A Jewel at the Heart of Quantum Physics

[bananas]

https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/

A Jewel at the Heart of Quantum Physics

Artist’s rendering of the amplituhedron, a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated — the probabilities of outcomes of particle interactions.

By: Natalie Wolchover
September 17, 2013

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.

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[chervilant]

1. The Calculus...

It is truly a thing of beauty.

[bananas]

2. SUSY 2013: The Amplituhedron

Hour-long video at http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Hamed_4-3.html

[DetlefK]

3. Geometry without locality and unitarity. Sounds... tricky.

locality = things interact by being at the same place at the same time

unitarity = if you do the opposite of what you did before, they will cancel out

[LuvNewcastle]

5. The locality problem is fascinating to me.

If locality isn't required for an action, that means one thing can physically affect something else on the other side of the world, or even the other side of the universe. We know this happens in an indirect way, but if it can happen directly, that would totally revolutionize our view of the world. I would like to know how that would apply to consciousness as well as more concrete things. If my thoughts here could be sent to someone in Japan, for instance, or even someone in the next room, that would be just about the most exciting thing I can think of.

[bananas]

9. Quora.com: Is this a watershed new discovery in physics - is space-time still fundamental?

http://www.quora.com/Physics/Is-this-a-watershed-new-discovery-in-physics-is-space-time-still-fundamental-now-that-we-have-the-amplituhedron-for-modeling-quantum-field-theory

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What this work is attempting to do (which it hasn't full achieved yet) is to replace our underlying formulation of quantum field theory with a new formulation.

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What Nima Arkani-Hamed [*] and collaborators are trying to do is, is to replace the building blocks of a theory with particles (rather than fields), elementary interactions and a new space called the Grassmannian. Most importantly, space-time does not appear in this formulation. In a class of theories, this has been shown to reproduce almost all of the results of the path integral formulation of quantum field theory. There are certain very field-y aspects that hasn't been reformulated, most notably vacuum expectation values (of fields) and instantons (to my knowledge). But that is huge progress.

The fact that space-time does not appear to be one of the elementary building blocks, but instead emerges as an interpretation of the results is a fascinating concept. We know that this has to be the case at some level, but I think that this particular avenue physicists find surprising (I think 5 years ago physicists would have muttered something about string field theory). The reason why this could be very important is that some of the deepest conceptual difficulties in quantum gravity are very difficult to formulate because they really require quantum space-time and our formulation takes in space-time as an input, while formally this problem isn't a contradiction, it does mean that space-time is getting in the way of doing calculations. This progress makes very little direct in-roadson these problems, it is beginning to at least create a formalism where space-time is not at the heart of the formulation.

* Full-disclosure: Nima Arkani-Hamed was my graduate advisor, is a close friend and is the godfather of daughter.

Via Frank Heile.

[Nitram]

4. Is it an 'object'...

...or a mathematical construct that could potentially lead to the discovery of an object?

[bananas]

6. It's a mathematical construct. nt

[bemildred]

7. I think it's a new method, is what it is.

I would use the analogy of integration by series approximation and integration where an indefinite integral is known. And if true, that seems like a really big deal with unforseeable consequences.

And then there is the pretty visualization up there ...

[bananas]

8. There's a new wikipedia entry for it

First time I've seen a new entry in wikipedia:

http://en.wikipedia.org/wiki/Amplituhedron

This article documents a current event. Information may change rapidly as the event progresses.

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[bemildred]

10. Wow.

That was amazing. I know just enough to know I have no idea what they are talking about. But it sounds really cool.