Tag Archives: string theory

High Energy? What does that mean?

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I am a high energy physicist who uses the high energy and low energy limits of a theory that, while valid up to high energies, is also a low-energy description of what at high energies ends up being string theory (string theorists, of course, being high energy physicists as well).

If all of that makes no sense to you, congratulations, you’ve stumbled upon one of the worst-kept secrets of theoretical physics: we really could use a thesaurus.

“High energy” means different things in different parts of physics. In general, “high” versus “low” energy classifies what sort of physics you look at. “High” energy physics corresponds to the very small, while “low” energies encompass larger structures. Many people explain this via quantum mechanics: the uncertainty principle says that the more certain you are of a particle’s position, the less certain you can be of how fast it is going, which would imply that a particle that is highly restricted in location might have very high energy. You can also understand it without quantum mechanics, though: if two things are held close together, it generally has to be by a powerful force, so the bond between them will contain more energy. Another perspective is in terms of light. Physicists will occasionally use “IR”, or infrared, to mean “low energy” and “UV”, or ultraviolet, to mean “high energy”. Infrared light has long wavelengths and low energy photons, while ultraviolet light has short wavelengths and high energy photons, so the analogy is apt. However, the analogy only goes so far, since “UV physics” is often at energies much greater than those of UV light (and the same sort of situation applies for IR).

So what does “low energy” or “high energy” mean? Well…

The IR limit: Lowest of the “low energy” points, this refers to the limit of infinitely low energy. While you might compare it to “absolute zero”, really it just refers to energy that’s so low that compared to the other energies you’re calculating with it might as well be zero. This is the “low energy limit” I mentioned in the opening sentence.

Low energy physics: Not “high energy physics”. Low energy physics covers everything from absolute zero up to atoms. Once you get up to high enough energy to break up the nucleus of an atom, you enter…

High energy physics: Also known as “particle physics”, high energy physics refers to the study of the subatomic realm, which also includes objects which aren’t technically particles like strings and “branes”. If you exclude nuclear physics itself, high energy physics generally refers to energies of a mega-electron-volt and up. For comparison, the electrons in atoms are bound by energies of around an electron-volt, which is the characteristic energy of chemistry, so high energy physics is at least a million times more energetic. That said, high energy physicists are often interested in low energy consequences of their theories, including all the way down to the IR limit. Interestingly, by this point we’ve already passed both infrared light (from a thousandth of an electron-volt to a single electron volt) and ultraviolet light (several electron-volts to a hundred or so). Compared to UV light, mega-electron volt scale physics is quite high energy.

The TeV scale: If you’re operating a collider though, mega-electron-volts (or MeV) are low-energy physics. Often, calculations for colliders will assume that quarks, whose masses are around the MeV scale, actually have no mass at all! Instead, high energy for particle colliders means giga (billion) or tera (trillion) electron volt processes. The LHC, for example, operates at around 7 TeV now, with 14 TeV planned. This is the range of scales where many had hoped to see supersymmetry, but as time has gone on results have pushed speculation up to higher and higher energies. Of course, these are all still low energy from the perspective of…

The string scale: Strings are flexible, but under enormous tension that keeps them very very short. Typically, strings are posed to be of length close to the Planck length, the characteristic length at which quantum effects become relevant for gravity. This enormously small length corresponds to the enormously large Planck energy, which is on the order of 1028 electron-volts. That’s about ten to the sixteen times the energies of the particles at the LHC, or ten to the twenty-two times the MeV scale that I called “high energy” earlier. For comparison, there are about ten to the twenty-two atoms in a milliliter of water. When extra dimensions in string theory are curled up, they’re usually curled up at this scale. This means that from a string theory perspective, going to the TeV scale means ignoring the high energy physics and focusing on low energy consequences, which is why even the highest mass supersymmetric particles are thought of as low energy physics when approached from string theory.

The UV limit: Much as the IR limit is that of infinitely low energy, the UV limit is the formal limit of infinitely high energy. Again, it’s not so much an actual destination, as a comparative point where the energy you’re considering is much higher than the energy of anything else in your calculation.

