Stop Listing the Amplituhedron as a Competitor of String Theory

The Economist recently had an article (paywalled) that meandered through various developments in high-energy physics. It started out talking about the failure of the LHC to find SUSY, argued this looked bad for string theory (which…not really?) and used it as a jumping-off point to talk about various non-string “theories of everything”. Peter Woit quoted it a few posts back as kind of a bellwether for public opinion on supersymmetry and string theory.

The article was a muddle, but a fairly conventional muddle, explaining or mis-explaining things in roughly the same way as other popular physics pieces. For the most part that didn’t bug me, but one piece of the muddle hit a bit close to home:

The names of many of these [non-string theories of everything] do, it must be conceded, torture the English language. They include “causal dynamical triangulation”, “asymptotically safe gravity”, “loop quantum gravity” and the “amplituhedron formulation of quantum theory”.

I’ve posted about the amplituhedron more than a few times here on this blog. Out of every achievement of my sub-field, it has most captured the public imagination. It’s legitimately impressive, a way to translate calculations of probabilities of collisions of fundamental particles (in a toy model, to be clear) into geometrical objects. What it isn’t, and doesn’t pretend to be, is a theory of everything.

To be fair, the Economist piece admits this:

Most attempts at a theory of everything try to fit gravity, which Einstein describes geometrically, into quantum theory, which does not rely on geometry in this way. The amplituhedron approach does the opposite, by suggesting that quantum theory is actually deeply geometric after all. Better yet, the amplituhedron is not founded on notions of spacetime, or even statistical mechanics. Instead, these ideas emerge naturally from it. So, while the amplituhedron approach does not as yet offer a full theory of quantum gravity, it has opened up an intriguing path that may lead to one.

The reasoning they have leading up to it has a few misunderstandings anyway. The amplituhedron is geometrical, but in a completely different way from how Einstein’s theory of gravity is geometrical: Einstein’s gravity is a theory of space and time, the amplituhedron’s magic is that it hides space and time behind a seemingly more fundamental mathematics.

This is not to say that the amplituhedron won’t lead to insights about gravity. That’s a big part of what it’s for, in the long-term. Because the amplituhedron hides the role of space and time, it might show the way to theories that lack them altogether, theories where space and time are just an approximation for a more fundamental reality. That’s a real possibility, though not at this point a reality.

Even if you take this possibility completely seriously, though, there’s another problem with the Economist’s description: it’s not clear that this new theory would be a non-string theory!

The main people behind the amplituhedron are pretty positively disposed to string theory. If you asked them, I think they’d tell you that, rather than replacing string theory, they expect to learn more about string theory: to see how it could be reformulated in a way that yields insight about trickier problems. That’s not at all like the other “non-string theories of everything” in that list, which frame themselves as alternatives to, or even opponents of, string theory.

It is a lot like several other research programs, though, like ER=EPR and It from Qubit. Researchers in those programs try to use physical principles and toy models to say fundamental things about quantum gravity, trying to think about space and time as being made up of entangled quantum objects. By that logic, they belong in that list in the article alongside the amplituhedron. The reason they aren’t is obvious if you know where they come from: ER=EPR and It from Qubit are worked on by string theorists, including some of the most prominent ones.

The thing is, any reason to put the amplituhedron on that list is also a reason to put them. The amplituhedron is not a theory of everything, it is not at present a theory of quantum gravity. It’s a research direction that might shed new insight about quantum gravity. It doesn’t explicitly involve strings, but neither does It from Qubit most of the time. Unless you’re going to describe It from Qubit as a “non-string theory of everything”, you really shouldn’t describe the amplituhedron as one.

The amplituhedron is a really cool idea, one with great potential. It’s not something like loop quantum gravity, or causal dynamical triangulations, and it doesn’t need to be. Let it be what it is, please!

9 thoughts on “Stop Listing the Amplituhedron as a Competitor of String Theory

  1. nonreligious

    While I concede that yes, things don’t look very good at all for natural SUSY (in the sense of the hierarchy problem), and that there is no direct experimental evidence for string theory (described nicely in Joe Conlon’s book), I was fairly ticked off by the tone of the article – which seemed fairly high handed for a piece which seemed to lack some basic understanding of the scientific background. It seems especially neglectful on the writer’s part not to mention that the amplituhedron construction arises in $N=4$ SYM – which I guess is pretty revealing in itself (and rather funny given their attitude).


  2. Madeleine Birchfield

    Very few string theorists from a decade ago are still working on actual string theory topics, Cumrun Vafa and the coterie around the Swampland project, and Lubos Motl being some of the few who do so. Many string theorists from a decade ago have stopped working on actual string theory and superstring theory because of issues with the landscape amongst other intractable problems, and instead have moved on to playing with low dimensional toy gauge-gravity duality models in quantum field theory such as AdS2/CFT3 in the hopes that those would help with condensed matter physics, or, for the theorists working at It from Qubit, have moved on to studying toy models in quantum information theory. I would also include those studying the amplituhedron, such as Nima Arkani-Hamed, in this group, as the amplituhedron is a tool derived from quantum field theory (N=4 SYM), and whose applications are largely in fields adjacent to quantum field theory (hadrodynamics, general relativity, etc). These string theorists are probably more accurately called quantum field theorists or quantum information theorists instead of string theorists at this point, as this work on gauge-gravity duality, holography, quantum information theory, and the amplituhedron is largely divorced from actual work on string theory, which has moved on to Swampland consistency conjectures and ties to pure mathematics.


    1. 4gravitons Post author

      See response to Peter Woit below. Also, the swampland’s connection to string theory is itself kind of 50/50: some of it is based on looking at various string compactifications, other parts are things like the weak gravity conjecture (or to take a recent example, Ooguri’s most recent paper on that topic) that are supposed to hold beyond string theory (unless you don’t think of WGC as a swampland constraint).

      Also, not to poke a hornet’s nest, but is Lubos Motl actually working on physics these days? He hasn’t published in 15 years.


  3. Peter Woit

    “Unless you’re going to describe It from Qubit as a “non-string theory of everything”, you really shouldn’t describe the amplituhedron as one.”

    Since It from Qubit has nothing to do with string theory (other than tribal affiliations of some people working on it), if it’s a “theory of everything” then it’s a “non-string theory of everything.” Of course the main problem here is that “It from Qubit” doesn’t seem to be a theory of anything, or even a theory, more like a vague dream that their might be a theory.


    1. 4gravitons Post author

      This is also a reply to Madeleine Birchfield’s comment above:

      Agreed that “It from Qubit” is not particularly stringy, and that much like the amplituhedron it’s not a “theory of everything” either. Given that, the article was pretty clearly just classifying by “tribal affiliation”, not by content. My point is if you’re going to do that, you should at least get the tribal affiliations right!


  4. Pingback: the Amplituhedron, go deeper – The nth Root

  5. Dale

    A bit asides the point of the main article, but does anyone have some good introductory sources on asymptotically safe gravity? I saw some stuff on it a while ago and it appealed to some of my more pure-math sensibilities since it side-steps perturbation.



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