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, but find a need for one in the process (“flowing”) theory of time. We then suggest why such a foliation might reasonably be unobservable.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
S. Gupta, “Gravitation and electromagnetism,” Phys. Rev. 96, 1683 (1954).
R. Kraichnan, “Special-relativistic derivation of generally covariant gravitation theory,” Phys. Rev. 98, 1118 (1955); also “Possibility of unequal gravitational and inertial masses,” Phys. Rev. 101, 482 (1956).
W. Thirring, “An alternative approach to the theory of gravitation,” Ann. Phys. (N.Y.) 16, 96 (1961).
L. Halpern, “On the structure of the gravitation self interaction,” Bull. Cl. Sci. Acad. R. Belg., 5e serie 49, 226 (1963).
R. P. Feynman, F. B. Morinigo, and W. G. Wagner, Feynman Lectures on Gravitation, B. Hatfield, ed. (Addison–Wesley, Reading, Mass., 1995).
V. Ogievetsky and I. Polubarinov, “Interacting field of spin 2 and the Einstein equations,” Ann. Phys. (N.Y.) 35, 167 (1965).
S. Deser, “Self-interaction and gauge invariance,” Gen. Rel. Gravit. 1, 9 (1970).
J. B. Pitts and W. C. Schieve, “Slightly bimetric gravitation,” submitted.
S. V. Babak and L. P. Grishchuk, “The energy-momentum tensor for the gravitational field,” Phys. Rev. D 61, 024038 (2000).
J. R. Fanchi, Parametrized Relativistic Quantum Theory (Kluwer Academic, Dordrecht, 1993).
M. C. Land and L. P. Horwitz, “Green's functions for off-shell electromagnetism and spacelike correlations,” Found. Phys. 21, 299 (1991).
M. C. Land and L. P. Horwitz, “The Lorentz force and energy-momentum for off-shell electromagnetism,” Found. Phys. Lett. 4, 61 (1991).
M. C. Land, “Particles and events in classical off-shell electrodynamics,” Found. Phys. 27, 19 (1997).
N. Shnerb and L. P. Horwitz, “Canonical quantization of four-and five-dimensional U(1) gauge theories,” Phys. Rev. A 48, 4068 (1993).
M. C. Land, N. Shnerb, and L. P. Horwitz, “On Feynman's approach to the foundations of gauge theory,” J. Math. Phys. 36, 3263 (1995).
L. P. Horwitz, “On the definition and evolution of states in relativistic classical and quantum mechanics,” Found. Phys. 22, 421 (1992).
D. Saad, L. P. Horwitz, and R. I. Arshansky, “Off-shell electromagnetism in manifestly covariant relativistic quantum mechanics,” Found. Phys. 19, 1125 (1989).
L. P. Horwitz and C. Piron, “Relativistic dynamics,” Helv. Phys. Acta 46, 316 (1973).
L. P. Horwitz, R. I. Arshansky, and A. C. Elitzur, “On the two aspects of time: The distinction and its implications,” Found. Phys. 18, 1159 (1988).
R. Arshansky, L. P. Horwitz, and Y. Lavie, “Particles vs. events: The concatenated structure of world lines in relativistic quantum mechanics,” Found. Phys. 13, 1167 (1983).
J. Frastai and L. P. Horwitz, “Off-shell fields and Pauli–Villars regularization,” Found. Phys. 25, 1495 (1995).
J. B. Pitts and W. C. Schieve, “On parametrized general relativity,” Found. Phys. 28, 1417 (1998).
J. B. Pitts and W. C. Schieve, “On the form of parametrized gravitation in flat spacetime,” Found. Phys. 29, 1977 (1999).
C. Misner, K. Thorne, and J. Wheeler, Gravitation (Freeman, New York, 1973).
P. G. O. Freund, A. Maheshwari, and E. Schonberg, “Finite-range gravitation,” Ap. J. 157, 857 (1969).
J. L. Anderson, Principles of Relativity Physics (Academic, New York, 1967).
J. L. Cook, “Solutions of the relativistic two-body problem,” Aust. J. Phys. 25, 117 (1972).
R. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
W. G. Unruh, “Unimodular theory of canonical quantum gravity,” Phys. Rev. D 40, 1048 (1989).
W. G. Unruh and R. M. Wald, “Time and the interpretation of canonical quantum gravity,” Phys. Rev. D 40, 2598 (1989).
One of us (J.B.P.) thanks L. P. Horwitz for correspondence on this matter
One of us (J.B.P.) thanks R. Matzner and M. Choptuik for making this point and D. Salisbury for related thoughts.