These are the definitions of “high energy” and “low energy”, “UV” and “IR” that one encounters most often in theoretical particle physics and string theory. Other parts of physics have their own idea of what constitutes high or low energy, and I encourage you to ask people who study those parts of physics if you’re curious.

What are Vacua? (A Point about the String Landscape)

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A couple weeks back, there was a bit of a scuffle between Matt Strassler and Peter Woit on the subject of predictions in string theory (or more properly, the question of whether any predictions can be made at all). As a result, Strassler has begun a series on the subject of quantum field theory, string theory, and predictions.

Strassler hasn’t gotten to the topic of string vacua yet, but he’s probably going to cover the subject in a future post. While his take on the subject is likely to be more expansive and precise than mine, I think my perspective on the problem might still be of interest.

Let’s start with the basics: one of the problems often cited with string theory is the landscape problem, the idea that string theory has a metaphorical landscape of around 10^500 vacua.

What are vacua?

Vacua is the plural of vacuum.

Ok, and?

A vacuum is empty space.

That’s what you thought, right? That’s the normal meaning of vacuum. But if a vacuum is empty, how can there be more than one of them, let alone 10^500?

“Empty” is subjective.

Now we’re getting somewhere. The problem with defining a concept like “empty space” in string theory or field theory is that it’s unclear what precisely it should be empty of. Naively, such a space should be empty of “stuff”, or “matter”, but our naive notions of “matter” don’t apply to field theory or string theory. In fact, there is plenty of “stuff” that can be present in “empty” space.

Think about two pieces of construction paper. One is white, the other is yellow. Which is empty? Neither has anything drawn on it, so while one has a color and the other does not, both are empty.

“Empty space” doesn’t come in multiple colors like construction paper, but there are equivalent parameters that can vary. In quantum field theory, one option is for scalar fields to take different values. In string theory, different dimensions can be curled up in different ways (as an aside, when string theory leads to a quantum field theory often these different curling-up shapes correspond to different values for scalar fields, so the two ideas are related).

So if space can have “stuff” in it and still count as empty, are there any limits on what can be in it?

As it turns out, there is a quite straightforward limit. But to explain it, I need to talk a bit about why physicists care about vacua in the first place.

Why do physicists care about vacua?

In physics, there is a standard modus operandi for solving problems. If you’ve taken even a high school physics course, you’ve probably encountered it in some form. It’s not the only way to solve problems, but it’s one of the easiest. The idea, broadly, is the following:

First get the initial conditions, and then use the laws of physics to see what happens next.

In high school physics, this is how almost every problem works: your teacher tells you what the situation is, and you use what you know to figure out what happens next.

In quantum field theory, things are a bit more subtle, but there is a strong resemblance. You start with a default state, and then find the perturbations, or small changes, around that state.

In high school, your teacher told you what the initial conditions were. In quantum field theory, you need another source for the “default state”. Sometimes, you get that from observations of the real world. Sometimes, though, you want to make a prediction that goes beyond what your observations tell you. In that case, one trick often proves useful:

To find the default state, find which state is stable.

If your system starts out in a state that is unstable, it will change. It will keep changing until eventually it changes into a stable state, where it will stop changing. So if you’re looking for a default state, that state should be one in which the system is stable, where it won’t change.

(I’m oversimplifying things a bit here to make them easier to understand. In particular, I’m making it sound like these things change over time, which is a bit of a tricky subject when talking about different “default” states for the whole of space and time. There’s also a cool story connected to this about why tachyons don’t exist, which I’d love to go into for another post.)

Since we know that the “default” state has to be stable, if there is only one stable state, we’ve found the default!

Because of this, we can lay down a somewhat better definition:

A vacuum is a stable state.

There’s more to the definition than this, but this should be enough to give you the feel for what’s going on. If we want to know the “default” state of the world, the state which everything else is just a small perturbation on top of, we need to find a vacuum. If there is only one plausible vacuum, then our work is done.

When there are many plausible vacua, though, we have a problem. When there are 10^500 vacua, we have a huge problem.

