Date: July 7th, 2012
Title: Encore: Symmetries in the Universe
Podcaster: Renee Hlozek and David Marsh
Organization: University of Oxford http://www-astro.physics.ox.ac.uk/~Hlozek/
This podcast is originally aired on November 14th, 2010
http://365daysofastronomy.org/2010/11/14/november-14th-symmetries-in-the-universe/
Description: Renée Hlozek interviews David Marsh about symmetries in the universe and how they affect our understanding of the fabric of space, time, of physical laws and the beginning of the universe. Starting from simple discussions about rotating squares, they proceed all the way to theories of quantum gravity that either extend or break symmetries in an attempt to describe the physics of the nascent universe.
Bio: David Marsh is a DPhil student reading Theoretical Physics at the University of Oxford. His main interests are the interface between particle physics and cosmology, and particularly those approaches based in extensions of the standard model and dark matter. He is originally from Liverpool and he enjoys skateboarding and the travel that goes along with it.
Originally from South Africa, Renée Hlozek is a DPhil student in Astrophysics at the University of Oxford. She uses observational data to test our current theories of cosmology and the nature of the universe. Her interests include reading, singing and cooking.
Today’s sponsor: “This episode of 365 days of astronomy was sponsored by iTelescope.net – Expanding your horizons in astronomy today. The premier on-demand telescope network, at dark sky sites in Spain, New Mexico and Siding Spring, Australia.”
Transcript:
RH: Hi, my name is Renée Hlozek.
DM: And my name is David Marsh.
RH: And we are going to talk to you today about symmetries, why they matter and why we are interested in them. Before we start to talk about how symmetries affect our physical model and our physical universe, it helps to just define what we are talking about in terms of symmetries at all, so David, why don’t you tell us – what is a symmetry?
DM: So, a symmetry is something that we can do to a system that leaves it unchanged, and an example is if we take a square, if we draw a square on a piece of paper and we want to keep the square looking the same, we can rotate it through 90 degrees, 180 degrees, 360 degrees, 270 degrees. You can also reflect it along any of its axes, along the middle, down the sides or along the diagonal and it still looks like a square. All these operations are called symmetry operations.
RH: So rotations and reflections are examples of symmetries. In physics we don’t only care about those type of symmetries, we care about translations in both time and space. And why is that important in physics, why do we care that things should be the same?
DM: Well, in physics we always care about continuous symmetries. What we talked about with the square was an example of a discrete symmetry and it’s just of a square, you know the world isn’t made of squares! In physics we care about the time translation, space translation and rotational symmetry of the world as a whole because we have to be able to repeat experiments in science. I have to be able to do an experiment here in Oxford, and you have to be able to repeat it in New York, so we need the world to be the same regardless of where we are. Similarly in time, I need to be able to do an experiment today, and tomorrow, and to get the same result.
RH: So we know that we can test, if you come up with a theory now, and tomorrow and we should get the same answer.
DM: Exactly. Now there are some caveats to this statement. So you can read about this in a book by Richard Feynman called The Character of Physical Law, which explains it nicely. When we say that we change something and the physical system remains the same, what we actually mean is that we change everything that could possibly affect the system.
RH: Isn’t that a cheat?
DM: So I might say that if I do an experiment to boil water here at sea level in Oxford, I’ll find that the water boils at 100 degrees. If I repeated the experiment up mount Everest I would get a different result, and we know that that is because it is at a lower pressure. So actually it is not the translation in space as a whole, and we know that we need to perform experiments at the same time of the year because the earth has moved around the sun. What we really mean is that if you take away all those factors, in the fabric of space itself if doesn’t matter where you are in that space, or when you are in that space – the laws of physics are still the same.
RH: So it is a more fundamental symmetry than just saying: “Oh we understand the difference in height between here and mount Everest” – it’s more fundamental. And one of the ways that symmetries are useful and important in physics is because global symmetries give rise to what we call conservation laws in physics. But in order to understand what a conservation law is, we need to look at an example.
