Online Segal Archive

Title: The Nature of Gravity

Descriptive symbol: UDT - Unspecified Document Type

Category of document: Scientific Papers

Sub-Category of document: Scientific Manuscripts


By I. E. Segal
Massachusetts Institute of Technology, Room 2-244
Cambridge, MA 02139
tel.: 617-253-4985 e-mail: fax: 617-253-4358 

Key words: Einstein Universe/ quantization/ Equivalence principle/
conformal invariance/ cosmology/ Mach’s Principle

31 August 1998

*Dedicated to the late Oswald Veblen, for his vision of the 
Intertwining of higher mathematics and fundamental physics

A conformally invariant theory of gravity which forms a natural extension of the Einstein Equivalence Principle (EEP), applies to mass points and subsumes Newtonian gravitational theory as a limiting form, is consistent both with the classical empirical tests and observational cosmology, is a component of a possible comprehensive quantum field theory and enjoys global energy conservation, is proposed. The gravitational energy-momentum vector is represented by the generators of the conformal group G into which the conventional relativistic energy-momentum generators ∂m are transformed by conformal inversion. The sum of the two energy components is equivalent to the generator of temporal evolution in the Einstein Universe E, to which the present underlying G-invariant spacetime is conformal, and is distinguished group-theoretically as the generator of the center of the maximal essentially compact subgroup of G, and so uniquely determined within conjugacy. 
The unification of gravitational and other forces is exemplified by a proposed G-invariant, convergent, and causal bilinear fundamental interaction between a fermion current and bosons in the context of quantum field theory, which extends electrodynamics.The corresponding particle theory converges to an extension of conventional relativistic theory as the (G-invariant) radius of space in E becomes infinite.The G-invariance of the fundamental forces is broken by the large-scale state of the Universe, down to approximate invariance under the isometry group of E. 
The time t in E is coincident with the local Minkowskian time xo within terms of third order, but t Æ ±p in natural G-invariant units as xoƱ•. The S-operator represents the action of the product of the antipodal map on the spherical space component of E with the transformation t -> t+p, which commutes with all elements of G. Mach’s principle is interpreted as the determination of mass from equilibrium statistical mechanics in the interacting cosmic quantum field.