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September 18, 2013 2:18 AM   Subscribe

Revelations in the field of quantum physics have resulted in the discovery of the Amplituhedron, a jewel-like higher dimensional object whose volume elegantly predicts fundamental physical processes that took the brilliant Dr. Richard Feynman hundreds of pages of abstruse mathematics to describe. The theoretical manifold not only enables simple pen-and-paper calculation of physics that would normally require supercomputers to work out, but also challenges basic assumptions about the nature of reality -- forgoing the core concepts of locality and unitarity and suggesting that space and time are merely emergent properties of a timeless, infinitely-sided "master amplituhedron," whose geometry represents the sum total of all physical interactions. More: The 152-page source paper on arXiv [PDF] - Lead author Nima Arkani-Hamed's hour-long lecture at SUSY 2013 - Scans of Arkani-Hamed's handwritten lecture notes - A far more detailed lecture series "Scattering Without Space Time": one, two, three - Arkani-Hamed previously on MeFi - A hot-off-the-presses Wikipedia page (watch this space)
posted by Rhaomi (128 comments total) 149 users marked this as a favorite

 
the tldr;/eli5 version of this as best I understand:

This is basically a new way to figure out the probabilities for the results of fundamental particles interacting that A) is dramatically simpler than Feynman diagrams and more importantly B) does not include space-time in the formula.

The reason that the second thing is important is that most physicists believe that space and time are not fundamental, and get in the way of figuring out quantum gravity, so this could pave the way to a Unified Theory of Everything.

The caveat is that right now they have only adapted it to a simplified model of particle physics and have not modified it to work with the standard model yet.

The people working on this are well-respected physicists at major institutions, so it's not crankery.
posted by empath at 2:45 AM on September 18, 2013 [33 favorites]


It still sounds amazing! Kind of like the mathematical version of a metaphor.
posted by Kevin Street at 2:50 AM on September 18, 2013 [1 favorite]


The Amplituhedron article says that the Amplituhedron has infinitely many sides, like a circle. But this thing is actually a polytope, right? Not a ball or disc. Circles only have one side.

Anyway, awesome post, and expect to see Amplituhedron on the cover of New Age books for the next thirty years.
posted by Elementary Penguin at 2:52 AM on September 18, 2013 [9 favorites]


Pffft, I've had one of those in the linen closet for years.
posted by robotot at 2:53 AM on September 18, 2013 [11 favorites]


"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning."  
- Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences (related)
posted by jeffburdges at 2:56 AM on September 18, 2013 [9 favorites]


Pffft, I've had one of those in the linen closet for years.

Tell me about it - you always start off thinking "ooh, a timeless hyper-shape whose volume elegantly predicts fundamental physical processes, that'd look lovely on the dresser", then it starts getting dirty and have you tried dusting an object with infinitely many sides? It's just not worth the effort.
posted by EndsOfInvention at 2:59 AM on September 18, 2013 [86 favorites]


I wish I understood things like this. I'm OK with Newton and Einstein, but my mind has always boggled trying to understand quantum theory.
posted by double block and bleed at 3:01 AM on September 18, 2013 [3 favorites]


According to Lubos Motl, there is another paper due to be published soon with more details. (which is to say that the 152 page paper linked here is _not_ the amplituhedron paper.)
posted by empath at 3:02 AM on September 18, 2013 [5 favorites]


These slides cover the amplituhedron as well.
posted by empath at 3:07 AM on September 18, 2013


My first reaction was "Time Cube, with better font choices", but it seems to be a real thing. Apparently my bullshit meter isn't correctly calibrated until my first cup of coffee.
posted by quillbreaker at 3:07 AM on September 18, 2013 [7 favorites]


Okay yeah he's got the same jaunty handwriting my lapsed-string-theorist brother developed during his doctorate. What is it with physicists and their fanciful capital letters?
posted by Mizu at 3:10 AM on September 18, 2013


the way this immediately got onto wikipedia shows just how problematic the idea of an encyclopedia is in the age of "viral" marketing. (wikipedia itself is cool, but the idea of an encyclopedia of knowledge is problematic)

the use of (infinite) dimensional grassmannians to study integrable systems (like "Yang-Mills" which seems to be the main subject of concern in this paper) is an established track of study in mathematics beginning with the Japanese mathematican Sato (Segal-Wilson on KdV is the canonical english language paper in the subject)

the "inverse scattering theory" approach to integrable systems is one of the jewels of Soviet mathematics and is completely surprising given the complexity of computing scattering amplitudes.

this research group is using a lot of mathematical power tools in virtuosic ways... sort of the physics version of juggling chain saws. (look in the references section for the shout-out to the Langlands conjecture and also Bob Macpherson showed them how some of the power tools worked.) there's actually very little which is "authoritative" about what they are doing... they themselves are probably the only people in the room who know what they are doing. everyone else is cheering them on because it relates to their research and they are using some cool tools.
posted by ennui.bz at 3:11 AM on September 18, 2013 [10 favorites]


Okay yeah he's got the same jaunty handwriting my lapsed-string-theorist brother developed during his doctorate. What is it with physicists and their fanciful capital letters?

When you're writing equations on chalk-boards, you need to learn to write letters so they'll be distinct. O,Q,P,R, etc.. all need to be obvious which is which at a glance, and it gets even worse when you start throwing in greek letters.
posted by empath at 3:14 AM on September 18, 2013 [3 favorites]


Is the cool multicolored illustration at the top of the article an actual diagram? Do the curved lines represent anything? Or is it just an artist's take on the 8-gluon example (which seems to be the only shape resembling it in any of the articles/papers/notes)?
posted by theodolite at 3:15 AM on September 18, 2013 [1 favorite]


So: a fractal snowflake in 196,833 dimensions, then?
posted by Sebmojo at 3:17 AM on September 18, 2013 [5 favorites]


Why would you even post stuff like this when physicsmatt is asleep?
posted by ryanrs at 3:20 AM on September 18, 2013 [9 favorites]


According to Lubos Motl, there is another paper due to be published soon with more details.

