Monthly Archives: March 2015

Only the Boring Kind of Parallel Universes

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PARALLEL UNIVERSES AT THE LHC??

No. No. Bad journalist. See what happens when you…

Mir Faizal, one of the three-strong team of physicists behind the experiment, said: “Just as many parallel sheets of paper, which are two dimensional objects [breadth and length] can exist in a third dimension [height], parallel universes can also exist in higher dimensions.

Bad physicist, bad! No biscuit for you!

Not nice at all!

For the technically-minded, Sabine Hossenfelder goes into thorough detail about what went wrong here. Not only do parallel universes have nothing to do with what Mir Faizal and collaborators have been studying, but the actual paper they’re hyping here is apparently riddled with holes.

BLACK holes! …no, actually, just logic holes.

But why did parallel universes even come up? If they have nothing to do with Faizal’s work, why did he mention them? Do parallel universes ever come up in real physics at all?

The answer to this last question is yes. There are real, viable ideas in physics that involve parallel universes. The universes involved, however, are usually boring ones.

The ideas are generally referred to as brane-world theories. If you’ve heard of string theory, you’ve probably heard that it proposes that the world is made of tiny strings. That’s all well and good, but it’s not the whole story. String theory has other sorts of objects in it too: higher dimensional generalizations of strings called membranes, branes for short. In fact, M theory, the theory of which every string theory is some low-energy limit, has no strings at all, just branes.

When these branes are one-dimensional, they’re strings. When they’re two-dimensional, they’re what you would normally picture as a membrane, a vibrating sheet, potentially infinite in size. When they’re three-dimensional, they fill three-dimensional space, again potentially up to infinity.

Filling three dimensional space, out to infinity…well that sure sounds a whole lot like what we’d normally call a universe.

In brane-world constructions, what we call our universe is precisely this sort of three-dimensional brane. It then lives in a higher-dimensional space, where its position in this space influences things like the strength of gravity, or the speed at which the universe expands.

Sometimes (not all the time!) these sorts of constructions include other branes, besides the one that contains our universe. These other branes behave in a similar way, and can have very important effects on our universe. They, if anything, are the parallel universes of theoretical physics.

It’s important to point out, though that these aren’t the sort of sci-fi parallel universes you might imagine! You aren’t going to find a world where everyone has a goatee, or even a world with an empty earth full of teleporting apes.

Pratchett reference!

That’s because, in order for these extra branes to do useful physical work, they generally have to be very different from our world. They’re worlds where gravity is very strong, or world with dramatically different densities of energy and matter. In the end, this means they’re not even the sort of universes that produce interesting aliens, or where we could send an astronaut, or really anything that lends itself well to (non-mathematical) imagination. From a sci-fi perspective, they’re as boring as can be.

Faizal’s idea, though, doesn’t even involve the boring kind of parallel universe!

His idea involves extra dimensions, specifically what physicists refer to as “large” extra dimensions, in contrast with the small extra dimensions of string theory. Large extra dimensions can explain the weakness of gravity, and theories that use them often predict that it’s much easier to create microscopic black holes than it otherwise would be. So far, these models haven’t had much luck at the LHC, and while I get the impression that they haven’t been completely ruled out, they aren’t very popular anymore.

The thing is, extra dimensions don’t mean parallel universes.

In fiction, the two get used interchangeably a lot. People go to “another dimension”, vaguely described as traveling along another dimension of space, and find themselves in a strange new world. In reality, though, there’s no reason to think that traveling along an extra dimension would put you in any sort of “strange new world”. The whole reason that our world is limited to three dimensions is because it’s “bound” to something: a brane, in the string theory picture. If there’s not another brane to bind things to, traveling in an extra dimension won’t put you in a new universe, it will just put you in an empty space where none of the types of matter you’re made of even exist.

It’s really tempting, when talking to laypeople, to fall back on stories. If you mention parallel universes, their faces light up with the idea that this is something they get, if only from imaginary examples. It gives you that same sense of accomplishment as if you had actually taught them something real. But you haven’t. It’s wrong, and Mir Faizal shouldn’t have stooped to doing it.

What Counts as a Fundamental Force?

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I’m giving a presentation next Wednesday for Learning Unlimited, an organization that presents educational talks to seniors in Woodstock, Ontario. The talk introduces the fundamental forces and talks about Yang and Mills before moving on to introduce my work.

While practicing the talk today, someone from Perimeter’s outreach department pointed out a rather surprising missing element: I never mention gravity!

Most people know that there are four fundamental forces of nature. There’s Electromagnetism, there’s Gravity, there’s the Weak Nuclear Force, and there’s the Strong Nuclear Force.