P. Miller, “On ‘becoming’ as a fifth dimension,” in Physics and the Ultimate Significance of Time, D. R. Griffin, ed. (SUNY Press, Albany, 1986).
L. Randall and R. Sundrum, “An alternative to compactification,” Phys. Rev. Lett. 83, 4690 (1999).
“Physics update: An alternative to compactification,” Physics Today 12, 9 (1999).
C. Piron and F. Reuse, “The relativistic two body problem,” Helv. Phys. Acta 48, 631 (1975).
M. A. Trump and W. C. Schieve, Classical Relativistic Many-Body Dynamics (Kluwer Academic, Dordrecht, 1999).
R. G. Cawley, “Observer theories based on Stueckelberg equations of motion,” Int. J. Theor. Phys. 3, 483 (1970).
J. P. Hsu and T. Y. Shi, “Hamiltonians within the relativistic dynamics with a scalar evolution variable,” Phys. Rev. D 26, 2745 (1982).
J. L. Cook, “General relativity in the equal proper time formalism,” Aust. J. Phys. 25, 469 (1972).
F. Selleri, “The relativity principle and the nature of time,” Found. Phys. 27, 1527 (1997).
I. Schmelzer, “General ether theory,” Los Alamos Preprints, xxx.lanl.gov, gr-qc–0001101.
M. Ferrero and E. Santos, “Empirical consequences of the scientific construction: The program of local hidden-variables theories in quantum mechanics,” Found. Phys. 27, 765 (1997).
L. E. Szabo and A. Fine, “A local hidden variable theory for the GHZ experiment,” Los Alamos Preprints, xxx.lanl.gov, quant-ph–0007102.
M. Genovese, G. Brida, C. Novero, and E. Predazzi, “Experimental test of local realism using non-maximally entangled states,” Los Alamos Preprints, xxx.lanl.gov, quant-ph– 0009067.
C. H. Brans, “Bell's theorem does not eliminate fully causal hidden variables,” Int. J. Theor. Phys. 27, 219 (1988).
T. Durt, “Three interpretations of the violations of Bell's inequalities,” Found. Phys. 27, 415 (1997).
T. Durt, “Why God might play dice,” Int. J. Theor. Phys. 35, 2271 (1996).
J. Bell, in The Ghost in the Atom, P. C. W. Davies and J. R. Brown, eds. (University Press, Cambridge, 1986).
R. K. Clifton, M. L. G. Redhead, and J. N. Butterfield, “Generalization of the Greenberger–Horne–Zeilinger algebraic proof of nonlocality,” Found. Phys. 21, 149 (1991).
J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (University Press, Cambridge, 1987).
P. Van Inwagen, An Essay on Free Will (University Press, Oxford, 1986). Though an advocate of free will, Van Inwagen finds no way to answer this “Mind” argument.
R. Kane, The Significance of Free Will (University Press, Oxford, 1998). Kane, a defender of free will, wrestles with this argument through much of the book.
J. Edwards, The Freedom of the Will (Soli Deo Gloria, Morgan, Pennsylvania, 1996). Reprint of (Thomas Nelson, London, 1845).
B. Metzger, The New Testament: Its Background, Growth, and Content, 2nd edn. (Abingdon, Nashville, 1983). Metzger cites Josephus.
C. J. Isham, “Canonical quantum gravity and the problem of time,” Los Alamos Preprints, xxx.lanl.gov, gr-qc–9210011.
D. Boulware and S. Deser, “Can gravitation have a finite range?” Phys. Rev. D 6, 3368 (1972).
M. Visser, “Mass for the graviton,” Gen. Rel. Gravit. 30, 1717 (1998).
R. Penrose, “On Schwarzschild causality––a problem for “Lorentz covariant” general relativity,” in Essays in General Relativity––A Festschrift for Abraham Taub, F. J. Tipler, ed. (Academic, New York, 1980).
