In times of crisis, when current theories are revealed as inadequate to task, and new physics is thought to be required—physics turns to re-evaluate its principles, and to seek new ones. This paper explores the various types, and roles of principles that feature in the problem of quantum gravity as a current crisis in physics. I illustrate the diversity of the principles being appealed to, and show that principles serve in a variety of roles in all stages of the crisis, including in motivating the need for a new theory, and defining what this theory should be like. In particular, I consider: the generalised correspondence principle, UV-completion, background independence, and the holographic principle. I also explore how the current crisis fits with Friedman’s view on the roles of principles in revolutionary theory-change, finding that while many key aspects of this view are not represented in quantum gravity (at the current stage), the view could potentially offer a useful diagnostic, and prescriptive strategy. This paper is intended to be relatively non-technical, and to bring some of the philosophical issues from the search for quantum gravity to a more general philosophical audience interested in the roles of principles in scientific theory-change.
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.
Almost as soon as GR was completed, Einstein was aware of the need for a quantum theory of gravity; Einstein (1916, p. 202) writes of a possible conflict between GR and the principles of quantum theory. See also the papers in Blum and Rickles (Forthcoming).
Note that, although each of these approaches is incomplete, and faces its own set of problems in addition to these general difficulties, it is still possible—and indeed, worthwhile—to engage with the philosophy of QG, as well as to consider what QG might tell us about other philosophical questions (See, e.g., Butterfield and Isham 2001; Callender and Huggett 2001; Rickles 2008a).
When I refer to “current principles”, I mean those that feature within, or led to the development of, existing theories (typically the current best theories of physics). This is in contrast with new principles that are being appealed to (e.g., the holographic principle), which have not yet led to, or featured within, any successful, accepted scientific theories.
As I discuss, the generalised correspondence principle does feature as a sort of meta-principle in what Friedman (2001) calls “communicative rationality”.
An effective theory in physics is one that is valid only at a given range of energy (length) scales, and is thus not considered fundamental.
Although UV-completion (the idea that a theory be formally predictive up to all possible high energy scales) is often presented as part of the definition of QG, Crowther and Linnemann (2017) argue against taking it as a criterion of acceptance in QG. Nevertheless, it plays a role in motivating the search for QG, and may usefully act as a guiding principle.
Note, too, that Dawid (2013) presents the UEA in conjunction with two other arguments, in order to establish limits on the underdetermination of the new theory, and together paint a picture that is much more nuanced than what I present here.
But see Footnote 8.
Dawid (2013), and string theorists, of course, would challenge this statement, asserting string theory’s success in doing exactly this. However, string theory is currently not at a stage where such assertions represent compelling arguments.
Including Brownian motion, radioactivity, the Michelson-Morley experiment, and experiments involving electrons accelerated to very high velocities.
Cf. Samaroo (2015).
An idea attributed to Reichenbach and Schlick, see Friedman (2001, pp. 76–79).
Although, as Crowther and Linnemann (2017) point out, QG need not be a fundamental theory, it would represent progress in this direction.
Almheiri et al. (2013).
Thanks to a referee for pointing this out.
However, physically relevant QFTs also contain non-observable fields, some of which are non-local.
GR treated in the framework of QFT is apparently perturbatively non-renormalisable, breaking down at energies approaching the Planck scale, and so cannot represent a theory of QG, if QG is required to describe physics at this scale. The idea of asymptotic safety is that this apparent problem with GR treated as a QFT may be an artifact of the misapplication of perturbation theory, and that the theory is in fact non-perturbatively renormalisable. Reviews: Niedermaier and Reuter (2006), Percacci (2009).
Actually, string theory is usually considered to possess an additional symmetry, conformal symmetry, making it a 2-dimensional conformal field theory.
Friedman (e.g., 2001, Lecture II, and Chapter 4).
E.g., Rovelli (2004).
The idea is essentially what Nickles (1973) calls “reduction2”.
See, Bokulich (2014).
Causal set theory sees the desideratum of “being quantum” in the same way that string theory views the principle of “being background indpendent”, i.e., an ultimate aspiration, but one that need not be implemented at the initial stages.
Perturbative renormalisability is insufficient to establish UV-completion, since a theory may be perturbatively renormalisable may still face a Landau Pole, as is the case in quantum electrodynamics.
Cf. Crowther and Linnemann (2017).
See references in Fn. 45.
