Foundations of Physics

, Volume 16, Issue 2, pp 143–169 | Cite as

The geometrodynamic content of the Regge equations as illuminated by the boundary of a boundary principle

  • Warner Allen Miller
Part I. Invited Papers Dedicated To John Archibald Wheeler


In this paper the principle that the boundary of a boundary is identically zero (∂○∂≡0) is applied to a skeleton geometry. It is shown that the left-hand side of the Regge equation may be interpreted geometrically as the sum of the moments of rotation associated with the faces of a polyhedral domain. Here the polyhedron, warped though it may be, is located in a lattice dual to the original skeleton manifold. This sum is related to the amount of energy-momentum (E-p) associated to the edge in question. In the establishment of this equation the ordinary Bianchi identity is rederived by applying the principle that the (∂○∂≡0) in its (1–2–3)-dimensional formulation to polyhedral domain. Steps toward the derivation of the contracted Bianchi identity using this principle in its (2–3–4)-dimensional form are discussed. Preliminary results in this direction indicate that there should be one vector identity per vertex of the skeleton geometry.

“Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve.”—Ref. 3, Chap. 1.


Manifold Bianchi Identity Dimensional Form Regge Equation Vector Identity 
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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Warner Allen Miller
    • 1
  1. 1.Center for Theoretical PhysicsUniversity of Texas at AustinAustin

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