The Amplituhedron – Turning physics inside out.

I like the seismics.

I just love the concept how recording a superposition of waves can transport information about the subsurface. We send out carefully engineered noise to record noise and apply statistics to these huge data sets and in the end get an image we can interpret in regard to its geologic formation.

This is amazing!

I like the more complex concepts of seismic anisotropy, where you look at your image of the waves and realize something’s wrong. The wave that travelled one way just doesn’t match up with a wave travelling the other wayLeon Thomsen (2001). Seismic anisotropy GEOPHYSICS, 66(1), 40?41. DOI: 10.1190/1.1444917. This happens for several reasons and they’re all fascinating to learn about.

However for this you have to be very careful when applying your statistics to your data. The process has to preserve the amplitudes so the strength of your waves, which can get quite tricky. However this true amplitude approach was the namesake of my url shortener amplt.deHubral, P. (1983). Computing true amplitude reflections in a laterally inhomogeneous earth. GEOPHYSICS, 48(8), 1051?1062. DOI: 10.1190/1.1441528.

Side glances

In this process I have also always had a glance at the newest stuff in physics and especially particle physics.
These are concepts I can barely grasp. It’s mind blowing how they smash together particles at almost light speed and since they can’t directly gain information from this, they have to look at the decay products of this to get information out it.

They also have no clue what they’ll get from their measurement and have to do some serious statistics to get valid conclusive results. Have you heard about the Higgs boson and the Higgs field? You cannot observe that particle! They had to calculate what decay products come from this particle to get an idea if that particle could even exist. And to top it off they had to do it several billions of times to get any statistically significant results.

I have always been fascinated by Feynman diagrams. They’re a graphic representation of these particle interactions. For any particle interaction you can draw all of these possible diagrams and add them up to predict what’s going to happen.

Feynman Diagram of an electron-electron interaction

The Challenge

However, there’s a problem with these. They’re too complex. For example there is a particle interaction of two gluons that result in 4 gluons. This happens a billion times at the LHC. This interaction has 220 Feynman diagrams that result in thousands of terms to calculate Page 34 and Even for supercomputers this gets a bit nasty. Physicists even proclaimed that this will not be solved in the forseeable future.

Signature quote of Barney Stinson in the series How I met you mother

Stephen Parke and Tommy Taylor from the Fermi National Accelerator Laboratory simplified the formula to a nine page formulaParke, S.J., & Taylor, T.R. (1986). Amplitude for n-gluon scattering Phys. Rev. Lett.; (United States); Journal Volume: 56:23 DOI: 10.1103/PhysRevLett.56.2459. (Yes I said that 9 pages was the simplified version…) However, they have tried the impossible and they succeded! They laid the foundation for the newest awesomeness that emerged from the world of physics lead by Nima Arkani-Hamed, which will probably change some things dramatically.

The Amplituhedron

Copyright Conan O’Brian, Sept 18, 2013

Okay, it’s not a bong. But the other statements are true. The newest discovery might prove time and space to be just illusionary dimensions. They have found the so-called amplituhedron. What’s so amazing about this?

Amplituhedron of a 8 gluon interaction. Source Simon Foundation

This amplituhedron is equivalent to a 500 page calculation of a particle interaction!
And they also calculated a master amplituhedron. This is an amplituhedron that has an infinite number of sides and might serve as a template.


I do not understand quantum mechanics. That stuff is pretty tough physics and even if you understand it, remember what Niels Bohr said:

“If quantum mechanics hasn?t profoundly shocked you, you haven?t understood it yet.” – Niels Bohr

However, I am just fascinated how a geometric object can simplify an entire field of research to the point of: “I could compute this formula on a supercomputer and wait a long time or just give me a pen and paper and I’ll draw this for you real quick and do the calculation this way.”

My mind is blown and if you like to read a more detailed description of the history of the amplituhedron head over to the Simons Foundation and if you want the paper, here’s the real dealNima Arkani-Hamed, Jacob L. Bourjaily, Freddy Cachazo, Alexander B. Goncharov, Alexander Postnikov, & Jaroslav Trnka (2012). Scattering Amplitudes and the Positive Grassmannian arXiv preprint arXiv:1212.5605 (2012) arXiv: 1212.5605v1.

via IFLS

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... is a geophysicist by heart. He works at the intersection of machine learning and geoscience. He is the founder of The Way of the Geophysicist and a deep learning enthusiast. Writing mostly about computational geoscience and interesting bits and pieces relevant to post-grad life.

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