Tag Archives: particle physics

A Paper About Ranking Papers

If you’ve ever heard someone list problems in academia, citation-counting is usually near the top. Hiring and tenure committees want easy numbers to judge applicants with: number of papers, number of citations, or related statistics like the h-index. Unfortunately, these metrics can be gamed, leading to a host of bad practices that get blamed for pretty much everything that goes wrong in science. In physics, it’s not even clear that these statistics tell us anything: papers in our field have been including more citations over time, and for thousand-person experimental collaborations the number of citations and papers don’t really reflect any one person’s contribution.

It’s pretty easy to find people complaining about this. It’s much rarer to find a proposed solution.

That’s why I quite enjoyed Alessandro Strumia and Riccardo Torre’s paper last week, on Biblioranking fundamental physics.

Some of their suggestions are quite straightforward. With the number of citations per paper increasing, it makes sense to divide each paper by the number of citations it contains: it means more to get cited by a paper with ten citations than by a paper with one hundred. Similarly, you could divide credit for a paper among its authors, rather than giving each author full credit.

Some are more elaborate. They suggest using a variant of Google’s PageRank algorithm to rank papers and authors. Essentially, the algorithm imagines someone wandering from paper to paper and tries to figure out which papers are more central to the network. This is apparently an old idea, but by combining it with their normalization by number of citations they eke a bit more mileage from it. (I also found their treatment a bit clearer than the older papers they cite. There are a few more elaborate setups in the literature as well, but they seem to have a lot of free parameters so Strumia and Torre’s setup looks preferable on that front.)

One final problem they consider is that of self-citations, and citation cliques. In principle, you could boost your citation count by citing yourself. While that’s easy to correct for, you could also be one of a small number of authors who cite each other a lot. To keep the system from being gamed in this way, they propose a notion of a “CitationCoin” that counts (normalized) citations received minus (normalized) citations given. The idea is that, just as you can’t make anyone richer just by passing money between your friends without doing anything with it, so a small community can’t earn “CitationCoins” without getting the wider field interested.

There are still likely problems with these ideas. Dividing each paper by its number of authors seems like overkill: a thousand-person paper is not typically going to get a thousand times as many citations. I also don’t know whether there are ways to game this system: since the metrics are based in part on citations given, not just citations received, I worry there are situations where it would be to someone’s advantage to cite others less. I think they manage to avoid this by normalizing by number of citations given, and they emphasize that PageRank itself is estimating something we directly care about: how often people read a paper. Still, it would be good to see more rigorous work probing the system for weaknesses.

In addition to the proposed metrics, Strumia and Torre’s paper is full of interesting statistics about the arXiv and InSpire databases, both using more traditional metrics and their new ones. Whether or not the methods they propose work out, the paper is definitely worth a look.

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Path Integrals and Loop Integrals: Different Things!

When talking science, we need to be careful with our words. It’s easy for people to see a familiar word and assume something totally different from what we intend. And if we use the same word twice, for two different things…

I’ve noticed this problem with the word “integral”. When physicists talk about particle physics, there are two kinds of integrals we mention: path integrals, and loop integrals. I’ve seen plenty of people get confused, and assume that these two are the same thing. They’re not, and it’s worth spending some time explaining the difference.

Let’s start with path integrals (also referred to as functional integrals, or Feynman integrals). Feynman promoted a picture of quantum mechanics in which a particle travels along many different paths, from point A to point B.

three_paths_from_a_to_b

You’ve probably seen a picture like this. Classically, a particle would just take one path, the shortest path, from A to B. In quantum mechanics, you have to add up all possible paths. Most longer paths cancel, so on average the short, classical path is the most important one, but the others do contribute, and have observable, quantum effects. The sum over all paths is what we call a path integral.

It’s easy enough to draw this picture for a single particle. When we do particle physics, though, we aren’t usually interested in just one particle: we want to look at a bunch of different quantum fields, and figure out how they will interact.

We still use a path integral to do that, but it doesn’t look like a bunch of lines from point A to B, and there isn’t a convenient image I can steal from Wikipedia for it. The quantum field theory path integral adds up, not all the paths a particle can travel, but all the ways a set of quantum fields can interact.