However, given the above discussion, one might wonder whether the principle should be viewed as being so significant—a thought that gains further weight with the recognition that particle physicists in the 1930s–70s managed to derive Einstein’s equations of GR from entirely unrelated principles, including universal coupling and avoidance of ghosts (e.g., Desser 1970; Nieuwenhuizen 1973). (Thanks to a referee for offering this food for thought).
See, e.g., Polchinski (2017).
Some work has been done in investigating the area scaling law. Oppenheim (2003), for example, uses an analogue model of a black hole with long-range interactions and shows how the entropy goes from scaling with volume to scaling with area as the strength of the interactions increases. Chandran et al. (2016) recounts the applicability of the area law for entanglement entropy, showing under what conditions it scales differently.
Almheiri, A., Marolf, D., Polchinski, J., & Sully, J. (2013). Black holes: Complementarity or firewalls? Journal of High Energy Physics, 2013(2), 62.
Anderson, E. (2012). Problem of time in quantum gravity. Annalen der Physik, 524(12), 757–786.
Bekenstein, J. (1981). A universal upper bound on the entropy to energy ratio for bounded systems. Physical Review D, 23(2), 287.
Belot, G. (2011). Background-independence. General Relativity and Gravitation, 43(10), 2865–2884.
Belot, G., & Earman, J. (2001). Presocratic quantum gravity. In C. Callender & N. Huggett (Eds.), Physics meets philosophy at the Planck scale (pp. 213–255). Cambridge: Cambridge University Press.
Belot, G., Earman, J., & Ruetsche, L. (1999). The hawking information loss paradox: The anatomy of a controversy. The British Journal for the Philosophy of Science, 50(2), 189–229.
Bergmann, P. G., & Komar, A. B. (1960). Poisson brackets between locally defined observables in general relativity. Physical Review Letters, 4, 432–433.
Bigatti, D., & Susskind, L. (2000). The holographic principle. In L. Thorlacius & T. Jonsson (Eds.), M-theory and quantum geometry (pp. 179–226)., Volume 556 of NATO science series Dordrecht: Kluwer Academic Publishers.
Blum, A. & Rickles, D. (Eds.). (Forthcoming). Quantum gravity in the first half of the twentieth century: A sourcebook. Berlin: Edition Open Access.
Bokulich, A. (2014). Bohr’s correspondence principle. The Stanford Encyclopedia of Philosophy, Spring 2014.
Bousso, R. (2002). The holographic principle. Reviews of Modern Physics, 74, 825–874.
Brown, H. (2005). Physical relativity: Space-time structure from a dynamical perspective. Oxford: Oxford University Press.
Butterfield, J. (Forthcoming). On dualities and equivalences between physical theories. In N. Huggett, B. L. Bihan, & C. Wüthrich (Eds.), Philosophy beyond spacetime. Oxford: Oxford University Press. https://arxiv.org/abs/1806.01505.
Butterfield, J., & Bouatta, N. (2015). Renormalization for philosophers. In T. Bigaj & C. Wüthrich (Eds.), Metaphysics in contemporary physics (pp. 437–485). Brill: Leiden.
Butterfield, J., & Isham, C. (1999). On the emergence of time in quantum gravity. In J. Butterfield (Ed.), The arguments of time (pp. 116–168). Oxford: Oxford University Press.
Butterfield, J., & Isham, C. (2001). Spacetime and the philosophical challenge of quantum gravity. In C. Callender & N. Huggett (Eds.), Physics meets philosophy at the Planck scale (pp. 33–89). Cambridge: Cambridge University Press.
Callender, C., & Huggett, N. (Eds.). (2001). Physics meets philosophy at the Planck scale: Contemporary theories in quantum gravity. Cambridge: Cambridge University Press.
Cao, T. Y., & Schweber, S. S. (1993). The conceptual foundations and the philosophical aspects of renormalization theory. Synthese, 97(1), 33–108.
Carlip, S. (2001). Quantum gravity: A progress report. Reports on Progress in Physics, 64(8), 885.
Carlip, S. (2017). Dimension and dimensional reduction in quantum gravity. Classical and Quantum Gravity, 34(19), 193001.
Chandran, A., Laumann, C., & Sorkin, R. (2016). When is an area law not an area law? Entropy, 18(7), 240–247.
Crowther, K. (2016). Effective spacetime: Understanding emergence in effective field theory and quantum gravity. Heidelberg: Springer.
Crowther, K., & Linnemann, N. (2017). Renormalizability, fundamentality and a final theory: The role of UV completion in the search for quantum gravity. British Journal for the Philosophy of Science. https://doi.org/10.1093/bjps/axx052.
