Articles & Reviews

Authored by RSF Research Staff

Article Review: A Jewel at the Heart of Quantum Physics

Nima Arkani-Hamed (architect of the amplituhedron) on removing spacetime from scattering amplitudes: On the Aharonov-Bohm effect – “it looks nonlocal, but we say don’t worry because we know in our heads we can introduce a vector potential and it couples locally, but that comes at the price of a great deal of Gauge redundancy... We can be non-redundant and give up manifest locality, or we can be redundant and keep locality”.

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Illustration by Andy Gilmore

The amplituhedron is a mathematical device that drastically simplifies calculations of particle-particle interactions – specifically the scattering amplitudes, which are the calculations of probabilities for different outcomes in scattering experiments (such as colliding particles together in a particle accelerator). The simplification comes from using a geometric structure, where instead of doing laborious calculations with thousands of terms (using what are called Feynman Diagrams), scattering amplitudes can be calculated from the volumes of some polytopes (in planar N=4 supersymmetric Yang-Mills theory – with a mathematical space known as the Positive Grassmannian, which is used to generalize and simplify particular physics calculations). Basically, it is a method for calculating probability amplitudes of subatomic particles by using n-dimensional polyhedrons in an abstract space, hence the appellation amplituhedron. amplituhedron-drawing_web Since the amplituhedron does not require locality (specificity of location in spacetime), or unitarity (all probabilities being between 0 and 1, basically consistency within quantum field theory calculations) it may at some point be a possible mechanism to describe quantum gravity. Because space and time result as emergent characteristics of the calculations, and are not intrinsic to them, it suggest that at a more fundamental level there is a geometric structure that is essentially timeless. This geometric structure is very reminiscent of the tetrahedral array described by Physicist Nassim Haramein, who has described the 64 tetrahedron matrix as the fundamental structure of spacetime geometry. Furthermore, Nassim Haramein has recently used a geometrical approach to generate solutions to quantum gravity, as well as resolve the seemingly huge discrepancy in the strength of the force of gravity with other natural forces, such as electromagnetism and the strong nuclear force. An approach that is very closely paralleled by the methods employed in the amplituhedron. This opens very exciting possibilities for both theoretical physics and technical developments.

By: William Brown

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