Now physicists were getting really nervous. Two symmetries that they believed were fundamental parts of our universe were broken. So the next big question on everyone's mind was, is CPT symmetry also going to fail and take down the standard model with it?
We've got three symmetries that I've mentioned so far. Three symmetries , three very good approximations to almost perfect symmetries in nature. Take matter, turn it into antimatter, look at it in a mirror, and reverse it in time.
degrees, half a turn, so that's three symmetries or I could move all the way around to two thirds of a turn, a fifth symmetry takes me five sixth of a turn around so there are five different symmetries that I can do to this starfish. Now actually there's a sixth symmetry that Galois identified here. This sixth symmetry is just leaving something where it is so that… it's strange. It means everything has one symmetry which is just picking it up and putting it down again. Now, it seems a bit silly but actually this is as powerful as the concept
So there is a kind of translation symmetry . And unlike the symmetries of the triangle, this is a continuous symmetry , meaning you can shift it by any amount you like. Over the next 12 years, Noether became a leading expert on symmetry .
Translational symmetry gives you conservation of momentum, rotational symmetry gives you conservation of angular momentum, and time translation symmetry gives you conservation of energy. But these are all symmetries of a static empty universe. The universe we live in is very different.
Why is it that we don't see, we don't hear about these people? This is called hidden symmetries in daily life.
Was it the fun? Was it the symmetries ? The wildness? The dramas?
This one really looks good. So those symmetries look really good.
horse could even carry one horse of his own size." I choose to believe that this experiment was never carried out. So some things are symmetries , some things aren't. But what about-- we have a human intuition about what should be a symmetry of nature.
We've got this combination. We've got three symmetries that I've mentioned so far. Three symmetries , three very good approximations to almost perfect symmetries in nature.
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy And these symmetries basically describe how the quantum mechanical waves of a system can be changed without any of
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy All built on symmetries .
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy Even if there those symmetries themselves don't look elegant, putting a little plot of all the particles in the standard model does start to look symmetric.
that's the same for symmetries as well. You are not allowed any symmetry in the same row here, in the main body of the table, or in the same column. And Galois developed some rules for the way symmetries must interact which enabled him to prove actually that if an object has six symmetries , then either its symmetries behave in the same way of the triangle or the six pointed starfish. So, it enabled him to abstract the idea of symmetry underlying something and this is perfect now when we go to the Alhambra. Because if we
It's trying to find, well, where are all of these points where you fix things, rotate them, or reflect them, and if you go now. So, you've got those points there but you see the same symmetries happening on this wall which looks very different. Rotate by a sixth of a turn around the point in the middle of the six pointed star and everything matches up. The third of a turn is actually where all of these 'z' pieces meet so again rotate by a third of a turn and eventually, ping, third of a turn and everything matches
You can tell whether these collisions happen forwards or backwards in time. Now the combination of all of these symmetries combined is called CPT symmetry . And CPT symmetry , it turns out, is kind of a big deal.
Together, these six actions capture all the symmetries of the equilateral triangle. - But you can also have more abstract symmetries , for example, with a mathematical function. If I shift this function up or down by some constant amount, call it a, then all of its y values will change.
So that is a kind of symmetry , exactly what Noether had spent her career studying. So she started thinking about the symmetries of the universe, beginning with the simplest possible case, an empty static universe. Imagine you are an astronaut in this universe.
- This doesn't violate any laws of physics because energy and momentum aren't conserved if there is no time or spatial symmetry . - So once you know that symmetries give you conservation laws, and so once those symmetries are gone, you don't have to worry about those conservation laws anymore, then you can start dropping these concepts of trying to force something that you want to say is fundamental into the theory,
Now if you shift the whole universe, rotate it, or let it evolve in time, things don't stay exactly the same. So you no longer have these global symmetries , but Noether realized there are still other symmetries left. See, no matter how you're moving, the laws of physics always look the same.
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy What do all of these symmetries that we've talked about, what ultimately do they mean?
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy And what Noether said is all these symmetries -- symmetries give rise to conserved quantities.
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy So if there are such beautiful symmetries in the universe-- and there are-- the question is, why isn't
It's a little bit like the rules for Sudoku. I don't know whether any of you do Sudoku's here but remember you are not allowed the same number in any column or any row. Well, that's the same for symmetries as well. You are not allowed any symmetry in the same row here, in the main body of the table, or in the same column. And Galois developed some rules for the way symmetries must interact which enabled him to prove actually that if an object has six symmetries , then either its symmetries behave in the same way of the
look at the tiles on the walls in the Alhambra, how can we say when two of those walls have the same underlying symmetry ? Now, they might look geometrically very different but Galois's language enables to say actually the symmetries of these two walls are the same symmetries , although they look very different. So, we've got this beautiful walls with these little twisted triangles and here I've got this six pointed star with this kind of 'z'. So let's look at the symmetries of these two walls. Remember, symmetry are the magic trick moves
elliptical orbits that are tilted at large angles with respect to each other. So the fact that the actual solar system has these symmetries that with circular orbits and aligned orbits seems to be telling us something about planet formation about the initial conditions
I think it's giving his predecessors a little bit too much credit, perhaps. So it is interesting to note that when we talk about symmetries in the universe, what we really mean is, what are some ways that you could adjust, say, the entire universe-- turning the universe, for example, or moving forward or backwards in time, or moving throughout space--
Won't ever appear. That makes the equations a lot simpler than they would be otherwise. Those things turn out not to matter in our symmetries of our universe. Other things seem like they might matter or might not matter.
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy But it says that every one of these symmetries that we've been talking about produces a conserved quantity.
