Physics & Engineering Physics Colloquium

Dennis Marks, Ph.D., professor emeritus, Department of Physics, Astronomy, Geosciences and Engineering Technology at Valdosta State University, will present “Geometry: From Fordham Prep to the Cosmos.”

Relativity is expressed geometrically, but quantum mechanics is expressed in terms of matrices. Geometric algebra expresses geometrical elements as matrices, thereby providing a common mathematical language for both relativity and quantum mechanics. The kind of matrix—dyreal, real, complex, quaternionic, or dyquaternionic—depends only on the metric signature “s” (the number of spatial dimensions minus the number of temporal dimensions). The rank of the matrix depends only on “n” (the total number of dimensions, spatial plus temporal). Geometric algebras are periodic in “s”, but recursive in “n”, thereby providing a way for larger geometries to grow from smaller geometries—either the Euclidean plane or the Minkowskian plane.

Qubits are unit vectors in the Euclidean plane, whose eigenvalues are the bits, +1 and -1. The dot product of two qubits gives the Bell correlation between them. The direct product of the geometric algebras of the two planes is the geometric algebra of 4-d space-time, with vectors (space-time), bi-vectors (spin-area), tri-vectors (momentumenergy), and 4-volume (action) that satisfy the Heisenberg (anti-) Commutation Relations as a consequence of the anti-commutativity of the basis vectors. The next four dimensions are compact and have the symmetries of the standard model of physics. After eight dimensions, the pattern of geometric algebras repeats, leading to an exponentially expanding 4-d space-time lattice with the physics of the standard model of physics at each node of the lattice. Thereafter, the universe continues growing in complexity from the bottom up.