That, in essence, is why many people despair of string theory ever making any testable predictions. String theory has around 10^500 plausible vacua (for a given, technical, meaning of plausible).

It’s important to remember a few things here.

First, the reason we care about vacuum states is because we want a “default” to make predictions around. That is, in a sense, a technical problem, in that it is an artifact of our method. It’s a result of the fact that we are choosing a default state and perturbing around it, rather than proving things that don’t depend on our choice of default state. That said, this isn’t as useful an insight as it might appear, and as it turns out there is generally very little that can be predicted without choosing a vacuum.

Second, the reason that the large number of vacua is a problem is that if there was only one vacuum, we would know which state was the default state for our world. Instead, we need some other method to pick, out of the many possible vacua, which one to use to make predictions. That is, in a sense, a philosophical problem, in that it asks what seems ostensibly to be a philosophical question: what is the basic, default state of the universe?

This happens to be a slightly more useful insight than the first one, and it leads to a number of different approaches. The most intuitive solution is to just shrug and say that we will see which vacuum we’re in by observing the world around us. That’s a little glib, since many different vacua could lead to very similar observations. A better tactic might be to try to make predictions on general grounds by trying to see what the world we can already observe implies about which vacua are possible, but this is also quite controversial. And there are some people who try another approach, attempting to pick a vacuum not based on observations, but rather on statistics, choosing a vacuum that appears to be “typical” in some sense, or that satisfies anthropic constraints. All of these, again, are controversial, and I make no commentary here about which approaches are viable and which aren’t. It’s a complicated situation and there are a fair number of people working on it. Perhaps, in the end, string theory will be ruled un-testable. Perhaps the relevant solution is right under peoples’ noses. We just don’t know.

Brown, Blue, and Birds

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I gave a talk at Brown this week, so this post may be shorter than usual. On the topic of Brown I don’t have much original to say: the people were friendly, the buildings were brownish-colored, and bringing a car there was definitely a bad idea. Don’t park at Brown. Not even then.

There’s a quote from Werner Heisenberg that has been making the rounds of the internet. It comes out of a 1976 article by Felix Bloch where he describes taking a walk with Heisenberg, when the discussion turned to the subject of space and time:

I had just read Weyl’s book Space, Time and Matter, and under its influence was proud to declare that space was simply the field of linear operations.

“Nonsense,” said Heisenberg, “space is blue and birds fly through it.”

Heisenberg’s point is that sometimes in physics you need to ask what your abstractions are really describing. You need to make sure that you haven’t stretched your definitions too badly away from their original inspiration.

When people first hear that string theory requires eleven dimensions, many wonder if this point applies. In mathematics, it’s well known that a problem can be described in many dimensions more than the physical dimensions of space. There’s a lovely example in the book Flatterland (a sequel to Flatland, a book which any math-y person should read at least once) of the dimensions of a bike. The bike’s motion through space gives three dimensions: up/down, backward/forward, and left/right. However, the bike can move in other ways: its gears can each be in a different position, as can its handlebars, as can the wheels…in the end, a bike can be envisioned as having many more “dimensions” than our normal three-dimensional space, each corresponding to some internal position.

Is string theory like this? No.

The first hint of the answer comes from something called F theory. String theory is part of something larger called M theory, and since M theory has eleven dimensions this is usually the number of dimensions given. But F theory contains string theory in a certain sense as well, only F theory contains twelve dimensions.

So why don’t string theorists say that the world has twelve dimensions?

As it turns out, the extra dimension added by F theory isn’t “really” a dimension. It’s much more like the mathematical dimensions of a bike’s gears and wheels than it is like the other eleven dimensions of M theory.

What’s the difference? What, according to a string theorist, is the definition of a dimension of space?

It’s simple: Space is “blue” (or colorless, I suppose). Birds (and particles, and strings, and membranes) fly in it.

