A Jewel at the Heart of Quantum Physics

https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics

by milkshakes • 13 years ago

285 91 13 years ago

gruseom2• 13 years ago

Is anyone here familiar with this work? I would like to hear more about it. At a minimum, this article is very much better than the usual science blog filler—it contains signs of a genuine conceptual breakthrough. For example:

“You can easily do, on paper, computations that were infeasible even with a computer before.”

That doesn't happen very often! Or this:

[T]he new geometric approach to particle interactions removes locality and unitarity from its starting assumptions. The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct.

That is exactly the kind of thing that happens when one model is replaced with a deeper one.

gaze3• 13 years ago

This isn't my field (a.k.a. I'm talking out of my ass), but I can give it my best shot. Usually with QFT you start with locality and unitarity as a sort of starting point. You might hope that you could come up with something much simpler where locality and unitarity come about naturally from the model itself (the goal of physics being to show that "it had to be this way".) QFT tells us how the world works by calculating scattering amplitudes. You throw n things in, and m things come out with some momentum, some spin, some color, etc. The way we started doing this was with Feynman diagrams... these diagrams tend to look like you have some particles banging off of some other particles, and they behave a little that way, but they're actually a notation for integrals in a series that you have to sum over. Hence the genius of the notation... they describe math while looking like something physically relevant. However, they're a little weird in that if you interpreted the diagram literally, you'd find that some of the diagrams involved in an interaction actually aren't physical! One might say that the degree of nonphysicality suppresses that diagram's contribution. Physicists describe these diagrams as "off-mass-shell." If you wish to describe an interaction, you figure out all the diagrams relevant to the interaction, calculate them and sum them. When the article says "tons of pages of calculations", what they mean is you need to sum over a LOT of Feynman diagrams to get an answer.

Now, there's some newish kinda diagram that's gone into use (I think maybe only for N=4 SYM?), which is also used to calculate interaction cross-sections. However, they're written in such a way that they always describe on-shell processes, hence why they're called on-shell diagrams. I think Zvi Bern had something to do with this. These diagrams have an underlying structure... and mathematicians have started writing similar diagrams recently (as in, they ran into a similar structure recently), but instead of the diagrams being to describe interactions, they're used to describe some structure called a positive grassmanian. The positive grassmanian in low dimensions relates to convex polygons... it's a simple thing. This guy had this interesting insight that an interaction crossection corresponds to some sort of volume... and in this case, it corresponds to the volume of this polytope described by the positive grassmanian... or something like that.

The positive grassmanian says nothing at all about unitarity or positivity, nothing about space or time, but it lets you calculate shit. That's very, very cool.

jessriedel2• 13 years ago

Do you know of a good review paper?

ISL• 13 years ago

Physicist here: This has a higher probability of being important than your usual science blog material. The Simons Foundation is a serious entity, backed with serious funds.

Arkani-Hamed had some compelling things to say recently at a talk and colloquium at our university; looking forward to learning more.

Tycho• 13 years ago

backed with serious funds

As I suspected, The Simons Foundation is backed by Jim Harris Simons, mathemetician and the most successful hedge fund manager of all time (Google Medallion Fund and Renaissance Technologies for more info). Cool.

redhat-reallyp11• 13 years ago

"it contains signs of a genuine conceptual breakthrough."

It contains claims of such signs, which seems to be the point of this fluff piece.

Alarm bells should go off when you read statements like this:

"...giving up space and time as fundamental constituents of nature and figuring out how the Big Bang and cosmological evolution of the universe arose out of pure geometry."

Ah yes, well that solves the mystery, doesn't it. The universe arose out of pure geometry.

A more concrete sign of the limitations of this work can be seen in the paragraph prior to the above quote:

"Physicists must also prove that the new geometric formulation applies to the exact particles that are known to exist in the universe, rather than to the idealized quantum field theory they used to develop it, called maximally supersymmetric Yang-Mills theory."

The problem is that maximally supersymmetric Yang-Mills theory conflicts with experiments (see e.g. http://news.discovery.com/space/lhc-discovery-maims-supersym...). This is why they hurry to qualify this point by saying:

"This model, which includes a 'superpartner' particle for every known particle and treats space-time as flat, 'just happens to be the simplest test case for these new tools,' Bourjaily said. 'The way to generalize these new tools to [other] theories is understood.'"

Well that's good, because they're going to need that generalization. Now all they need is to actually produce it.

