Tag Archives: particle physics

What if there’s nothing new?

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In the weeks after the folks at the Large Hadron Collider announced that they had found the Higgs, people I met would ask if I was excited. After all, the Higgs was what particle physicists were searching for, right?

 As usual in this blog, the answer is “Not really.”

We were all pretty sure the Higgs had to exist; we just didn’t know what its mass would be. And while many people had predictions for what properties the Higgs might have (including some string theorists), fundamentally they were interested for other reasons.

Those reasons, for the most part, are supersymmetry. If the Higgs had different properties than we expected, it could be evidence for one or another proposed form of supersymmetry. Supersymmetry is still probably the best explanation for dark matter, and it’s necessary in some form or another for string theory. It also helps with other goals of particle physics, like unifying the fundamental forces and getting rid of fine-tuned parameters.

Fundamentally, though, the Higgs isn’t likely to answer these questions. To get enough useful information we’ll need to discover an actual superpartner particle. And so far…we haven’t.

That’s why we’re not all that excited about the Higgs anymore. And that’s why, increasingly, particle physics is falling into doom and gloom.

Sure, when physicists talk about the situation, they’re quick to claim that they’re just as hopeful as ever. We still may well see supersymmetry in later runs of the LHC, as it still has yet to reach its highest energies. But people are starting, quietly and behind closed doors, to ask: what if we don’t?

What happens if we don’t see any new particles in the LHC?

There are good mathematical reasons to think that some form of supersymmetry holds. Even if we don’t see supersymmetric particles in the LHC, they may still exist. We just won’t know anything new about them.

That’s a problem.

We’ve been spinning our wheels for too long, and it’s becoming more and more obvious. With no new information from experiments, it’s not clear what we can do anymore.

And while, yes, many theorists are studying theories that aren’t true, sometimes without even an inkling of a connection to the real world, we’re all part of the same zeitgeist. We may not be studying reality itself, but at least we’re studying parts of reality, rearranged in novel ways. Without the support of experiment the rest of the field starts to decay. And one by one, those who can are starting to leave.

Despite how it may seem, most of physics doesn’t depend on supersymmetry. If you’re investigating novel materials, or the coolest temperatures ever achieved, or doing other awesome things with lasers, then the LHC’s failure to find supersymmetry will mean absolutely nothing to you. It’s only a rather small area of physics that will progressively fall into self-doubt until the only people left are the insane or the desperate.

But those of us in that area? If there really is nothing new? Yeah, we’re screwed.

What are colliders for, anyway?

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Above is a thoroughly famous photo from ATLAS, one of six different particle detectors that sit around the ring of the Large Hadron Collider (or LHC for short). Forming a 26 kilometer ring spanning a chunk of southern France and Switzerland, the LHC is the biggest experiment of its kind, with the machine alone costing around 4 billion dollars.

But what is “its kind”? And why does it need to be so huge?

Aesthetics, clearly.

Explaining what a particle collider like the LHC does is actually fairly simple, if you’re prepared for some rather extreme mental images: using incredibly strong magnetic fields, the LHC accelerates protons until they’re moving at 99.9999991% of the speed of light, then lets them smash into each other in the middle of sophisticated detectors designed to observe and track everything that comes out of the collision.

That’s all well and awesome, but why do the protons need to be moving so fast? Are they really really hard to crack open, or something?

This gets at a common misunderstanding of particle physics, which I’d like to correct here.

When most people imagine what a particle collider does, they picture it smashing particles together like hollow shells, revealing the smaller particles trapped inside. You may have even heard particle colliders referred to as “atom smashers”, and if you’re used to hearing about scientists “splitting the atom”, this all makes sense: with lots of energy, atoms can be broken apart into protons and neutrons, which is what they are made of. Protons are made of quarks, and quarks were discovered using particle colliders, so the story seems to check out, right?

The thing is, lots of things have been discovered using particle colliders that definitely aren’t part of protons and neutrons. Relatives of the electron like muons and tau particles, new varieties of neutrinos, heavier quarks…pretty much the only particles that are part of protons or neutrons are the three lightest quarks (and that’s leaving aside the fact that what is or is not “part of” a proton is a complicated question in its own right).

So where do the extra particles come from? How do you crash two protons together and get something out that wasn’t in either of them?

You…throw Einstein at them?