DM: Right, a global symmetry, like you said is a symmetry that applies to everything. For example the global symmetry of translation invariance which means I can perform tests on physical laws here and perform them somewhere else and I will get the same results, gives rise to the conservation of momentum, which we are familiar with. The way conservation of momentum manifests is you can imagine siting with your friend, you are on two wheeley chairs, and you are both sitting stationary, so there is no movement between the two of you. You push away each other, you push away from your friend, you’ll move backwards and your friend will move forwards. So the total momentum if you add up going forwards as “plus” and going backwards as “minus” adds to zero, so we have conserved momentum. And that conservation law that seems disconnected from the symmetry of being able to repeat physical laws in different places, are actually two sides of the same coin. And this was something that we learned about a century ago from the German mathematician Emmy Noether.
RH: So symmetries play an important role in physics, and it is clear that when we come up with new theories, that scientists look for symmetries, they pay attention to symmetries in these theories.
DM: One way we can extend the symmetries, is we extend our symmetries to what is called a local symmetry or a gauge symmetry in physics. So a local symmetry is my freedom to choose a direction, say, to choose a co ordinate system at any point in space. If I want to choose what direction I am going to call forwards. You and I want to agree, and we are separated, but we know that in relativity there is a maximum speed, the speed of light. So if I choose a direction to be forwards and you haven’t had time to receive my message I sent to you via light to tell you which direction I’ve chosen, you can choose whatever direction you want. But at some point we communicate, and decide on a consistent direction to choose. So local symmetries extend the symmetries massively, because now instead of just having a freedom in space to set up a co ordinate system, which is, you know a system of rods and clocks, and things we choose to measure the world by, you have a freedom at every point in space, continuously, so the symmetry group has suddenly grown massively, and it is these symmetries in physics that give us more than just conservation laws, they actually give us the dynamics of the system, they give us the laws of motion. Conservation laws are somehow static, but laws of motion are somehow different. We get laws of motion from gauge symmetries. An example is General relativity as a gauge theory to do with a group called the Lorentz group, because symmetries always come from groups, and the other example is the standard model of particle physics, that we use to describe quantum mechanics, this is also described by a gauge symmetry, by three other very simple groups called SU(3), SU(2) and U(1).
RH: So when you talk about a group, going back to our earlier example, we can represent all the different rotations you can make of a square for example by a group, and there is something of an analogy to the groups you were talking about earlier.
DM: Exactly, it is a very well studied area of mathematics – group theory is very well defined.
RH: Ok, you have explained to us local versus global symmetries, but why don’t you tell us how we can extend, either both extend symmetries or break symmetries to come up with new physical theories.
DM: So, we have got two very good theories that describe the physical world. We’ve got the standard model of particle which is a gauge theory and has one group and we have general relativity which is a gauge theory and has a different group which describes its symmetries. And as you know one of the outstanding questions in physics is how do we put the two together?
We can always extend our understanding of the world by imagining what other symmetries might there be that we don’t know, or what would happen if the symmetries we do know were broken. So, one important example of this is actually in the standard model of particle physics, so you may know that one of the main goals of the LHC at CERN is to search for the Higgs boson. And what the Higgs boson does is it breaks one of the gauge symmetries of the standard model of particle physics. So an example of a broken symmetry is if we take our square and I ask you to choose a corner of that square that is special and to mark it with a dot. You can choose any of the corners, so it is somehow random, or spontaneous. But once you have chosen that corner, the number of symmetry operations you can make on the square that leave it unchanged is now smaller. You can no longer rotate it through 90 degrees for it to remain symmetric, you need to rotate it through a full 360 degrees to bring the marked corner back to where it started.
RH: So you reduce the number of symmetries within the system
DM: You’ve only hidden them, and then the mechanism that chooses the corner, and the mechanism that hides the symmetries is the Higgs mechanism. An example of where we are extending symmetries is in particle physics when we talk about supersymmetry. Supersymmetry takes the idea of special relativity and makes the group bigger, and it is a unique extension of the symmetry group, and then you have a whole bunch more predictive power. You can predict much more things if you have a bigger symmetry group, there are very many more physical laws, more things you can predict.