This is the sort of thing that leads these gee-whiz models to end up on the ash heap of history.

Don't get me wrong, it would be fantastic if the amplituhedron revolutionizes quantum theory. But based on the red flags in this article, I wouldn't hold my breath.

gaze3• 13 years ago

Things that work on simple models motivate work on more complex models. He STARTS OUT by saying N=4 SYM is a toy model. The klein-gordon equation is unphysical but motivated a lot of good physics.

gruseom2• 13 years ago

What you're saying makes it sound comparable to a compelling software demo that only works on simplified test cases.

bsullivan012• 13 years ago

what are your qualifications? No offense meant, but I am trying to see if this is real or not.

Quite a few smart people seem excited by it, yet you dismiss it

loup-vaillant6• 13 years ago

Ah yes, well that solves the mystery, doesn't it. The universe arose out of pure geometry.

That was a serious hypothesis before this. Heard about Tegmark's level IV multiverse? It's the idea that every mathematical structure just "exists", like "poof magic", and the simpler ones would, like, have greater weight. Kind of a literal interpretation of Occam's Razor, really. A corrolary is, the simpler the laws of physics are, the more probable the above hypothesis is. And suddenly we learn that the true laws of physics might be much simpler than we anticipated? This is huge.

Or not.

The idea of a timeless universe, where our subjective notion of time just arise from its structure has been around for quite some… time.

Likewise, Occam's Razor itself suggests that the true laws of physics are simpler than we think. Plus, current human laws of physics are either false or incomplete. I fully expect future physics to be further simplified. Claims of massive simplification are therefore not that surprising.

---

That said, I agree with your specific objections (the "work in progress" warnings).

ssivark7• 13 years ago

I've been keenly following this area of research and have heard some of the talks and read some papers. I concur with the sketch given by @gaze.

1. The notion of unitarity is a "common sense" rule that implies that you can consistently assign probabilities to possible outcomes in a quantum mechanical experiment (http://en.wikipedia.org/wiki/Unitarity_%28physics%29)

2. The notion of locality states that what happens on Jupiter better not affect how fast your code compiles this morning (or how experiments run on earth). This is an important postulate, because if this weren't true, we might as well give up on doing science as there would be arbitrarily many external influences we couldn't take into account.

All our experiments so far are perfectly consistent with these two principles. Quantum field theory is the brainchild of the marriage of unitarity (from quantum mechanics) and the idea of locality (in field theory). Our world view today ("Standard model of particle physics") is based on this.

In practice, calculating answers using this theory is painfully difficult. YOu will add up thousand pages worth of algebraic terms and then your answer will 'miraculously' reduce to a few terms. This and other observations have inspired researchers to search for underlying structure... leading to what is now being called the 'amplitude revolution' by some people.

bennyg• 13 years ago

Are the terms they reduce to constant, i.e. are they the same variables like spin or charge, no matter the problem? I'm not a physicist - not even close - but I do love a good mathematically general abstraction across a problem space.

slacka• 13 years ago

2. The notion of locality states that what happens on Jupiter better not affect how fast your code compiles this morning (or how experiments run on earth). This is an important postulate, because if this weren't true, we might as well give up on doing science as there would be arbitrarily many external influences we couldn't take into account.

Unfortunately for science, the principle of locality has been violated multiple times with experiments involving quantum entanglement.[1]

I think you are confusing Micro-causality with Einsteinian locality[2], the theory that influences propagate at most as fast as light. Micro-causality is the locality that's associated with quantum field theory and what was discussed in this article. Many theories in the history of science have been proven wrong. And if one of these is, then it will no lead to the end of science as we know it.

[1] http://arstechnica.com/science/2007/04/new-experiments-with-...

[2] http://www.rzuser.uni-heidelberg.de/~as3/nonlocality.html

Steuard• 13 years ago

This isn't really my specialty (string theory), but it's close enough "next door" that our conferences tend to have speakers on this topic on a regular basis. (There's a lot of overlap in individual researchers, too.)

I'm not going to try to one-up the article's non-expert description, but it's worth emphasizing that this isn't a "bold new idea of the week". (Rare among science journalism, I know.) This is a longstanding research program with a substantial number of contributors that's been making clear, gradual progress for a decade or two.

gngeal• 13 years ago

That is exactly the kind of thing that happens when one model is replaced with a deeper one.

