Quantizing Geometry or Geometrizing the Quantum?

Abstract

The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an approach the quantum mechanical laws should emerge from the geometrical theory. A toy model that incorporates the idea is presented and its necessary formulation in configuration space is emphasized.Comment: Talk given at QTRF 5 conference, 5 pages, typos corrected, reference adde

Geometric description of the Schrödinger equation in (3n+1)-dimensional configuration space

“…Please note that those equations are just a rewriting of the initial equation (3). Please note further that in addition to analogous manipulations, the de Broglie Bohm (dBB) interpretation consists in associating physical reality to the trajectories (8). Since the dBB theory is deterministic and non-local, equation (8) confirms the non-local nature of dBB theory i.e., position of one particle depends on the position of all other particles constituting the system.…”

“…It is thus natural that there are numerous attempts to reformulate quantum mechanics in a more geometrical way [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

On the Noncommutative Eikonal

“…Geometric treatments of quantum mechanics have also been studied in depth; for a sample see, e.g. [2,[20][21][22][23][24][25][26][27].…”

Two particle entanglement and its geometric duals

“…Thus it naturally led many physicists to the attempt to reformulate quantum mechanics in a geometric language, like GR. References [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] are a few such efforts towards the geometrical rewriting of quantum laws.…”