John R. Urani

Philosophical midwifery and the birthpangs of modern cosmology

Philosophical considerations sometimes direct developments in physics. Such influence most frequently operates during the genesis of new fields. The birth of modern cosmology provides clear evidence of the interaction between philosophical issues and the shape and direction of a new physical discipline. Philosophical controversy between E. A. Milne and other astrophysicists, including A. S. Eddington, James Jeans, and H. P. Robertson, directly affected the models, methods, and very nature of cosmological science for future generations. Today’s standard space‐time metric, for example, resulted from responses by Robertson and A. G. Walker to philosophical challenges presented in Milne’s proposals to scrap the very idea of expanding ‘‘space.’’ Analysis of published works, unpublished manuscripts and correspondence, and personal interviews illustrates the role philosophical considerations played in development of this new field in physics.

A generalization of the Dirac equation to accelerating reference frames

Using a recently developed global isometry method for treating accelerating observers, the induced tangent space transformation on flat Lorentzian R4 is mapped homomorphically onto a time‐dependent D(1/2,0) ⊕ D(0,1/2) representation of SL (2,C). The Dirac equation is shown to take on pseudoterms via this mapping. Eliminating the pseudoterms by identifying an affine connection, an exact analytic expression for the covariant derivative is found for general cases of arbitrary C2 timelike observers. The transformation properties of the connection are shown to satisfy the conditions imposed by a general tetrad formalism. The specific case of the rotating observer is considered wherein the exact expression for the boosted Dirac equation is found.

A global isometry approach to accelerating observers in flat space–time

A global two‐point diffeomorphic extension of Lorentz transformations is constructed which preserves the global Lorentzian metric structure of flat R4. This global mapping induces, as a tangent‐space mapping, instantaneous Lorentz transformations parametrized by interframe velocity functions. The elimination of pseudoterms from particle and electromagnetic field equations leads to an exact analytic expression for the affine connection needed for covariant differentiation. Examination of invariant particle equations gives an obvious proof of the equivalence principle in terms of the symmetric part of the acceleration‐group connection. Transformation properties of the connection coefficients are shown to be in accord with general covariance requirements. The specific case of the rotating observer is treated exactly where it is seen that the affine connection merely supplies the exact Thomas precession term. Recent work by DeFacio et al. is found to be especially convenient for comparison with the present wo...

Field equations and the tetrad connection

A fundamental result of Geroch is that a space‐time admits a spinor structure if and only if it is parallelizable. A nonsymmetric, metric‐compatible curvature‐free connection is associated with a global orthonormal tetrad field on such a parallelizable space‐time. This connection is used to examine reported inconsistencies for S> 1/2 spinor field equations on general space‐times. It is shown that the assumed Levi–Civita transport of Clifford units causes the inconsistencies at the Klein–Gordon stage. The relation of the torsion tensor of the parallelization connection to the space‐time topology is indicated and the Lorentz covariance of the modified Klein–Gordon equations is demonstrated. A particularly simple plane‐wave solution form for free‐field equations is shown to result for locally flat space‐times for which the torsion tensor is necessarily zero.

Dirac general covariance and tetrads. I. Clifford and Lie bundles and torsion

The isomorphic map of Clifford and Lie bundles to arbitrary coordinate atlases using a global orthonormal tetrad field on a parallelizable space‐time is used to construct a fully covariant Dirac spinor theory. The Klein–Gordon equation exhibits a natural spin‐torsion coupling of the Einstein–Cartan form, the torsion coming from the tetrad field. The tetrad connection coefficients are explicitly derived in addition to their relationship to the usual Levi–Civita coefficients. Various topological conditions for vanishing torsion are given. The Dirac and adjoint Dirac equations are obtained from a simple Lagrangian and the structure of the adjoint equation is discussed.

Tetrads and arbitrary observers

Recent results concerning globally isometric mappings for arbitrary observers in flat space‐time are generalized to space‐times admitting a time orientation. Critical to the method is the use of an orthonormal tetrad which, when it is defined globally, allows the construction of a global isometry which generalizes the pointwise boost on flat space‐time. Connection coefficients are obtained, thereby defining acceleration covariant differentiation for both particle and tensor field equations. An application to orbiting observers in exterior Schwarzschild geometries is presented.

An extension of special relativity to accelerating frames and some of its philosophical implications

A rigorous extension of the full Lorentz group is found which is parameterized by interframe velocities v(t) and which reduces to Special Relativity for acceleration-free cases and to Galilean relativity for low velocity cases. Full group properties are exhibited. Four-momentum is defined and particle masses are shown to be invariants. Four-force is introduced and pseudoforces are shown to enter the equations of particle dynamics. Maxwells equations are shown to take on pseudocurrent terms in accelerating frames. A four-vector Green function solution to the modified Maxwell equations is presented. Finally, a discussion is offered concerning philosophical questions such as the operational definition of time.

Consistent spinor equations

Long-recognized curvature inconsistencies forS≥3/2 spinor equations are shown to result from an inconsistent transport law for the Infeld-Van der Waerden σ-symbols implied by conventional spinor derivatives. A curvature-free connection for the σ-symbols and a simple spinor form of the Levi-Civita connection for spinor fields yields consistent equations for any spin with no curvature restrictions.