Relevant quote: "Point of view is worth 80 IQ points." (Alan Kay)

Lerc• 13 years ago

As a Layman, the concept seems reminiscent of Garrett Lisi's E8 idea. Are they comparable approaches?

yk• 13 years ago

I did not read the paper, but from the article; probably not. So the E8 idea is stab at a quantum field theory of gravity. On the other hand these amplituhedron idea seems to be 'just' a different idea to calculate usual qft calculations easier. The only connection which may be there is, that apparently the amplituhedron idea can be turned on its head and then serve as a new way of looking onto qft. And this may or may not lead into a interesting direction for quantum gravity theories.

freyrs3• 13 years ago

The paper from the arxiv mentioned in the article: http://arxiv.org/pdf/1212.5605v1.pdf

selimthegrim4• 13 years ago

I was talking to a friend in the physics department at Stanford a few months ago about how one of the people whose work is cited in this paper (Greg Moore of Rutgers) had found analytic expressions purely rooted in geometry for Bethe Ansatz[1] results in (1+1) dimensional systems. Based on that, I told my friend I believed these "physical mathematics types" (as they call themselves) were on to something. He concurred that their methods would be very important in the future.

(This was in May, lol)

[1] BA is a nifty numerical method involving a lot of number crunching to find scattering matrices for these theories, and is very useful in low-dimensional electronic systems.

ssivark7• 13 years ago

I think there's a lot of exciting research going on in the context of integrable systems (~Bethe Ansatz) and N=2 quantum field theories. However, some people are also working on integrability in N=4 theories, which might be relevant to the ideas in this article. It's a thought some people (including Arkani-Hamed) have expressed, but it's too early to tell.

biot2• 13 years ago

In other words, you made a comment four months ago that simple, geometric models are likely to be important?

ssivark7• 13 years ago

And here's a (long!) recent review about developments in this area over the past few years -- http://arxiv.org/abs/1308.1697

Sniffnoy• 13 years ago

A note -- when linking to arXiv, please link to the abstract[1], not directly to the PDF. The abstract has other information about the paper, and one can see different versions of the paper, and of course one can click through to the actual paper. Going the other way requires manually editing the URL.

[1]http://arxiv.org/abs/1212.5605v1

ttctciyf• 13 years ago

(non physicist, non mathematician) The current excitement seems to be to do with a forthcoming paper from Arkani Hamed and his student Jaroslav Trnka. The pdf at http://www.staff.science.uu.nl/~tonge105/igst13/Trnka.pdf has some details of that, I think.

Edit to add:

The pdf is slides from a talk by Trnka. Video of a later talk on the same topic by Arkani Hamed is at http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Ha... - he sounds very excited!

noonespecial• 13 years ago

Every once in a while I get the feeling that the greatest discoveries are still ahead and these next few decades might be the real "golden age of science". The "individual genius" phase is just behind us and the "collaborative brilliance" phase is just beginning.

WalterSear• 13 years ago

Not to mention modern computational power.

xenophanes• 13 years ago

Why do you think there will be or should be a golden age, rather then continuous progress forever?

http://beginningofinfinity.com

Osmium• 13 years ago

I always think of "golden ages" as arising naturally from a random distribution of "big breakthroughs" and similar. It's not unlikely that you'd get some clumps of many breakthroughs followed by time with very few breakthroughs. And we call these clumps "golden ages." And of course, the fact that they're not independent events, but that one breakthrough might precipitate another, just reinforces this.

So I don't think "golden ages" are going away any time soon.

derleth• 13 years ago

To expand on what Osmium said, a "golden age" is more like a "goldrush age": A big breakthrough opens up a new conceptual frontier, and the golden age is scientists rushing in to homestead and start mining the new landscape.

This isn't to say that all progress is done in goldrushes, but the most basic and, therefore, best-known work of a given field will be done in that period.

has2k12• 13 years ago

It is possible that Gravity as we know it is an illusion. For example, the Newtonian take on Gravity was that it was a force. That according to Einstein was illusory, Gravity was really a geometric manifestation due to the curvature of space-time. With that take Gravity as we know it is different from the Gravity as was once known. However the Newtonian view that Gravity is a force can and still does facilitate useful everyday computations.

The go to illusion when we think of illusions is the mirage, you can see as water complete with the wavy nature of water and if you had no way of getting closer to inspect it, it might as well be the real thing. Depending on your philosophical take either it is always an illusion, or it becomes an illusion when you find out that it is not water.

