QFT in curved space-time, however, is not a unification. It is a mongrel, and as such deserves to be put down.—M. J. Duff
Abstract
It was recognized almost from the original formulation of general relativity that the theory was incomplete because it dealt only with classical, rather than quantum, matter. What must be done in order to complete the theory has been a subject of considerable debate over the last century, and here I just mention a few of the various options that have been suggested for a quantum theory of gravity. The aim of what follows is twofold. First, I address worries about the consistency and physical plausibility of hybrid theories of gravity—theories involving a classical gravitational field and quantum matter fields. Such worries are shown to be unfounded. These hybrid theories—mongrel gravity—in fact comprise the only current, actual theories of gravity that incorporate quantum matter, and they also offer legitimate promise as tools for discovering the full theory of gravity. So my second aim is to highlight these theories as providing an interesting example of scientific revolution in action. I begin to try to draw some philosophical lessons from mongrel gravity theories, but more importantly I try to convince philosophers of physics that they should pay more attention to them.
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Notes
An anonymous referee points out quite rightly that this characterization is not entirely fair to Ptolemy’s theory and the uses to which it was put. It does however capture reasonably well the attitudes of many philosophers of science toward the followers of Ptolemy in the waning days of the theory. And it is only the latter that I wish to capture here. Lakatos (1978, Ch 4) is a fairly typical, account—though one might well understand Lakatos there as providing grounds to regard the Copernican program itself as the mongrel, transitional form in the development of astronomy from Ptolemy to Kepler and on to Newton. I cannot consider this possibility here.
One may well demur on the appropriateness of claiming that there is something that is the “current theory”. And in fact a very helpful anonymous referee does so demur. I have, however, argued elsewhere for the claim that transitional forms should count as theories—in part because doing so is important for developing an account of continuity of science across revolutionary divides.(Mattingly, 2005a, b) A more complete defense of my use of “current theory” will have to await another occasion.
It is perhaps worth pointing out that the existence of such a technique illustrates again the mathematical consistency of combined quantum and classical systems.
I do not here call into question their conclusion about what constitutes our best choice of equations of motion, but there seems to be no clear argument for that conclusion in their work.
But see the critical discussion in (Sudarshan, 2004).
See also Jones (1993) for an interesting discussion of the correct way to understand the transition to the classical limit.
It might be of interest to note that in conversation Hu has concurred with this interpretation of his program.
References
Anderson, A. (1995). Quantum backreaction on “Classical” variables. Physical Review Letters, 74(5), 621–625.
Anderson, A. (1996). Anderson replies. Physical Review Letters, 76(21), 4090–4091.
Bohr, N., & Rosenfeld, L. (1933). On the question of the measurability of electromagnetic field quantities. In J. Wheeler, & W. Zurek (Eds.), Quantum theory and measurement (pp. 479–522) (1983). Princeton: Princeton University Press.
Borzeszkowski, H. -H. von., & Treder, H. -J. (1988). The meaning of quantum gravity. Dordrecht: D. Reidel Publishing Company.
Caro, J., & Salcedo, L. L. (1999). Impediments to mixing classical and quantum dynamics. Physical Review A, 60(2), 842–852.
Callender, C., & Huggett, N. (2001). Introduction. In C. Callender, & N. Huggett (Eds.), Physics meets philosophy at the planck scale (pp. 1–30). Cambridge: Cambridge University Press.
DeWitt, B. (1962). The quantization of geometry. In L. Witten (Ed.), Gravitation: an introduction to current research (pp. 266–381). New York: John Wiley & Sons.
Diósi, L., & Halliwell, J. (1998). Coupling classical and quantum variables using continuous quantum measurement theory. Physical Review Letters, 81(14), 2846–2849.
Duff, M. J. (1981). Inconsistency of quantum field theory in curved space-time. In C. J. Isham, R. Penrose, & D. W. Sciama (Eds.), Quantum gravity 2: A second Oxford symposium (pp. 81–105). Oxford: Oxford University Press.
Eppley. K., & Hannah, E. (1977). The necessity of quantizing the gravitational field. Foundations of Physics, 7, 51–65.
Fulling, S. (1989). Aspects of quantum field theory in curved space-time. Cambridge: Cambridge University Press.