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy And the answer seems to be that for all of these symmetries in the universe, there's also sort of a corresponding effect that makes the universe
left right reflectional symmetry but it does have symmetry . But what does it mean to have symmetry ? Also, how can I say, articulate, that two of these walls have the same symmetries ? How can I say if the Moorish artists discovered all the symmetries that are possible on the walls in the Alhambra? Now, actually, to be able to articulate these ideas, the Moors didn't have this sophisticated language to be able to talk about these questions. In fact, it took a mathematician called Évariste Galois, who is a French revolutionary who
this is actually the tiles that we met when we entered the Alhambra. This is actually the ceiling in that first room in the Alhambra and this is the tiles on the floor. Now again, these pictures look very different but the underlying symmetries , thanks to Galois's language, we can say are actually the same. And this group of symmetries we call 4,4,2. Nothing to do with football but because of the fact that there's a place where I can rotate by a quarter of a turn, a different place here, and here again somewhere we have
And part of the reason this has been so difficult is because our laws of physics are full of symmetry . In the mid 1950s, there were three symmetries all particles were believed to obey. Charge, parity, and time reversal symmetry .
So something else I could do is I could rotate this triangle by 120 degrees or by 240 degrees or by 360 degrees. Together, these six actions capture all the symmetries of the equilateral triangle. - But you can also have more abstract symmetries , for example, with a mathematical function.
Euler and Lagrange found that the principle of least action is obeyed, so long as this set of differential equations is satisfied. So Noether used action to see how physics was affected by different symmetries . - So suppose we do an experiment where the result is the same now as some tiny time interval epsilon later, then how does this affect the action?
But what Galois realizes is not just the individual moves, but how they interact with each other which is key. So, I'm going to push you a little bit mathematically now so brace yourselves, but I want to explain this language that Galois developed to explore the symmetries of these two objects. So, two simple objects. I've got a six pointed star with a little twist on it and a triangle. So the magic trick moves, the symmetries , are the things that I can do to these objects which leaves them exactly where they were so first of all, I could rotate
or a third of a turn anti-clockwise and I've got, now I can reflect this as you said. I can reflect in the line through 'x' or I can reflect in the line through 'y' or I can reflect in the line through 'z.' So, five symmetries again, plus the extra symmetry where I'm just picking it up and put it back down again. So, both of these objects have six symmetries . So, should we say they have the same symmetries because they have the same amount of symmetry ?
in the line through 'z.' So, five symmetries again, plus the extra symmetry where I'm just picking it up and put it back down again. So, both of these objects have six symmetries . So, should we say they have the same symmetries because they have the same amount of symmetry ? Well, now you feel there's some difference between these objects, but how can we articulate why the symmetries of these things really are different?
The first clue that such asymmetries might exist came in the mid 1950s. Up until then, every interaction that had been studied conserved the individual symmetries of C, P and T. And so conserved CPT as a whole.
We can transform the points of space around as much as we like. And since these transformations aren't global but local, these are called local symmetries . In a second theorem, Noether proved that for these local symmetries , you no longer get proper conservation laws like we're used to in classical physics.
And since these transformations aren't global but local, these are called local symmetries . In a second theorem, Noether proved that for these local symmetries , you no longer get proper conservation laws like we're used to in classical physics. Instead, you get something that only works locally: a continuity equation.
since the higher education of women began." - The reason that Noether's theorem is so important is that everybody just changed their state of mind. All of a sudden, the physicists were thinking about physics in terms of these symmetries . - Physicists started applying these ideas to the quantum world too, realizing that charged particles like electrons also have symmetries .
It would have the wrong orientation. So one of the things that's going to be very interesting for us about sort of understanding symmetries in the universe is to recognize, symmetries are very beautiful. They're going to give us guidance.
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy There are, however, other symmetries that we can look at.
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy Our modern understanding of physics is all of those fundamental forces that we talk about are fundamentally built on symmetries .
So in this case, we might imagine Maxwell's demon takes the high-energy particles and tries to sort them to the left side of the partition and the low-energy So one of the things that modern-day particle physicists do is they come up with models based on symmetries .
But I hadn't really figured out why I liked this image. I hung it. It wasn't quite as surreal as some of the impossible symmetries or floating stones that I'm known for. It helped a lot-- well, it felt good-- when my father came in and patted me on the back one morning.
it by a sixth of a turn and it looks like it did before. Okay, I can rotate it by a third of a turn and it still looks like it did before I moved it, or I can rotate 180 degrees, half a turn, so that's three symmetries or I could move all the way around to two thirds of a turn, a fifth symmetry takes me five sixth of a turn around so there are five different symmetries that I can do to this starfish. Now actually there's a sixth symmetry that Galois identified here. This sixth symmetry is just leaving something where it is so that…
followed by rotation 'c', which is a third of a turn, and the combined effect of those is if I'd just done half a turn in one go. So, this table shows me how the symmetries interact with each other and this was the inspirational move of Galois is that this is key to understanding the symmetries of this object. If I do this in a different order, doesn't matter really, do the third of a turn followed by a sixth of a turn, it still ends up in the same place. So, there's some symmetry in the way the symmetries interact, but that's
doesn't matter really, do the third of a turn followed by a sixth of a turn, it still ends up in the same place. So, there's some symmetry in the way the symmetries interact, but that's not true for the triangle. Let's do two symmetries of the triangle. We're going to rotate by a third of a turn anti-clockwise then reflect in 'x'. The combined effect is if I've just reflected in 'z' but now do these in a different order; do the reflection first and then rotate by a third of a turn and it ends up in a different place. It's as if I'd