Listed here by their most significant uses.

What ties these things together, though? What makes them all “fundamental forces”?

Mathematically, gravity is the odd one out here. Electromagnetism, the Weak Force, and the Strong Force all share a common description: they’re Yang-Mills forces. Gravity isn’t. While you can sort of think of it as a Yang-Mills force “squared”, it’s quite a bit more complicated than the Yang-Mills forces.

You might be objecting that the common trait of the fundamental forces is obvious: they’re forces! And indeed, you can write down a force law for gravity, and a force law for E&M, and umm…

[Mumble Mumble]

Ok, it’s not quite as bad as xkcd would have us believe. You can actually write down a force law for the weak force, if you really want to, and it’s at least sort of possible to talk about the force exerted by the strong interaction.

All that said, though, why are we thinking about this in terms of forces? Forces are a concept from classical mechanics. For a beginning physics student, they come up again and again, in free-body diagram after free-body diagram. But by the time a student learns quantum mechanics, and quantum field theory, they’ve already learned other ways of framing things where forces aren’t mentioned at all. So while forces are kind of familiar to people starting out, they don’t really match onto anything that most quantum field theorists work with, and it’s a bit weird to classify things that only really appear in quantum field theory (the Weak Nuclear Force, the Strong Nuclear Force) based on whether or not they’re forces.

Isn’t there some connection, though? After all, gravity, electromagnetism, the strong force, and the weak force may be different mathematically, but at least they all involve bosons.

Well, yes. And so does the Higgs.

The Higgs is usually left out of listings of the fundamental forces, because it’s not really a “force”. It doesn’t have a direction, instead it works equally at every point in space. But if you include spin 2 gravity and spin 1 Yang-Mills forces, why not also include the spin 0 Higgs?

Well, if you’re doing that, why not include fermions as well? People often think of fermions as “matter” and bosons as “energy”, but in fact both have energy, and neither is made of it. Electrons and quarks are just as fundamental as photons and gluons and gravitons, just as central a part of how the universe works.

I’m still trying to decide whether my presentation about Yang-Mills forces should also include gravity. On the one hand, it would make everything more familiar. On the other…pretty much this entire post.

What Can Pi Do for You?

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Tomorrow is Pi Day!

And what a Pi Day! 3/14/15 (if you’re in the US, Belize, Micronesia, some parts of Canada, the Philippines, or Swahili-speaking Kenya), best celebrated at 9:26:53, if you’re up by then. Grab a slice of pie, or cake if you really must, and enjoy!

If you don’t have some of your own, download this one!

Pi is great not just because it’s fun to recite digits and eat pastries, but because it serves a very important role in physics. That’s because, often, pi is one of the most “natural” ways to get larger numbers.

Suppose you’re starting with some sort of “natural” theory. Here I don’t mean natural in the technical sense. Instead, I want you to imagine a theory that has very few free parameters, a theory that is almost entirely fixed by mathematics.

Many physicists hope that the world is ultimately described by this sort of theory, but it’s hard to see in the world we live in. There are so many different numbers, from the tiny mass of the electron to the much larger mass of the top quark, that would all have to come from a simple, overarching theory. Often, it’s easier to get these numbers when they’re made out of factors of pi.

Why is pi easy to get?

In general, pi shows up a lot in physics and mathematics, and its appearance can be mysterious the uninitiated, as this joke related by Eugene Wigner in an essay I mentioned a few weeks ago demonstrates:

THERE IS A story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. “How can you know that?” was his query. “And what is this symbol here?” “Oh,” said the statistician, “this is pi.” “What is that?” “The ratio of the circumference of the circle to its diameter.” “Well, now you are pushing your joke too far,” said the classmate, “surely the population has nothing to do with the circumference of the circle.”

While it may sound silly, in a sense the population really is connected to the circumference of the circle. That’s because pi isn’t just about circles, pi is about volumes.

Take a bit to check out that link. Not just the area of a circle, but the volume of a sphere, and that of all sorts of higher-dimensional ball-shaped things, is calculated with the value of pi. It’s not just spheres, either: pi appears in the volume of many higher-dimensional shapes.

Why does this matter for physics? Because you don’t need a literal shape to get a volume. Most of the time, there aren’t literal circles and spheres giving you factors of pi…but there are abstract spaces, and they contain circles and spheres. A electric and magnetic fields might not be shaped like circles, but the mathematics that describes them can still make good use of a circular space.