If people think a theory is crackpot, maybe it's best not to give them ammunition by citing the blog of a climate-change 'skeptic' who has a whole category "freedom vs PC" (PC = "political correctness") and uses "feminist" as a derogatory term and considers himself to be both an expert in economics and string theory. Because that blog has pushed my opinion from "probably crackpot" to "oh yeah, totally crackpot".
posted by Pyry at 3:25 AM on September 18, 2013 [6 favorites]


Because that blog has pushed my opinion from "probably crackpot" to "oh yeah, totally crackpot".

The institute for Advanced Study at Princeton doesn't hire crackpots. Motl is just a physicist/blogger who talks to a lot of other physicists, and if you read his post, he is actually somewhat skeptical about this being a major breakthrough. (Note the post title refers to 'good PR'). I am sure that physics bloggers with less baggage like Sean Carroll will post about it also when they wake up in the morning.
posted by empath at 3:30 AM on September 18, 2013 [1 favorite]


I love that it's like - "here, laypeople, this insanely complicated mathematical object has been characterised as a pretty multi-coloured jewel so you can understand it so much easier."

It's nice that physicists try to explain it in simplified terms, but the process my brain follows to understand this is roughly the same as a fish trying to work out how to use a can opener.
posted by MuffinMan at 3:36 AM on September 18, 2013 [11 favorites]


There's a long history in science of domain experts acting like complete crackpots when pontificating on matters outside of their domain. Being crackpots everywhere else doesn't invalidate statements they make within their domain of expertise however.
posted by pharm at 3:41 AM on September 18, 2013 [5 favorites]


For a second I parsed that as, "The IAS hired Lubos Motl, so he's not a crackpot" and I was like O_O.
posted by Elementary Penguin at 3:41 AM on September 18, 2013


> It's nice that physicists try to explain it in simplified terms, but the process my brain follows to understand this is roughly the same as a fish trying to work out how to use a can opener.

How to use a can opener if you're a fish:
1. Wait. It will be dark. That's OK.
2. Eventually you will hear a loud noise. Then there might be light. The human has opened the can.
posted by ardgedee at 3:46 AM on September 18, 2013 [35 favorites]


This is not easy stuff to summarize, except in a poetic way.

For those of us who have had some QFT there's a helpful 250-page paper just published last month to bring you up to the basics of what is involved here.
posted by vacapinta at 3:46 AM on September 18, 2013 [4 favorites]


...have you tried dusting an object with infinitely many sides? It's just not worth the effort.

That's why I keep a Klein bottle full of compressed air in one of my desk drawers.
posted by Kid Charlemagne at 3:57 AM on September 18, 2013 [24 favorites]


a jewel-like higher dimensional object

If you open one of the flaps, it tells you whether you'll have a swimming pool when you grow up.
posted by obiwanwasabi at 4:00 AM on September 18, 2013 [17 favorites]


I spent all summer reading Nima+co's giant paper from last year, and I've also worked through a good portion of the recent review (that vacapinta links to). So I've got a few comments; I'm going to split them up for clarity.

Mizu: What is it with physicists and their fanciful capital letters?

Are you by any chance talking about the letter capital N here? If so, it's actually because in the toy model theory they're talking about, regular block capital N means one thing (the number of color charges in the theory; for electromagnetism this is one, for QCD it is 3, but you can write down a theory with any N). But curly capital N means another: curly capital N tells you how many supersymmetries (in this case, 4).

Which brings up a point about this being a toy model: the polytope picture is most easily applicable to a theory with curly N=4 supersymmetries (note our universe has, exactly, 0- and maybe approximately 1, but we haven't seen it yet), and block N=infinity color charges. (Actual physics we can test in a collider doesn't produce more than 3, but there are proposals for more). So yeah, it's not our world. But maybe it does tell us more about how to calculate things which are.
posted by nat at 4:01 AM on September 18, 2013 [4 favorites]


Ctrl+F for "M'Kraan Crystal". Nothing.

You people disappoint me.
posted by X-Himy at 4:05 AM on September 18, 2013 [6 favorites]


empath: (which is to say that the 152 page paper linked here is _not_ the amplituhedron paper.)

Ok, I'm not Lubos Motl, and yeah, there is supposed to be another mammoth paper coming out. I really hope it does so soon; I'm starting to work on this area and it's pretty hard to work on it when all you have for the most recent picture is a bunch of talk slides and rumors.

Note to authors: not every paper has to be 100+ pages! It's ok to write small bits as you go along, and possibly it's even *polite* to do so; nobody else can really work on offshoots of your work until you put it out in written form. Grrrr.


Speaking of polite, Lubos Motl is a total asshat, incredibly sexist, and I'm infinitely glad I've never overlapped with him anywhere. That having been said, he does know his physics, so as long as he's somehow managing to present it without reference to politics, gender, or other fields of science he's not so well versed in, he's probably right.
posted by nat at 4:07 AM on September 18, 2013 [3 favorites]


From the beamer slides linked above: "triangles" are not known to mathematicians

I knew we were missing something.
posted by gleuschk at 4:09 AM on September 18, 2013 [2 favorites]


Elementary Penguin: The Amplituhedron article says that the Amplituhedron has infinitely many sides, like a circle. But this thing is actually a polytope, right? Not a ball or disc. Circles only have one side.

Think a regular polygon with N sides. Increase N. Bigger N gets, closer you to get a circle. Circle can be thought of as N=infinity. See Flatland.