How do we actually calculate that?

One way is with Feynman diagrams, and (often, but not always) loop integrals.

4grav2loop

I’ve talked about Feynman diagrams before. Each one is a picture of one possible way that particles can travel, or that quantum fields can interact. In some (loose) sense, each one is a single path in the path integral.

Each diagram serves as instructions for a calculation. We take information about the particles, their momenta and energy, and end up with a number. To calculate a path integral exactly, we’d have to add up all the diagrams we could possibly draw, to get a sum over all possible paths.

(There are ways to avoid this in special cases, which I’m not going to go into here.)

Sometimes, getting a number out of a diagram is fairly simple. If the diagram has no closed loops in it (if it’s what we call a tree diagram) then knowing the properties of the in-coming and out-going particles is enough to know the rest. If there are loops, though, there’s uncertainty: you have to add up every possible momentum of the particles in the loops. You do that with a different integral, and that’s the one that we sometimes refer to as a loop integral. (Perhaps confusingly, these are also often called Feynman integrals: Feynman did a lot of stuff!)

\frac{i^{a+l(1-d/2)}\pi^{ld/2}}{\prod_i \Gamma(a_i)}\int_0^\infty...\int_0^\infty \prod_i\alpha_i^{a_i-1}U^{-d/2}e^{iF/U-i\sum m_i^2\alpha_i}d\alpha_1...d\alpha_n

Loop integrals can be pretty complicated, but at heart they’re the same sort of thing you might have seen in a calculus class. Mathematicians are pretty comfortable with them, and they give rise to numbers that mathematicians find very interesting.

Path integrals are very different. In some sense, they’re an “integral over integrals”, adding up every loop integral you could write down. Mathematicians can define path integrals in special cases, but it’s still not clear that the general case, the overall path integral picture we use, actually makes rigorous mathematical sense.

So if you see physicists talking about integrals, it’s worth taking a moment to figure out which one we mean. Path integrals and loop integrals are both important, but they’re very, very different things.

Why Your Idea Is Bad

By A. Physicist

 

Your idea is bad…

 

…because it disagrees with precision electroweak measurements

…………………………………..with bounds from ATLAS and CMS

…………………………………..with the power spectrum of the CMB

…………………………………..with Eötvös experiments

…because it isn’t gauge invariant

………………………….Lorentz invariant

………………………….diffeomorphism invariant

………………………….background-independent, whatever that means

…because it violates unitarity

…………………………………locality

…………………………………causality

…………………………………observer-independence

…………………………………technical naturalness

…………………………………international treaties

…………………………………cosmic censorship

…because you screwed up the calculation

…because you didn’t actually do the calculation

…because I don’t understand the calculation

…because you predict too many magnetic monopoles

……………………………………too many proton decays

……………………………………too many primordial black holes

…………………………………..remnants, at all

…because it’s fine-tuned

…because it’s suspiciously finely-tuned

…because it’s finely tuned to be always outside of experimental bounds

…because you’re misunderstanding quantum mechanics

…………………………………………………………..black holes

………………………………………………………….effective field theory

…………………………………………………………..thermodynamics

…………………………………………………………..the scientific method

…because Condensed Matter would contribute more to Chinese GDP

…because the approximation you’re making is unjustified

…………………………………………………………………………is not valid

…………………………………………………………………………is wildly overoptimistic

………………………………………………………………………….is just kind of lazy

…because there isn’t a plausible UV completion

…because you care too much about the UV

…because it only works in polynomial time

…………………………………………..exponential time

…………………………………………..factorial time

…because even if it’s fast it requires more memory than any computer on Earth

…because it requires more bits of memory than atoms in the visible universe

…because it has no meaningful advantages over current methods

…because it has meaningful advantages over my own methods

…because it can’t just be that easy

…because it’s not the kind of idea that usually works

…because it’s not the kind of idea that usually works in my field

…because it isn’t canonical

…because it’s ugly

…because it’s baroque

…because it ain’t baroque, and thus shouldn’t be fixed

…because only a few people work on it

…because far too many people work on it

…because clearly it will only work for the first case

……………………………………………………………….the first two cases

……………………………………………………………….the first seven cases

……………………………………………………………….the cases you’ve published and no more

…because I know you’re wrong

…because I strongly suspect you’re wrong

…because I strongly suspect you’re wrong, but saying I know you’re wrong looks better on a grant application

…….in a blog post

…because I’m just really pessimistic about something like that ever actually working

…because I’d rather work on my own thing, that I’m much more optimistic about

…because if I’m clear about my reasons

……and what I know

…….and what I don’t

……….then I’ll convince you you’re wrong.

