Tag Archives: gravity

Thoughts from the Winter School

There are two things I’d like to talk about this week.

First, as promised, I’ll talk about what I worked on at the PSI Winter School.

Freddy Cachazo and I study what are called scattering amplitudes. At first glance, these are probabilities that two subatomic particles scatter off each other, relevant for experiments like the Large Hadron Collider. In practice, though, they can calculate much more.

For example, let’s say you have two black holes circling each other, like the ones LIGO detected. Zoom out far enough, and you can think of each one as a particle. The two particle-black holes exchange gravitons, and those exchanges give rise to the force of gravity between them.


In the end, it’s all just particle physics.


Based on that, we can use our favorite scattering amplitudes to make predictions for gravitational wave telescopes like LIGO.

There’s a bit of weirdness to this story, though, because these amplitudes don’t line up with predictions in quite the way we’re used to. The way we calculate amplitudes involves drawing diagrams, and those diagrams have loops. Normally, each “loop” makes the amplitude more quantum-mechanical. Only the diagrams with no loops (“tree diagrams”) come from classical physics alone.

(Here “classical physics” just means “not quantum”: I’m calling general relativity “classical”.)

For this problem, we only care about classical physics: LIGO isn’t sensitive enough to see quantum effects. The weird thing is, despite that, we still need loops.

(Why? This is a story I haven’t figured out how to tell in a non-technical way. The technical explanation has to do with the fact that we’re calculating a potential, not an amplitude, so there’s a Fourier transformation, and keeping track of the dimensions entails tossing around some factors of Planck’s constant. But I feel like this still isn’t quite the full story.)

So if we want to make predictions for LIGO, we want to compute amplitudes with loops. And as amplitudeologists, we should be pretty good at that.

As it turns out, plenty of other people have already had that idea, but there’s still room for improvement.

Our time with the students at the Winter School was limited, so our goal was fairly modest. We wanted to understand those other peoples’ calculations, and perhaps to think about them in a slightly cleaner way. In particular, we wanted to understand why “loops” are really necessary, and whether there was some way of understanding what the “loops” were doing in a more purely classical picture.

At this point, we feel like we’ve got the beginning of an idea of what’s going on. Time will tell whether it works out, and I’ll update you guys when we have a more presentable picture.


Unfortunately, physics wasn’t the only thing I was thinking about last week, which brings me to my other topic.

This blog has a fairly strong policy against talking politics. This is for several reasons. Partly, it’s because politics simply isn’t my area of expertise. Partly, it’s because talking politics tends to lead to long arguments in which nobody manages to learn anything. Despite this, I’m about to talk politics.

Last week, citizens of Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen were barred from entering the US. This included not only new visa applicants, but also those who already have visas or green cards. The latter group includes long-term residents of the US, many of whom were detained in airports and threatened with deportation when their flights arrived shortly after the ban was announced. Among those was the president of the Graduate Student Organization at my former grad school.

A federal judge has blocked parts of the order, and the Department of Homeland Security has announced that there will be case-by-case exceptions. Still, plenty of people are stuck: either abroad if they didn’t get in in time, or in the US, afraid that if they leave they won’t be able to return.

Politics isn’t in my area of expertise. But…

I travel for work pretty often. I know how terrifying and arbitrary border enforcement can be. I know how it feels to risk thousands of dollars and months of planning because some consulate or border official is having a bad day.

I also know how essential travel is to doing science. When there’s only one expert in the world who does the sort of work you need, you can’t just find a local substitute.

And so for this, I don’t need to be an expert in politics. I don’t need a detailed case about the risks of terrorism. I already know what I need to, and I know that this is cruel.

And so I stand in solidarity with the people who were trapped in airports, and those still trapped abroad and trapped in the US. You have been treated cruelly, and you shouldn’t have been. Hopefully, that sort of message can transcend politics.


One final thing: I’m going to be a massive hypocrite and continue to ban political comments on this blog. If you want to talk to me about any of this (and you think one or both of us might actually learn something from the exchange) please contact me in private.

Fun with Misunderstandings

Perimeter had its last Public Lecture of the season this week, with Mario Livio giving some highlights from his book Brilliant Blunders. The lecture should be accessible online, either here or on Perimeter’s YouTube page.

These lectures tend to attract a crowd of curious science-fans. To give them something to do while they’re waiting, a few local researchers walk around with T-shirts that say “Ask me, I’m a scientist!” Sometimes we get questions about the upcoming lecture, but more often people just ask us what they’re curious about.