We’re using the same age-old distinction that Heisenberg was, in a way. What is space? Space is just a place where things can move, in the same way they move in our usual three dimensions. Space is where you have momentum, where that momentum can change your position. Space is where forces act, the set of directions in which something can be pulled or pushed in a symmetric way. Space can’t be reduced, at least not without a lot of tricks: a bird flying isn’t just another description of a lizard crawling, not in the way a bicycle’s gears moving can be thought of as turning through our normal three dimensions without any extra ones. And while F theory doesn’t fit this criterion, M theory really does. The membranes of M theory fly around in eleven dimensional space-time, just like a bird moves through three space and one time dimensions.

Space for a string theorist isn’t any crazier or more abstract than it is for you. It’s just a place where things can move.

The (2, 0) Theory: Where does it come from?

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Part One of a Series on the (2, 0) Theory

By semi-popular demand, I’m doing a guide on the (2, 0) theory. Over the course of this guide I’ll try to explain where the (2, 0) theory comes from, what its name means, and, more elusively, what it’s actually about.

The (2, 0) theory doesn’t get much press coverage, and when it does, it’s a bit silly. The article I just linked compares it to Star Wars’ Emperor Palpatine, in analogy with what George Musser and perhaps others call the Darth Vader theory, or N=4 super Yang-Mills.

The metaphor, as far as I can parse it, is the following: while N=4 super Yang-Mills is solid, powerful, and important (like Darth Vader), the (2, 0) theory is mysterious and yet somehow even more central (like the Emperor).

The thing is, while the (2, 0) theory is indeed sexy and mysterious, it isn’t especially central. Laymen haven’t heard of it for good reason: it’s really only specialists in the field who have a reason to be interested in it. So really, it’s more like the Mara Jade theory.

If you don’t know who this is, that’s my point

The (2, 0) theory is very much a theory, in the same sense as N=4 super Yang-Mills. It isn’t a “theory of everything”, and it isn’t supposed to describe the real world. With that in mind, let’s talk about the sort of world it does describe.

There are two ways to “define” the (2, 0) theory. One of them is to take a particular type of string theory (type IIB) with ten dimensions (nine space dimensions and one dimension for time), and twist four of those dimensions into a particular shape (called a K3 surface). There are six dimensions left (five space, one time), and in those six dimensions the world obeys the (2, 0) theory.

That definition may not seem particularly illuminating, and it really isn’t. You can get almost any theory in physics by taking some type of string theory and twisting up some of the dimensions in a particular way, so unless you’re familiar with that particular type of string theory or the particular shape of the dimensions, you don’t learn anything from that definition.

The second definition, though, is more appealing. The (2, 0) theory can be defined as the world-volume theory of a five-dimensional object called an M5-brane.

A world-volume theory is a theory that describes what it is like to live inside of the volume of some object, so that the object is your whole world. To understand what that means, think about Flatland.

Think upward, not northward

In Edwin A. Abbott’s Flatland, the characters are two-dimensional shapes living in a two-dimensional world. Because their whole world is two-dimensional, they cannot imagine a third dimension. Despite that, there is a third dimension, as demonstrated by a sphere who floats through the world one day and upsets the main character’s life. The theory of physics in Flatland, then, is the world-volume theory of a two-dimensional plane in three-dimensional space.

Imagine that the two-dimensional plane of Flatland was flexible, that is, more like a two-dimensional membrane. Such a membrane could move back and forth in the third dimension, rippling up and down.

Now remember that, in Flatland, nobody can imagine a third dimension. So if you are within Flatland, and the world around you is bouncing up and down, can you notice?

The answer is a counter-intuitive yes. It’s easy if there is gravity in the third dimension: when the world curves up, it would get harder to climb up, while if the world curves down, it would be easier. Even if there isn’t gravity, though, you can still notice the changes in energy. It takes energy to set the world vibrating, and that energy has to come from somewhere. That energy can come from movement within your dimension. What a Flatlander would observe, then, would be processes that seem to violate conservation of energy, by losing more energy than they put in: instead, that energy would go to making the world wiggle.

What a Flatland scientist would observe, then, would be a world in which there is some number that can change from place to place, and that can oscillate, carrying energy as it does so. Those of you who remember my older posts might recognize what’s going on here: this is precisely the way in which you discover the existence of a scalar field!

