Physicists Uncover Geometric ‘Theory Space’ | Hacker News Reader

Physicists Uncover Geometric ‘Theory Space’

quantamagazine.org

266 pointssrameshc88 comments

I work directly in this field. This article covers a lot of a material that is at the forefront of theoretical high energy physics where we are neck-deep in the 'fog of war.' Truthfully, I can think of few subjects more difficult to describe to people not in the field than the conformal bootstrap; there are a lot of technical details that are easy to get hung up on but are crucial for understanding the big picture.

From the article, it looks very promising! Forgive me for my lack of understanding, but the article made it sound like it could supplant the notion of quarks and/or other elementary particles. Is that correct?

Yes, not that they do exist but perhaps the notion of how a quantum field theory of quarks is really nearly the same thing in some ways as an Ising model, etc. The ultimate goal is to understand how these disparate physical systems are similarly mathematically structured and how to get from one to the next, and to find out the limits of the space of theories. (The signposts and roads analogy in the article is a good one.)

That was Chew's original motivation, explaining the hadron/meson zoo without quarks and gluons, but it's not likely to happen any time soon. The conformal bootstrap program is about analyzing _conformal_ QFTs, those which look the same at every magnification setting. (The theory of hadrons is not conformal; if you zoom in, the particles get bigger.) In conformal QFTs, it turns out something like Chew's vision does hold. This implies a huge set of constraints, and it turns out you can use these constraints to find solutions to the equations of motion of these theories. This is a bit of a miracle, since it's extremely hard to solve these equations directly. It's also rather valuable, since conformal QFTs describe a lot of natural physical system (like the triple point phase of water). Being able to solve these theories with sufficiently good approximations means that you can compare theoretical and experimental predictions.

Can you recommend some reading material, maybe a textbook, for folks who want to get into the details?

That would take multiple textbooks and probably a couple years at minimum.

Jared Kaplan, one of the researchers mentioned in the article, has a good set of notes here: http://sites.krieger.jhu.edu/jared-kaplan/files/2016/05/AdSC...

David Tong does a good job explaining background physics and his notes can be found here: http://www.damtp.cam.ac.uk/user/tong/teaching.html

The fourth chapter of his string theory notes are about as approachable an introduction to conformal field theory that there is. His QFT notes are good too.

Any chance you can attempt to ELI5 or ELI15 it?

I'll give it a shot!

Why are we interested in conformal field theories (CFTs)? One reason is it appears that all quantum field theories (QFTs) can be viewed as points along a “path” between a high-energy CFT to a low-energy CFT (c.f. the roadmap analogy in the article). Therefore, studying CFTs lets us study the space of well-defined QFTs, which are the mathematical framework in which to construct models in particle physics.

At the same time, we can describe seemingly unrelated theories like the 3d Ising model as CFTs. The conformal bootstrap approach has enabled researchers to recently calculate the critical exponents for the 3d Ising model, which effectively “solves” the theory as the critical exponents are universal and characterize all the physical properties of a theory.

The whole business about the “unknown polyhedron” and mapping “the geometry of theory space” means figuring out where these theories (e.g. Ising and other thing) live on this (higher-dimensional) map in relation to each other and potentially how to get from one to the other.

The article briefly talks about the AdS/CFT or holographic principle and how we can use CFTs to study gravity (this is more what I'm interested in) but this is a whole other can of worms. Needless to say, it's also super exciting! Two examples of the types of 'big' questions being looked at are gravity as 'emerging' from a CFT and probing the black hole information paradox / beyond the horizon.

Hope this helps!

Barrel of monkeys for physics math.

Out of curiosity, was Robert B. Laughlins (Nobel price for Laughlin wavefunction explaining the fractional quantum Hall effect) on right track and is his work any way relevant to what is currently happening?