Long-time readers will know that I find this one of the most fun parts of the job. In particular, there’s a unique challenge in figuring out just why someone asked a question. Often, there’s a hidden misunderstanding they haven’t recognized.

The fun thing about these misunderstandings is that they usually make sense, provided you’re working from the person in question’s sources. They heard a bit of this and a bit of that, and they come to the most reasonable conclusion they can given what’s available. For those of us who have heard a more complete story, this often leads to misunderstandings we would never have thought of, but that in retrospect are completely understandable.

One of the simpler ones I ran into was someone who was confused by people claiming that we were running out of water. How could there be a water shortage, he asked, if the Earth is basically a closed system? Where could the water go?

The answer is that when people are talking about a water shortage, they’re not talking about water itself running out. Rather, they’re talking about a lack of safe drinking water. Maybe the water is polluted, or stuck in the ocean without expensive desalinization. This seems like the sort of thing that would be extremely obvious, but if you just hear people complaining that water is running out without the right context then you might just not end up hearing that part of the story.

A more involved question had to do with time dilation in general relativity. The guy had heard that atomic clocks run faster if you’re higher up, and that this was because time itself runs faster in lower gravity.

Given that, he asked, what happens if someone travels to an area of low gravity and then comes back? If more time has passed for them, then they’d be in the future, so wouldn’t they be at the “wrong time” compared to other people? Would they even be able to interact with them?

This guy’s misunderstanding came from hearing what happens, but not why. While he got that time passes faster in lower gravity, he was still thinking of time as universal: there is some past, and some future, and if time passes faster for one person and slower for another that just means that one person is “skipping ahead” into the other person’s future.

What he was missing was the explanation that time dilation comes from space and time bending. Rather than “skipping ahead”, a person for whom time passes faster just experiences more time getting to the same place, because they’re traveling on a curved path through space-time.

As usual, this is easier to visualize in space than in time. I ended up drawing a picture like this:


Imagine person A and person B live on a circle. If person B stays the same distance from the center while person A goes out further, they can both travel the same angle around the circle and end up in the same place, but A will have traveled further, even ignoring the trips up and down.

What’s completely intuitive in space ends up quite a bit harder to visualize in time. But if you at least know what you’re trying to think about, that there’s bending involved, then it’s easier to avoid this guy’s kind of misunderstanding. Run into the wrong account, though, and even if it’s perfectly correct (this guy had heard some of Hawking’s popularization work on the subject), if it’s not emphasizing the right aspects you can come away with the wrong impression.

Misunderstandings are interesting because they reveal how people learn. They’re windows into different thought processes, into what happens when you only have partial evidence. And because of that, they’re one of the most fascinating parts of science popularization.

Mass Is Just Energy You Haven’t Met Yet

How can colliding two protons give rise to more massive particles? Why do vibrations of a string have mass? And how does the Higgs work anyway?

There is one central misunderstanding that makes each of these topics confusing. It’s something I’ve brought up before, but it really deserves its own post. It’s people not realizing that mass is just energy you haven’t met yet.

It’s quite intuitive to think of mass as some sort of “stuff” that things can be made out of. In our everyday experience, that’s how it works: combine this mass of flour and this mass of sugar, and get this mass of cake. Historically, it was the dominant view in physics for quite some time. However, once you get to particle physics it starts to break down.

It’s probably most obvious for protons. A proton has a mass of 938 MeV/c², or 1.6×10⁻²⁷ kg in less physicist-specific units. Protons are each made of three quarks, two up quarks and a down quark. Naively, you’d think that the quarks would have to be around 300 MeV/c². They’re not, though: up and down quarks both have masses less than 10 MeV/c². Those three quarks account for less than a fiftieth of a proton’s mass.

The “extra” mass is because a proton is not just three quarks. It’s three quarks interacting. The forces between those quarks, the strong nuclear force that binds them together, involves a heck of a lot of energy. And from a distance, that energy ends up looking like mass.

This isn’t unique to protons. In some sense, it’s just what mass is.

The quarks themselves get their mass from the Higgs field. Far enough away, this looks like the quarks having a mass. However, zoom in and it’s energy again, the energy of interaction between quarks and the Higgs. In string theory, mass comes from the energy of vibrating strings. And so on. Every time we run into something that looks like a fundamental mass, it ends up being just another energy of interaction.

If mass is just energy, what about gravity?

When you’re taught about gravity, the story is all about mass. Mass attracts mass. Mass bends space-time. What gets left out, until you actually learn the details of General Relativity, is that energy gravitates too.