Crowther, K., & Rickles, D. (2014). Introduction: Principles of quantum gravity. Studies In History and Philosophy of Modern Physics, 46, 135–141.
Dawid, R. (2013). String theory and the scientific method. Heidelberg: Cambridge University Press.
Dawid, R. (2017). String dualities and empirical equivalence. Studies In History and Philosophy of Modern Physics, 59, 21–29.
de Haro, S. (2017). Dualities and emergent gravity: Gauge/gravity duality. Studies In History and Philosophy of Modern Physics, 59, 109–125.
Deser, S., & van Nieuwenhuizen, P. (1974). One-loop divergences of quantized Einstein–Maxwell fields. Physical Review D, 10(2), 401.
Desser, S. (1970). Self-interaction and gauge invariance. General Relativity and Gravitation, 1, 9–18.
Dvali, G., Giudice, G. F., Gomez, C., & Kehagias, A. (2011). Uv-completion by classicalization. Journal of High Energy Physics, 2011(8), 1–31.
Earman, J. (2006). The implications of general covariance for the ontology and ideology of spacetime. In D. Dieks (Ed.), The Ontology of Spacetime (pp. 3–23). Amsterdam: Elsevier.
Einstein, A. (1916). Approximate integration of the field equations of gravitation. In The collected papers of Albert Einstein. Volume 6: The Berlin years: Writings, 1914–1917 (English translation supplement). http://einsteinpapers.press.princeton.edu/vol6-trans/213.
Einstein, A. (1919). Time, space, and gravitation (pp. 13–14). London: The Times.
Friedman, M. (1983). Foundations of space-time theories. Princeton: Princeton University Press.
Friedman, M. (2001). Dynamics of reason: The 1999 Kant lectures of Stanford University. Stanford: CSLI Publications.
Giulini, D. (2007). Remarks on the notions of general covariance and background independence. In I.-O. Stamatescu & E. Seiler (Eds.), Lecture notes in physics (Vol. 721, pp. 105–120). Berlin: Springer.
Haba, Z. (2002). Renormalization in quantum brans-dicke gravity. arXiv preprint arXiv:hep-th/0205130.
Hagar, A. (2014). Discrete or continuous? The quest for fundamental length in modern physics. Cambridge: Cambridge University Press.
Hartmann, S. (2002). On correspondence. Studies in History and Philosophy of Modern Physics, 33(1), 79–94.
Hawking, S. (1974). Black hole explosions? Nature, 248, 30–31.
Hawking, S. (1975). Particle creation by black holes. Communications in Mathematical Physics, 43, 199–220.
Hossenfelder, S. (2013). Minimal length scale scenarios for quantum gravity. Living Reviews in Relativity, 16, 2.
Huggett, N., & Callender, C. (2001). Why quantize gravity (or any other field for that matter)? Philosophy of Science, 68(3), S382–S394.
Huggett, N., & Vistarini, T. (2015). Deriving general relativity from string theory. Philosophy of Science, 82(5), 1163–1174.
Huggett, N., Vistarini, T., & Wüthrich, C. (2013). Time in quantum gravity. In H. Dyke & A. Bardon (Eds.), A companion to the philosophy of time, Blackwell companions to philosophy (pp. 242–261). Chichester: Wiley-Blackwell.
Huggett, N., & Wüthrich, C. (2013). Emergent spacetime and empirical (in)coherence. Studies in History and Philosophy of Modern Physics, 44(3), 276–285.
Kiefer, C. (2006). Quantum gravity: General introduction and recent developments. Annals of Physics, 15(1), 129–148.
Kiefer, C. (2007). Why quantum gravity? In I. O. Stamatescu & E. Seiler (Eds.), Approaches to Fundamental Physics (pp. 123–130). Berlin: Springer.
Kuhn, T. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.
Maldacena, J. (1998). The large N limit of superconformal field theories and supergravity. Advances in Theoretical and Mathematical Physics, 2, 231–252.
Mathur, S. (2009). The information paradox: A pedagogical introduction. Classical and Quantum Gravity, 26, 224001.
Mattingly, J. (2005). Is quantum gravity necessary? In A. Kox & J. Eisenstaedt (Eds.), The universe of general relativity (pp. 327–338). Basel: Birkhäuser.
Mattingly, J. (2006). Why Eppley and Hannah’s thought experiment fails. Physical Review D, 73, 062025.
