Category Archives: Misc

Gravitational Waves, and Valentine’s Day Physics Poem 2016

By the time this post goes up, you’ll probably have seen Advanced LIGO’s announcement of the first direct detection of a gravitational wave. We got the news a bit early here at Perimeter, which is why we were able to host a panel discussion right after the announcement.

From what I’ve heard, this is the real deal. They’ve got a beautifully clear signal, and unlike BICEP, they kept this under wraps until they could get it looked at by non-LIGO physicists. While I think peer review gets harped on a little too much in these sorts of contexts, in this case their paper getting through peer review is a good sign that they’re really seeing something.

Pictured: a very clear, very specific something

I’ll have more to say next week: explanations of gravitational waves and LIGO for my non-expert audience, and impressions from the press release and PI’s panel discussion for those who are interested. For now, though, I’ll wait until the dust (metaphorical this time) settles. If you’re hungry for immediate coverage, I’m sure that half the blogs on my blogroll have posts up, or will in the next few days.

In the meantime, since Valentine’s Day is in two days, I’ll continue this blog’s tradition and post one of my old physics poems.

When a sophisticated string theorist seeks an interaction

He does not go round and round in loops

As a young man would.

Instead he turns to topology.

Mature, the string theorist knows

That what happens on

(And between)

The (world) sheets,

Is universal.

That the process is the same

No matter which points

Which interactions

One chooses.

Only the shapes of things matter.

Only the topology.

For such a man there is no need.

To obsess

To devote

To choose

One point or another.

The interaction is the same.

The world, though

Is not an exercise in theory.

Is not a mere possibility.

And if a theorist would compute

An experiment

A probability

He must pick and choose

Obsess and devote

Label his interactions with zeroes and infinities

Because there is more to life

Than just the shapes of things

Than just topology.

Trust Your Notation as Far as You Can Prove It

1 Reply

Calculus contains one of the most famous examples of physicists doing something silly that irritates mathematicians. See, there are two different ways to write down a derivative, both dating back to the invention of calculus: Newton’s method, and Leibniz’s method.

Newton cared a lot about rigor (enough that he actually published his major physics results without calculus because he didn’t think calculus was rigorous enough, despite inventing it himself). His notation is direct and to the point: if you want to take the derivative of a function f of x, you write,

$f'(x)$

Leibniz cared a lot less about rigor, and a lot more about the scientific community. He wanted his notation to be useful and intuitive, to be the sort of thing that people would pick up and run with. To write a derivative in Leibniz notation, you write,

$\frac{df}{dx}$

This looks like a fraction. It’s really, really tempting to treat it like a fraction. And that’s the point: it’s to tell you that treating it like a fraction is often the right thing to do. In particular, you can do something like this,

$y=\frac{df}{dx}$

$y dx=df$

$\int y dx=\int df$

and what you did actually makes a certain amount of sense.

The tricky thing here is that it doesn’t always make sense. You can do these sorts of tricks up to a point, but you need to be aware that they really are just tricks. Take the notation too seriously, and you end up doing things you aren’t really allowed to do. It’s always important to stay aware of what you’re really doing.

There are a lot of examples of this kind of thing in physics. In quantum field theory, we use path integrals. These aren’t really integrals…but a lot of the time, we can treat them as such. Operators in quantum mechanics can be treated like numbers and multiplied…up to a point. A friend of mine was recently getting confused by operator product expansions, where similar issues crop up.

I’ve found two ways to clear up this kind of confusion. One is to unpack your notation: go back to the definitions, and make sure that what you’re doing really makes sense. This can be tedious, but you can be confident that you’re getting the right answer.

The other option is to stop treating your notation like the familiar thing it resembles, and start treating it like uncharted territory. You’re using this sort of notation to remind you of certain operations you can do, certain rules you need to follow. If you take those rules as basic, you can think about what you’re doing in terms of axioms rather than in terms of the suggestions made by your notation. Follow the right axioms, and you’ll stay within the bounds of what you’re actually allowed to do.

Either way, familiar-looking notation can help your intuition, making calculations more fluid. Just don’t trust it farther than you can prove it.

Newtonmas 2015

6 Replies

Merry Newtonmas!

I’ll leave up my poll a bit longer, but the results are already looking pretty consistent.

A strong plurality of my readers have PhDs in high energy or theoretical physics, a little more than a quarter. Another big chunk (a bit over a fifth) are physics grad students. All together, that means almost half of my readers have some technical background in what I do.

In the comments, Cliff suggests this is a good reason to start writing more technical posts. Looking at the results, I agree, it looks like there would definitely be an audience for that sort of thing. Technical posts take a lot more effort than general audience posts, so don’t expect a lot of them…but you can definitely look forward to a few technical posts next year.

On the other hand, between people with some college physics and people who only saw physics in high school, about a third of my audience wouldn’t get much out of technical posts. Most of my posts will still be geared to this audience, since it’s kind of my brand at this point, but I do want to start experimenting with aiming a few posts to more specific segments.