Also awesome name, are you by any chance named after the diagram?
posted by nat at 4:12 AM on September 18, 2013 [2 favorites]


Wouldn't a sphere have been a better analogy?
posted by empath at 4:15 AM on September 18, 2013 [1 favorite]


The first link especially seems to be overstating things, that unitarity will be 'removed'. It sounds more like you don't need to work in the same ways to enforce it.

I think I wouldn't be alone in the physics community for thinking that if you actually wrote down a theory that didn't provide probabilities that summed to 1 then it is, to put it politely, off to a bad start.

I've not had to use QM in anger for a long time though.
posted by edd at 4:18 AM on September 18, 2013 [2 favorites]


Think a regular polygon with N sides. Increase N. Bigger N gets, closer you to get a circle. Circle can be thought of as N=infinity. See Flatland.

Sure, but all the talk about triangles and sides had me thinking infinite dimensional polytope. *sigh* I'm going to have to read a 250 QM paper to understand this, aren't I? The problem I have is that I totally understand the math but I have no understanding of the physics so reading physics stuff is always really weird for me.

Also awesome name, are you by any chance named after the diagram?

Beatles reference.
posted by Elementary Penguin at 4:22 AM on September 18, 2013 [2 favorites]


The first link especially seems to be overstating things, that unitarity will be 'removed'. It sounds more like you don't need to work in the same ways to enforce it.

That's good to hear. I was really really confused that people in the thread were like "these are serious people doing serious science" while the idea of not having unitarity at all is equivalent to "does not make a lick of sense".
posted by Jpfed at 4:23 AM on September 18, 2013


From the first link: But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway.

Time is an illusion. Space-time doubly so.
posted by logicpunk at 4:23 AM on September 18, 2013 [5 favorites]


"Also awesome name, are you by any chance named after the diagram?"
posted by nat

"Semolina pilchard climbing up the Eiffel Tower
Elementary penguin singing Hare Krishna
Man you should have seen them kicking Edgar Alan Poe
I am the eggman, they are the eggmen
I am the walrus, goo goo goo joob goo goo goo joob"
posted by marienbad at 4:23 AM on September 18, 2013 [1 favorite]


Dang, beaten to it by the Penguin!
posted by marienbad at 4:24 AM on September 18, 2013


empath: sure, Sphere then, these are polytopes; but they're polytopes in a multidimensional Grassmanian, so does it really matter?

edd: Might be nice to get unitarity out, rather than put it in though, yes? Same with locality. They are both features we like, but why impose them by hand when you can get them to come out of simpler axioms for free?

Also, unitarity combined with black holes is kind of annoying. See discussion on firewalls and complementarity (there must have been one on mefi, but I can't find it right now and have to get ready for work-- anybody know?). I still like it, but it is in conflict with some other things (like effective field theory) that we expect to be true.
posted by nat at 4:25 AM on September 18, 2013


Wow, seriously never managed to parse those lyrics well enough to catch the words. Penguin diagrams were named much later, although I believe entirely independently.
posted by nat at 4:26 AM on September 18, 2013 [2 favorites]


Tardis.
posted by Kerasia at 4:27 AM on September 18, 2013 [2 favorites]


they're polytopes in a multidimensional Grassmanian

Can you explain this in terms that someone who knows basic linear algebra and some group theory would understand?
posted by empath at 4:38 AM on September 18, 2013 [1 favorite]


nat: well, exactly. It's much nicer to have them an unavoidable result of the theory. It's a bit too easy to read the article like they've been done away with altogether though, which would be a very different situation.
The black holes business is annoying, but also still very unclear. I'd still be willing to eat some item of clothing if you could get a physical situation where probabilities didn't sum to 1 though. I believe hats are commonplace, and Jim Al-Khalili has the boxer shorts covered with that neutrinos faster than light claim, so I'll have to think of something else for this hypothetical future snack.
posted by edd at 4:40 AM on September 18, 2013


No, but Wikipedia can. (Better than me, anyhow).
posted by nat at 4:40 AM on September 18, 2013 [1 favorite]


Hah. No. What I got from that is that grassmanians are a subset of vector spaces of dimension r embedded in a larger dimensional space n, which I kind of grok, but I don't know what it would mean to have a polytope in that space.
posted by empath at 4:43 AM on September 18, 2013


I see there are no tags on this post. Perhaps we should consider adding 'Borges'.
posted by victory_laser at 4:57 AM on September 18, 2013 [2 favorites]


On the back part of the step, toward the right, I saw a small iridescent sphere of almost unbearable brilliance. At first I thought it was revolving; then I realised that this movement was an illusion created by the dizzying world it bounded. The Aleph's diameter was probably little more than an inch, but all space was there, actual and undiminished. Each thing (a mirror's face, let us say) was infinite things, since I distinctly saw it from every angle of the universe. I saw the teeming sea; I saw daybreak and nightfall; I saw the multitudes of America; I saw a silvery cobweb in the center of a black pyramid; I saw a splintered labyrinth (it was London); I saw, close up, unending eyes watching themselves in me as in a mirror; I saw all the mirrors on earth and none of them reflected me....
On preview, beaten to the punch by victory_laser. Eponysterical.
posted by kewb at 4:58 AM on September 18, 2013 [2 favorites]


It has been known for more than 200 years that space and time are merely pure forms of sensibility, but people won't believe it until it's in Nature!
posted by thelonius at 5:02 AM on September 18, 2013 [2 favorites]


References to complicated yet fundamental theoretical physics spoken as if they were common knowledge, a reverence to Dr. Feynman, and an overt disdain for Wikipedia entries?!?

