Amplituhedron

Charles Vorbach                                                        May 19, 2014

Earth Science/CD Odd                                              Mrs. McClellan

Wolchover, Natalie. "A Jewel at the Heart of Quantum Physics." Quanta Magazine. Simons Foundation, 17 Sept. 2013. Web. 19 May 2014. <http://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/>.

My current event report is on the article "A Jewel at the Heart of Quantum Physics", published in Quanta Magazine. The author Natalie Wolchover described the discovery of a dramatic simplification in calculating the scattering amplitudes of particle interactions. In particle physics, scattering amplitudes are the probabilities certain particles will turn into other particles with different energies during an interaction. These values were previously sought using formulas with thousands, millions, or even billions of terms but now they can be found using a special multidimensional solid called an amplituhedron. Using basic information about the particles as the vertices, mathematicians construct amplituhedron. Then they can decode the scattering amplitudes from the object’s volume – an enormous improvement over old methods. The saga of a search for efficient calculations began with Feynman diagrams in the 1950s. Each of these branching drawings represent a scattering of a particle. By gradually summing all possible drawings, physicists form a complete picture of the amplitudes. As virtual particles are introduced however, the calculations are made extraordinarily complex by loops where particles created are immediately destroyed. In 1984, several physicists wrote many interactions were so complex, “that they may not be evaluated in the foreseeable future”. However there were hints of an underlying simplicity. Two mathematicians reduced one interaction from billions of terms to nine pages with some tricky algebra. Then they guessed, but couldn’t prove, an equivalent one term expression. Finally in the 2000s the BCFW recursion relations were discovered. This set of formulas used strangle variables called twisters and described interactions in terms of a complex geometric object called a positive Grassmanian. When added up, these objects constructed the amplituhedron.  Perhaps the most important aspect of this discovery is its autonomy. Neither locality, the principle particles only interact from adjoining positions, nor unitarity, that all possible outcomes add up to 1, prerequisite the calculation. By bypassing these rules which currently seem to obstruct a unified theory of quantum gravity, the amplituhedron brings future discoveries closer.

The amplituhedron is a major innovation in the calculation particle scattering. Not only does it simplify the process, but it reveals a new and previously unknown structure to amplitudes. Exact description of physical processes is vital to our fundamental understanding of nature. Knowing the relationship between scattering and volume provides insight into particle interactions sure to reveal other discoveries. Another important effect is opening of Amplitudeology other scientists. Quantum mechanics is one of science’s most esoteric fields, but the amplituhedron uses (relatively) simple geometry to explain a complex phenomenon. It crosses scientific disciplines and broadens the subject. Furthermore the amplituhedron aids in the search for a Grand Unified Theory of Particle Physics. By bypassing core, but likely flawed principles the amplituhedron seeks to isolate even more fundamental rules. The amplituhedron promises to clarify, expand, and invigorate much of quantum mechanics.

The article “A Jewel at the Heart of Quantum Physics” is one of the best written popular scientific articles I have ever read, but it still had a common flaw. The article described extraordinary complex concepts in lay terms and mercifully avoided the mathematics behind them. Every idea was explained thoroughly within the context of story and related to the amplituhedron. However after doing background research into my topic, I found the discovery was somewhat exaggerated.  Use of the amplituhedron slightly faster than the BCFW recursion relations but only works in a theory called Planar N=4 Super Yang-Mills and can only calculate up to 3 loops of virtual particles. This makes it a constricted tool. While overstating the amplituhedron’s potential, the article still provided an exceptional overview of scattering amplitudes and ranks as my favorite scientific article.