Beyond that, I’ve got a smattering of readers in other parts of physics, and a few mathematicians. Aside from the occasional post defending physics notation, there probably won’t be much aimed at either group, but do let me know what I can do to make things more accessible!

Want to Open up Your Work? Try a Data Mine!

Who Plagiarizes an Acknowledgements Section?

4 Replies

I’ve got plagiarists on the brain.

Maybe it was running into this interesting discussion about a plagiarized application for the National Science Foundation’s prestigious Graduate Research Fellowship Program. Maybe it’s due to the talk Paul Ginsparg, founder of arXiv, gave this week about, among other things, detecting plagiarism.

Using arXiv’s repository of every paper someone in physics thought was worth posting, Ginsparg has been using statistical techniques to sift out cases of plagiarism. Probably the funniest cases involved people copying a chunk of their thesis acknowledgements section, as excerpted here. Compare:

“I cannot describe how indebted I am to my wonderful girlfriend, Amanda, whose love and encouragement will always motivate me to achieve all that I can. I could not have written this thesis without her support; in particular, my peculiar working hours and erratic behaviour towards the end could not have been easy to deal with!”

“I cannot describe how indebted I am to my wonderful wife, Renata, whose love and encouragement will always motivate me to achieve all that I can. I could not have written this thesis without her support; in particular, my peculiar working hours and erratic behaviour towards the end could not have been easy to deal with!”

Why would someone do this? Copying the scientific part of a thesis makes sense, in a twisted way: science is hard! But why would someone copy the fluff at the end, the easy part that’s supposed to be a genuine take on your emotions?

The thing is, the acknowledgements section of a thesis isn’t exactly genuine. It’s very formal: a required section of the thesis, with tacit expectations about what’s appropriate to include and what isn’t. It’s also the sort of thing you only write once in your life: while published papers also have acknowledgements sections, they’re typically much shorter, and have different conventions.

If you ever were forced to write thank-you notes as a kid, you know where I’m going with this.

It’s not that you don’t feel grateful, you do! But when you feel grateful, you express it by saying “thank you” and moving on. Writing a note about it isn’t very intuitive, it’s not a way you’re used to expressing gratitude, so the whole experience feels like you’re just following a template.

Literally in some cases.

That sort of situation: where it doesn’t matter how strongly you feel something, only whether you express it in the right way, is a breeding ground for plagiarism. Aunt Mildred isn’t going to care what you write in your thank-you note, and Amanda/Renata isn’t going to be moved by your acknowledgements section. It’s so easy to decide, in that kind of situation, that it’s better to just grab whatever appropriate text you can than to teach yourself a new style of writing.

In general, plagiarism happens because there’s a disconnect between incentives and what they’re meant to be for. In a world where very few beginning graduate students actually have a solid research plan, the NSF’s fellowship application feels like a demand for creative lying, not an honest way to judge scientific potential. In countries eager for highly-cited faculty but low on preexisting experts able to judge scientific merit, tenure becomes easier to get by faking a series of papers than by doing the actual work.

If we want to get rid of plagiarism, we need to make sure our incentives match our intent. We need a system in which people succeed when they do real work, get fellowships when they honestly have talent, and where we care about whether someone was grateful, not how they express it. If we can’t do that, then there will always be people trying to sneak through the cracks.

What Can Pi Do for You?

7 Replies

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.

Valentine’s Day Physics Poem 2015

1 Reply

In the third installment of an ongoing tradition (wow, this blog is old enough to have traditions!), I present 2015’s Valentine’s Day Physics Poem. Like the others, I wrote this one a long time ago. I’ve polished it up a bit since.

Perturbation Theory

When you’ve been in a system a long time, your state tends to settle

Time-energy uncertainty

That unrigorous interloper

Means the longer you wait, the more fixed you are

And I’ve been stuck

In a comfy eigenstate

Since what I might as well call t=0.

Yesterday though,

Out of the ether

Like an electric field

New potential entered my Hamiltonian.

And my state was perturbed.

Just a small, delicate perturbation

And an infinite series scrolls out

Waves from waves from waves

It’s a new system now

With new, unrealized energy

And I might as well

Call yesterday

t=0.

Our old friend

Time-energy uncertainty

Tells me not to change,

Not to worry.

Soon, probability thins

The Hamiltonian pulls us back

And we all return

Closer and closer

To a fixed, settled, normal state.

This freedom

This uncertainty

This perturbation

Is limited by Planck’s constant

Is vanishingly small.

Yet rigor

And happiness

Demand I include it.

So the Higgs is like, everywhere, right?

19 Replies

When I tell people I do particle physics, they generally jump to the first thing they’ve heard of, the Higgs boson. Unfortunately, what most people have heard about the Higgs boson is misleading.

The problem is the “crowded room” metaphor, a frequent favorite of people trying to describe the Higgs. The story goes that the Higgs works like trying to walk through a crowded room: an interesting person (massive particle) will find that the crowd clusters around them, so it becomes harder to make progress, while a less interesting person (less massive or massless particle) will have an easier time traveling through the crowd.