Sheldon, are you trolling the people on the little people blogs again?!?
posted by Blue_Villain at 5:07 AM on September 18, 2013 [3 favorites]


I'd still be willing to eat some item of clothing if you could get a physical situation where probabilities didn't sum to 1 though. I believe hats are commonplace...

the sum of probabilities over all possible states is 1, a priori. no amount of measurement could prove or disprove that statment.

they're polytopes in a multidimensional Grassmanian

i *think* the amplituhedron is ultimately a "polytope" in a multidimensional infinite dimensional grassmannian. most of the heavy lifting is in getting comfortable with grassmannians... which really only require some basic linear algebra well, and tensor algebra since grassmannians are most straightforwardly (that is, I prefer pluecker coordinates... sue me) coordinatized using antisymmetric forms i.e. wedge products.

the grassmannian G(k,N) is the set of k-dimensional subspaces of a given N-dimensional vector space (the vector space could be over R, C, of even H is you want to push things.) this set happens to be a smooth manifold. in particular G(1,N) is N-1 dimensional projective space, which is to say that the geometry of a given grassmanian depends a lot on what "k" and "N" happen to be. but you can choose coordinates by looking at the wedge products of basis elements for the subspaces.

you can also look at G(k,N) is a "symmetric" space i.e. a Lie group modulo some subgroup of stabilizers, which in this case would be elements of GL(N) which fix k-dimensional subspaces.

what he means by "positive" grassmannian could be different things and i didn't pick that up scanning the articles....
posted by ennui.bz at 5:15 AM on September 18, 2013 [5 favorites]


Question: Is this "just math" (sorry, math geeks), e.g., that this makes certain computations work really well, or are they saying something about the nature of reality?
posted by CheeseDigestsAll at 5:41 AM on September 18, 2013 [1 favorite]


They're going to spool through the possibilities, come up with some major breakthroughs and then rudely sublimate without sharing any of it.
posted by Slackermagee at 5:42 AM on September 18, 2013 [3 favorites]


I see there are no tags on this post. Perhaps we should consider adding 'Borges'.

Oh, it's already there. This post has infinite tags, your browser probably just isn't displaying them properly.
posted by oulipian at 5:46 AM on September 18, 2013 [7 favorites]


Question: Is this "just math" (sorry, math geeks), e.g., that this makes certain computations work really well, or are they saying something about the nature of reality?

If they can make this work with actual particle physics, then it suggests in the same way that newtonian physics emerge from quantum mechanics, quantum mechanics and even space and time itself could be an emergent property of some more fundamental theory.
posted by empath at 5:52 AM on September 18, 2013 [1 favorite]


A timeless hyper-shape whose volume elegantly predicts fundamental physical processes.

Okay, back to sleep for me.
posted by pwally at 5:57 AM on September 18, 2013


When you're writing equations on chalk-boards, you need to learn to write letters so they'll be distinct. O,Q,P,R, etc.. all need to be obvious which is which at a glance, and it gets even worse when you start throwing in greek letters.

And of course nothing derails note-taking during a lecture like a well-placed ξ, and good luck if it lives in the same equation as ϵ because you're never going to successfully parse what you wrote.

Someone should do a study to see if good penmanship correlates with success in advanced physics and mathematics classes....
posted by RonButNotStupid at 5:58 AM on September 18, 2013


All modern physics is "just math that makes certain computations work really well", CheeseDigestsAll, that's how we understand reality. You might argue relativity came from physical intuition, except actually the math was worked out first and inspired the interpretation, and arguing that for say relativistic electromagnetism doesn't work so well anyways.
posted by jeffburdges at 5:59 AM on September 18, 2013 [3 favorites]


Now it's just a matter of time for the Amplituhedron crochet pattern.

See what I did there?
posted by slogger at 6:02 AM on September 18, 2013 [1 favorite]


So: a fractal snowflake in 196,833 dimensions, then?

That was a reference to the Fischer–Griess Monster group. More here.
posted by zamboni at 6:04 AM on September 18, 2013 [1 favorite]


I keep waiting for the post that ends with "and so now we can have FTL travel." I would also accept "and now we are going to start teleporting shit like you wouldn't believe."

For me, that's what quantum theory is about. I firmly believe that if we slap it just right one of those two things is going to fall out. I leave the math up to those who are more capable than I am.
posted by BeReasonable at 6:05 AM on September 18, 2013 [8 favorites]


Is this related to the monolith puzzle in Fez in any way?
posted by Riton at 6:21 AM on September 18, 2013 [5 favorites]



When you're writing equations on chalk-boards, you need to learn to write letters so they'll be distinct. O,Q,P,R, etc.. all need to be obvious which is which at a glance, and it gets even worse when you start throwing in greek letters.


Heh, there is a very good reason that math undergrads are very unlikely to use a computer to take notes. Didn't own a laptop until after school, because why bother? Not to mention the geometric diagrams.

This is ...above my comprehension, but my undergrad focused on enumerative geometry-type stuff, so in theory I should be able to figure it out. Back to the textbooks for me! And thanks everyone who is trying to explain it.
posted by Lemurrhea at 6:23 AM on September 18, 2013


and so now we can start investigating what other parts of the Divine Comedy are accurate?
posted by Potomac Avenue at 6:23 AM on September 18, 2013


All modern physics is "just math that makes certain computations work really well".

I guess I was thinking more along the lines of approximating the area under a curve with rectangles. But I'm getting that if this holds up, it's the real deal (or at least our best approximation so far.)
posted by CheeseDigestsAll at 6:24 AM on September 18, 2013


I think I need to go find some DMT or something.
posted by aramaic at 6:28 AM on September 18, 2013 [3 favorites]


Wow, just think about playing an RPG with amplituhedral dice. A die with infinitely many sides and a structure that relates to the basic rules of reality would be really useful for D&D.
posted by branduno at 6:43 AM on September 18, 2013 [5 favorites]


Thank you, you just helped name Carbon 7's next 20 songs or so.
posted by Devils Rancher at 6:43 AM on September 18, 2013


and so now we can start investigating what other parts of the Divine Comedy are accurate?

