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A Jewel at the Heart of Quantum Physics

285 points by milkshakes 13y ago

gruseom 13y 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.
- gaze 13y 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.
  - jessriedel 13y ago
    Do you know of a good review paper?
    - ssivark 13y ago
      http://arxiv.org/abs/1308.1697 http://arxiv.org/abs/1308.1697
      - jessriedel 13y ago
        This is very useful, thank you.
- ISL 13y 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 13y 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-reallyp 13y 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-supersymmetry-again-130724.htm 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.
  - gaze 13y 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.
    - selimthegrim 13y ago
      In condensed-matter physics, toy models play with you! http://arxiv.org/abs/cond-mat/0007254 http://arxiv.org/abs/cond-mat/0007254
    - redhat-reallyp 13y ago
- ssivark 13y 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 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 13y 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 13y 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-quantum-entanglement-suggest-that-reality-might-be-overrated/ http://arstechnica.com/science/2007/04/new-experiments-with-... [2] http://www.rzuser.uni-heidelberg.de/~as3/nonlocality.html http://www.rzuser.uni-heidelberg.de/~as3/nonlocality.html
- Steuard 13y 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 13y 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 13y ago
As a Layman, the concept seems reminiscent of Garrett Lisi's E8 idea. Are they comparable approaches?
- yk 13y 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 13y ago
The paper from the arxiv mentioned in the article: http://arxiv.org/pdf/1212.5605v1.pdf http://arxiv.org/pdf/1212.5605v1.pdf
- selimthegrim 13y 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.
  - ssivark 13y 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.
    - selimthegrim 13y ago
      You don't know any of Neitzke's grad students by any chance, do you? A certain fellow with a fondness for army boots and camo fatigues used to live down the hall from me at Caltech....
      - ssivark 13y ago
        A certain fellow working down the hall from me is quirky enough to match that description :-)
  - biot 13y ago
noonespecial 13y 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 13y ago
  Not to mention modern computational power.
- xenophanes 13y ago
  Why do you think there will be or should be a golden age, rather then continuous progress forever? http://beginningofinfinity.com http://beginningofinfinity.com
  - Osmium 13y 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 13y 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.
    - raverbashing 13y ago
      Yes There's no continuum because some things are harder, others are easy. Computers have evolved pretty much "continually" since the personal computer era, but they took some time to be invented. Quantum mechanics evolved "quickly" once we found out there was such a thing as quantum mechanics, up until them it was a lot of "banging heads" and freewheeling. Not to mention delays because of other constraints: wars, political instabilities, etc
ivan_ah 13y ago
A video lecture by Nima Arkani-Hamed here on the topic: http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Hamed_4-3.html http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Ha...
- Create 13y 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 13y 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 13y 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 13y 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_everything.html http://www.ted.com/talks/garrett_lisi_on_his_theory_of_every...
- gaze 13y 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 13y ago
Rejecting unitarity is a bold thing to do. What can it mean for the probabilities of alternatives to sum to more than 1?
- ssivark 13y 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 13y 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 13y 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 13y 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".
  - ars 13y ago
    > and objects move along geodesics You say that like it's so obvious. But why do they move in the first place?
    - textminer 13y ago
      Good discussion of your question: http://physics.stackexchange.com/questions/24359/why-do-objects-follow-geodesics-in-spacetime http://physics.stackexchange.com/questions/24359/why-do-obje...
      - ars 13y ago
        That answers why they move along geodesics. It doesn't answer why they move.
      - textminer 13y ago
        I thought those seemed part and parcel. :) "I'm in the gravity well of a star" leads to "this alters the geodesic of spacetime that the I tumble down", which made me wonder "wait, why does it tumble down geodesics to begin with". The answers seems to be "physics doesn't have to abide by your intuition or need for narratives, human"
011011100 13y ago
Discussion by people who are more likely to know what's going on: http://physics.stackexchange.com/questions/77730/what-is-the-actual-significance-of-the-amplituhedron http://physics.stackexchange.com/questions/77730/what-is-the...
deleted 13y ago
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scotty79 13y 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 13y 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 13y 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 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 13y 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 13y 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 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/lectures.pdf 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.
polaris9000 13y ago
It is discoveries like this one that always makes me wish I had pursued physics or mathematics back in college. There are so many things in Nature yet to be discovered! Imagine all of the mysteries that await us in the future. Take, for example, the theoretical graviton particle. What will happen once it is finally "discovered"? Thanks for the article; It is articles like this that make me want to go back to school and major in physics or mathematics.
wbhart 13y 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 13y 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 13y 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?