This metaphor gives people the impression that each of us is surrounded by an invisible sea of particles, like an invisible crowd constantly jostling us.

I see Higgs people!

People get very impressed by the idea of some invisible, newly discovered stuff that extends everywhere and surrounds everything. The thing is, this really isn’t the unique part of the Higgs. In fact, every fundamental particle works like this!

In physics, we describe the behavior of fundamental particles (like the Higgs, but also everything from electrons to photons) with a framework called Quantum Field Theory. In Quantum Field Theory, each particle has a corresponding field, and each field extends everywhere, over all space and time. There’s an electron field, and the electron field is absolutely everywhere. The catch is, most of the time, most of these fields are at zero. The electron field tells you that there are zero electrons in a generic region of space.

Particles are ripples in these fields. If the electron field wobbles a bit higher than normal somewhere, that means there’s an electron there. If it wobbles a bit lower than normal instead, then it’s an anti-electron. (Note: this is a very fast-and-loose way to describe how antimatter works, don’t take it for more than it’s worth.)

When the Higgs field ripples, you get a Higgs particle, the one discovered at the LHC. The “crowd” surrounding us isn’t these ripples (which are rare and hard to create), but the field itself, which surrounds us in the same way every other field does.

With all that said, there is a difference between the Higgs field and other fields. The Higgs field is the only field we’ve discovered (so far) that isn’t usually zero. This is because the Higgs is the only field we’ve discovered that is allowed to be something other than zero.

Symmetry is a fundamental principle in physics. At its simplest, symmetry is the idea that nothing should be special for no good reason. One consequence is that there are no special directions. Up, down, right, left, the laws of physics don’t care which one you choose. Only the presence of some object (like the Earth) can make differences like up versus down relevant.

What does that have to do with fields?

Think about a magnetic field. A magnetic field pulls in a specific direction.

So far, so good…

Now imagine a magnetic field everywhere. Which way would it point? If it was curved like the one in the picture, what would it be curved around?

There isn’t a good choice. Any choice would single out one direction, making it special. But nothing should be special for no good reason, and unless there was an object out there releasing this huge magnetic field there would be no good reason for it to be pointed that way. Because of that, the default value of the magnetic field over all space has to be zero.

You can make a similar argument for fields like the electron field. It’s even harder to imagine a way for electrons to be everywhere and not pick some “special” direction.

The Higgs, though, is special. The Higgs is what’s known as a scalar field. That means that it doesn’t have a direction. At any specific point it’s just a number, a scalar quantity. The Higgs doesn’t have to be zero everywhere because even if it isn’t, no special direction is singled out. One metaphor I’ve used before is colored construction paper: the paper can be blue or red, and either way it will still be empty until someone draws on it.

A bit less exciting than ghosts, huh?

The Higgs is special because it’s the first fundamental scalar field we’ve been able to detect, but there are probably others. Most explanations of cosmic inflation, for example, rely on one or more new scalar fields. (Just like “mass of the fundamental particles” is just a number, “rate the universe is inflating” is also just a number, and can also be covered by a scalar field.) It’s not special just because it’s “everywhere”, and imagining it as a bunch of invisible particles careening about around you isn’t going to get you anywhere useful.

Now, if you find the idea of being surrounded by invisible particles interesting, you really ought to read up on neutrinos….

Welcome to the New Site!

4 Replies

Welcome to the newly improved 4gravitons.wordpress.com!

I’ll be keeping redirects up from the old blog at 4gravitonsandagradstudent.wordpress.com, so old links should still work. Those of you following on WordPress Reader, I think the blog should be properly transferred there as well.

In addition to the spiffy new graphics, the blog has a number of handy new features. I’ve added categories to all of the posts from the following list: (2, 0) Theory, Amateur Philosophy, Amplitudes Methods, Astrophysics/Cosmology, General QFT, Gravity, Life as a Physicist, Science Communication, String Theory, Yang-Mills, and Misc. There’s a menu in the sidebar that lets you pick a category and look at posts from only that category.

I’ve also added a variety of tags, many of which are listed in the tag cloud in the sidebar. Bigger tags indicate more content.

There’s a blogroll now, of blogs I think are worth reading, including a mix of established folks and interesting people I’ve run into.

I’ve put the guide to N=8 supergravity up in the menus at the top, along with a collection of my posts on physics careers, and some general quantum field theory posts that I reference a lot. Each is in a separate section under Handy Handbooks. The posts have been cleaned up a bit, so if you missed them the first time be sure to take a gander.

Finally, I’ve added a Contact page, in case you want to ask me questions that don’t make sense as comments.

Take some time to explore the new features! And welcome to the next phase in the trials and tribulations of four gravitons and a postdoc!

Caltech Amplitudes Workshop, and Valentines Poem 2014

4 gravitons

Stories about physics from someone who's been there