T. Jacobson and D. Mattingly, “Gravity with a dynamical preferred frame,” Los Alamos Preprints, xxx.lanl.gov, gr-qc–0007031.
Q. Smith, “Problems with the new tenseless theory of time,” Phil. Studies 52, 371 (1987).
M. Dorato, Time and Reality: Spacetime Physics and the Objectivity of Temporal Becoming (CLUEB, Bologna, 1995).
C. J. Isham and J. C. Polkinghorne, “The debate over the block universe,” in Quantum Cosmology and the Laws of Nature: Scientific Perspectives on Divine Action, 2nd edn., R. J. Russell, N. Murphey, and C. J. Isham, eds. (Vatican Observatory, Vatican City State, and the Center for Theology and the Natural Sciences, Berkeley, 1999).
R. M. Chisholm and D. W. Zimmerman, “Theology and tense,” Nouûs 31, 262 (1997).
J. Perry, “The problem of the essential indexical,” Nouûs 13, 3 (1979).
D. H. Mellor, Real Time (University Press, Cambridge, 1981).
Q. Smith, Language and Time (Oxford University Press, New York, 1993).
W. L. Craig, lectures given at Talbott Seminary, Biola University (1995).
W. L. Craig, The Tensed Theory of Time, and The Tenseless Theory of Time (Synthese Library, Kluwer Academic, Dordrecht, 2000).
W. L. Craig, Time and the Metaphysics of Relativity, and God, Time and Eternity (Kluwer Academic, Dordrecht, 2000).
A. N. Prior, “Thank goodness that's over,” Philosophy 34, 12 (1959).
A. N. Prior, “The formalities of omniscience,” Philosophy 37, 114 (1962).
D. Lewis, “Attitudes de dicto and de se,” Phil. Rev. 88, 513 (1979).
N. Wolterstorff, “God everlasting,” in Contemporary Philosophy of Religion, S. M. Cahn and D. Shatz. (Oxford University Press, New York, 1982).
N. Kretzmann, “Omniscience and immutability,” J. Phil. 63, 409 (1966).
D. H. Mellor, “ 'Thank goodness that' over',” Ratio 23, 20 (1981). Mellor is attempting to refute this line of argument.
H. Reichenbach, The Direction of Time (University of California Press, Berkeley, 1956).
D. R. Griffin, Physics and the Ultimate Significance of Time (SUNY Press, Albany, 1986).
T. Maudlin, Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics (Blackwell, Oxford, 1994).
F. Shojai and M. Golshani, “On the general covariance in Bohmian quantum gravity,” Int. J. Mod. Phys. A 13, 2135 (1998).
S. Goldstein and S. Teufel, “Quantum spacetime without observers: Ontological clarity and the conceptual foundations of quantum gravity,” Los Alamos Preprints, xxx.lanl.gov, quant-ph–9902018, to appear in Physics Meets Philosophy at the Planck Scale, C. Callender and N. Huggett, eds. (Cambridge University Press, forthcoming).
J. Butterfield and C. J. Isham, “Spacetime and the philosophical challenge of quantum gravity,” Los Alamos Preprints, xxx.lanl.gov, gr-qc–9903072, to appear in Physics Meets Philosophy at the Planck Scale, C. Callender and N. Huggett, eds. (Cambridge University Press, forthcoming).
One of us (J.B.P.) thanks C. Rovelli for stimulating correspondence on this issue.
H. P. Stapp, “Einstein time and process time,” in Physics and the Ultimate Significance of Time, D. R. Griffin, ed. (SUNY Press, Albany, 1986).
J. T. Wilcox, “A question from physics for certain theists,” J. Religion 41, 293 (1961).
L. S. Ford, “Is process theism consistent with relativity theory?” J. Religion 48, 124 (1968).
R. G. Gruenler, The Inexhaustible God (Baker, Grand Rapids, 1983).
W. L. Craig, “God and real time,” Religious Studies 26, 335 (1990).
C. Møller, The Theory of Relativity (Clarendon, Oxford, 1952).
About this article
Cite this article
Pitts, J.B., Schieve, W.C. Flat Spacetime Gravitation with a Preferred Foliation. Foundations of Physics 31, 1083–1104 (2001). https://doi.org/10.1023/A:1017578424131