Weyl relativity: a novel approach to Weyl's ideas
- Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, 18008 Granada (Spain)
- The Cosmology and Gravity Group and the Laboratory for Quantum Gravity and Strings, Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, Rondebosch 7701 (South Africa)
In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the conformal invariance of the gravitational field. We highlight that changing the local symmetry group of spacetime permits to construct a theory in which these two symmetries are combined into a putative gauge symmetry but with second-order field equations and non-trivial mass scales, unlike the original higher-order construction by Weyl. We prove that the gravitational field equations are equivalent to the (trace-free) Einstein field equations, ensuring their compatibility with known tests of general relativity. As a corollary, the effective cosmological constant is rendered radiatively stable due to Weyl invariance. A novel phenomenological consequence characteristic of this construction, potentially relevant for cosmological observations, is the existence of an energy scale below which effects associated with the non-integrability of spacetime distances, and an effective mass for the electromagnetic field, appear simultaneously (as dual manifestations of the use of Weyl connections). We explain how former criticisms against Weyl's ideas lose most of their power in its present reincarnation, which we refer to as Weyl relativity, as it represents a Weyl-invariant, unified description of both the Einstein and Maxwell field equations.
- OSTI ID:
- 22676174
- Journal Information:
- Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 06; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1475-7516
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
COMPATIBILITY
CONFORMAL INVARIANCE
COSMOLOGICAL CONSTANT
DISTANCE
EFFECTIVE MASS
EINSTEIN FIELD EQUATIONS
ELECTROMAGNETIC FIELDS
ELECTROMAGNETISM
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
MAXWELL EQUATIONS
SPACE-TIME
SYMMETRY GROUPS
UNIFIED FIELD THEORIES
WEYL UNIFIED THEORY