 

……….or maybe you’ll convince me?

 

Unreasonably Big Physics

The Large Hadron Collider is big, eight and a half kilometers across. It’s expensive, with a cost to construct and operate in the billions. And with an energy of 6.5 TeV per proton, it’s the most powerful collider in the world, accelerating protons to 0.99999999 of the speed of light.

The LHC is reasonable. After all, it was funded, and built. What does an unreasonable physics proposal look like?

It’s probably unfair to call the Superconducting Super Collider unreasonable, after all, it did almost get built. It would have been a 28 kilometer-wide circle in the Texas desert, accelerating protons to an energy of 20 TeV, three times the energy of the LHC. When it was cancelled in 1993, it was projected to cost twelve billion dollars, and two billion had already been spent digging the tunnel. The US hasn’t invested in a similarly sized project since.

A better example of an unreasonable proposal might be the Collider-in-the-Sea. (If that link is paywalled, this paper covers most of the same information.)

mcint2-2656157-large

If you run out of room on land, why not build your collider underwater?

Ok, there are pretty obvious reasons why not. Surprisingly, the people proposing the Collider-in-the-Sea do a decent job of answering them. They plan to put it far enough out that it won’t disrupt shipping, and deep enough down that it won’t interfere with fish. Apparently at those depths even a hurricane barely ripples the water, and they argue that the technology exists to keep a floating ring stable under those conditions. All in all, they’re imagining a collider 600 kilometers in diameter, accelerating protons to 250 TeV, all for a cost they claim would be roughly comparable to the (substantially smaller) new colliders that China and Europe are considering.

I’m sure that there are reasons I’ve overlooked why this sort of project is impossible. (I mean, just look at the map!) Still, it’s impressive that they can marshal this much of an argument.

Besides, there are even more impossible projects, like this one, by Sugawara, Hagura, and Sanami. Their proposal for a 1000 TeV neutrino beam isn’t intended for research: rather, the idea is a beam powerful enough to send neutrinos through the Earth to destroy nuclear bombs. Such a beam could cause the bombs to detonate prematurely, “fizzling” with about 3% the explosion they would have normally.

In this case, Sugawara and co. admit that their proposal is pure fantasy. With current technology they would need a ring larger than the Collider-in-the-Sea, and the project would cost hundreds of billions of dollars. It’s not even clear who would want to build such a machine, or who could get away with building it: the authors imagine a science fiction-esque world government to foot the bill.

There’s a spectrum of papers that scientists write, from whimsical speculation to serious work. The press doesn’t always make the difference clear, so it’s a useful skill to see the clues in the writing that show where a given proposal lands. In the case of the Sugawara and co. proposal, the paper is littered with caveats, explicitly making it clear that it’s just a rough estimate. Even the first line, dedicating the paper to another professor, should get you to look twice: while this sometimes happens on serious papers, often it means the paper was written as a fun gift for the professor in question. The Collider-in-the-Sea doesn’t have these kinds of warning signs, and it’s clear its authors take it a bit more seriously. Nonetheless, comparing the level of detail to other accelerator proposals, even those from the same people, should suggest that the Collider-in-the-Sea isn’t entirely on the same level. As wacky as it is to imagine, we probably won’t get a collider that takes up most of the Gulf of Mexico, or a massive neutrino beam capable of blowing up nukes around the world.

Tutoring at GGI

I’m still at the Galileo Galilei Institute this week, tutoring at the winter school.

At GGI’s winter school, each week is featuring a pair of lecturers. This week, the lectures alternate between Lance Dixon covering the basics of amplitudeology and Csaba Csaki, discussing ways in which the Higgs could be a composite made up of new fundamental particles.

Most of the students at this school are phenomenologists, physicists who make predictions for particle physics. I’m an amplitudeologist, I study the calculation tools behind those predictions. You’d think these would be very close areas, but it’s been interesting seeing how different our approaches really are.

Some of the difference is apparent just from watching the board. In Csaki’s lectures, the equations that show up are short, a few terms long at most. When amplitudes show up, it’s for their general properties: how many factors of the coupling constant, or the multipliers that show up with loops. There aren’t any long technical calculations, and in general they aren’t needed: he’s arguing about the kinds of physics that can show up, not the specifics of how they give rise to precise numbers.

In contrast, Lance’s board filled up with longer calculations, each with many moving parts. Even things that seem simple from our perspective take a decent amount of board space to derive, and involve no small amount of technical symbol-shuffling. For most of the students, working out an amplitude this complicated was an unfamiliar experience. There are a few applications for which you need the kind of power that amplitudeology provides, and a few students were working on them. For the rest, it was a bit like learning about a foreign culture, an exercise in understanding what other people are doing rather than picking up a new skill themselves. Still, they made a strong go at it, and it was enlightening to see the pieces that ended up mattering to them, and to hear the kinds of questions they asked.

Our Bargain

Sabine Hossenfelder has a blog post this week chastising particle physicists and cosmologists for following “upside-down Popper”, or assuming a theory is worth working on merely because it’s falsifiable. She describes her colleagues churning out one hypothesis after another, each tweaking an old idea just enough to make it falsifiable in the next experiment, without caring whether the hypothesis is actually likely to be true.

Sabine is much more of an expert in this area of physics (phenomenology) than I am, and I don’t presume to tell her she’s wrong about that community. But the problem she’s describing is part of something bigger, something that affects my part of physics as well.

There’s a core question we’d all like to answer: what should physicists work on? What criteria should guide us?

Falsifiability isn’t the whole story. The next obvious criterion is a sense of simplicity, of Occam’s Razor or mathematical elegance. Sabine has argued against the latter, which prompted a friend of mine to comment that between rejecting falsifiability and elegance, Sabine must want us to stop doing high-energy physics at all!

That’s more than a little unfair, though. I think Sabine has a reasonably clear criterion in mind. It’s the same criterion that most critics of the physics mainstream care about. It’s even the same criterion being used by the “other side”, the sort of people who criticize anything that’s not string/SUSY/inflation.

The criterion is quite a simple one: physics research should be productive. Anything we publish, anything we work on, should bring us closer to understanding the real world.

And before you object that this criterion is obvious, that it’s subjective, that it ignores the very real disagreements between the Sabines and the Luboses of the world…before any of that, please let me finish.

We can’t achieve this criterion. And we shouldn’t.

We can’t demand that all physics be productive without breaking a fundamental bargain, one we made when we accepted that science could be a career.

1200px-13_portrait_of_robert_hooke

The Hunchback of Notre Science

It wasn’t always this way. Up until the nineteenth century, “scientist” was a hobby, not a job.

After Newton published his theory of gravity, he was famously accused by Robert Hooke of stealing the idea. There’s some controversy about this, but historians agree on a few points: that Hooke did write a letter to Newton suggesting a 1/r^2 force law, and that Hooke, unlike Newton, never really worked out the law’s full consequences.

Why not? In part, because Hooke, unlike Newton, had a job.

Hooke was arguably the first person for whom science was a full-time source of income. As curator of experiments for the Royal Society, it was his responsibility to set up demonstrations for each Royal Society meeting. Later, he also handled correspondence for the Royal Society Journal. These responsibilities took up much of his time, and as a result, even if he was capable of following up on the consequences of 1/r^2 he wouldn’t have had time to focus on it. That kind of calculation wasn’t what he was being paid for.

We’re better off than Hooke today. We still have our responsibilities, to journals and teaching and the like, at various stages of our careers. But in the centuries since Hooke expectations have changed, and real original research is no longer something we have to fit in our spare time. It’s now a central expectation of the job.

When scientific research became a career, we accepted a kind of bargain. On the positive side, you no longer have to be independently wealthy to contribute to science. More than that, the existence of professional scientists is the bedrock of technological civilization. With enough scientists around, we get modern medicine and the internet and space programs and the LHC, things that wouldn’t be possible in a world of rare wealthy geniuses.

We pay a price for that bargain, though. If science is a steady job, then it has to provide steady work. A scientist has to be able to go in, every day, and do science.

And the problem is, science doesn’t always work like that. There isn’t always something productive to work on. Even when there is, there isn’t always something productive for you to work on.

Sabine blames “upside-down Popper” on the current publish-or-perish environment in physics. If physics careers weren’t so cut-throat and the metrics they are judged by weren’t so flawed, then maybe people would have time to do slow, careful work on deeper topics rather than pumping out minimally falsifiable papers as fast as possible.

There’s a lot of truth to this, but I think at its core it’s a bit too optimistic. Each of us only has a certain amount of expertise, and sometimes that expertise just isn’t likely to be productive at the moment. Because science is a job, a person in that position can’t just go work at the Royal Mint like Newton did. (The modern-day equivalent would be working for Wall Street, but physicists rarely come back from that.) Instead, they keep doing what they know how to do, slowly branching out, until they’ve either learned something productive or their old topic becomes useful once more. You can think of it as a form of practice, where scientists keep their skills honed until they’re needed.

So if we slow down the rate of publication, if we create metrics for universities that let them hire based on the depth and importance of work and not just number of papers and citations, if we manage all of that then yes we will improve science a great deal. But Lisa Randall still won’t work on Haag’s theorem.

In the end, we’ll still have physicists working on topics that aren’t actually productive.

img_0622

A physicist lazing about unproductively under an apple tree

So do we have to pay physicists to work on whatever they want, no matter how ridiculous?

No, I’m not saying that. We can’t expect everyone to do productive work all the time, but we can absolutely establish standards to make the work more likely to be productive.

Strange as it may sound, I think our standards for this are already quite good, or at least better than many other fields.

First, there’s falsifiability itself, or specifically our attitude towards it.

Physics’s obsession with falsifiability has one important benefit: it means that when someone proposes a new model of dark matter or inflation that they tweaked to be just beyond the current experiments, they don’t claim to know it’s true. They just claim it hasn’t been falsified yet.

This is quite different from what happens in biology and the social sciences. There, if someone tweaks their study to be just within statistical significance, people typically assume the study demonstrated something real. Doctors base treatments on it, and politicians base policy on it. Upside-down Popper has its flaws, but at least it’s never going to kill anybody, or put anyone in prison.

Admittedly, that’s a pretty low bar. Let’s try to set a higher one.

Moving past falsifiability, what about originality? We have very strong norms against publishing work that someone else has already done.

Ok, you (and probably Sabine) would object, isn’t that easy to get around? Aren’t all these Popper-flippers pretending to be original but really just following the same recipe each time, modifying their theory just enough to stay falsifiable?

To some extent. But if they were really following a recipe, you could beat them easily: just write the recipe down.

Physics progresses best when we can generalize, when we skip from case-by-case to understanding whole swaths of cases at once. Over time, there have been plenty of cases in which people have done that, where a number of fiddly hand-made models have been summarized in one parameter space. Once that happens, the rule of originality kicks in: now, no-one can propose another fiddly model like that again. It’s already covered.

As long as the recipe really is just a recipe, you can do this. You can write up what these people are doing in computer code, release the code, and then that’s that, they have to do something else. The problem is, most of the time it’s not really a recipe. It’s close enough to one that they can rely on it, close enough to one that they can get paper after paper when they need to…but it still requires just enough human involvement, just enough genuine originality, to be worth a paper.

The good news is that the range of “recipes” we can code up increases with time. Some spaces of theories we might never be able to describe in full generality (I’m glad there are people trying to do statistics on the string landscape, but good grief it looks quixotic). Some of the time though, we have a real chance of putting a neat little bow on a subject, labeled “no need to talk about this again”.

This emphasis on originality keeps the field moving. It means that despite our bargain, despite having to tolerate “practice” work as part of full-time physics jobs, we can still nudge people back towards productivity.