Beatrice sure sets him straight about the light and dark patches on the Moon. There's a lot about geography that they didn't teach us in school, also.
posted by thelonius at 6:53 AM on September 18, 2013 [1 favorite]


Today I learned there is a physicist on the faculty at Berkeley whose name is Lawrence Hall. Weird.
posted by bukvich at 7:28 AM on September 18, 2013 [3 favorites]


So is this basically Borges' Aleph then? Did a postmodernist get there before the physicists did?

And does Betteridge's law apply to MeFi comments too?
posted by saulgoodman at 7:29 AM on September 18, 2013 [1 favorite]


Oh, hey, Nima was my friend(and her husband)'s graduate advisor. They are both extremely smart people. If I can remotely understand any of this, I'll have to ask them about it when I visit them next month.
posted by maryr at 7:54 AM on September 18, 2013


[Apologies to empath for stepping on toes with this unintended double. FWIW, his post shared most of the same links, and if the Amplituhedron teaches us anything, its that there's something to be said for concise and efficient explanations over wordier fare. :P]
posted by Rhaomi at 8:24 AM on September 18, 2013 [1 favorite]


Talking about The Amplituhedron is like dancing about fhqwhgads.
posted by petebest at 8:28 AM on September 18, 2013 [2 favorites]


Wow, just think about playing an RPG with amplituhedral dice. A die with infinitely many sides and a structure that relates to the basic rules of reality would be really useful for D&D.

They'd probably still come up 1 at the worst possible moments.
posted by Foosnark at 8:30 AM on September 18, 2013 [4 favorites]


The vague statement about discarding unitarity (so that probabilities no longer add up to one) was really bugging me. Exhaustive and exclusive event probabilities add to one by definition, so ...?

Thanks to nat, edd, and others above for pointing out that they're hoping that unitarity emerges as a consequence of the theory, rather than being baked in. This para in the article was also illuminating:

Unitarity says the quantum mechanical probabilities of all possible outcomes of a particle interaction must sum to one. To prove it, one would have to observe the same interaction over and over and count the frequencies of the different outcomes. Doing this to perfect accuracy would require an infinite number of observations using an infinitely large measuring apparatus, but the latter would again cause gravitational collapse into a black hole. In finite regions of the universe, unitarity can therefore only be approximately known.

This sounds more reasonable.
posted by RedOrGreen at 8:47 AM on September 18, 2013 [2 favorites]


This sounds a lot like mysticism. Is it? Pretty much "physical reality as a undifferentiated whole in which division makes no sense emerges from a ground state of eternal, infinite Possibility."

I like mysticism a lot, and wasn't really aware of a formal physics flavor of it, so I'll definitely be looking into this despite formal physics being an elephant I have to content myself to trusting the descriptions of a blind man with. Thanks! This seems really fascinating.
posted by byanyothername at 8:48 AM on September 18, 2013


Any sufficiently advanced theoretical physics is indistinguishable from something you came up with when you were really high during math class.
posted by Elementary Penguin at 8:51 AM on September 18, 2013 [12 favorites]


...For those of us who have had some QFT...

I presume that QFT stands for Quantum Fisics Theory?
posted by goethean at 8:59 AM on September 18, 2013 [1 favorite]


I like mysticism a lot, and wasn't really aware of a formal physics flavor of it (...)

Physics is completely indiscernible from mysticism at my level of intellect.
posted by Devils Rancher at 9:01 AM on September 18, 2013 [3 favorites]


I am going to keep track of how many weeks it is until the New Agers start selling Amplituhedron crystals that keep you in resonance with the multiverse, or Grassmannian yoga that must be performed on grass in order to be at one with the higher dimensions.

ref: Tachyon crystals, Tachyon Reiki, Quantum Crystals, Quantum Yoga
posted by memebake at 9:14 AM on September 18, 2013 [4 favorites]


Tachyon Reiki sounds like it should be the name of a JRPG protagonist.
posted by Elementary Penguin at 9:17 AM on September 18, 2013 [3 favorites]


Dammit, those tachyon crystals that they're selling are the very ones that fell out of my time machine when I crashed in this era. Give those back!
posted by Galaxor Nebulon at 9:25 AM on September 18, 2013 [1 favorite]


An Amplituhedron is Forever.
posted by Kabanos at 9:39 AM on September 18, 2013 [4 favorites]


Mind, this thing won't achieve true cultural relevance until it shows up as a purchasable item in Bejeweled Blitz.
posted by prize bull octorok at 9:51 AM on September 18, 2013 [2 favorites]


I like listening to Arkani-Hamed lecture. I don't comprehend most of it, but every once in a while he gets around to grounding all of the math into what it's getting at and it seems to make sense. thanks for the post.
posted by OHenryPacey at 10:22 AM on September 18, 2013


So... the last I heard about quantum physics, every atom was actually made of constantly-vibrating strings. And now reality is also encoded in an infinitely complex higher-dimensional crystal?

Physics seems to be at a point where I just sort of have to throw up my hands and say "sure, ok, why the hell not?" Next week in quantum physics discoveries: the fifth dimension only makes sense when expressed as bagpipe music! The speed of light is actually a box of crayons! The past is a pumpkin of infinitely variable size! The space between your atoms is pizza!
posted by showbiz_liz at 10:27 AM on September 18, 2013 [17 favorites]


And now reality is also encoded in an infinitely complex higher-dimensional crystal?

Duh.
posted by AElfwine Evenstar at 10:32 AM on September 18, 2013


Wow, just think about playing an RPG with amplituhedral dice. A die with infinitely many sides and a structure that relates to the basic rules of reality would be really useful for D&D.

