Tag Archives: quantum gravity

Flexing the BICEP2 Results

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The physics–verse has been abuzz this week with news of the BICEP2 experiment’s observations of B-mode polarization in the Cosmic Microwave Background.

There are lots of good sources on this, and it’s not really my field, so I’m just going to give a quick summary before talking about a few aspects I find interesting.

BICEP2 is a telescope in Antarctica that observes the Cosmic Microwave Background, light left over from the first time that the universe was clear enough for light to travel. (If you’re interested in a background on what we know about how the universe began, Of Particular Significance has an article here that should be fairly detailed, and I have a take on some more speculative aspects here.) Earlier experiments that observed the Cosmic Microwave Background discovered a surprising amount of uniformity. This led to the proposal of a concept called inflation: the idea that at some point the early universe expanded exponentially, smearing any non-uniformities across the sky and smoothing everything out. Since the rate the universe expands is a number, if that number is to vary it naturally should be a scalar field, which in this case is called the inflaton.

During inflation, distances themselves get stretched out. Think about inflation like enlarging an image. As you’ve probably noticed (maybe even in early posts on this blog), enlarging an image doesn’t always work out well. The resulting image is often pixelated or distorted. Some of the distortion comes from glitches in the program that enlarges the image, while some of it is just what happens when the pixels of the original image get enlarged to the point that you can see them.

Enlarging the Cosmic Microwave Background

Quantum fluctuations in the inflaton field itself are the glitches in the program, enlarging some areas more than others. The pattern they create in the Cosmic Microwave Background is called E-mode polarization, and several other experiments have been able to detect it.

Much weaker are the effect of the “pixels” of the original image. Since the original image is spacetime itself, the pixels are the quantum fluctuations of spacetime: quantum gravity waves. Inflation enlarged them to the point that they were visible on a large-distance scale, fundamental non-uniformity in the world blown up big enough to affect the distribution of light. The effect this had on light is detectably different: it’s called B-mode polarization, and this is the first experiment to detect it on the right scale for it to be caused by gravity waves.

Measuring this polarization, in particular how strong it is, tells us a lot about how inflation occurred. It’s enough to rule out several models, and lend support to several others. If the results are corroborated this will be real, useful evidence, the sort physicists love to get, and folks are happily crunching numbers on it all over the world.

All that said, this site is called four gravitons and a grad student, and I’m betting that some of you want to ask this grad student: is this evidence for gravitons, or for gravity waves?

Sort of.

We already had good indirect evidence for gravity waves: pairs of neutron stars release gravity waves as they orbit each other, which causes them to slow down. Since we’ve observed them slowing down at the right rates, we were already confident gravity waves exist. And if you’ve got gravity waves, gravitons follow as a natural consequence of quantum mechanics.

The data from BICEP2 is also indirect. The gravity waves “observed” by BICEP2 were present in the early universe. It is their effect on the light that would become the Cosmic Microwave Background that is being observed, not the gravity waves directly. We still have yet to directly detect gravity waves, with a gravity telescope like LIGO.

On the other hand, a “gravity telescope” isn’t exactly direct either. In order to detect gravity waves, LIGO and other gravity telescopes attempt to measure their effect on the distances between objects. How do they do that? By looking at interference patterns of light.

In both cases, we’re looking at light, present in the environment of a gravity wave, and examining its properties. Of course, in a gravity telescope the light is from a nearby environment under tight control, while the Cosmic Microwave Background is light from as far away and long ago as anything within the reach of science today. In both cases, though, it’s not nearly as simple as “observing” an effect. “Seeing” anything in high energy physics or astrophysics is always a matter of interpreting data based on science we already know.

Alright, that’s evidence for gravity waves. Does that mean evidence for gravitons?

I’ve seen a few people describe BICEP2’s results as evidence for quantum gravity/quantum gravity effects. I felt a little uncomfortable with that claim, so I asked Matt Strassler what he thought. I think his perspective on this is the right one. Quantum gravity is just what happens when gravity exists in a quantum world. As I’ve said on this site before, quantum gravity is easy. The hard part is making a theory of quantum gravity that has real predictive power, and that’s something these results don’t shed any light on at all.

