What's Wrong with This Retrit?

Presenter

Avash Subedi

Campus

UMass Boston

Sponsor

Christopher Fuchs, Department of Physics, UMass Boston

Schedule

Session 3, 1:30 PM - 2:15 PM [Schedule by Time][Poster Grid for Time/Location]

Location

Poster Board A62, Campus Center Auditorium, Row 4 (A61-A80) [Poster Location Map]

Abstract

After 25 years of struggle, the theory of quantum mechanics finally achieved completion in 1925. The theory lays the foundation for all that we understand of the atomic world and is regarded as one of the most important theories of physics.  Next year thus marks the theory’s hundredth anniversary, but there remain a number of mysteries about it. A perennial is why it relies on complex numbers. These are like regular numbers encountered in everyday life except that they also include an imaginary component. The imaginary component are special numbers that we cannot observe physically but have unique and convenient properties. We can use them to model waves and rotations. The mystery of why complex numbers instead of real numbers has never been completely understood. A new interpretation of quantum mechanics, known as QBism, provides a novel way to tackle this problem. In QBism, the geometry of equiangular lines plays an important role. Equiangular lines are lines that all intersect at a single point and such that the angle between any two lines are the same as any two others. A three-level quantum system that involves complex numbers  in regular quantum mechanics with complex numbers one can have a set with 9 equiangular lines. If quantum mechanics depended on real numbers instead, one can only get a set with 6 equiangular lines. We call this unique system a retrit. In this paper, we will explore the geometry of 6 equiangular lines and pose the question of why having only real numbers are not sufficient in quantum mechanics.

Keywords

Quantum Mechanics, Physics, Geometry, Mathematics, Quantum Information

Research Area

Physics and Nanotechnology

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