Mattingly, J. (2009). Mongrel gravity. Erkenntnis, 70(3), 379–395.
Nickles, T. (1973). Two concepts of intertheoretic reduction. The Journal of Philosophy, 70(7), 181–201.
Niedermaier, M., & Reuter, M. (2006). The asymptotic safety scenario in quantum gravity. Living Reviews in Relativity, 9(5), 173.
Norton, J. (2003). General covariance, gauge theories and the Kretschmann objection. In K. Brading & E. Castellani (Eds.), Symmetries in physics: Philosophical reflections (pp. 110–123). Cambridge: Cambridge University Press.
Oppenheim, J. (2003). Thermodynamics with long-range interactions: From Ising models to black holes. Physical Review E, 68, 016108.
Orlando, D., & Reffert, S. (2009). The renormalizability of Hořava–Lifshitz-type gravities. Classical and Quantum Gravity, 26(15), 155021.
Percacci, R. (2009). Asymptotic safety. In D. Oriti (Ed.), Approaches to quantum gravity: Towards a new understanding of space, time and matter (pp. 111–128). Cambridge: Cambridge University Press.
Pitts, J. B. (2006). Absolute objects and counterexamples: Jones–Geroch dust, Torretti constant curvature, tetrad-spinor, and scalar density. Studies in History and Philosophy of Modern Physics, 37, 347–371.
Pitts, J. B. (2014). Change in Hamiltonian general relativity from the lack of a time-like killing vector field. Studies in History and Philosophy of Modern Physics, 47, 68–89.
Pitts, J. B. (2017). Equivalent theories redefine Hamiltonian observables to exhibit change in general relativity. Classical and Quantum Gravity, 34(5), 055008.
Poincaré, H. (1905a). The principles of mathematical physics. The Monist, 15(1), 1–24.
Poincaré, H. (1905b). Science and hypothesis. New York: Walter Scott.
Poincaré, H. (1907). The value of science. New York: Science Press.
Polchinski, J. (2017). Dualities of fields and strings. Studies in History and Philosophy of Modern Physics, 59, 6–20.
Pons, J., Salisbury, D., & Sundermeyer, K. (2010). Observables in classical canonical gravity: Folklore demystified. Journal of Physics: Conference Series, 222(1), 012018.
Pons, J. M. (2005). On Dirac’s incomplete analysis of gauge transformations. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 36(3), 491–518.
Pooley, O. (2015). Background independence, diffeomorphism invariance, and the meaning of coordinates. In D. Lehmkuhl (Ed.), Towards a theory of spacetime theories (pp. 105–143). Basel: Birkhäuser.
Pooley, O. (2017). Background independence, diffeomorphism invariance, and the meaning of coordinates. In D. Lehmkuhl, G. Schiemann, & E. Scholz (Eds.), Towards a theory of spacetime theories (pp. 105–144). Basel: Birkhäuser.
Post, H. (1971). Correspondence, invariance and heuristics: In praise of conservative induction. Studies in History and Philosophy of Science Part A, 2(3), 213–255.
Radder, H. (1991). Heuristics and the generalized correspondence principle. British Journal for the Philosophy of Science, 42, 195–226.
Read, J. (2016). Background independence in classical and quantum gravity. Master’s thesis, University of Oxford.
Read, J. & Møller-Nielsen, T. (2018). Motivating dualities. Synthese. https://doi.org/10.1007/s11229-018-1817-5.
Rickles, D. (2006a). Time and structure in canonical gravity. In D. Rickles, S. French, & J. Saatsi (Eds.), The structural foundations of quantum gravity (pp. 152–196). Oxford: Oxford University Press.
Rickles, D. (2006b). Who’s afraid of background independence? In D. Dieks (Ed.), The ontology of spacetime (pp. 133–152). Amsterdam: Elsevier.
Rickles, D. (2008a). Quantum gravity: A primer for philosophers. In D. Rickles (Ed.), The Ashgate companion to contemporary philosophy of physics, chapter 5 (pp. 262–365). Aldershot: Ashgate.
Rickles, D. (2008b). Symmetry, structure, and spacetime. Amsterdam: Elsevier.
Rickles, D. (2011). A philosopher looks at string dualities. Studies in History and Philosophy of Modern Physics, 42(1), 54–67.
Rickles, D. (2012). Time, observables, and structure. In E. Landry & D. Rickles (Eds.), Structural realism (pp. 135–145)., Volume 77 of the Western Ontario series in philosophy of science Dordrecht: Springer.