 

One final point: it’s possible you’re completely ok with the idea of physicists spending most of their time “practicing”, but just wish they wouldn’t make such a big deal about it. Maybe you can appreciate that “can I cook up a model where dark matter kills the dinosaurs” is an interesting intellectual exercise, but you don’t think it should be paraded in front of journalists as if it were actually solving a real problem.

In that case, I agree with you, at least up to a point. It is absolutely true that physics has a dysfunctional relationship with the media. We’re too used to describing whatever we’re working on as the most important thing in the universe, and journalists are convinced that’s the only way to get the public to pay attention. This is something we can and should make progress on. An increasing number of journalists are breaking from the trend and focusing not on covering the “next big thing”, but in telling stories about people. We should do all we can to promote those journalists, to spread their work over the hype, to encourage the kind of stories that treat “practice” as interesting puzzles pursued by interesting people, not the solution to the great mysteries of physics. I know that if I ever do anything newsworthy, there are some journalists I’d give the story to before any others.

At the same time, it’s important to understand that some of the dysfunction here isn’t unique to physics, or even to science. Deep down the reason nobody can admit that their physics is “practice” work is the same reason people at job interviews claim to love the company, the same reason college applicants have to tell stirring stories of hardship and couples spend tens of thousands on weddings. We live in a culture in which nothing can ever just be “ok”, in which admitting things are anything other than exceptional is akin to calling them worthless. It’s an arms-race of exaggeration, and it goes far beyond physics.

(I should note that this “culture” may not be as universal as I think it is. If so, it’s possible its presence in physics is due to you guys letting too many of us Americans into the field.)

 

We made a bargain when we turned science into a career. We bought modernity, but the price we pay is subsidizing some amount of unproductive “practice” work. We can negotiate the terms of our bargain, and we should, tilting the field with incentives to get it closer to the truth. But we’ll never get rid of it entirely, because science is still done by people. And sometimes, despite what we’re willing to admit, people are just “ok”.

One, Two, Infinity

Physicists and mathematicians count one, two, infinity.

We start with the simplest case, as a proof of principle. We take a stripped down toy model or simple calculation and show that our idea works. We count “one”, and we publish.

Next, we let things get a bit more complicated. In the next toy model, or the next calculation, new interactions can arise. We figure out how to deal with those new interactions, our count goes from “one” to “two”, and once again we publish.

By this point, hopefully, we understand the pattern. We know what happens in the simplest case, and we know what happens when the different pieces start to interact. If all goes well, that’s enough: we can extrapolate our knowledge to understand not just case “three”, but any case: any model, any calculation. We publish the general case, the general method. We’ve counted one, two, infinity.

200px-infinite-svg

Once we’ve counted “infinity”, we don’t have to do any more cases. And so “infinity” becomes the new “zero”, and the next type of calculation you don’t know how to do becomes “one”. It’s like going from addition to multiplication, from multiplication to exponentiation, from exponentials up into the wilds of up-arrow notation. Each time, once you understand the general rules you can jump ahead to an entirely new world with new capabilities…and repeat the same process again, on a new scale. You don’t need to count one, two, three, four, on and on and on.

Of course, research doesn’t always work out this way. My last few papers counted three, four, five, with six on the way. (One and two were already known.) Unlike the ideal cases that go one, two, infinity, here “two” doesn’t give all the pieces you need to keep going. You need to go a few numbers more to get novel insights. That said, we are thinking about “infinity” now, so look forward to a future post that says something about that.

A lot of frustration in physics comes from situations when “infinity” remains stubbornly out of reach. When people complain about all the models for supersymmetry, or inflation, in some sense they’re complaining about fields that haven’t taken that “infinity” step. One or two models of inflation are nice, but by the time the count reaches ten you start hoping that someone will describe all possible models of inflation in one paper, and see if they can make any predictions from that.

(In particle physics, there’s an extent to which people can actually do this. There are methods to describe all possible modifications of the Standard Model in terms of what sort of effects they can have on observations of known particles. There’s a group at NBI who work on this sort of thing.)

The gold standard, though, is one, two, infinity. Our ability to step back, stop working case-by-case, and move on to the next level is not just a cute trick: it’s a foundation for exponential progress. If we can count one, two, infinity, then there’s nowhere we can’t reach.