Nima Arkani-Hamed thinks space-time is doomed.
That doesn’t mean he thinks it’s about to be destroyed by a supervillain. Rather, Nima, like many physicists, thinks that space and time are just approximations to a deeper reality. In order to make sense of gravity in a quantum world, seemingly fundamental ideas, like that particles move through particular places at particular times, will probably need to become more flexible.
But while most people who think space-time is doomed research quantum gravity, Nima’s path is different. Nima has been studying scattering amplitudes, formulas used by particle physicists to predict how likely particles are to collide in particular ways. He has been trying to find ways to calculate these scattering amplitudes without referring directly to particles traveling through space and time. In the long run, the hope is that knowing how to do these calculations will help suggest new theories beyond particle physics, theories that can’t be described with space and time at all.
Ten years ago, Nima figured out how to do this in a particular theory, one that doesn’t describe the real world. For that theory he was able to find a new picture of how to calculate scattering amplitudes based on a combinatorical, geometric space with no reference to particles traveling through space-time. He gave this space the catchy name “the amplituhedron“. In the years since, he found a few other “hedra” describing different theories.
Now, he’s got a new approach. The new approach doesn’t have the same kind of catchy name: people sometimes call it surfaceology, or curve integral formalism. Like the amplituhedron, it involves concepts from combinatorics and geometry. It isn’t quite as “pure” as the amplituhedron: it uses a bit more from ordinary particle physics, and while it avoids specific paths in space-time it does care about the shape of those paths. Still, it has one big advantage: unlike the amplituhedron, Nima’s new approach looks like it can work for at least a few of the theories that actually describe the real world.
The amplituhedron was mysterious. Instead of space and time, it described the world in terms of a geometric space whose meaning was unclear. Nima’s new approach also describes the world in terms of a geometric space, but this space’s meaning is a lot more clear.
The space is called “kinematic space”. That probably still sounds mysterious. “Kinematic” in physics refers to motion. In the beginning of a physics class when you study velocity and acceleration before you’ve introduced a single force, you’re studying kinematics. In particle physics, kinematic refers to the motion of the particles you detect. If you see an electron going up and to the right at a tenth the speed of light, those are its kinematics.
Kinematic space, then, is the space of observations. By saying that his approach is based on ideas in kinematic space, what Nima is saying is that it describes colliding particles not based on what they might be doing before they’re detected, but on mathematics that asks questions only about facts about the particles that can be observed.
(For the experts: this isn’t quite true, because he still needs a concept of loop momenta. He’s getting the actual integrands from his approach, rather than the dual definition he got from the amplituhedron. But he does still have to integrate one way or another.)
Quantum mechanics famously has many interpretations. In my experience, Nima’s favorite interpretation is the one known as “shut up and calculate”. Instead of arguing about the nature of an indeterminately philosophical “real world”, Nima thinks quantum physics is a tool to calculate things people can observe in experiments, and that’s the part we should care about.
From a practical perspective, I agree with him. And I think if you have this perspective, then ultimately, kinematic space is where your theories have to live. Kinematic space is nothing more or less than the space of observations, the space defined by where things land in your detectors, or if you’re a human and not a collider, in your eyes. If you want to strip away all the speculation about the nature of reality, this is all that is left over. Any theory, of any reality, will have to be described in this way. So if you think reality might need a totally new weird theory, it makes sense to approach things like Nima does, and start with the one thing that will always remain: observations.
4 gravitons 
“So if you think reality might need a totally new weird theory, it makes sense to approach things like Nima does, and start with the one thing that will always remain: observations.”
That’s, in a proper dualism manner, both duh and totally wrong. Except probabilities go to infinity 😉
The duh hopefully does not need elaboration.
The totally wrong … it’s not unlike saying a fish could figure out the ocean by taking mouthful of sea water and observe what happens when it spits that water out at various pressures and angles. Absolutely everything, from our senses and their imperfect design and biased processing to every instrument ever conceived is part of what we are observing.
Good luck.
One can do amazing things with a mouthful of [sea] water. We are nowhere near to filling up the set of possible things we can do with it. Simply because the set has infinite size. And that’s just water.
Yet, it’s the most entertaining thing a human being can do. If ye do it for any other reason, my condolences.
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“This is the first in a series of papers” 🙂
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And it was!
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What are the core insights that make it possible to do this without Feynman diagrams (or their path integral equivalents)?
Is he exploiting symmetries that make terms cancel out?
Is he doing a principle of least action analysis and then working out another way to determine the amount of stochastic variation from a deterministic calculation based upon that principle?
What real world problems are outside his techniques’ domain of applicability?
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Your first question is more difficult to answer than you might think. Nima tends to present his results as fully-formed “miracles” springing out of beautiful formalism, so it can be hard to track down how it relates to prior work.
I think the answer has to do with the mathematics he’s using to count curves. Previously people were aware that you could have a “stringy” picture of particle physics amplitudes where instead of drawing individual diagrams you summarize them with a single topology for each number of loops. But in those approaches it was hard to do more than a couple loops, and often one needed to “cut” the loops open in some way to avoid over-counting paths that twist around the loops. Nima’s new work brings in more sophisticated mathematics that lets one count those paths in the right way to get the correct particle physics result out.
I don’t think symmetries play much of a role here, he’s not canceling terms, rather he’s summarizing many terms in terms of their topological properties.
Your question about a principle of least action/stochastic variation sounds like you’re imagining something like stochastic electrodynamics, and this is really a very different kind of thing. Nima isn’t starting from a physical picture or attempt at a physical picture like that, instead he’s starting by assuming some of the mathematical properties of the normal Feynman diagram approach (a sum over diagrams with a certain topology, momentum flowing through the diagram) and then finding a more minimal way to express the problem given those assumptions that doesn’t explicitly describe the individual Feynman diagrams or details of the intermediate states. He’s certainly not replacing the path integral or the overall quantum picture, but he’s finding a way to describe the result of summing diagrams that is a relatively simple and minimal math problem.
At the moment, he’s able to handle a very specific list of theories. I think the expectation is this can be more general, but you get less of a “pure math problem” and more need to actually use physics information the more realistic you want to go. Of the theories he can do, the realistic ones are one that describes pions (I don’t know how often this is actually used anymore to do this though) and one that describes interactions of pure Yang-Mills (so just gluons, no quarks). A different group figured out how to include fermions, though only in an unrealistic context where they interact with colored scalars.
It’s important to note that at this point, it’s unclear if this will actually offer any savings for practical calculations. People are more optimistic about it doing so than they were for the amplituhedron (in particular, the new technique lines up rather nicely with a new technique for numerically doing Feynman diagram integrals), but I don’t think anyone’s working on applying this to SM calculations yet.
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