Normally you don’t notice this, because mass contributes so much more to energy than anything else. That’s really what E=m is really about: it’s a unit conversion formula. It tells you that if you want to know how much energy a given mass “really is”, you multiply it by the speed of light squared. And that’s a large enough number that most of the time, when you notice energy gravitating, it’s because that energy looks like a big chunk of mass. (It’s also why physicists like silly units like MeV/c² for mass: we can just multiply by c² and get an energy!)

It’s really tempting to think about mass as a substance, of mass as always conserved, of mass as fundamental. But in physics we often have to toss aside our everyday intuitions, and this is no exception. Mass really is just energy. It’s just energy that we’ve “zoomed out” enough not to notice.

Source Your Common Sense

When I wrote that post on crackpots, one of my inspirations was a particularly annoying Twitter conversation. The guy I was talking to had convinced himself that general relativity was a mistake. He was especially pissed off by the fact that, in GR, energy is not always conserved. Screw Einstein, energy conservation is just common sense! Right?

Think a little bit about why you believe in energy conservation. Is it because you run into a lot of energy in your day-to-day life, and it’s always been conserved? Did you grow up around something that was obviously energy? Or maybe someone had to explain it to you?

Teacher Pointing at Map of World

Maybe you learned about it…from a physics teacher?

A lot of the time, things that seem obvious only got that way because you were taught them. “Energy” isn’t an intuitive concept, however much it’s misused that way. It’s something defined by physicists because it solves a particular role, a consequence of symmetries in nature. When you learn about energy conservation in school, that’s because it’s one of the simpler ways to explain a much bigger concept, so you shouldn’t be surprised if there are some inaccuracies. If you know where your “common sense” is coming from, you can anticipate when and how it might go awry.

Similarly, if, like one of the commenters on my crackpot post, you’re uncomfortable with countable and uncountable infinities, remember that infinity isn’t “common sense” either. It’s something you learned about in a math class, from a math teacher. And just like energy conservation, it’s a simplification of a more precise concept, with epsilons and deltas and all that jazz.

It’s not possible to teach all the nuances of every topic, so naturally most people will hear a partial story. What’s important is to recognize that you heard a partial story, and not enshrine it as “common sense” when the real story comes knocking.

Don’t physicists use common sense, though? What about “physical intuition”?

Physical intuition has a lot of mystique behind it, and is often described as what separates us from the mathematicians. As such, different people mean different things by it…but under no circumstances should it be confused with pure “common sense”. Physical intuition uses analogy and experience. It involves seeing a system and anticipating the sorts of things you can do with it, like playing a game and assuming there’ll be a save button. In order for these sorts of analogies to work, they generally aren’t built around everyday objects or experiences. Instead, they use physical systems that are “similar” to the one under scrutiny in important ways, while being better understood in others. Crucially, physical intuition involves working in context. It’s not just uncritical acceptance of what one would naively expect.

So when your common sense is tingling, see if you can provide a source. Is that source relevant, experience with a similar situation? Or is it in fact a half-remembered class from high school?

Things You Don’t Know about the Power of the Dark Side

Last Wednesday, Katherine Freese gave a Public Lecture at Perimeter on the topic of Dark Matter and Dark Energy. The talk should be on Perimeter’s YouTube page by the time this post is up.

Answering twitter questions during the talk made me realize that there’s a lot the average person finds confusing about Dark Matter and Dark Energy. Freese addressed much of this pretty well in her talk, but I felt like there was room for improvement. Rather than try to tackle it myself, I decided to interview an expert on the Dark Side of the universe.


Twitter doesn’t know the power of the dark side!

Lord Vader, some people have a hard time distinguishing Dark Matter and Dark Energy. What do you have to say to them?

Fools! Light side astronomers call “dark” that which they cannot observe and cannot understand. “Fear” and “anger” are different heights of emotion, but to the Jedi they are only the path to the Dark Side. Dark Energy and Dark Matter are much the same: both distinct, both essential to the universe, and both “dark” to the telescopes of the light.

Let’s start with Dark Matter. Is it really matter?

You ask an empty question. “Matter” has been defined in many ways. When we on the Dark Side refer to Dark Matter, we merely mean to state that it behaves much like the matter you know: it is drawn to and fro by gravity, sloshing about.

It is distinct from your ordinary matter in that two of the forces of nature, the strong nuclear force and electromagnetism, do not concern it. Ordinary matter is bound together in the nuclei of atoms by the strong force, or woven into atoms and molecules by electromagnetism. This makes it subject to all manner of messy collisions.