The Theory of Everything, R. B. Laughlin and David Pines http://www.pnas.org/content/97/1/28.full

A Different Universe: Reinventing Physics from the Bottom Down, R. B. Laughlin https://www.amazon.com/Different-Universe-Reinventing-Physic...

http://large.stanford.edu/publications/

I'm not well-versed in his work but it seems like Laughlin is an advocate for the approaches to looking at the system instead of the components. One could say that is what the conformal bootstrap does when it's used to solve a theory by calculating its critical exponents. I'd definitely be interested in seeing if we could calculate the critical exponent of the IR fixed point of turbulence.

But like a Fourier transform is able to take something complex and express using simpler mathematical language.

I would assume we could take something extremely abstract and explain it using simpler abstractions that more people could understand; similar to a Fourier transform.

I really enjoy this magazine, but them and a couple others seem to have an "earth shattering" theory announcement nearly every week and it is often hard to tell from the articles if these are truly fundamental discoveries or I'm just being taken for clickbait.

I don't understand the point of most of these pop-sci articles. They are too difficult to understand for the layman, but they are too handwavy and contain too many silly analogies and too little insight for those who are truly interested.

One of the reasons I gave up on New Scientist. We would be much better served by more in-depth articles that don’t claim to ‘change everything’ but instead inform.

Then it means they are for the layman. Layman isn't after understanding, but curiosity, wonder, anger, whatever fuels his emotional needs at the moment.

Are you talking about cave people, or fellow human beings?

Curiosity and wonder are the motivation for understanding, even among researchers.

Or do you believe that researchers do their work for a PhD and for the compensation?

Not sure why you mention anger. I picture an angry plumber ripping up an issue of Popular Science while sitting in a La-Z-Boy and drinking a Rolling Rock.

> Curiosity and wonder are the motivation for understanding, even among researchers.

Right, and the layperson is just interested in those first two things, whereas the researcher follows through to the point of understanding. Or maybe they don't. Someone who does research is not necessarily interested in understanding every single field either.

The cave man was exactly as human as you.

Nowhere does his post condemn the satisfying of emotional needs. In fact, given that emotions are primary action catalysts, his post asserts Quanta is doing very important cultural work.

This is such a bizarre way to totally miss the point.

Let me respond to the left turn you just took. There are genetic and social differences between our prehistoric ancestors and modern humans. Where exactly we draw the line of who is a "caveman" and who is not, is ancillary to the point:

You're evaluating the statement, a "then" statement, without considering the antecedents from its parent comment.

He uses "laypeople" to describe a group of people who are not truly interested, who are not seeking understanding, and who use pop-sci literature to abate basal emotions like anger.

> In fact, given that emotions are primary action catalysts, his post asserts Quanta is doing very important cultural work.

By that logic, every magazine for people who are not truly interested and don't seek understanding is potentially culturally important if it can connect with emotions. I don't buy it.

Cave people is such a nebulous term that I probably shouldn't have responded to that part of your post :\

He says the layperson isn't seeking understanding, yes. To conflate that, and curiosity, wonder, and anger, with being -not truly interested-, baffles me. Maybe you disagree that interest manifests in ways besides seeking understanding?

Thanks for clarification, it was precisely my point: layman won't understand true detail but they won't care, because the sense of interest in those articles comes from other 'rewards' (more emotional).

I think this attitude vastly underestimates how messy of a process knowing actually is. To give just one point here: understanding a topic---even a single assertion---isn't like a switch, something you lack one moment and have the next. A researcher who can use knowledge about a topic in a wide variety of contexts (especially beyond their mechanical training) and who can map it into a wide variety of other systems has, for the most part, a better understanding than a researcher who can't. And of a course a layman who can't even work in a single system but has acquired a few "analogical" notions can have more understanding than someone who doesn't even recognize the concept.

