In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cℓ3 of the three-dimensional Euclidean space as a model for (3+1)-dimensional space-time, representing a point in space-time via a paravector (3-dimensional vector plus a 1-dimensional scalar).
The Clifford algebra Cℓ3 has a faithful representation, generated by Pauli matrices, on the spin representation C2; further, Cℓ3 is isomorphic to the even subalgebra of the 3+1 Clifford algebra, Cℓ0
3,1.
APS can be used to construct a compact, unified and geometrical formalism for both classical and quantum mechanics.
APS should not be confused with spacetime algebra (STA), which concerns the Clifford algebra Cℓ1,3(R) of the four dimensional Minkowski spacetime.
Read more about Algebra Of Physical Space: Special Relativity, Classical Electrodynamics, Relativistic Quantum Mechanics, Classical Spinor
Famous quotes containing the words algebra of, algebra, physical and/or space:
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)
“Not too many years ago, a child’s experience was limited by how far he or she could ride a bicycle or by the physical boundaries that parents set. Today ... the real boundaries of a child’s life are set more by the number of available cable channels and videotapes, by the simulated reality of videogames, by the number of megabytes of memory in the home computer. Now kids can go anywhere, as long as they stay inside the electronic bubble.”
—Richard Louv (20th century)
“This moment exhibits infinite space, but there is a space also wherein all moments are infinitely exhibited, and the everlasting duration of infinite space is another region and room of joys.”
—Thomas Traherne (1636–1674)