E equals m c squared. This equation, famous to the point of cliché, is often misinterpreted. One useful way to think about it is that it describes mass as a type of energy, and clarifies how to convert between units of mass and units of energy. Then E in the equation is merely the contribution to the energy of a particle from its mass, while the full energy also includes kinetic energy, the energy of motion.

Energy is conserved, that is, cannot be created or destroyed. Mass, on the other hand, being merely one type of energy, is not necessarily conserved. The reason why mass seems to be conserved in day to day life is because it takes a huge amount of energy to make any appreciable mass: the c in m c squared is the speed of light, after all. That’s why if you’ve got a radioactive atom it will decay into lighter elements, never heavier ones.

However, this changes with enough kinetic energy. If you get something like a proton accelerated to up near the speed of light, its kinetic energy will be comparable to (or even much higher than) its mass. With that much “spare” energy, energy can transform from one form into another: from kinetic energy into mass!

Of course, it’s not quite that simple. Energy isn’t the only thing that’s conserved: so is charge, and not just electric charge, but other sorts of charge too, like the colors of quarks.  All in all, the sorts of particles that are allowed to be created are governed by the ways particles can interact. So you need not just one high energy particle, but two high energy particles interacting in order to discover new particles.

And that, in essence, is what a particle collider is all about. By sending two particles hurtling towards each other at almost the speed of light you are allowing two high energy particles to interact. The bigger the machine, the faster those particles can go, and thus the more kinetic energy is free to transform into mass. Thus the more powerful you make your particle collider, the more likely you are to see rare, highly massive particles that if left alone in nature would transform unseen into less massive particles in order to release their copious energy. By producing these massive particles inside a particle collider we can make sure they are created inside of sophisticated particle detectors, letting us observe what they turn into with precision and extrapolate what the original particles were. That’s how we found the Higgs, and it’s how we’re trying to find superpartners. It’s one of the only ways we have to answer questions about the fundamental rules that govern the universe.

What’s so hard about Quantum Field Theory anyway?

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As I have mentioned before a theory in theoretical physics can be described as a list of quantum fields and the ways in which they interact. It turns out this is all you need to start drawing Feynman Diagrams.

Feynman Diagrams are tools physicists use to calculate the probability of things happening: radioactive particles decaying, protons colliding, electrons changing course in a magnetic field…basically anything small enough that quantum mechanics is important. Each Feynman Diagram depicts the paths that a group of particles take over time, interacting as they go. It’s important to remember, however, that Feynman Diagrams are not literally what’s going on: rather, they are tools for calculation.

To start making a Feynman Diagram, think about what you need present in order to start whatever process you’re investigating. For the examples given above, this means a radioactive particle, two protons, and an electron and a magnetic field, respectively. For each particle or field that you start out with, draw a line on the left of the diagram.

4gravincoming

If you’re making a Feynman Diagram you’re looking for a probability of some particular outcome. Draw lines corresponding to the particles and fields in that outcome on the left of the diagram. For example, if you were looking at a radioactive decay, you’d want the new particles the original particle decayed into. For an electron moving in a magnetic field, you want the electron’s new path.

4gravoutgoing

Now come the interactions. Each way that the particles and fields can interact is a potential way that lines can come together. For example, electrons are affected by the photons that make up electric and magnetic fields. Specifically, an electron can absorb a photon, changing its path. This gives us an interaction: an electron and a photon go in, and an electron comes out.

4gravinteraction

You’ve got the basic building blocks: particles as lines, and interactions where the lines come together. Now, just link them all up! Something like this:

4gravclassical

Then again, you could also do it like this:

4gravanom

Or this:

4grav2loop

Or this:

4gravcomplicated

You get the idea. To use these diagrams, a physicist assigns a number to each line and each interaction, depending on various traits of the particles involved including their energy and angles of travel. For each diagram, all these numbers are multiplied together. Then, because in quantum mechanics every possible event has to be included, you add up all the numbers from all of the diagrams. Every single one.

Not just the simple diagram on the top, but also the more complicated one below it, and the one below that, and every way you could possibly link up all of the particles going in and coming out, each more and more complicated. An infinite list of diagrams. Only by adding all of those diagrams together can a physicist find the true, complete probability of a quantum event.

Adding an infinite set of increasingly complicated diagrams is tricky. By tricky, I mean nearly absolutely impossible and so insane in principle that mathematicians aren’t even sure that it has any real meaning.

