This physical breakthrough could change our understanding of spacetime

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Over at Quanta Magazine, Natalie Wolchover has authored a stunning feature on the "amplituhedron" – a jewel-shaped, geometric object that could give scientists a new perspective on the quantum world, while "[challenging] the notion that space and time are fundamental constituents of nature."


Above: Artist Andy Gilmore's rendering of the amplituhedron, via Quanta Magazine

What does that mean, exactly? Allow Wolchover to explain. We've included an excerpt here, but you'll find the entire piece (which is praiseworthy for its crisp and lucid encapsulation of what is, admittedly, some rather esoteric subject matter) over at Quanta Magazine:

Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.

“This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work.

The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression.

“The degree of efficiency is mind-boggling,” said Jacob Bourjaily, a theoretical physicist at Harvard University and one of the researchers who developed the new idea. “You can easily do, on paper, computations that were infeasible even with a computer before.”

The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe. Attempts thus far to incorporate gravity into the laws of physics at the quantum scale have run up against nonsensical infinities and deep paradoxes. The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.

“Both are hard-wired in the usual way we think about things,” said Nima Arkani-Hamed, a professor of physics at the Institute for Advanced Study in Princeton, N.J., and the lead author of the new work, which he is presenting in talks and in a forthcoming paper. “Both are suspect.”


Corpore Metal

I've been reading about the amplituhedron over the last two days after hearing about it. The major implications, I think, are as follows:

  1. In understanding particle inactions, it vastly simplifies calculations and predictions that would taken hundrends of thousands or millions of Feynman diagrams in the past.
  2. By discarding locality, unitarity, space and time, it may, and that's a very shaky "may," finally give us a quantum field theory of gravity. Something that has proved nearly impossible for more than 70 years.

In the past, Feynman diagrams (Which are themselves very powerful and elegant simplifying tools) didn't help us in understanding some specific particle interactions because the number of terms that needed to be calculated were so huge that even our most powerful supercomputers couldn't crack a solution. If this new concept is right, it is a staggeringly elegant mathematical simplification and the Standard Model will be vastly simplified by incorporating it.

The second implication is also huge. For many, many decades we've had lots of problems trying to bring together general relativity with quantum theory into a quantum field theory of gravity. If the amplituhedron (Or some other Grassmannian.) is valid, it may produce a quantum gravity model as natural consequence.

Of course, in doing that, we may have to discard concepts like time, space (Which frankly a bit undermined by relativity anyway.) and locality (Which is heavily undermined by quantum theory anyway.) and unitarity (Which really is just an arbitrary restriction in working out probability.)