So God DOES play dice with the universe!
posted by maryr at 10:34 AM on September 18, 2013 [2 favorites]


I was tripping on mushrooms pretty hard one time, and I think I came to similar conclusions about reality. In particular the multi-faceted geometric shape part of it.
posted by Aubergine at 10:35 AM on September 18, 2013 [1 favorite]


... the fifth dimension only makes sense when expressed as bagpipe music!

lol

I think what they have here is "one weird trick that lets you calculate scattering amplitudes"
posted by memebake at 10:35 AM on September 18, 2013 [7 favorites]


It's true, everyone. Very specialized domains of knowledge are difficult to understand without at least a little grounding. That doesn't make them fairy magic beyond mortal comprehension, and implying as much really does you and society a disservice.
posted by gilrain at 10:36 AM on September 18, 2013 [2 favorites]


I do apologize for my levity
posted by showbiz_liz at 10:45 AM on September 18, 2013 [1 favorite]


THANK YOU.

Yeah, I apologize. I could easily have phrased my objection more kindly. Also, my minor gripe is really with how the thread has gone overall, not you.
posted by gilrain at 10:46 AM on September 18, 2013


robotot: "Pffft, I've had one of those in the linen closet for years."

It's that little plastic sphere tumbler thingy you put in the dryer to keep your cloths soft, right?
posted by Hairy Lobster at 10:48 AM on September 18, 2013


I don't know about everyone else, but I was being 100% serious.
posted by aramaic at 10:48 AM on September 18, 2013 [1 favorite]


Translating hard problems to easier domains is a tremendous way to solve them, but it doesn't mean the now easy problem actually exists in that domain. For example, you can port pretty much any hard problem to a domain called SAT, where you're saying things like:

Bit 1 and 2 are 0, bit 3 is 1.
Bit 2 and 3 are 1, bit 4 is 0.
Bit 1 and 5 are 1, bit 3 is 0.

Find values for bits 1 through 5, in which all the above are true (SATisfiable) -- or prove the above is impossible (UNSATisfiable).

You can do this porting, and solve really (really) hard to solve problems. But that doesn't mean the world, even the math world, is made of SAT. It just means SAT's a powerful domain for complexity management, and that if actually solving problems is your goal, translating to this domain is useful.

(A corollary is that complexity management isn't really done that well in the rest of math.)
posted by effugas at 11:03 AM on September 18, 2013 [1 favorite]


showbiz_liz: "The space between your atoms is pizza!"

But... what is the space between pizza atoms?
posted by Hairy Lobster at 11:04 AM on September 18, 2013


In Soviet Universe, the space between pizza atoms is you.
posted by Anything at 11:06 AM on September 18, 2013


Physics is completely indiscernible from mysticism at my level of intellect.
I know you're poking fun, but "mysticism" is one of those words, like "anarchism," that is one of the highest, fullest, most refined and intelligent expressions of its area of expertise but in common usage it usually means the exact opposite of what it is. Whenever something looks like mysticism to me, I try to point at it, because the ideas that the miraculous is always present, that Divinity is personal but not solipsistic, that the divisions between beings is ultimately illusory and that it makes more sense for the spiritual to be about cultivating awe and universal adoration than cataloging the numbers of angels all resonate with me on a very inarticulately innate level. Taken as a whole, this is probably the most beautiful worldview I've encountered in life. It's a shame that the very useful word to describe it in our language is more often used as a derogatory term for its antithesis.

Does it really fall on me to make the Planetary reference? I prefer The Invisibles' flavor anyway, for being more consciously classical mysticism dressed up as pop culture sci-fi, but the whole "uberdimensional jeweled infinity that is the ground state of the world and all possibility" is pretty much a dead ringer for the Snowflake.
posted by byanyothername at 11:53 AM on September 18, 2013 [2 favorites]


I just want to see if any of this leads to brand new approaches to Zeno's paradoxes. Backatya Ancients!
posted by VikingSword at 12:00 PM on September 18, 2013


But that doesn't mean the world, even the math world, is made of SAT.

Yeah, the whole "but what really is the nature of reality?" question is for metaphysics, not physics. "Truth" for physics is completely utilitarian: does the model yield testable hypotheses that are validated by experiment? That's it.
posted by mr_roboto at 12:31 PM on September 18, 2013 [3 favorites]


So God DOES play dice with the universe!

Except that he never actually throws the dice and they just kind of sit there forever/timelessly showing every possible combination of values at once.

(Caveats about mistaking the map for the territory aside.)
posted by saulgoodman at 12:58 PM on September 18, 2013 [1 favorite]


....It's a shame that the very useful word to describe it in our language is more often used as a derogatory term for its antithesis....
posted by byanyothername at 19:53 on September 18 [1 favorite +][!]


Eponysterical.
posted by solotoro at 1:26 PM on September 18, 2013 [1 favorite]


This made me think of Indra's Net and the Avatamsaka Sutra of Huayan Buddhism.
posted by kokaku at 1:33 PM on September 18, 2013 [1 favorite]


goethean: QFT = "Quantum Field Theory" -- basically, the modern version of quantum mechanics used in particle physics.

To help tie the thread together, my QFT course was in fact taught by Lawrence Hall (who works at Lawrence Berkeley Lab as well as at UCB, though he's probably also lectured at Lawrence Hall at some point). It was long enough ago that I've pretty much forgotten it all, unfortunately.
posted by janewman at 1:34 PM on September 18, 2013


Does it really fall on me to make the Planetary reference? I prefer The Invisibles' flavor anyway, for being more consciously classical mysticism dressed up as pop culture sci-fi, but the whole "uberdimensional jeweled infinity that is the ground state of the world and all possibility" is pretty much a dead ringer for the Snowflake.

Oh Jon. Do you take me for a Republic serial villain? I did it in the fourteenth post.