Exactly because of how knowing works, I think articles like this can have an important place. They can open up new concepts for us (often little more than an empty node that can later be filled in). For experts in the broader field, they can give a quick impression of what other people are working on which might stimulate digging into more detail. And for experts on this topic, taking such writing seriously can have benefits like keeping their work in perspective and stimulating creativity (see Feynman's point about teaching physics 101).

And yes, these articles satisfy emotional needs. But what good thing doesn't?

Edit: I was mostly responding to the parent->parent, not so much disagreeing with the parent, who raised a good point.

That's right. Sometimes part of the fun is having an understanding of what the theory is useful for, and how it could impact science overall in the medium and long term, even if we don't get anything at all about the workings of the theory itself.

Nice condescension you have going on there. You don't think that reading about these articles might actually inspire someone to study mathematics? Introduce and explain difficult topics to laypeople, thus making mathematical research more accessible?

I didn't mean to condescend. And while I am convinced online article won't inspire anyone to study a field as arcane and useless to most people as math, I was simply extending on parent's observation: a lot of content out there is written in a way that non-expert can't use, and experts have no use because it's too basic.

> And while I am convinced online article won't inspire anyone to study a field as arcane and useless to most people as math

An individual seeking more information about physics will likely understand that complex math will be deeply involved.

The problem tackled by a pop-sci article shouldn't be to inspire the individual to develop a thorough background in math but to inspire a different way of thinking or to introduce new concepts.

I'm truly interested. There was enough insight to deepen my understanding.

The article provides some historical background, introduces a few key topics and the researchers involved as well as some idea of how it all fits into a bigger picture.

That's a tall order and I think quantamagazine does a good job with this.

For a properly prepared and motivated person, the quantamagazine article could be a starting point for further reading, for example, like lengthy review articles in subject-matter journals. But far more common, I think, it's just an interesting cursory read for anybody who happens to stumble upon this in their news feed. That's OK.

I'd argue the target audience is the "layman" in a tangential field. So, they have enough background that what the article talks about doesn't go above their head, and they can get a quick overview of the subject, but it doesn't require them having to read up on a bunch of materials outside their field. Think people like mathematicians that work in tandem with physicists in their institutions, but don't read into it as much themselves.

Do you have any specifics in how the article doesn't meet your standards or which aspects were poorly communicated?

My decently informed layman's understanding [1] led me to believe this article was a very well written description of some fascinating developments. As of now, I want to read more articles like it.

To be fair, I may be representative of a smaller niche. I agree that many laypeople might struggle with the technical parts.

However, I would love to know specifically how I may be mistaken in what I am taking away from these articles, if anything.

[1] I majored in math and am an avid follower of physics and cosmology.

For what it's worth: The bootstrap revival is a pretty big deal, much more important and more immediately useful than almost everything else Wolchover writes about. It's a new set of techniques for analyzing existing theories, and it applies equally well to theorist's toys like supersymmetric QFT and to experimental workhorse models like the 3d Ising Model. Rychkov, Poland, Simons-Duffin and (now many) others have been working at it for just a couple of years, and they've already set the gold standard for the computation of a lot of important and difficult quantities.

You shouldn't think of them as earth-shattering announcements. Think of these articles as the highlights reel of the 10-year progress report in some area of physics/math. Most of these are not ideas that will have any revolutionary impact over the next couple of years. But, over the next decade, we expect these ideas to lead to some very fruitful insights.

This is one of the hardest parts of communicating research to the layperson -- it can often come across as deceptively simple. Ten minutes of simplified communication summarizes ten years of blood, sweat and tears by dozens of people.

EDIT: I'm pretty optimistic about the Bootstrap idea in particular; I'm not trying to downplay its importance. But I wanted to convey that the way it'll end up helping might be very different from the leaps anticipated in the article, as it would be for any such article on any area of research.

Definitely far from clickbait in this particular case. It's hard to tell unless you are somewhat close to the field tho.

Adding to the other reply pointing out this is quite fundamental work, the point of these articles isn't really to announce new breakthroughs that happened last week, but rather to sketch major research themes that's been going on for the past couple of decades, but received little to no media coverage because they're highly technical.