RH: Ok, you have been talking about symmetries and how they relate to the fabric of space, but we know that we live in an expanding universe. We know that the universe is not the same now as it was at the beginning of time, so how can we square up our idea of symmetries with the expanding universe that we live in?
DM: That is a very interesting question. We can say: “why is energy conserved?” If energy is related to time translation, how do you frame that question in an evolving universe. And really to answer these questions we have to go back and say: “What happened at the beginning?” What set off the laws? Because we know the universe cools down as it expands, and that is just like knowing that the pressure changes as we go up Mount Everest. We can account for that, and that doesn’t mean that our laws are wrong, even though the universe wasn’t the same today as it was in the past. But to really answer these questions we end up asking what happened at the beginning of the universe. What happened when you got very very small, what symmetries were manifest then and ways in which we can answer that question lead us onto some very interesting theories. So we say: “why is the universe so flat, and so homogeneous?” And the way we answer that question is to say that inflation happened, and inflation was something that happened when the universe was very very young, in a very hot dense state, an unknown force, that we call inflation, led now to the flatness of the universe.
So we end up having to go back and back and back to answer these questions, and eventually we reach a point where we have to answer these questions with quantum gravity. We have to answer that question in: “what possible universes could there be, given the symmetries our universe must have?” These questions can be answered in many different contexts.
DM: So these ideas of breaking and extending symmetries bring together two different parts of physics – they bring together cosmology and particle physics, because when we start to ask the question: “what happened at the big bang?, Why is there a direction to time?, where did time and space begin?” we also need to ask the question: “what happens to gravity on very small scales?” So we get led to the question of quantum gravity. And the question of the origin of the universe and the question of quantum gravity both become tied up into the question of what symmetries did this primeval atom have and when we get onto quantum gravity there are two ways: extend your symmetries or break your symmetries, to answer the question. In the ‘breaking the symmetries’ camp, there is a theory called Hořava-Lifshitz gravity that says what if the theory of quantum gravity broke the symmetries of general relativity in such a way that we could compute with it, that we could make predictions, and that is an active area of research.
Then in the idea of extending symmetry you may be aware of String theory. String theory says that I am no longer going to consider the symmetries of a point particle, I’m going to consider the symmetries of a string, and it turns out that this is incredibly rich and we get led into things called dualities. So there are symmetries that relate different string theories that lead us to believe that maybe they are part of a theory called M-theory. In string theory the whole theory is defined by symmetries – so when you get rid of your extra 6 dimensions (string theory lives in 10 dimensions), the symmetries of the six extra dimensions determine all the physics in our dimensions and there is a huge amount of symmetry. This leads us to think about things like multiverses, where all of these different shapes of these extra dimensions are realised and then this, in turn, gives a way that we can answer questions about why is our universe homogeneous, why is our universe isotropic, why is it the shape that it is – because we can conceive of it as part of a landscape, so we can extend our symmetries and then ask why do we live where we are, what is special about our place in the landscape?
RH: So we live in one particular universe, but we know that actually there would be a whole landscape of different possible realisations of the universe.
DM: And all those different realisations are related to different symmetries, and that can help us to answer some of the fundamental questions about our particular universe. Or even if the landscape turns out not to be real, that logical framework that we have used to ask how symmetric could physical laws possibly be can lead us to ask questions about the universe, its evolution and ultimately its fate.
And these symmetries, they are more fundamental symmetries than just moving from: “am I going to boil water here or am I going to boil water up mount Everest?” – they are to do with the fabric of physical law itself.
RH: So we have gone from looking at rotations of a square to understanding the fabric of space and time and our physical law
DM: All by looking at symmetries.
RH: I hope you have enjoyed our journey into symmetries and what they mean for you!
DM: Thanks
RH: Cheers
End of podcast:
365 Days of Astronomy
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