Though as pointed out further up the page, the Snowflake is apparently a reference to this.
posted by Sebmojo at 2:17 PM on September 18, 2013 [2 favorites]


A Twitter search for 'Amplituhedron' brings a host of posts reminding us that 'Time & Space' are illusory... Well, I read The Effing Post and that sure wasn't what this layperson got from it. I then came back here and sure enough the Mefite Maths Monster Group set me right.

Thanks to all the math junkies for another non-trivial night of excellence.
posted by artof.mulata at 7:40 PM on September 18, 2013


A Twitter search for 'Amplituhedron' brings a host of posts reminding us that 'Time & Space' are illusory

It's not that they're illusory, they're no more illusory than, say 'wind' is. Wind is an emergent phenomena of the actions of many atoms. Time and space may similarly emerge from some underlying phenomenon.
posted by empath at 7:46 PM on September 18, 2013 [1 favorite]


...they're no more illusory than, say 'wind' is.

I know, I know. It's amazing how one source, probably Gawker's joking on the matter, leads to a slew of 'Is the sky falling? Only a Sky God of Inner Light can save you!'
posted by artof.mulata at 8:00 PM on September 18, 2013


Yeah, the whole "but what really is the nature of reality?" question is for metaphysics, not physics. "Truth" for physics is completely utilitarian: does the model yield testable hypotheses that are validated by experiment? That's it.

Physics, that realm which recently gotten eaten by String Theorists, probably shouldn't be lecturing anyone on testable hypothesi. Though I suspect our opinions align here :)

My point is that you can create incredibly parsimonious mathematical structures within which deeply valid predictions can be made, and still the map (how you solved the equation) tells you nothing at all about the territory (what is actually happening in the universe).

Mapping from math can be both too complex and too simple. Alas.
posted by effugas at 10:16 PM on September 18, 2013 [1 favorite]


/eyes mice suspiciously
posted by obiwanwasabi at 10:35 PM on September 18, 2013 [3 favorites]


Somehow the article's 2D representation of the 4D object is not helpful.

“In a sense, we would see that change arises from the structure of the object. But it’s not from the object changing. The object is basically timeless.”

Sounds very Platonic. But "amplituhedron" ? that's gotta go.

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.

Hope that happens faster than it has for string theory. In the meantime, new measurements of the weak force are consistent with the poor beleagured Standard Model and its space-time bigotry.
posted by Twang at 11:23 PM on September 18, 2013


In the meantime, new measurements of the weak force are consistent with the poor beleagured Standard Model and its space-time bigotry.

Don't know if you're joking, but nobody doubts the standard model models the electroweak force very well. It's gravity that's the problem.
posted by empath at 1:11 AM on September 19, 2013


I see nobody's posted this yet, so here's Peter Woit's summary: "a rather excessive Quanta headline about a 'jewel at the heart of quantum mechanics', ensuring that the next stage of publicity (e.g. Slashdot) will launch the hype level into outer space, escaping any relationship to reality."

Very much worth reading if you want to understand this topic! And Woit in general is a good antidote to "multiverse mania", over-promotion of string theory, etc.
posted by crazy_yeti at 5:03 AM on September 19, 2013 [2 favorites]


Peter Woit says that the Quanta headline is excessive, while also saying the same Quanta article gives 'a good overview'. He then says "I’m nowhere near expert enough to provide this [a non-hyped version of what the real recent advances are.]". This left me even more confused.
posted by memebake at 8:18 AM on September 19, 2013


I watched the whole hour talk, not getting 95% of it... what did make some sense to me was the idea of having a triangle with 3 corners holding it up, and the center of mass of the thing having to be somewhere in between the supports.... of course even writing out what I just learned is something I don't have the language to do accurately or efficiently.... but I'll try anyway:

If you have a triangle supported by 3 strings, and randomly drop sand on it, one of them will break first, the probability of a given string breaking is somehow related to where the center of mass is, and the directions and strengths of the supporting strings. This to me seems like the closest analog to quantum mechanics for someone that I've heard in a long time.

I've got some vague physics notions from this, which I can't express, and I feel it was time well spent. Thanks!
posted by MikeWarot at 3:50 PM on September 19, 2013 [1 favorite]


Bohemian Gravity! by A Capella Science
posted by jeffburdges at 7:12 AM on September 20, 2013


I just need The Doctor to explain it all to me in the next 'Who' episode and I'll understand it.
posted by Gadgetenvy at 12:07 PM on September 20, 2013 [1 favorite]


Doctor Who is known for its accurcate science.
posted by maryr at 12:21 PM on September 20, 2013 [2 favorites]


But "amplituhedron" ? that's gotta go.

Seriously. It's half Greek and half Latin!
posted by whir at 2:47 PM on September 20, 2013


Totally! The team's sociopathic disregard for properly monolingual terms is so dysfunctional, it makes me want to give up on physics and go watch automobile racing on television.
posted by Rhaomi at 6:58 PM on September 20, 2013 [5 favorites]


Guh, every time there's a physics thread I actually know something about on Mefi I have to go and do *actual work* so I can't sit around and comment. Somebody asked about Kerr black holes once and I'm still sad I didn't manage to comment..

anyhow, a few responses now that I've read the thread:

RonButNotStupid: And of course nothing derails note-taking during a lecture like a well-placed ξ, and good luck if it lives in the same equation as ϵ because you're never going to successfully parse what you wrote.