A note of agreement with what seems like your main query, we might as well drop the word illusion when it comes to the physical description of the universe. Any framework of description is full of illusions that may never be proven otherwise.

I took QFT some years back and it also went over my head. There is still that mental gap of where the only way you can think about time is via time-(in)dependent wave function.

rational_me• 13 years ago

I took QFT some years back and it also went over my head. There is still that mental gap of where the only way you can think about time is via time-(in)dependent wave function.

Total bullshit. The wave function is time dependent.

VLM• 13 years ago

Perhaps another analogy for an illusion of a force would be centrifugal force?

redhat-reallyp11• 13 years ago

"Illusion" is a misleading way to put it.

We experience gravity as a force - we can measure it with devices designed to measure forces. It's not an illusion. However, the model of gravity as a force between massive objects does not capture certain aspects of gravity - it's an incomplete model.

That doesn't actually mean that gravity is "really a geometric manifestation due to the curvature of space-time". Gravity appears to behave that way, but what do you mean by "really" in that sentence? What we can say with confidence is that the spacetime curvature model is a more precise and complete model of gravity than the mass/force model.

Perhaps if we figure out how to unify quantum phenomena with gravitation, we'll find a different model for gravity in that context. Will you then say that gravity wasn't "really" spacetime curvature? That wouldn't make sense, because all that will have changed is that we would have another model for interpreting and understanding gravity.

When people say gravity is an "illusion" or that forces are "fictitious", what they're really getting at is that these observed phenomena are not fundamental - that they're consequences of some underlying phenomena. But they're real consequences, not illusory or fictitious.

(Of course "fictitious" is a technical term used in physics, but it doesn't mean "does not exist in reality" but rather means something more like "is not fundamental".)

ivan_ah• 13 years ago

A video lecture by Nima Arkani-Hamed here on the topic:

http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Ha...

Create• 13 years ago

"How should we make it attractive for them [young people] to spend 5,6,7 years in our field, be satisfied, learn about excitement, but finally be qualified to find other possibilities?" -- H. Schopper

(btw: entire careers have been based on susy, without a spec of experimental evidence: on might say, it is not even wrong)

happy4crazy• 13 years ago

I'm not remotely qualified to comment on the content, but I was very lucky to have Nima as a professor in college. He was an incredibly exciting lecturer--he practically glowed with intellectual energy.

zokier• 13 years ago

Interesting thing that he mentions in the beginning something like "Amplituhedron is so simple I could explain it to high-school students". I'd sure love to hear that explanation as my knowledge of physics/maths is not much better than that of hs students.

edit: Also the hand-written presentation slides are lovely.

devx• 13 years ago

So this guy was right? The geometry-based particle interaction theory sounds similar to what this guy was saying a few years back on TED:

http://www.ted.com/talks/garrett_lisi_on_his_theory_of_every...

gaze3• 13 years ago

Completely different thing. Garrett Lisi threw us some weird looking thing that when you turn it to the left and spin it 3 times and do a backflip looks like an electron... and if you turn it up and around and up town it looks like a quark. However, if you're gonna propose a structure like this, it better behave in a way that any way you look at it, it better look like something you might see in the universe. This thing predicted WAY too much shit to have physical relevance.

The thing in this post is a new way to calculate scattering amplitudes that has nothing to do with space, time, and isn't motivated by unitarity or locality.

tlb• 13 years ago

Rejecting unitarity is a bold thing to do. What can it mean for the probabilities of alternatives to sum to more than 1?

ssivark7• 13 years ago

No, they do not reject unitarity. The theory is still unitary. However, unitarity is not built-in to the theory... the theory talks about some other ideas and structures, and it turns out that all the answers you compute respect unitarity -- like it should!

TeMPOraL• 13 years ago

I understand it's kind of like "let's start without unitarity and locality baked in explicitly in the model and see where it leads and if they come out implicitly in the results".

Xcelerate• 13 years ago

This is really cool. I didn't understand most of it, even though I'm taking QFT right now. Shows you how deep the subject goes.