That’s why, when I describe the mathematical formulas I work with, formulas that often produce factors of pi, mathematicians will often ask if they’re the volume of some particular mathematical space. It’s why Nima Arkani-Hamed is trying to understand related formulas by thinking of them as the volume of some new sort of geometrical object.

All this is not to say you should go and plug factors of pi together until you get the physical constants you want. Throw in enough factors of pi and enough other numbers and you can match current observations, sure…but you could also match anything else in the same way. Instead, it’s better to think of pi as an assistant: waiting in the wings, ready to translate a pure mathematical theory into the complicated mess of the real world.

So have a Happy Pi Day, everyone, and be grateful to our favorite transcendental number. The universe would be a much more boring place without it.

How to Predict the Mass of the Higgs

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Did Homer Simpson predict the mass of the Higgs boson?

No, of course not.

Apart from the usual reasons, he’s off by more than a factor of six.

If you play with the numbers, it looks like Simon Singh (the popular science writer who reported the “discovery” Homer made as a throwaway joke in a 1998 Simpsons episode) made the classic physics mistake of losing track of a factor of 2\pi. In particular, it looks like he mistakenly thought that the Planck constant, h, was equal to the reduced Planck constant, \hbar, divided by 2\pi, when actually it’s \hbar times 2\pi. So while Singh read Homer’s prediction as 123 GeV, surprisingly close to the actual Higgs mass of 125 GeV found in 2012, in fact Homer predicted the somewhat more embarrassing value of 775 GeV.

D’Oh!

That was boring. Let’s ask a more interesting question.

Did Gordon Kane predict the mass of the Higgs boson?

I’ve talked before about how it seems impossible that string theory will ever make any testable predictions. The issue boils down to one of too many possibilities: string theory predicts different consequences for different ways that its six (or seven for M theory) extra dimensions can be curled up. Since there is an absurdly vast number of ways this can be done, anything you might want to predict (say, the mass of the electron) has an absurd number of possible values.

Gordon Kane and collaborators get around this problem by tackling a different one. Instead of trying to use string theory to predict things we already know, like the mass of the electron, they assume these things are already true. That is, they assume we live in a world with electrons that have the mass they really have, and quarks that have the mass they really have, and so on. They assume that we live in a world that obeys all of the discoveries we’ve already made, and a few we hope to make. And, they assume that this world is a consequence of string (or rather M) theory.

From that combination of assumptions, they then figure out the consequences for things that aren’t yet known. And in a 2011 paper, they predicted the Higgs mass would be between 105 and 129 GeV.

I have a lot of sympathy for this approach, because it’s essentially the same thing that non-string-theorists do. When a particle physicist wants to predict what will come out of the LHC, they don’t try to get it from first principles: they assume the world works as we have discovered, make a few mild extra assumptions, and see what new consequences come out that we haven’t observed yet. If those particle physicists can be said to make predictions from supersymmetry, or (shudder) technicolor, then Gordon Kane is certainly making predictions from string theory.

So why haven’t you heard of him? Even if you have, why, if this guy successfully predicted the mass of the Higgs boson, are people still saying that you can’t make predictions with string theory?

Trouble is, making predictions is tricky.

Part of the problem is timing. Gordon Kane’s paper went online in December of 2011. The Higgs mass was announced in July 2012, so you might think Kane got a six month head-start. But when something is announced isn’t the same as when it’s discovered. For a big experiment like the Large Hadron Collider, there’s a long road between the first time something gets noticed and the point where everyone is certain enough that they’re ready to announce it to the world. Rumors fly, and it’s not clear that Kane and his co-authors wouldn’t have heard them.

Assumptions are the other issue. Remember when I said, a couple paragraphs up, that Kane’s group assumed “that we live in a world that obeys all of the discoveries we’ve already made, and a few we hope to make“? That last part is what makes things tricky. There were a few extra assumptions Kane made, beyond those needed to reproduce the world we know. For many people, some of these extra assumptions are suspicious. They worry that the assumptions might have been chosen, not just because they made sense, but because they happened to give the right (rumored) mass of the Higgs.

If you want to predict something in physics, it’s not just a matter of getting in ahead of the announcement with the right number. For a clear prediction, you need to be early enough that the experiments haven’t yet even seen hints of what you’re looking for. Even then, you need your theory to be suitably generic, so that it’s clear that your prediction is really the result of the math and not of your choices. You can trade off aspects of this: more accuracy for a less generic theory, better timing for looser predictions. Get the formula right, and the world will laud you for your prediction. Wrong, and you’re Homer Simpson. Somewhere in between, though, and you end up in that tricky, tricky grey area.

Like Gordon Kane.