An M5-brane is a five-dimensional membrane that lives in M theory, a theory with eleven dimensions (ten space and one time). The world-volume theory of an M5-brane, then, is the theory of what it is like to have your whole world inside the five dimensions of the M5-brane, just like a person in Flatland has their whole world within the two dimensions of Flatland. And just like the two-dimensional Flatland would have one scalar field corresponding to its ability to vibrate in the third dimension, the five space dimensions of the (2, 0) theory have five scalar fields, corresponding to the five other directions (ten minus five) in which the M5-brane can move.

So the (2, 0) theory is the theory of what it’s like to live on a five-dimensional membrane in a ten-dimensional space, and because of that, the theory contains five scalar fields. But if it was just five scalar fields, it would hardly be mysterious. What else does the theory contain? And what does “(2, 0)” mean anyway? Tune in next week to find out!

Edit: I am informed by George Musser (@gmusser on twitter) that the Darth Vader thing was apparently all Nima Arkani-Hamed’s idea. So don’t blame him for the somewhat misleading metaphor!

Duality: Find out what it means to me

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There’s a cute site out there called Why String Theory. Started by Oxford and the Royal Society, Why String Theory contains lots of concise and well-illustrated explanations of string theory, and it even wades into some of the more complex topics like AdS/CFT and string dualities in general. Their explanation of dualities is a nice introduction to why dualities matter in string theory, but I don’t think it does a very good job of explaining what a duality actually is or how one works. As your fearless host, I’m confident that I can do better.

Why String Theory defines dualities as when “different mathematical theories describe the same physics.” How does that work, though? In what sense are the theories different, if they describe the same thing? And if they describe the same thing, why do we need both of them?

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You’ve probably seen the above image before, or one much like it. Look at it one way, and you see a goblet. Another, and you see two faces.

Now imagine that instead of a flat image, these are 3D objects, models you have in your house. You’ve got a goblet, and a pair of clay faces. You’re still pretty sure they fit together like they do in the image, though. Maybe they said they fit together on the packaging, maybe you stuck them together and it didn’t look like there were any gaps. Whatever the reason, you’re confident enough about this that you’re willing to assume it’s true.

Now suppose you want to figure out how long the noses on the faces are. In case you’ve never measured a human nose, I can let you know that it’s tricky. You could put a ruler along the nose, but it would be diagonal rather than straight, so you wouldn’t get an accurate measurement. Even putting the ruler beneath the nose doesn’t work for rounded noses like these.

That said, measuring the goblet is easy. You can run measuring tape around the neck of the goblet to find the circumference, and then calculate the diameter. And if you measure the goblet in this way, you also know how long the faces’ noses are.

You could go further, and build up a list of things you can measure on one object that tell you about the other one. The necks match up to the base of the goblet, the foreheads to the mouth, etc. It would be like a dictionary, translating between two languages: the language of measurements of the faces, and the language of measurements of the goblet.

That sort of “dictionary” is the essence of duality. When two theories have a duality (are dual to each other), you can make a “dictionary” to translate measurements in one theory to measurements in the other. That doesn’t mean, however, that the theories are clearly connected: like 3D models of the faces and the goblet, it may be that without looking at the particular “silhouette” defined by duality the two views are radically different. Rather than physical objects, the theories compare mathematical “objects”, so rather than physical obstructions like the solidity of noses we have to deal with mathematical ones, situations where one quantity or another is easier or harder to calculate depending on how the math is set up. For example, many dualities relate things that require calculations at very high loops to things that can be calculated with fewer loops (for an explanation of loops, check out this post).

As Why String Theory points out, one of the most prominent dualities is called AdS/CFT, and it relates N=4 super Yang-Mills (a Conformal Field Theory, or CFT) to string theory in something called Anti-de Sitter (AdS) space (tricky to describe, but essentially a world in which space is warped like a hyperbola). Another duality relates N=4 super Yang-Mills Feynman diagrams with n particles coming in from outside to diagrams with an n-sided shape and particles randomly coming in from the edges of the shape (these latter diagrams are called Wilson loops). In general N=4 super Yang-Mills is involved in many, many dualities, which is a big part of why it’s so dang cool.

