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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

by 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)

by gruseom 13y ago

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)