure thought in coming up with physical theories. So Einstein famously introduced these thought experiments, he asked himself, "What happens if I rush off the light ray or what happens to time when a clock is traveling on a fast moving train?" Things like that.

So, it's a very different way of doing physics, less driven by experimental data, but by just purity of thought. And symmetry is trying to see how the power of symmetry is actually restricted to types of physical laws which can be written down.

And so, this attitude of letting yourself be guided by symmetry has become vital. I think Einstein was one of the first. Of course, at a practical level, it has just permeated all of modern physics. A world without relativity to me is unimaginable.

James - We've heard about how symmetry is used in our theories of relativity which we use to describe gravity.

This is useful if we want to think about very big things like planets moving around the sun. But what if we want to zoom right in and look at much smaller things, maybe atoms?

I'm going to head across the road from the Institute of Astronomy where I'll get to the Cavendish Laboratories. Historically, these labs have played a very important role in the build- up to what we now call a standard model...

Andy - I'm Professor Andy Parker. I'm the head of the Cavendish Laboratory. So, the standard model is our current understanding of all the particles and forces between them that make up atoms or normal matter and indeed, everything in the universe.

So, we have quarks which are the constituents inside protons and neutrons, and therefore, make up the atomic nucleus and the bulk of the weight of the atom.

And then outside of that are electrons which circle the nucleus like little planets, and a bunch of other particles similar to electrons, and those two types of particles make up the matter in the standard model, and the forces between them make up the interactions.

James - However, the journey to this theory was by no means an easy ride.

Andy - When we first turned on large accelerators, we started to make new particles by colliding things and those new particles were coming out sometimes once a week, almost discovering what seem to be a new fundamental particle. And people were talking about a zoo of particles.

James - The trouble was, it wasn't what you might expect from a zoo. There was no plaque telling you which species was which and everything was mixed in together - lions with toucans, and kangaroos, all in one enclosure.

Scientists needed a way to categorise these new particles, a bit like a zoo has a reptile house and an aviary.

The standard model has helped us to do this using symmetry and more recently, the Higgs Boson - the particle which explains why things have mass.

Andy - In fact, the Large Hadron Collider which discovered the Higgs has just restarted and we're collecting data right now. With the LHC data, we should be able to perhaps discover something really exciting.