Plate trick
Encyclopedia
In mathematics
and physics
, the plate trick, also known as Feynman
's plate trick, Dirac
's belt trick, spinor spanner or quaternionic handshake is any of several particular physical demonstrations of the mathematical theorem that SU(2) double-covers SO(3), or sometimes this fact itself. The usual demonstration, as indicated by the name, is to hold a plate on one's flat palm, then perform two subsequent rotations of the arm holding the plate which results in the original position.
Topologists usually call this the belt trick, although some knot theorists, such as Louis Kauffman
have dubbed it the quaternionic handshake. The reference to quaternion
s is because the action of SU(2) considered as the unit quaternions, on the 2-sphere, considered as pure unit quaternions, gives the double covering.
The plate trick is the mathematical physics reason why particles in a four-dimensional spacetime
are either fermion
s or boson
s. See the Spin-statistics theorem
for more details.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, the plate trick, also known as Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
's plate trick, Dirac
Paul Dirac
Paul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...
's belt trick, spinor spanner or quaternionic handshake is any of several particular physical demonstrations of the mathematical theorem that SU(2) double-covers SO(3), or sometimes this fact itself. The usual demonstration, as indicated by the name, is to hold a plate on one's flat palm, then perform two subsequent rotations of the arm holding the plate which results in the original position.
Topologists usually call this the belt trick, although some knot theorists, such as Louis Kauffman
Louis Kauffman
Louis H. Kauffman is an American mathematician, topologist, and professor of Mathematics in the Department of Mathematics, Statistics, and Computer science at the University of Illinois at Chicago...
have dubbed it the quaternionic handshake. The reference to quaternion
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space...
s is because the action of SU(2) considered as the unit quaternions, on the 2-sphere, considered as pure unit quaternions, gives the double covering.
The plate trick is the mathematical physics reason why particles in a four-dimensional spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
are either fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s or boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
s. See the Spin-statistics theorem
Spin-statistics theorem
In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin of a particle is its intrinsic angular momentum...
for more details.
External links
- Air on the Dirac Strings
- Animation of Dirac belt trick
- Video of Kauffman's quaternionic handshake
- Abstruse Goose Reference
- The Spinor Spanner The American Mathematical Monthly, Vol. 80, No. 9, Nov., 1973