Because of this, everything that physicists calculate is an approximation. This approximation is possible because each interaction multiplies the total for a diagram by a “small” number, which gets smaller the weaker the force involved, from around 1/2 for the strong nuclear force to about 1/12 for electricity and magnetism. If you limit the number of points of interaction, you limit the number of possible diagrams. For our example, limiting things to one point of interaction gives only the first diagram. If you allow up to three points, you get the second diagram, and so on. Each time you add two more interactions, your diagram gets another loop, and the contribution to the total is smaller, so that even just four loops with a force as weak as electricity and magnetism gets you all but a billionth of the total, which is about as accurate as the experiments are anyway.

What this means, though, is that we’re only at the very edge of a vast ocean of knowledge. We know the rules, the laws of physics if you will, but we can only tiptoe loop by loop towards the full formulas, sitting infinitely far away.

That, in essence, is what I work on. I look for patterns in the numbers, tricks in the calculation, ways to yank ourselves up by our bootstraps to higher and higher loops, and maybe, just maybe, for a shortcut up to infinity.

Because just because we know the rules, doesn’t mean we know how the game is played.

That’s Quantum Field Theory.

Supersymmetry, to the Rescue!

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Part Three of a Series on N=4 Super Yang-Mills Theory

This is the third in a series of articles that will explain N=4 super Yang-Mills theory. In this series I take that phrase apart bit by bit, explaining as I go. Because I’m perverse and out to confuse you, I started with the last bit here, and now I’m working my way up.

N=4 Super Yang-Mills Theory

Ah, supersymmetry…trendy, sexy, mysterious…an excuse to put “super” in front of words…it’s a grand subject.

If I’m going to manage to explain supersymmetry at all, then I need to explain spin. Luckily, you don’t need to know much about spin for this to work. While I could start telling you about how particles literally spin around like tops despite having a radius of zero, and how quantum mechanics restricts how fast they spin to a few particular values measured by Planck’s constant…all you really need to know is the following:

Spin is a way to categorize particles.

In particular, there are:
Spin 1: Yang-Mills fields are spin 1, carrying forces with a direction and strength.
Spin ½: This spin covers pretty much all of the particles you encounter in everyday matter: electrons, neutrons, and protons, as well as more exotic stuff like neutrinos. If you want to make large-scale, interesting structures like rocks or lifeforms you pretty much need spin ½ particles.
Spin 0: A spin zero field (also called a scalar) is a number, like a temperature, that can vary from place to place. The Higgs field is an example of a spin zero field, where the number is part of the mass of other particles, and the Higgs boson is a ripple in that field, like a cold snap would be for temperature.

While they aren’t important for this post, you can also have higher numbers for spin: gravity has spin 2, for example.

With this definition in hand, we can start talking about supersymmetry, which is also pretty straightforward if you ignore all of the actual details.

Supersymmetry is a relationship (or symmetry) between particles with spin X, and particles with spin X-½

For example, you could have a relationship between a spin 1 Yang-Mills field and a spin ½ matter particle, or between a spin ½ matter particle and a spin 0 scalar.

“Relationship” is a vague term here, much like it is in romance, and just like in romance you’d do well to clarify precisely what you mean by it. Here, it means something like the following: if you switch a particle for its “superpartner” (the other particle in the relationship) then the physics should remain the same. This has two important consequences: superpartners have the same mass as each-other and superpartners have the same interactions as each-other.

The second consequence means that if a particle has electric charge -1, its superpartner also has electric charge -1. If you’ve got gluons, each with a color and an anti-color, then their superpartners will also have both a color and an anti-color. Astute readers will have remembered that quarks just have a color or an anti-color, and realized the implication: quarks cannot be the superpartners of gluons.

Other, even more well-informed readers will be wondering about the first consequence. Such readers might have heard that the LHC is looking for superpartners, or that superpartners could explain dark matter, and that in either case superpartners have very high mass. How can this be if superpartners have to have the same mass as their partners among the regular particles?

The important point to make here is that our real world is not supersymmetric, even if superpartners are discovered at the LHC, because supersymmetry is broken. In physics, when a symmetry of any sort is broken it’s like a broken mirror: it no longer is the same on each side, but the two sides are still related in a systematic way. Broken supersymmetry means that particles that would be superpartners can have different masses, but they will still have the same interactions.