In Defense of Pure Theory

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I’d like to preface this by saying that this post will be a bit more controversial than usual. I have somewhat unconventional opinions about the nature and purpose of science, and what I say below shouldn’t be taken as representative of the field in general.

A bit more than a week ago, Not Even Wrong had a post on the Fundamental Physics Prize. Peter Woit is often…I’m going to say annoying…and this post was no exception.

The Fundamental Physics Prize, for those not in the know, is a fairly recently established prize for physicists, mostly theoretical physicists.  Clocking in at three million dollars, the prize is larger than the Nobel, and is currently the largest prize of its sort. Woit has several objections to the current choice of award recipient (Alexander Polyakov). I sympathize with some of these objections, in particular the snarky observation that a large number of the awardees are from Princeton’s Institute for Advanced Study. But there is one objection in particular that I feel the need to rebut, if only due to its wording: the gripe that “Viewers of the part I saw would have no idea that string theory is not tested, settled science.”

There are two problems with this statement. The first is something that Woit is likely aware of, but it probably isn’t obvious to everyone reading this. To be clear, the fact that a certain theory is not experimentally tested is not a barrier to its consideration for the Fundamental Physics Prize. Far from it, the purpose of the Fundamental Physics Prize is precisely to honor powerful insights in theoretical physics that have not yet been experimentally verified. The Fundamental Physics Prize was created, in part, to remedy what was perceived as unfairness in the awarding of the Nobel Prize, as the Nobel is only awarded to theorists after their theories have received experimental confirmation. Since the whole purpose of this prize is to honor theories that have not been experimentally tested, griping that the prizes are being awarded to untested theories is a bit like griping that Oscars aren’t awarded to scientists, or objecting that viewers of the Oscars would have no idea that the winners haven’t done anything especially amazing for humanity. If you’re watching the ceremony, you probably know what it’s for.

Has this been experimentally verified?

The other problem is a difference of philosophy. When Woit says that string theory is not “tested, settled science” he is implying that in order to be “settled science”, a theory must be tested, and while I can’t be sure of his intent I’m guessing he means tested experimentally. It is this latter implication I want to address: whether or not Woit is making it here, it serves to underscore an important point about the structure of physics as an institution.

Past readers will be aware that a theory can be valuable even if it doesn’t correspond to the real world because of what it can teach us about theories that do correspond to the real world. And while that is an important point, the point I’d like to make here is a bit more controversial. I would like to argue that pure theory, theory unconnected with experiment, can be important and valuable and “settled science” in and of itself.

First off, let’s talk about how such a theory can be science, and in particular how it can be physics. Plenty of people do work that doesn’t correspond to the experimentally accessible real world.  Mathematicians are the clearest example, but the point also arguably applies to fields like literary analysis. Physics is ostensibly supposed to be special, though: as part of science, we expect it to concern itself with the real world, otherwise one would argue that it is simply mathematics. However, as I have argued before, the difference between mathematics and physics is not one of subject matter, but of methods. This makes sense, provided you think of physics not as some sort of fixed school of thought, but as an institution. Physicists train new physicists, and as such physicists learn methods common to other physicists. That which physicists like to do, then, is physics, which means that physics is defined much more by the methods used to do it than by its object of study.

How can such a theory be settled, then? After all, if reality is out, what possible criteria could there be for deciding what is or is not a “good” theory?

The thing about physics as an institution is that physics is done by physicists, and physicists have careers. Over the course of those careers, those physicists need to publish papers, which need to catch the attention and approval of other physicists. They also need to have projects for grad students to do, so as to produce more physicists. Because of this, a “good” theory cannot be worked on alone. It has to be a theory with many implications, a theory that can be worked on and understood consistently by different people. It also needs to constrain further progress, to make sure that not just anyone can create novel results: this is what allows papers to catch the attention of other physicists! If you have all that, you have all of the relevant advantages of reality.