Dark Matter, in contrast, is pure, partaking neither of nuclear nor chemical reactions. It passes through each of us with no notice. Only the weak nuclear force and gravity affect it. The latter has brought it slowly into clumps and threads through the universe, each one a vast nest for groupings of stars. Truly, Dark Matter surrounds us, penetrates us, and binds the galaxy together.

Could Dark Matter be something we’re more familiar with, like neutrinos or black holes? What about a modification of gravity?

Many wondered as much, when the study of the Dark Side was young. They were wrong.

The matter you are accustomed to composes merely a twentieth of the universe, while Dark Matter is more than a quarter. There is simply not enough of these minor contributions, neutrinos and black holes, to account for the vast darkness that surrounds the galaxy, and with each astronomer’s investigation we grow more assured.

As for modifying gravity, do you seek to modify a fundamental Force?

If so, you should be wary. Forces, by their nature, are accompanied by particles, and gravity is no exception. Take care that your tinkering does not result in a new sort of particle. If so, you may be unknowingly walking the path of the Dark Side, for your modification may be just another form of Dark Matter.

What sort of things could Dark Matter be? Can Dark Matter decay into ordinary matter? Could there be anti-Dark Matter?

As of yet, your scientists are still baffled by the nature of Dark Matter. Still, there are limits. Since only rare events could produce it from ordinary matter, the universe’s supply of Dark Matter must be ancient, dating back to the dawn of the cosmos. In that case, it must decay only slowly, if at all. Similarly, if Dark Matter had antimatter forms then its interactions must be so weak that it has not simply annihilated with its antimatter half across the universe. So while either is possible, it may be simpler for your theorists if Dark Matter did not decay, and was its own antimatter counterpart. On the other hand, if Dark Matter did undergo such reactions, your kind may one day be able to detect it.

Of course, as a master of the Dark Side I know the true nature of Dark Matter. However, I could only impart it to a loyal apprentice…

Yeah, I think I’ll pass on that. They say you can only get a job in academia when someone dies, but unlike the Sith they don’t mean it literally.

Let’s move on to Dark Energy. What can you tell us about it?

Dark “Energy”, like Dark Matter, is named for what people on your Earth cannot comprehend. Nothing, not even Dark Energy, is “made of energy”. Dark Energy is “energy” merely because it behaves unlike matter.

Matter, even Dark Matter, is drawn together by the force of gravity. Under its yoke, the universe would slow down in its expansion and eventually collapse into a crunch, like the throat of an incompetent officer.

However, the universe is not collapsing, but accelerating, galaxies torn away from each other by a force that must compose more than two thirds of the universe. It is rather like the Yuuzhan Vong, a mysterious force from outside the galaxy that scouts persistently under- or over-estimate.

Umm, I’m pretty sure the Yuuzhan Vong don’t exist anymore, since Disney got rid of the Expanded Universe.

That perfidious Mouse!

Well folks, Vader is now on a rampage of revenge in the Disney offices, so I guess we’ll have to end the interview. Tune in next week, and until then, may the Force be with you!

You Go, LIGO!

Well folks, they did it. LIGO has detected gravitational waves!


What’s a gravitational wave?

Gravitational waves are ripples in space and time. As Einstein figured out a century ago, masses bend space and time, which causes gravity. Wiggle masses in the right way and you get a gravity wave, like a ripple on a pond.

Ok, but what is actually rippling? It’s some stuff, right? Dust or something?

In a word, no. Not everything has to be “stuff”. Energy isn’t “stuff”, and space-time isn’t either, but space-time is really what vibrates when a gravitational wave passes by. Distances themselves are changing, in a way that is described by the same math and physics as a ripple in a pond.

What’s LIGO?

LIGO is the Laser Interferometer Gravitational-Wave Observatory. In simple terms, it’s an observatory (or rather, a pair of observatories in Washington and Louisiana) that can detect gravitational waves. It does this using beams of laser light four kilometers long. Gravitational waves change the length of these beams when they pass through, causing small but measurable changes in the laser light observed.

Are there other gravitational wave observatories?

Not currently in operation. LIGO originally ran from 2002 to 2010, and during that time there were other gravitational wave observatories also in operation (VIRGO in Italy and GEO600 in Germany). All of them (including LIGO) failed to detect anything, and so LIGO and VIRGO were shut down in order for them to be upgraded to more sensitive, advanced versions. Advanced LIGO went into operation first, and made the detection. VIRGO is still under construction, as is KAGRA, a detector in Japan. There are also plans for a detector in India.