That said, I’m a bit conflicted. They really are seeing a quantum effect in gravity, and as far as I’m aware this really is the first time such an effect has been observed. Gravity is so weak, and quantum gravity effects so small, that it takes inflation blowing them up across the sky for them to be visible. Now, I don’t think there was anyone out there who thought gravity didn’t have quantum fluctuations (or at least, anyone with a serious scientific case). But seeing into a new regime, even if it doesn’t tell us much…that’s important, isn’t it? (After writing this, I read Matt Strassler’s more recent post, where he has a paragraph professing similar sentiments).

On yet another hand, I’ve heard it asserted in another context that loop quantum gravity researchers don’t know how to get gravitons. I know nothing about the technical details of loop quantum gravity, so I don’t know if that actually has any relevance here…but it does amuse me.

A Wild Infinity Appears! Or, Renormalization

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Back when Numberphile’s silly video about the zeta function came up, I wrote a post explaining the process of regularization, where physicists take an incorrect infinite result and patch it over to get something finite. At the end of that post I mentioned a particular variant of regularization, called renormalization, which was especially important in quantum field theory.

Renormalization has to do with how we do calculations and make predictions in particle physics. If you haven’t read my post “What’s so hard about Quantum Field Theory anyway?” you should read it before trying to tackle this one. The important concepts there are that probabilities in particle physics are calculated using Feynman Diagrams, that those diagrams consist of lines representing particles and points representing the ways they interact, that each line and point in the diagram gives a number that must be plugged in to the calculation, and that to do the full calculation you have to add up all the possible diagrams you can draw.

Let’s say you’re interested in finding out the mass of a particle. How about the Higgs?

You can’t weigh it, or otherwise see how gravity affects it: it’s much too light, and decays into other particles much too fast. Luckily, there is another way. As I mentioned in this post, a particle’s mass and its kinetic energy (energy of motion) both contribute to its total energy, which in turn affects what particles it can turn into if it decays. So if you want to find a particle’s mass, you need the relationship between its motion and its energy.

Suppose we’ve got a Higgs particle moving along. We know it was created out of some collision, and we know what it decays into at the end. With that, we can figure out its mass.

higgstree

There’s a problem here, though: we only know what happens at the beginning and the end of this diagram. We can’t be certain what happens in the middle. That means we need to add in all of the other diagrams, every possible diagram with that beginning and that end.

Just to look at one example, suppose the Higgs particle splits into a quark and an anti-quark (the antimatter version of the quark). If they come back together later into a Higgs, the process would look the same from the outside. Here’s the diagram for it:

higgsloop

When we’re “measuring the Higgs mass”, what we’re actually measuring is the sum of every single diagram that begins with the creation of a Higgs and ends with it decaying.

Surprisingly, that’s not the problem!

The problem comes when you try to calculate the number that comes out of that diagram, when the Higgs splits into a quark-antiquark pair. According to the rules of quantum field theory, those quarks don’t have to obey the normal relationship between total energy, kinetic energy, and mass. They can have any kinetic energy at all, from zero all the way up to infinity. And because it’s quantum field theory, you have to add up all of those possible kinetic energies, all the way up. In this case, the diagram actually gives you infinity.

(Note that not every diagram with unlimited kinetic energy is going to be infinite. The first time theorists calculated infinite diagrams, they were surprised.

For those of you who know calculus, the problem here comes after you integrate over momentum. The two quarks each give a factor of one over the momentum, and then you integrate the result four times (for three dimensions of space plus time), which gives an infinite result. If you had different particles arranged in a different way you might divide by more factors of momentum and get a finite value.)

The modern understanding of infinite results like this is that they arise from our ignorance. The mass of the Higgs isn’t actually infinity, because we can’t just add up every kinetic energy up to infinity. Instead, at some point before we get to infinity “something else” happens.

We don’t know what that “something else” is. It might be supersymmetry, it might be something else altogether. Whatever it is, we don’t know enough about it now to include it in the calculations as anything more than a cutoff, a point beyond which “something” happens. A theory with a cutoff like this, one that is only “effective” below a certain energy, is called an Effective Field Theory.