Comprehensive list of "earth shattering" theories in fundamental physics of the last 50 years, discovery of the standard model as a gauge theory, first discussion of gauge theories in the 20ies, completion with observation of the Higgs boson in 2012, dark matter, first discussed by Zwicky in the 1920ies, since WMAP (~2000) a well established observation. Dark Energy, first discussed by Einstein in the twenties (actually I think a decade earlier) and observed by the High-Z-Supernova-Project in 1998. And neutrino mass, discussed as a curiosity for a long time and observed first in the 60ies and confirmed in 2001.

So anybody who uses the description "earth shattering" more than once a decade is probably overselling the importance of individual papers.

Reading this made me realize how I sound explaining my job to my mother. The sounds of cars rushing over my head and "What?" echoing between my ears...

This "bootstrap" appears to not be the "bootstrap" regularly encountered in statistics, just fyi if you were confused like me for the entirety of this article.

Correct. Both terms do, however, refer to Baron von Munchausen's levitation technique.

What about "the bootstrap method"? That name is commonly associated with the data resampling technique. Did the journalist make an error in saying that it was also used for this thing in theoretical particle physics?

These are all based on a saying from the early 19th century about the foolishness of trying to do something impossible, e.g. “It is conjectured that Mr. Murphee will now be enabled to hand himself over the Cumberland river or a barn yard fence by the straps of his boots.” (1834)

An earlier tall tale (from the 18th century or before) is that the fictional Baron Munchausen pulled himself out of a swamp by his own hair. Often the bootstrap saying is claimed to come from this source, but there’s not much proof of that, and it’s probably a misattribution.

In computing, the idea of “bootstrapping” (“booting”) dates from the 1950s, and refers to a computer starting with some simple capabilities which can read some data in and go through a series of steps each of which increases its capability, until it has been fully initialized. Metaphorically, the computer is pulling itself up by its own bootstraps rather than getting an external boost.

There are many other later uses of this idea of “bootstrapping”, including in statistics (from the late 1970s) and theoretical physics.

Cool, I didn't know the literature references. However what I was asking was whether the specific phrase "the bootstrap method" was used for this thing in theoretical physics. I only know the statistical concept, which _is_ called "the bootstrap method"; this physics thing sounds to me more like a "theory" or "model" than a "method" and I wondered if perhaps the journalist had got "the bootstrap method" from google hits (which are overwhelmingly dominated by the statistical concept) and thus muddied the waters slightly. A fairly unimportant question, to be sure.

The journalist did not invent the physics use of the term 'bootstrap method'. As the article makes clear, it came from some Berkeley physicists in the 1960s.

He conjectured that each particle is composed of other particles, and those others are held together by exchanging the first particle in a process that conveys a force. Thus, particles’ properties are generated by self-consistent feedback loops.

Can someone rephrase that to me?

He basically posited that particles self-validate themselves recursively: particle A is made up of components B and C tied together by the exchange of streams of... particle A.

Versus particle A is made up of components B and C tied together by the exchange of streams of ...?

...as opposed to hadrons (and other composte particles) made up by trios of quarks bound together by streams of gauge bosons (gluons that also recursively interact with themselves, generating more gluons), W and Z gauge bosons, and electromagnetic gauge bosons (photons).

That sounds a bit confusing, I’m sure, but aside from the gluons creating other gluons, there’s no recursion. In Chen’s view, it was alternating “turtles all the way down”...

What about size in all that? Say a boson has a size? What about the particles in Chen's view?

Also, can we differentiate a boson, say A, from a boson B? How (specifically, how sure are we that's two different objects)? In Chen's view?

Finally, how does space and time look like in boson's world, roughly?

Fundamental particles are pointlike and dimensionless. They have wave-particle duality and have characteristic wavelengths however on the order of 10^-16 m or so for hadrons and quarks are about 2000 smaller.