When people look for supersymmetry at the LHC, they’re looking for new particles with the same interactions as the old particles, but generally much higher mass. When I talk about supersymmetry, though, I’m talking about unbroken supersymmetry: pairs of particles with the same interactions and the same mass. And N=4 super Yang-Mills is full of them.

How full? N=4 full. And that’s next week’s topic.

Yang-Mills: Plays Well With Itself

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Part Two of a Series on N=4 Super Yang-Mills Theory

This is the second in a series of articles that will explain N=4 super Yang-Mills theory. In this series I take that phrase apart bit by bit, explaining as I go. Because I’m perverse and out to confuse you, I started with the last bit here, and now I’m working my way up.

N=4 Super Yang-Mills Theory

So first these physicists expect us to accept a nonsense word like quark, and now they’re calling their theory Yang-Mills? What silly word are they going to foist on us next?

Umm…Yang and Mills are people.

Chen Ning Yang and Robert Mills were two physicists, famous for being very well treated by the Chinese government and for not being the father of nineteenth century Utilitarianism, respectively.

Has a wife 56 years younger than him

Did not design the Panopticon

In the 1950’s, Yang and Mills were faced with a problem: how to describe the strong nuclear force, the force that holds protons and neutrons in the nuclei of atoms together. At the time, the nature of this force was very mysterious. Nuclear experiments were uncovering new insight about the behavior of the strong force, but those experiments showed that the strong force didn’t behave like the well-understood force of electricity and magnetism. In particular, the strong force seemed to treat neutrons and protons in a related way, almost as if they were two sides of the same particle.

In 1954, Yang and Mills proposed a solution to this problem. In order to do so, they had to suggest something novel: a force that interacts with itself. To understand what that means and why that’s special, let’s discuss a bit about forces.

Each fundamental force can be thought of in terms of a field extending across space and time. The direction and strength of this field in each place determines which way the force pushes. When this field ripples, things that we observe as particles are created, the result of waves in the field. Particles of light, or photons, are waves in the field of the fundamental force of electricity and magnetism.

The electric force attracts charges with opposite sign, and repels charges when they have the same sign. Photons, however, have no charge, so they pass right through electric and magnetic fields. This is what I mean when I say that electricity and magnetism is a force that doesn’t interact with itself.

The strong force is different. Yang and Mills didn’t know this at the time, but we know now that the strong force acts on fundamental particles inside protons and neutrons called quarks, and that quarks come in three colors, unimaginatively named red, blue, and green, while their antiparticles are classified as antired, antiblue, or antigreen. Like all other forces, the strong force gives rise to a particle, in this case called a gluon. Unlike photons, gluons are not neutral! While they have no electric charge, they are affected by the strong force. Each gluon has a color and an anti-color: red/anti-green, blue/anti-red, etc. This means that while the strong force binds quarks together, it also binds itself together as well, keeping it from reaching outside of atoms and affecting the everyday world like electricity does.

Quarks and Gluons in a Proton

Yang and Mills’ description wasn’t perfect for the strong force (they had two types of charge rather than three) but it was fairly close to how the weak force worked, as other physicists realized in 1956. It was realized much later (in the 70’s) that a modification of Yang and Mills’ proposal worked for the strong force as well. In recognition of their insight, today the names Yang and Mills are attached to any force that interacts with itself.

A Yang-Mills theory, then, is a theory that contains a fundamental force that can interact with itself. This force generates particles (often called force-carrying bosons) which have something like charge or color with respect to the Yang-Mills force. If you remember the definition of a theory, you’ll see that we have everything we need: we have specified a particle (the force-carrying boson) and the ways in which it can interact (specifically, with itself).

Tune in next week when I explain the rest of the phrase, in a brief primer on the superheroic land of supersymmetry.

Who Am I?

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I call myself a String Theorist, someone who describes the world in terms of subatomic lengths of string that move in ten dimensions (nine of space and one of time),

But in practice I’m more of a Particle Theorist, describing the world not in terms of short lengths of string but rather with particles that each occupy a single point in space,

More specifically, I’m an Amplitudeologist, part of a trendy new tribe including the likes of Zvi Bern, Lance Dixon, Nima Arkani-Hamed, John Joseph Carrasco (jjmc on twitter), and sometimes Sheldon Cooper,

In terms of my career, I’m a Graduate Student, less like a college student and more like an apprentice, learning not primarily through classes but rather through working to advance my advisor’s research,

And what do I work on? Things like this.