Ha. I still remember the first college math class I took. I knew what \xi looked like in print, because I was bored in high school physics and memorized the Greek alphabet from the back of the book, but I don't think I'd ever seen it written. PDE class that was pretty dang tough for me, teacher talking very fast and I wasn't used to people having accents, and saying something that sounded like "z" and looked like a tornado. I wrote z in my notes. And then, after 40 minutes, he introduces another quantity, which was actually called "z". I swore audibly.
I later took Greek and thus managed to get a better handwritten \xi, but telling \xi and \zeta apart... ah well. I can't tell v from r in my handwriting either. or \gamma and 2.


ennui.bz: what he means by "positive" grassmannian could be different things and i didn't pick that up scanning the articles.... Ah. The positive grassmanian is just the region of the space where the homogenous coordinates are positive. It's not quite right, but if the good coordinates on the plane are the regular x,y coordinates, then you're just taking the region where x>0 and y>0. (The grassmanian is a weirder space so good coordinates on it are harder to describe).

Also empath, I'm assuming ennui's explanation of Grassmannians was more useful than the Wikipedia one; if not, lemme know and I can try something. Been a little buried this past week, something about trying to write papers in hopes of future employment.


memebake: "one weird trick that lets you calculate scattering amplitudes"

Hah, I am seriously going to use this description, it kind of cracks me up. Of course, there's a reason a bunch of people are working on this stuff now; often a simpler or easier way to calculate a physics quantity indicates deep underlying physics, or at the very least allows you to calculate a whole bunch of things you couldn't previously. In this case I'd personally be happy with either (bonus points if you can do it with less supersymmetry).


effugasPhysics, that realm which recently gotten eaten by String Theorists

Ok so as a string theorist, I can't pass this up. If you think physics has been eaten by string theorists, then you haven't got any idea of what percentage of current physicists are string theorists, or what percentage of even current high energy theorist positions are going to string theorists (say, over the past five years).
Also strings isn't *in principle* untestable. Rather most formulations of it are practically so, but there's a fundamental difference there. Gah, also, "string theory" is not one coherent object. It's not like "newton's theory of gravity" or "Einstein's theory of special relativity". Really, string theory is a set of techniques which might be useful for quantizing gravity, just like differential equations are a set of techniques, or field theory is a set of techniques.


Twang: "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."

Hope that happens faster than it has for string theory.


Well so does everyone. The easiest consistent string theories to write down are in 10 dimensions and have supersymmetry. I don't live in 10 (big) dimensions, nor does our world have supersymmetry (at our energy scale, at least). So people trying to build models of, say, collider physics from string theory have to find ways to compactify the extra dimensions, and break the supersymmetry, and not break something else in the process. It turns out this is hard (not least because it turns out there are way too many ways to do it and no method to choose between the ways).

Here, the theory they are discussing (termed \cal{N}=4 superyangmills at large N: this means it's a souped up version of quantum chromodynamics, the theory which describes the strong force between quarks; it's souped up because regular QCD is \cal{N}=0 and thus not-super just regular Yang-Mills, and number of charges N=3, not infinity) has all sorts of extra symmetry. They rely pretty strongly on this extra symmetry, and so it's a bit hard to imagine how the methods are useful for the case of actual real QCD.

But on the other hand, in the history of physics, many times people first learned how to do calculations say in only 2 dimensions, or only with electric field but no magnetic field, or only magnetic but no electric, and only from these first forays did they later learn how to do full on electromagnetism in the (3+1) dimensions we actually live in.

So yeah, I guess the hope here is this represents a new set of techniques, which arose out of the study of this sort of special problem, but might be much more broadly applicable (and people are actively working on making them applicable more broadly).
posted by nat at 9:03 PM on September 20, 2013 [3 favorites]


I think maybe I should make a feature request in MetaTalk for pb to put LaTeX support into the comments.
posted by Elementary Penguin at 2:28 AM on September 21, 2013 [4 favorites]


Kevin Street: "It still sounds amazing! Kind of like the mathematical version of a metaphor."

The tricky part is: mathematics IS a metaphor.

2 is just a description of what we're thinking about.

"divided by" isn't a real-world action. No matter what you do, if something is split into two parts, something is lost: 2/2 < 1, in every real-world incident, from cutting cheese to splitting atoms.

"e^x" is never calculated by the universe.
posted by IAmBroom at 11:52 AM on September 21, 2013


ennui.bz: "the way this immediately got onto wikipedia shows just how problematic the idea of an encyclopedia is in the age of "viral" marketing. (wikipedia itself is cool, but the idea of an encyclopedia of knowledge is problematic)"

Interesting. I just realized that Wikipedia demonstrates market inefficiency.

If it were updated by everyone at once who had an interest in the topic, every time it merited change, the odds are immensely in favor of a more accurate Wikipedia. I believe. Instead, it is vandalized by A, then reverted 10 minutes later by B, then 15 days later given a political bias by a staffmember on behalf of C, then corrected back a month after that towards a less-biased POV by D...
posted by IAmBroom at 11:57 AM on September 21, 2013


MuffinMan: "It's nice that physicists try to explain it in simplified terms, but the process my brain follows to understand this is roughly the same as a fish trying to work out how to use a can opener."

FREE OUR BRETHREN FROM THE CANS OF MAN!

RETURN OUR PEOPLE'S BODIES FOR PROPER BURIAL AT SEA!
posted by IAmBroom at 11:58 AM on September 21, 2013 [1 favorite]


Twang: "“In a sense, we would see that change arises from the structure of the object. But it’s not from the object changing. The object is basically timeless.”

Sounds very Platonic.
"

Hmmm.... Never thought about it before, but Plato's Ideal Objects are sort of relevant at the quantum level.

There's no platonic "chair", but AFAWK there's a platonic "photon".
posted by IAmBroom at 1:03 PM on September 21, 2013 [1 favorite]


So God DOES play dice with the universe!

I always just assumed that was so-called free will.
posted by philip-random at 12:10 AM on September 22, 2013


I [rolls d20] agree with philip-random, but [rolls d20] also steal his watch.
posted by obiwanwasabi at 1:39 AM on October 1, 2013 [1 favorite]


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