On Measuring Standards in Weyl’s Geometry

Abstract

In Weyl's geometry the nonintegrability problem and difficulties in defining measuring standards are reconsidered. Approaches removing the nonintegrability of length in the interior of atoms are given, so that atoms can serve as measuring standards. The Weyl space becomes a well founded framework for classical theories of electromagnetism and gravitation.

Creation of fundamental particles in Wesson’s IMT

“…Following the ideas of Weyl [12][13][14] and Dirac [15], developed by Nathan Rosen [16] and the present writer [17][18][19][20][21], the Weyl-Dirac version of Wesson's IMT was proposed recently [9][10][11]. In Wesson's original IMT one considers a 5D manifold {M} (the bulk), mapped by coordinates x N (N = 01234) and possessing the metric tensor g AB = g B A .…”

“…Among others theories Wesson's Induced Matter Theory (IMT) [3][4][5][6][7][8] provides an elegant answer based on the creation of matter by geometry of the 5-dimensional (5D) bulk. In the Weyl-Dirac modification [9][10][11] of Wesson's IMT the bulk induces on the 4D brane both, gravitation and electromagnetism, as well gravitational matter and electric current. Now, as a considerable amount of conventional matter appears in the form of particles, it would be interesting to look for a mechanism of creating fundamental particles in the framework of the Weyl-Dirac modification of Wesson's IMT.…”

Creation of Neutral Fundamental Particles in the Weyl–Dirac Version of Wesson’s IMT

“…The situation resembles the 4D Weyl geometry (9 -11) , where the light cone is the principal phenomenon describing the space- Following the ideas of Weyl (9,10,11) and Dirac (12) , developed by Nathan Rosen (13) and the present writer (14) , the Weyl-Dirac version of Wesson's IMT was proposed recently (7) and in it the measurability of length was proved (8) .…”

“…Wesson's Induced Matter Theory (IMT) (1,2,3,4,5,6) provides an elegant answer based on the creation of matter by geometry of the 5-dimensional bulk. In the Weyl-Dirac modification (7,8) of Wesson's IMT the bulk induces on the 4D brane both, gravitation and electromagnetism, as well gravitational matter and electric current. Now, as a considerable amount of conventional matter appears in the form of particles, we are looking for a mechanism of creating fundamental particles.…”

“…We make use of a recently proposed Weyl-Dirac (W-D) modification of Wesson's IMT (7,8) , where the 5-dimensional (5D) bulk, in addition to the metric tensor AB g , possesses a Dirac gauge function Ω and a Weyl vector C w . On the brane, the five dimensional C w has its four dimensional (4D) counterpart µ w , the latter being regarded as the potential four vector of the Maxwell field.…”