While we don’t know what happens at higher energies, we still need a way to complete our calculations if we want to use them in the real world. That’s where renormalization comes in.

When we use renormalization, we bring in experimental observations. We know that, no matter what is contributing to the Higgs particle’s mass, what we observe in the real world is finite. “Something” must be canceling the divergence, so we simply assume that “something” does, and that the final result agrees with the experiment!

"Something"

“Something”

In order to do this, we accepted the experimental result for the mass of the Higgs. That means that we’ve lost any ability to predict the mass from our theory. This is a general rule for renormalization: we trade ignorance (of the “something” that happens at high energy) for a loss of predictability.

If we had to do this for every calculation, we couldn’t predict anything at all. Luckily, for many theories (called renormalizable theories) there are theorems proving that you only need to do this a few times to fix the entire theory. You give up the ability to predict the results of a few experiments, but you gain the ability to predict the rest.

Luckily for us, the Standard Model is a renormalizable theory. Unfortunately, some important theories are not. In particular, quantum gravity is non-renormalizable. In order to fix the infinities in quantum gravity, you need to do the renormalization trick an infinite number of times, losing an infinite amount of predictability. Thus, while making a theory of quantum gravity is not difficult in principle, in practice the most obvious way to create the theory results in a “theory” that can never make any predictions.

One of the biggest virtues of string theory (some would say its greatest virtue) is that these infinities never appear. You never need to renormalize string theory in this way, which is what lets it work as a theory of quantum gravity. N=8 supergravity, the gravity cousin of N=4 super Yang-Mills, might also have this handy property, which is why many people are so eager to study it.

What’s A Graviton? Or: How I Learned to Stop Worrying and Love Quantum Gravity

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I’m four gravitons and a grad student. And despite this, I haven’t bothered to explain what a graviton is. It’s time to change that.

Let’s start like we often do, with a quick answer that will take some unpacking:

Gravitons are the force-carrying bosons of gravity.

I mentioned force-carrying bosons briefly here. Basically, a force can either be thought of as a field, or as particles called bosons that carry the effect of that field. Thinking about the force in terms of particles helps, because it allows you to visualize Feynman diagrams. While most forces come from Yang-Mills fields with spin 1, gravity has spin 2.

Now you may well ask, how exactly does this relate to the idea that gravity, unlike other forces, is a result of bending space and time?

First, let’s talk about what it means for space itself to be bent. If space is bent, distances are different than they otherwise would be.

Suppose we’ve got some coordinates: x and y. How do we find a distance? We use the Pythagorean Theorem:

d^2=x^2+y^2

Where d is the full distance. If space is bent, the formula changes:

d^2=g_{x}x^2+g_{y}y^2

Here g_{x} and g_{y} come from gravity. Normally, they would depend on x and y, modifying the formula and thus “bending” space.

Let’s suppose instead of measuring a distance, we want to measure the momentum of some other particle, which we call \phi because physicists are overly enamored of Greek letters. If p_{x,\phi} is its momentum (physicists also really love subscripts), then its total momentum can be calculated using the Pythagorean Theorem as well:

p_\phi^2= p_{x,\phi}^2+ p_{y,\phi}^2

Or with gravity:

p_\phi^2= g_{x}p_{x,\phi}^2+ g_{y} p_{y,\phi}^2

At the moment, this looks just like the distance formula with a bunch of extra stuff in it. Interpreted another way, though, it becomes instructions for the interactions of the graviton. If g_{x} and g_{y} represent the graviton, then this formula says that one graviton can interact with two \phi particles, like so:

graviton

Saying that gravitons can interact with \phi particles ends up meaning the same thing as saying that gravity changes the way we measure the \phi particle’s total momentum. This is one of the more important things to understand about quantum gravity: the idea that when people talk about exotic things like “gravitons”, they’re really talking about the same theory that Einstein proposed in 1916. There’s nothing scary about describing gravity in terms of particles just like the other forces. The scary bit comes later, as a result of the particular way that quantum calculations with gravity end up. But that’s a tale for another day.