String theory has not been experimentally tested, but it meets all of these criteria. String theory has been a major force in theoretical physics for the past thirty years because it can fuel careers and lead to discussion in a way that nothing else on the table can. It has been tested mathematically in numerous ways, ways which demonstrate its robustness as a theory of quantum gravity. In this sense, string theory is a prime example of tested, settled science.

Nature Abhors a Constant

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Why is a neutrino lighter than an electron? Why is the strong nuclear force so much stronger than the weak nuclear force, and why are both so much stronger than gravity? For that matter, why do any particles have the masses they do, or forces have the strengths they do?

To some people, these sorts of questions are meaningless. A scientist’s job is to find out the facts, to measure what the constants are. To ask why, though…why would you want to do that?

Maybe a sense of history?

See, physics has a history of taking what look like arbitrary facts (the orbits of the planets, the rate objects fall, the pattern of chemical elements) and finding out why they are that way. And there’s no reason not to expect this trend to continue.

The point can be made even more strongly: increasingly, it is becoming clear that nature abhors a constant.

To explain this, I first have to clarify what I mean by a constant. If you were asked to think of a constant, you’d probably think of the speed of light. The thing is, the speed of light is actually not the sort of constant I have in mind. The speed of light is three hundred million meters per second…but it’s also 671 million miles per hour, or one light year per year. Choose the right units, and the speed of light is just one. To go a bit further: the speed of light is merely an artifact of how we choose our units of distance and time, so it’s not a “real” constant at all!

So what would a “real” constant look like? Well, imagine if there were two fundamental speeds: a maximum, like the speed of light and a minimum, which nothing could go slower than. You could pick units so that one of the speeds was one, or so that the other was…but they couldn’t both be one at the same time. Their ratio stays the same, no matter what units you’re using. That’s the sign of a true constant. To say it another way: a “real” constant is dimensionless.

It is these “real” constants that nature so abhors, because whenever such a “real” constant appears to exist, it is likely to be due to a scalar field.

To remind readers, a scalar field is a type of quantum field consisting of a number that can vary through space. Temperature is an iconic illustration of a scalar field: at any given point you can define temperature by a number, and that number changes as you move from place to place.

Now constants, being constant, are not known for changing from place to place. Just because we don’t see mass or charge being different in different places, though, doesn’t mean they aren’t scalar fields.

To illustrate, imagine that you live far in the past, far enough that no-one knows that air has weight. Through careful experimentation, though, you can observe air pressure: everything is pressed upon in all directions by some mysterious force. Even if you don’t have access to mountains and therefore can’t see that air pressure varies by height, maybe you have begun to guess that air pressure is related to the weight of the air. You have a possible explanation for your constant pressure, in terms of a scalar pressure field. But how do you test your idea? Well, the big difference between a scalar and a constant is that a scalar can vary. Since there’s so much air above you, it’s hard to get air pressure to vary: you have to put enough energy in to the air to make it happen. More specifically, you vibrate the air: you create sound waves! By measuring how fast the sound waves go, you can test out your proposed number for the mass of the air, and if everything lines up right, you have successfully replaced a mysterious constant with a logical explanation.

This is almost exactly what happened with the Higgs. Scientists observed that particle masses seemed to be arbitrary numbers, and proposed a scalar field to explain them. (As a matter of fact, the masses involved actually cannot just be constants; the mathematics involved doesn’t allow it. They must be scalar fields). In order to test out the theory, we built the Large Hadron Collider, and used it to cause ripples in the seemingly constant masses, just like sound waves in air. In this case, those ripples were the Higgs particle, which served as evidence for the Higgs field just as sound waves serve as evidence for the mass of air.

And this sort of method keeps going. The Higgs explains mass in many cases, but it doesn’t explain the differences between particle masses, and it may be that new fields are needed to explain those. The same thing goes for the strengths of forces. Scalar fields are the most likely explanations for inflation, and in string theory scalars control the size and shape of the extra dimensions. So if you’ve got a mysterious constant, nature likely has a scalar field waiting in the wings to explain it.

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.