## James T. Wheeler

Associate Professor

Employed at USU 1989

BS (1972) Kalamazoo College

MS (1980) University of Maryland

PhD (1986) University of Chicago

Research Interests:

- Gravitational field theory
- Quantum field theory
- Extended gravity

Telephone #: (435) 797-3349

E-mail address: jwheeler@cc.usu.edu

Expanding on General Relativity
**Expanding on
General Relativity**
**Scale invariance, and the consequent
conformal symmetry of nature, are such natural extensions of the Poincaré
symmetry of general relativity that dozens of attempts have been made over
the last century to build a coherent conformal theory of gravity. These
extensions have held out various hopes ranging from the unification of
gravity with electromagnetism (Weyl) to finding deep connections with quantum
theory (London), to tools for imposing cosmic censorship (Penrose), to
introducing a time-dependent gravitational constant (Dirac). Still later,
it was hoped that the extra fields introduced by enlarging the symmetry
of general relativity would lead to unification with other fundamental
interactions besides electromagnetism.**

**Unfortunately, these efforts have uniformly
been plagued by difficulties. First, the standard gravity theory built
on the conformal group does not reduce to general relativity. A theory
equivalent to GR is achieved only by introducing extra, compensating fields.
Second, it has been shown that the most of the new fields arising from
the enlarged symmetry cannot lead to new physics. Third, the one new field
that can lead to new physical predictions (the "Weyl vector") predicts
expanding or contracting forms of matter, and as a result has defied any
interpretation consistent with experience. These failures have even led
some to argue that scale invariance cannot be a physical symmetry.**

**Why does such a clear symmetry of nature
resist physical interpretation? We may be starting to find some answers.
Our work investigates how a new theory of gravity based on the conformal
group solves the three problems listed above, while leading to an interesting
class of geometries. These new spaces have a direct interpretation as curved
generalizations of phase space. Like quantum mechanics, this model suggests
that the true arena for physics is more like phase space than spacetime.
Moreover, in the phase space interpretation, the extra dimensions of the
theory also require a constant with the units of action. If this constant
is Planck's, then these spaces might even shed light on quantum gravity.**