> Finally, how does space and time look like in boson's world, roughly?

Fundamental particles don't really have a size. The size of a particle depends on what force you use to examine it.

Remember that particles can only interact by the fundamental forces, so your typical expectation of a "size" is incorrect. If two particles don't have any forces in common they can pass right through each other - i.e. they don't have an edge that says "I'm here".

So looked at gravitationally or electromagnetically particles have infinite size, and their "existence" (to each other) is not binary "I'm here/I'm not here", but rather they are partially there, in ratio to how strong their interaction is.

Their size as measured by the strong force will be different from their size measured by the weak force.

Composite particles are different - they are made of fundamental particles in some particular spacing. The fundamental particles they are made of have no size, but the spacing between them does have a size, so that's the size they are given.

It would help you to stop thinking of particles as objects, but rather as areas of force, which get weaker the farther away you are. Like a kind of fuzzy ball that fades out, but never goes to zero.

Wow. Your explanation just helped me SO MUCH to visualize all this stuff. Thanks

If two particles don't have any forces in common they can pass right through each other - i.e. they don't have an edge that says "I'm here".

Your explanation was so much fun. Thank you.

What are the types of force? Gravitational, electromagnetic, what else?

What forces is made a quark of?

> what else?

Strong force and Weak force. See: https://en.wikipedia.org/wiki/Fundamental_forces

> What forces is made a quark of?

Quarks experience all 4 forces. That doesn't mean it's made of those forces though.

Particles are figments of their own imaginations.

I was having flashbacks to the end of Final Fantasy X. So I'm the son of a dream of myself made by a dead civilization about its own death?

Funny, I was thinking of Turing’s Theta fixed-point combinator.

Terry Pratchett would have thoroughly enjoyed that concept.

As somebody schooled in applied mathematics, it never fails to strike me how totally inscrutable and abstruse these pieces sound. It reads like a passage straight out of Harry Potter.

Because it's made up, just like Harry Potter.

"Theory Space" the name alone should give you red flags.

Sounds like another term for 'scientists discovered' what Aristotle already knew 2400 years ago... the term "potentiality".

That’s where I have to disagree... as most mathematicians I tend towards the idea that mathematical structures are discovered (even though techniques might be invented). There’s clearly an underlying pattern to physics, and the two main theories have to be reconciled somehow since the Universe hangs together pretty coherently; it’s just as obvious (to me, at least) that they’re mapping something with these procedures and that what they’re finding is not a side-effect of the procedure that gets randomly instantiated by the algorithm.

Why should 'theory space' throw red flags?

If you have a set of 'theories' with some structure attached to it, you have a 'theory space'.

Usually the structure in "space" is topological, i.e. some concept of a "neighborhood".

And indeed there is a concept of "neighborhood" here: a set of parameters characterizing the conformal field theory in question.

My personal red flag is the lack of formula or theorem. For me a beautiful formula is often more enlightening than a lengthy explanation. Fancy names occur in very serious mathematical articles.

There’s plenty of underlying mathematics and formulae (albeit being conjectures, probably not many overarching theorems for these specific theories yet). However I expect they decided against printing anything ’mathematical’, probably because the notation would be so dense with additional meanings it would be likewise indistinguishable from gibberish (for the layman, at least).

Please don't post snarky, shallow dismissals to HN. That's just what we're hoping to avoid here.

Fortunately qubex righted the ship with some high-quality replies and showed us all how it's done. But alas that is the exception.

https://news.ycombinator.com/newsguidelines.html

The article provides good links to sources like the 3.5 page Nature article below describing the progress in bootstrapping.

   Progress Article The conformal bootstrap
   https://www.nature.com/articles/nphys3761
   Nature Physics 12, 535–539 (2016)
   doi:10.1038/nphys3761

I’m just commenting on how difficult it is to render these concepts by means of metaphors, analogies, and colloquialisms.