Other sorts of experiments can detect gravitational waves on different scales. eLISA is a planned space-based gravitational wave observatory, while Pulsar Timing Arrays could use distant neutron stars as an impromptu detector.

What did they detect? What could they detect?

The gravitational waves that LIGO detected came from a pair of black holes merging. In general, gravitational waves come from a pair of masses, or one mass with an uneven and rapidly changing shape. As such, LIGO and future detectors might be able to observe binary stars, supernovas, weird-shaped neutron stars, colliding galaxies…pretty much any astrophysical event involving large things moving comparatively fast.

What does this say about string theory?

Basically nothing. There are gravity waves in string theory, sure (and they play a fairly important role), but there were gravity waves in Einstein’s general relativity. As far as I’m aware, no-one at this point seriously thought that gravitational waves didn’t exist. Nothing that LIGO observed has any bearing on the quantum properties of gravity.

But what about cosmic strings? They mentioned those in the announcement!

Cosmic strings, despite the name, aren’t a unique prediction of string theory. They’re big, string-shaped wrinkles in space and time, possible results of the rapid expansion of space during cosmic inflation. You can think of them a bit like the cracks that form in an over-inflated balloon right before it bursts.

Cosmic strings, if they exist, should produce gravitational waves. This means that in the future we may have concrete evidence of whether or not they exist. This wouldn’t say all that much about string theory: while string theory does have its own explanations for cosmic strings, it’s unclear whether it actually has unique predictions about them. It would say a lot about cosmic inflation, though, and would presumably help distinguish it from proposed alternatives. So keep your eyes open: in the next few years, gravitational wave observatories may well have something important to say about the overall history of the universe.

Why is this discovery important, though? If we already knew that gravitational waves existed, why does discovering them matter?

LIGO didn’t discover that gravitational waves exist. LIGO discovered that we can detect them.

The existence of gravitational waves is no discovery. But the fact that we now have observatories sensitive enough to detect them is huge. It opens up a whole new type of astronomy: we can now observe the universe not just by the light it sheds (and neutrinos), but through a whole new lens. And every time we get another observational tool like this, we notice new things, things we couldn’t have seen without it. It’s the dawn of a new era in astronomy, and LIGO was right to announce it with all the pomp and circumstance they could muster.


My impressions from the announcement:

Speaking of pomp and circumstance, I was impressed by just how well put-together LIGO’s announcement was.

As the US presidential election heats up, I’ve seen a few articles about the various candidates’ (well, usually Trump’s) use of the language of political propaganda. The idea is that there are certain visual symbols at political events for which people have strong associations, whether with historical events or specific ideas or the like, and that using these symbols makes propaganda more powerful.

What I haven’t seen is much discussion of a language of scientific propaganda. Still, the overwhelming impression I got from LIGO’s announcement is that it was shaped by a master in the use of such a language. They tapped in to a wide variety of powerful images: from the documentary-style interviews at the beginning, to Weiss’s tweed jacket and handmade demos, to the American flag in the background, that tied LIGO’s result to the history of scientific accomplishment.

Perimeter’s presentations tend to have a slicker look, my friends at Stony Brook are probably better at avoiding jargon. But neither is quite as good at propaganda, at saying “we are part of history” and doing so without a hitch, as the folks at LIGO have shown themselves to be with this announcement.

I was also fairly impressed that they kept this under wraps for so long. While there were leaks, I don’t think many people had a complete grasp of what was going to be announced until the week before. Somehow, LIGO made sure a collaboration of thousands was able to (mostly) keep their mouths shut!

Beyond the organizational and stylistic notes, my main thought was “What’s next?” They’ve announced the detection of one event. I’ve heard others rattle off estimates, that they should be detecting anywhere from one black hole merger per year to a few hundred. Are we going to see more events soon, or should we settle into a long wait? Could they already have detected more, with the evidence buried in their data, to be revealed by careful analysis? (The waves from this black hole merger were clear enough for them to detect them in real-time, but more subtle events might not make things so easy!) Should we be seeing more events already, and does not seeing them tell us something important about the universe?

Most of the reason I delayed my post till this week was to see if anyone had an answer to these questions. So far, I haven’t seen one, besides the “one to a few hundred” estimate mentioned. As more people weigh in and more of LIGO’s run is analyzed, it will be interesting to see where that side of the story goes.

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.