10 found
Order:
  1.  77
    Null Cones and Einstein's Equations in Minkowski Spacetime.J. Brian Pitts & W. C. Schieve - 2004 - Foundations of Physics 34 (2):211-238.
    If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using a generalized eigenvector formalism based on the Segré classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Securing the correct relationship between the two null cones dynamically plausibly is achieved using the naive gauge freedom. New variables tied to the generalized eigenvector (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  2.  40
    Null cones in lorentz-covariant general relativity.J. Brian Pitts & W. C. Schieve - unknown
    The oft-neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity is considered. Consistency requires that the flat metric's null cone be respected, but this does not automatically happen. After reviewing the history of this problem, we introduce a generalized eigenvector formalism to give a kinematic description of the relation between the two null cones, based on the Segre' classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Then we propose a (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  3.  79
    Nonsingularity of Flat Robertson–Walker Models in the Special Relativistic Approach to Einstein's Equations.J. Brian Pitts & W. C. Schieve - 2003 - Foundations of Physics 33 (9):1315-1321.
    Recently the neglected issue of the causal structure in the flat space-time approach to Einstein's theory of gravity has been substantially resolved. Consistency requires that the flat metric's null cone be respected by the null cone of the effective curved metric. While consistency is not automatic, thoughtful use of the naive gauge freedom resolves the problem. After briefly recapitulating how consistent causality is achieved, we consider the flat Robertson–Walker Big Bang model. The Big Bang singularity in the spatially flat Robertson–Walker (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  4.  56
    On Parametrized General Relativity.J. Brian Pitts & W. C. Schieve - 1998 - Foundations of Physics 28 (9):1417-1424.
    A physical framework has been proposed which describes manifestly covariant relativistic evolution using a scalar time τ. Studies in electromagnetism, measurement, and the nature of time have demonstrated that in this framework, electromagnetism must be formulated in terms of τ-dependent fields. Such an electromagnetic theory has been developed. Gravitation must also use of τ-dependent fields, but many references do not take the metric's dependence on τ fully into account. Others differ markedly from general relativity in their formulation. In contrast, this (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  5. Flat Spacetime Gravitation with a Preferred Foliation.J. B. Pitts & W. C. Schieve - 2001 - Foundations of Physics 31 (7):1083-1104.
    Paralleling the formal derivation of general relativity as a flat spacetime theory, we introduce in addition a preferred temporal foliation. The physical interpretation of the formalism is considered in the context of 5-dimensional “parametrized” and 4-dimensional preferred frame contexts. In the former case, we suggest that our earlier proposal of unconcatenated parametrized physics requires that the dependence on τ be rather slow. In the 4-dimensional case, we consider and tentatively reject several areas of physics that might require a preferred foliation, (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6.  55
    On the Form of Parametrized Gravitation in Flat Spacetime.J. Brian Pitts & W. C. Schieve - 1999 - Foundations of Physics 29 (12):1977-1985.
    In a framework describing manifestly covariant relativistic evolution using a scalar time τ, consistency demands that τ-dependent fields be used. In recent work by the authors, general features of a classical parametrized theory of gravitation, paralleling general relativity where possible, were outlined. The existence of a preferred “time” coordinate τ changes the theory significantly. In particular, the Hamiltonian constraint for τ is removed From the Euler-Lagrange equations. Instead of the 5-dimensional stress-energy tensor, a tensor comprised of 4-momentum density mid flux (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  88
    For Lawrence Horwitz on his sixty-fifth birthday.W. C. Schieve - 1996 - Foundations of Physics 26 (12):1575-1578.
  8.  59
    Classical Scattering in the Covariant Two-Body Coulomb Potential.M. A. Trump & W. C. Schieve - 1998 - Foundations of Physics 28 (8):1211-1236.
    The problem of two relativistically-moving pointlike particles of constant mass is undertaken in an arbitrary Lorentz frame using the classical Lagrangian mechanics of Stückelberg, Horwitz, and Piron. The particles are assumed to interact at events along their world lines at a common “world time,” an invariant dynamical parameter which is not in general synchronous with the particle proper time. The Lorentz-scalar interaction is assumed to be the Coulomb potential (i.e., the inverse square spacetime potential) of the spacetime event separation. The (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  9.  30
    Perihelion precession in the special relativistic two-body problem.M. A. Trump & W. C. Schieve - 1998 - Foundations of Physics 28 (9):1407-1416.
    The classical two-body system with Lorentz-invariant Coulomb work function V = -k/ρ is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stückelberg. Particular solutions for the reduced motion are obtained which correspond to bound attractive, unbound attractive, and repulsive scattering motion. A lack of perihelion precession is found in the bound attractive orbit, and the semiclassical hydrogen spectrum subsequently contains no fine structure corrections. It is argued that this prediction is indicative of the correct classical special relativistic (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  10.  46
    The synchronization problem in covariant relativistic dynamics.Matthew Trump & W. C. Schieve - 1997 - Foundations of Physics 27 (1):1-17.
    In the classical Stueckelberg-Horwitz-Piron relativistic Hamiltonian mechanics, a significant aspect of evolution of the classical n-body particle system with mutual interaction is the method by which events along distinct particle world lines are put into correspondence as a dynamical state. Approaches to this procedure are discussed in connection with active and passive symmetry principles.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark