New research, which turns out to not really be all that new, suggests that space and time do not exist. The research also suggests that a jewel (an “amplituhedron”) is the center of our universe and that from said jewel every feature of our known reality can be quantified. This is crazy, right? Like, why-the-hell-am-I-sitting-at-this-desk-right-now-as-I-tumble-through-a-universe-that-is-governed-by-features-that-are-incomprehensible-to-my-human-mind crazy. But maybe not, actually.
To find out, I spoke with Jacob Bourjaily, a theoretical physicist at Harvard who is closely familiar and very much involved with this strand of research. In December, he co-authored a paper titled “Scattering Amplitudes and the Positive Grassmannian.”
Yeah. Yeahhhhh.
Space and time may not exist. This is a REALLY BIG DEAL, right?
It is a “really big deal” for sure, but this itself is not a (or the) novel idea involved in the research described in the article. It has been generally known (in the theoretical physics community) for decades that locality and unitarity (a continuous notion of “spacetime”) must ultimately break down in theories with gravity. The problem is that, until very recently, all of the standard, mathematical tools available to describe nature made locality and unitarity essentially unbreakable, foundational ideas.
So we’ve known for a long time that these ideas need to be modified, but it has never been clear how to modify the standard tools.
The “amplitudehedron” research is related to this indirectly because it provides a complete reformulation of the standard toolbox—one that is mathematically identical to the traditional one, but one for which locality and unitarity arise indirectly. Because they are not built-in features of the description, there is optimism that these new ideas can eventually be modified to correctly describe theories with gravity. (It is worth mentioning that we don’t yet know how to do this; it is really just a long-term motivation for the need to reformulate the old-school foundations of quantum mechanics (and it is such a reformulation which has recently been accomplished).)
“The new developments have provided a reformulation of quantum field theory, and they make the simplicity of predictions manifest, dramatically expanding our ability to make predictions for experiment in the future.”
To a person who upon considering all of this, at best, feels an overwhelming rush of anxiety and at worst, now feels unmoored to existence, just floating through a universe without any familiar organizing principles, what would you say? I mean, without space and time … what is there?
Don’t worry! As described above, the new ideas are merely a (perfect) reformulation of existing ideas. By a “perfect” reformulation, I mean that predictions made using the “amplitudehedron” are mathematically guaranteed to match the predictions obtained using the standard techniques (Feynman diagrams).
Considering that the new ideas reproduce exactly the same predictions as old-fashioned ones, you may wonder why anyone cares. There are two principal reasons why these developments are important and exciting (and depending on your philosophical preferences, one may be much more important than the other).
Firstly, it turns out that this new description is dramatically more efficient than the standard one. Making predictions for experiments using Feynman diagrams (the standard toolbox) is a massively complex, difficult task. And it can be amazingly frustrating: making predictions even for relatively simple experiments can require adding up hundreds of thousands of terms, and in almost every case, these terms collapse into something shockingly simple (like a single, provocatively simple term).
The new methods make this ultimate simplicity completely manifest. Predictions that would have required supercomputers using Feynman diagrams can now be done on a napkin. And so these ideas represent a massive technological advance in our ability to make predictions for quantum mechanical processes.
The second reason is related to your questions about spacetime (locality and unitarity). As I described above, although the new tools reformulate the standard ones, these ideas don’t involve locality or unitarity in any important way—they only emerge indirectly at the end of computations. Because of this, we hope that this is a framework that can somehow, ultimately be modified to incorporate gravity and provide a deeper description of nature.
OK, so beyond that—because if we can’t get beyond that, my hands will cease to type—one of the biggest takeaways, it seems, is that this may totally simplify our understanding of our existence. How so?
Simplify is right. The amplitudehedron picture as we have it now will make precisely the same predictions for experiment as would have been made using traditional techniques. But these new ideas are incredibly more concise. Of course, Feynman diagrams are quite compelling (and arguably “simple”) in their own way, and are certainly very intuitive. But they completely obfuscate the ultimate simplicity taken by virtually all predictions made for experiments.
The amplitudehedron picture makes it clear why predictions for experiments are so simple. And it does this in a very beautiful way, using novel ideas deeply based in geometry.
The amplituhedron is a jewel. This is more a “mathematical concept of a jewel,” rather than the common conception of a jewel you could find naturally occurring somewhere, right?
Yes. The amplitudehedron is a (rather abstract, and somewhat distant) generalization of the ordinary notion of a “polyhedron”—like a jewel. It is a relatively “simple” space, described by its faces, its edges, etc.; but it doesn’t live in ordinary space, but rather in an auxiliary space called the “Grassmannian.”
How would this affect a normal person’s day-to-day life? Or, more than anything, does it just inform the context within which we exist?
For the past half-century, quantum field theory has provided the ultimate foundation for our understanding of the Laws of Nature. It is like “F=ma”: a framework that allows us to make predictions for any system of particles and forces we happen to discover in nature. While experiments at colliders have uncovered a host of new particles and forces, quantum field theory—as a framework—has remained unchanged, and is itself independent of these discoveries.
Despite all its successes, quantum field theory has two principle shortcomings: it remains enormously difficult, and it must be ultimately modified to incorporate gravity. To get a sense of the seemingly excessive difficulty of quantum field theory, it is not unusual for computations relevant to collider experiments to require efforts involving many years of supercomputer time, and yet these predictions almost universally turn out to be shockingly simple and elegant.
The new developments have provided a reformulation of quantum field theory, and they make the simplicity of predictions manifest, dramatically expanding our ability to make predictions for experiment in the future.
What about the still-unanswered “why does the world exist” question? There’s always a “yeah, but why did that happen?” that precedes whatever explanation someone might give. Does this put us any closer to finding a first cause of the universe?
I don’t know. In many ways, this research applies to any world described in terms of quantum mechanics and relativity. These tools will of course prove useful for making predictions for the Standard Model of particle physics (relevant to our universe), but are valid also for any other conceivable set of forces and particles (whose interactions are guided by quantum mechanics and relativity). The new ideas don’t really inform or depend on our understanding of the content and forces observed in our universe.
Obviously, this is still in the initial stages. What’s next, before I start re-evaluating everything?
There is still a lot of work to do. For one thing, the amplitudehedron is only thoroughly understood in the context of certain, very simple quantum field theories. I think it is safe to say that we understand how to generalize these ideas to all quantum field theories (such as the Standard Model); but more complicated theories involve many complications, and it remains to be seen how elegantly these complications can be dealt with. (I have no doubt that the amplitudehedron story will eventually result in a reformulation of any quantum field theory, but strictly speaking, we only have strong evidence that the reformulation exists for a small set of especially nice theories.)
There is also the question of what this reformulation teaches us about quantum theories with gravity. Not having locality and unitarity manifest is a great step in the right direction, but it is far from obvious how we should modify the amplitudehedron to actually change our understanding of the laws of nature.