Rideout, D., & Zohren, S. (2006). Evidence for an entropy bound from fundamentally discrete gravity. Classical and Quantum Gravity, 23(22), 6195.
Rovelli, C. (1991). What is observable in classical and quantum gravity? Classical and Quantum Gravity, 8(2), 297.
Rovelli, C. (2002). GPS observables in general relativity. Physical Review D, 65, 044017.
Rovelli, C. (2004). Quantum Gravity. Cambridge: Cambridge University Press.
Samaroo, R. (2015). Friedman’s thesis. Studies in History and Philosophy of Modern Physics, 52, 129–138.
Shankar, R. (1999). The triumph and limitations of quantum field theory. In T. Y. Cao (Ed.), Conceptual foundations of quantum field theory (pp. 47–55). Cambridge: Cambridge University Press.
Smolin, L. (2001). The strong and weak holographic principles. Nuclear Physics B, 601(12), 209–247.
Smolin, L. (2006). The case for background independence. In D. Rickles, S. French, & J. Saatsi (Eds.), The structural foundations of quantum gravity (pp. 196–239). Oxford: Oxford University Press.
Smolin, L. (2017). Four principles for quantum gravity. In J. Bagla & S. Engineer (Eds.), Gravity and the quantum (pp. 427–450)., Volume 187 of fundamental theories of physics Berlin: Springer.
Stelle, K. (1977). Renormalization of higher-derivative quantum gravity. Physical Review D, 16(4), 953.
Susskind, L. (1995). The world as a hologram. Journal of Mathematical Physics, 36(11), 6377–6396.
’t Hooft, G. (1993). Dimensional reduction in quantum gravity. https://arxiv.org/abs/gr-qc/9310026.
’t Hooft, G. & Veltman, M. (1974). One-loop divergencies in the theory of gravitation. In Annales de l’IHP Physique théorique (Vol. 20, pp. 69–94).
Teh, N. (2013). Holography and emergence. Studies in History and Philosophy of Modern Physics, 44(3), 300–311.
Thbault, K. P. (2012). Three denials of time in the interpretation of canonical gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 43(4), 277–294.
Van Nieuwenhuizen, P. (1973). On ghost-free tensor lagrangians and linearized gravitation. Nuclear Physics B, 60, 478–492.
Wallace, D. (2017a). The case for black hole thermodynamics, part i: Phenomenological thermodynamics. https://arxiv.org/abs/1710.02724.
Wallace, D. (2017b). The case for black hole thermodynamics, part ii: Statistical mechanics. https://arxiv.org/abs/1710.02725.
Wallace, D. (2018). Why black hole information loss is paradoxical. https://arxiv.org/abs/1710.03783v2.
Weinberg, S. (1979). Ultraviolet divergencies in quantum theories of gravitation. In S. Hawking & W. Israel (Eds.), General relativity, an Einstein Centenary survey (pp. 790–831). Cambridge: Cambridge University Press.
Weinberg, S. (1999). What is quantum field theory and what did we think it was? In T. Y. Cao (Ed.), Conceptual foundations of quantum field theory (pp. 241–251). Cambridge: Cambridge University Press.
Wheeler, J. (1984). Quantum gravity: The question of measurement. In S. Christensen (Ed.), Quantum theory of gravity: Essays in honor of the 60th birthday of Bryce S. DeWitt (pp. 224–233). Bristol: Adam Hilger.
Wheeler, J., & Ford, K. (1998). Geons, black holes and quantum foam. New York: W.W. Norton & Company.
Wüthrich, C. (2005). To quantize or not to quantize: Fact and folklore in quantum gravity. Philosophy of Science, 72, 777–788.
Wüthrich, C. (2017). Raiders of the lost spacetime. In D. Lehmkuhl (Ed.), Towards a theory of spacetime theories (pp. 297–335). Basel: Birkhäuser.
Zee, A. (2010). Quantum field theory in a nutshell. Princeton: Princeton University Press.
Thanks to Niels Linnemann, Ashton Green, Christian Wüthrich, James Read, and three anonymous reviewers for comments and suggestions.
Rights and permissions
About this article
Cite this article
Crowther, K. Defining a crisis: the roles of principles in the search for a theory of quantum gravity. Synthese 198 (Suppl 14), 3489–3516 (2021). https://doi.org/10.1007/s11229-018-01970-4
- Constitutive principles
- Scientific revolution
- Theory change
- Holographic principle