Ah yes. It's a problem. Writing about complex mathematical subject and providing actual information is very difficult.

One article that can be recommended is Terence Tao's excellent article about universality.

A second draft of a non-technical article on universality https://terrytao.wordpress.com/2010/09/14/a-second-draft-of-...

I’ve worked on how dynamic networks of agents (i.e. financial markets made up of traders) exhibit universality. That said, Tao’s article is excellent.

On SciHub: http://sci-hub.la/10.1038/nphys3761

Great point. Why do they do that?

I’m not sure who their target audience is, but I thought everyone benefits from simple as possible but no simpler.

I don't know if I'm part of the target audience envisioned by the author and editors, but the article served me well. The landscape of physics, while beautifully unified, is nevertheless so vast that I'm essentially a layman outside of the areas in which I've done research. I'd heard about all the things mentioned in the article, but now have a better appreciation of how they fit together and arose historically. I thought everything was well and honestly explained.

If anyone is interested, the animation seems to be from David Ope

http://dvdp.tumblr.com/

It's definitely by him. There's even a link to his site in the corner... https://davidope.com/

Any links to material introducing how animations like his are created?

Reading the comments, it seems like sometimes animation or illustration just shouldn't be too good, otherwise the message is ruined.

Secular scientifically oriented mind considers theoretical physics as a fundamental. Alas, very few can really understand what the high priests at the Institute for Advanced Study are actually doing.

Visualizations and animations provide the analog of religious iconography. They convey the feeling of sublime to 'mere mortals'. Person may not be able to understand the Latin sermon, but there are beautiful pictures on the wall to look at.

Like the inscrutable algos & images of "social" media walls?

I have always thought of the modern way to do science very 'unscientific', i.e. science as the activity scientists perform as opposed to the classical tripartite definition ('Justified True Belief'), as it is simply not feasible that all scientists can perform experiments for every bit of knowledge and must accept some propositions by authority or consensus.

Your comment gave me a good insight into this idea, thanks!

The "unscientific" side might be best explained by a little editorializing.

Theory, experiment and now computation have ended up split between specilaists because the required knowledge for each can no longer practically fit into one education. The effect of this is that since one brain has been separated into many heads, lots of partly-formed ideas must be communicated between them to replace what used to be internal musing.

Lots of published theory has little experimental or numerical footing; theory is the superego of the split mind and plays the closest role to imagining goals and setting courses.

Experiment would be lost without theory: experimental papers are relatively light on interpretation and usually serve to "check out" theorized results. To continue the metaphor they're the Id: sometimes experiments come up with results that no rational mind could have expected, grabbing the wheel and bringing theory crashing back down to earth, and upon reaching the earth again launching it off in amazing new directions.

Computational physicists (I'm including anyone who spends most of their time with numbers in this) are left as the integrating Ego, trying to write code that models the theories and analyses the data and on a good day gives the same answers for both.

Finally, I should add that all of these intermediate results are very carefully worded to be true, claiming no more than can be claimed. The system would still work if they were phrased assertively but there's such a strong culture of truth that nobody does that. So, you can trust the papers, but not so much the magazine write-ups which usually clobber the careful stepping.

The vast majority of theoretical physicists know that they need strong experimental confirmation. It is disingenuous to imply that this isn't the case.

What are you trying to get at? Vague poetic denigration may be fun to write, but it isn't an effective way to communicate.

This was not a jab at scientists, but at people who eat up scientific factoids without having much understanding of science thereof.

If that was the intention, there are certainly much better ways of responding to such people, than to snidely put them down.

I'm not really sure what the expectation is either... Theoretical physics is not exactly something you pick up in afternoon.

I just burned 10 minutes of my day staring at that animated GIF.

Same. It's only 16 frames.

Slightly larger: https://media.wired.com/photos/59266b77af95806129f4f65b/mast...

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