Hawking, S. (1975). Particle creation by black holes. Communications in Mathematical Physics, 43, 199–220.
Hu, B. L. (2002). A kinetic theory approach to quantum gravity. International Journal of Theoretical Physics, 41, 2091–2119.
Hu, B. L., & Verdaguer, E. (2001). Recent advances in stochastic gravity: Theory and issues. arXiv.org:gr-qc/0110092v1, Erice Lectures.
Hu, B. L., & Verdaguer, E. (2003). Stochastic gravity: A primer. Classical and Quantum Gravity, 20, R1–R42.
Jones, K. R. W. (1993). General method for deforming quantum dynamics into classical dynamics while keeping \(\hbar\) fixed. Physical Review A 48(1), 822–825.
Jones, K. R. W. (1994). Exclusion of intrinsically classical domains and the problem of quasiclassical emergence. Physical Review A 50(2), 1062–1070.
Jones, K. R. W. (1996). Comment on “Quantum Backreaction on ‘Classical’ Variables”. Physical Review Letters, 76(21), 4087.
Kibble, T. W. B. (1981). Is a semiclassical theory of gravity viable? In C. J. Isham, R. Penrose, & D. W. Sciama (Eds.), Quantum gravity 2, a second Oxford Symposium (pp. 63–80). Oxford: Clarendon.
Koopman, B. O. (1931). Hamiltonian systems and transformations in Hilbert space. Proceedings of the National Academy of Science, 17, 315–318.
Lakatos, I. (1970). Falsification and the methodology of scientific research programs. In I. Lakatos & A. Musgrave (Eds.), Criticism and the growth of knowledge (pp. 91–196). Cambridge University Press: Cambridge.
Lakatos, I. (1978). The methodology of scientific research programmes: Philosophical papers (Vol. 1). Cambridge: Cambridge University Press.
Mattingly, J. (2005a). Is quantum gravity necessary? Paper presented at the Fifth International Conference on the History and Foundations of General Relativity, Notre Dame (1999). Published in J. Eisenstaedt & A. J. Kox (Eds.), The universe of general relativity: Einstein studies (pp. 325–337). Boston: Birkhäuser.
Mattingly, J. (2005b). The structure of scientific theory change. Philosophy of Science, 72, 365–389.
Mattingly, J. (2006). Why Eppley and Hannah’s thought experiment fails. Physical Review, D 73, 6402547.
Mattingly, J. (2009). The paracletes of quantum gravity. In M. Dickson & M. Domski (Eds.), Discourse on a new method: Reinvigorating the marriage of history and philosophy of science. Open Court Press.
Page, D. N., & Geilker, C. D. (1981). Indirect evidence for quantum gravity. Physical Review Letters, 47 979–982.
Peres, A. (1993). Quantum theory: Concepts and methods. Norwell, MA: Kluwer Academic.
Peres, A., & Terno, D. (1996). Evolution of the Liouville density of a chaotic system. Physical Review E53, 284–290.
Peres, A., & Terno, D. (2001). Hybrid classical-quantum dynamics. Physical Review A, 63, 022101.
Sergi, A. (2005). Non-Hamiltonian commutators in quantum mechanics. Physical Review E, 72, 066125.
Sudarshan, E. (2004). Consistent measurement of a quantum dynamical variable using classical apparatus. arXiv.org:quant-ph/0402134.
Terno, D. (2004). Inconsistency of quantum-classical dynamics, and what it implies. arXiv:quant-ph/0402092v1.
Wald, R. (1977). The back reaction effect in particle creation in curved spacetime. Communications in Mathematical Physics, 54(1), 1–19.
Wald, R. (1994). Quantum field theory in curved spacetime and black hole thermodynamics. Chicago: University of Chicago Press.
Wüthrich, C. (2005). To quantize or not to quantize: Fact and folklore in quantum gravity. Philosophy of Science, 72(5), 777–788.
Acknowledgements
J. Mattingly is happy to acknowledge, and even happier to have received, very good advice from two anonymous referees. Their insights and careful reading have resulted in important improvements to this paper.
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Mattingly, J. Mongrel Gravity. Erkenn 70, 379–395 (2009). https://doi.org/10.1007/s10670-009-9156-z
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DOI: https://doi.org/10.1007/s10670-009-9156-z