On another note, if I see the word "illusion" or "illusory" one more time in these science blogs, I'm going to have a fit. This must be the meaningless new buzzword of the day. 1) Spacetime is not an "illusion" 2) Gravity is not an "illusion" 3) <insert sciency word> is not an "illusion". That doesn't even make sense.

crntaylor• 13 years ago

I think what they mean is that the force we call gravity is an illusion that we experience because we perceive spacetime as flat. In a curved spacetime, you don't need to posit a force to explain motion due to a nearby mass - the mass curves spacetime, and objects move along geodesics in the curved spacetime. So while it would be incorrect to say "gravity is an illusion" I think it makes sense to say "the force of gravity is an illusion".

ars3• 13 years ago

and objects move along geodesics

You say that like it's so obvious. But why do they move in the first place?

tokipin• 13 years ago

He's probably quite aware of what the intended meaning is. The point is that since we're in effect always talking about 'verisimilitudes', calling this or that an "illusion" is silly, because it implies that we didn't realize our models are just models ("You mean to tell me the Standard Model isn't a 1-to-1 mapping from reality to our brains??? NOOOOO * worldview shattered * ").

For example, the spacetime explanation for gravity is also a model, and is also likely to be an "illusion." Making note of that is theoretical physics 101... or at least it should be.

011011100• 13 years ago

Discussion by people who are more likely to know what's going on:

http://physics.stackexchange.com/questions/77730/what-is-the...

scotty79• 13 years ago

From what I get they managed to vastly simplify calculations of super-symmetric Yang-Mills theory by representing results as volumes of geometric object.

Super-symmetric Yang-Mills theory is not shown to represent reality (yet?) but they hope they can use similar method to simplify calculations of the quantum field theories that are currently believed to represent reality.

evanb• 13 years ago

It's worse than that--- N=4SYM is known not to represent reality. However, it has some features that make calculations particularly easy to do. The analogous calculations are doable for other theories, but are trickier. So they've done the simplest example with this new framework.

snarfy• 13 years ago

It reminds me of heim theory. Supposedly, in heim theory you could derive particle mass by from quantum numbers by a relationship in a six dimensional geometric structure.

http://en.wikipedia.org/wiki/Heim_theory

Wiki doesn't have a lot of info, but it's mostly been debunked from what I've read.

robbiep• 13 years ago

My favourite line, and something I wasn't aware of (as a layman)

In 1986, it became apparent that Feynman’s apparatus was a Rube Goldberg machine.

I think Feynman would have loved to have heard his doodles to be described in such a way (maybe he did, he had a few years left in him at that point!)

mrcactu5• 13 years ago

Nima Arkani-Hamed is a nortorious loudmouth.

I went to his lecture from 1-3 and we got an encore from 3-5 and another from 5-6. It is no surprise his paper is verbose clocking at 154 pages.

Scattering Amplitudes and the Positive Grassmannian http://arxiv.org/abs/1212.5605

Alejandro Morales has some lecture notes on a course on the Positive Grassmanian The professor was Alexander Postnikov at MIT.

http://www.thales.math.uqam.ca/~ahmorales/18.318lecs/lecture...

Feynman famously said "I think I can safely say that nobody understands quantum mechanics." That was in 1965 but it's still true.

The scattering amplitudes in a certain case of N=4 Super Yang-Mills theory are more symmetric than people first expected. This has applications to "total positivity" and "integrable systems".

This will not help you build an app, but it's beautiful and represents an important shift in mathematics.

wbhart• 13 years ago

The article states about unitarity and locality that "both are suspect". I'm happy for locality to be suspect, but in what sense is unitarity suspect? Surely only in the sense that it is apparently a consequence of more fundamental things. And when you think about it, that's philosophically amazing, that probabilities summing to one may have an underlying (timeless?) explanation. Or maybe I should infer that there has been some exaggeration!?

stan_rogers• 13 years ago

It's that "only" in "... only in the sense that ..." upon which the whole thing hangs. Presupposing unitarity (and locality) and constraining models to conform to that presupposition may be that complication, that blinder, that prevents discovery of the simpler underlying rule from which either or both emerge. And either or both may be necessary consequences of the much simpler, underlying rule (if there is one to be found), at least on the observable side of any predicted phenomena, but that can't be determined unless one is willing to first throw away the constraints that keep you from finding it. (In effect, it's analogous to simply adding two natural numbers directly rather than using Peano arithmetic and checking at each iteration that an increment occurs. Either way you will arrive at the same answer, but the unconstrained rules for addition allows for negative numbers and fractions.)

axilmar• 13 years ago

What are the consequences of it regarding P = NP? can this be used as a proof that P = NP since a 9 page formula is reduced to a simple function? can we use geometry to solve programs in the NP space?

A Jewel at the Heart of Quantum Physics

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