285 points by milkshakes 13y 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.

gaze 13y 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.
- jessriedel 13y ago
  Do you know of a good review paper?
  - ssivark 13y ago
    http://arxiv.org/abs/1308.1697 http://arxiv.org/abs/1308.1697
    - jessriedel 13y ago
      This is very useful, thank you.
ISL 13y 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 13y 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-reallyp 13y 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-supersymmetry-again-130724.htm 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.
- gaze 13y 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.
  - selimthegrim 13y ago
    In condensed-matter physics, toy models play with you! http://arxiv.org/abs/cond-mat/0007254 http://arxiv.org/abs/cond-mat/0007254
  - redhat-reallyp 13y ago
ssivark 13y 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 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 13y 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 13y 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-quantum-entanglement-suggest-that-reality-might-be-overrated/ http://arstechnica.com/science/2007/04/new-experiments-with-... [2] http://www.rzuser.uni-heidelberg.de/~as3/nonlocality.html http://www.rzuser.uni-heidelberg.de/~as3/nonlocality.html
Steuard 13y 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 13y 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 13y ago

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

yk 13y 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 13y ago

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

selimthegrim 13y 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.
- ssivark 13y 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.
  - selimthegrim 13y ago
    You don't know any of Neitzke's grad students by any chance, do you? A certain fellow with a fondness for army boots and camo fatigues used to live down the hall from me at Caltech....
    - ssivark 13y ago
      A certain fellow working down the hall from me is quirky enough to match that description :-)
- biot 13y ago

noonespecial 13y 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 13y ago
Not to mention modern computational power.
xenophanes 13y ago
Why do you think there will be or should be a golden age, rather then continuous progress forever? http://beginningofinfinity.com http://beginningofinfinity.com
- Osmium 13y 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 13y 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.
  - raverbashing 13y ago
    Yes There's no continuum because some things are harder, others are easy. Computers have evolved pretty much "continually" since the personal computer era, but they took some time to be invented. Quantum mechanics evolved "quickly" once we found out there was such a thing as quantum mechanics, up until them it was a lot of "banging heads" and freewheeling. Not to mention delays because of other constraints: wars, political instabilities, etc

ivan_ah 13y ago

A video lecture by Nima Arkani-Hamed here on the topic: http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Hamed_4-3.html http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Ha...

Create 13y 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 13y 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 13y 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 13y 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_everything.html http://www.ted.com/talks/garrett_lisi_on_his_theory_of_every...

gaze 13y 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 13y ago

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

ssivark 13y 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 13y 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 13y 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 13y 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".
- ars 13y ago
  > and objects move along geodesics You say that like it's so obvious. But why do they move in the first place?
  - textminer 13y ago
    Good discussion of your question: http://physics.stackexchange.com/questions/24359/why-do-objects-follow-geodesics-in-spacetime http://physics.stackexchange.com/questions/24359/why-do-obje...
    - ars 13y ago
      That answers why they move along geodesics. It doesn't answer why they move.
    - textminer 13y ago
      I thought those seemed part and parcel. :) "I'm in the gravity well of a star" leads to "this alters the geodesic of spacetime that the I tumble down", which made me wonder "wait, why does it tumble down geodesics to begin with". The answers seems to be "physics doesn't have to abide by your intuition or need for narratives, human"

011011100 13y ago

Discussion by people who are more likely to know what's going on: http://physics.stackexchange.com/questions/77730/what-is-the-actual-significance-of-the-amplituhedron http://physics.stackexchange.com/questions/77730/what-is-the...

deleted 13y ago

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scotty79 13y 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 13y 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 13y 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 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 13y 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 13y 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 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/lectures.pdf 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.

polaris9000 13y ago

It is discoveries like this one that always makes me wish I had pursued physics or mathematics back in college. There are so many things in Nature yet to be discovered! Imagine all of the mysteries that await us in the future. Take, for example, the theoretical graviton particle. What will happen once it is finally "discovered"? Thanks for the article; It is articles like this that make me want to go back to school and major in physics or mathematics.

wbhart 13y 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 13y 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 13y 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?