Abstract
An astonishing thesis in the philosophy of quantum gravity is that spacetime ”disappears” at the fundamental level of reality, and that the geometrical notions of ”length” and ”duration” are derived from the dynamics of the basic non–geometrical building blocks of the theory. Unveiling here the analysis of the concepts of spacetime, measure, and magnitude, given by the philosopher Nicolai Hartmann, I argue that the ”disappearance” thesis is too strong. The fundamental geometrical notions are, on the contrary, primitive and cannot be derived from the fundamental building blocks; they must be presupposed ab initio not only for epistemological, but also for methodological reasons.
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Notes
Unsolvable in principle was for Hartmann synonym of irrational, and irrationality was what characterized the metaphysical problems in a strict sense. He thought, however, that the causes for irrationality were not in reality itself (there are no conspiracies in Nature), but in human understanding, which – pace Aristotle – was not designed originally to reach the heights of philosophy, logic, or theoretical science, but rather to solve practical problems of survival.
For the sphere of the physical objects, according to Hartmann’s ontology, every degree of freedom can be a good example of the quantity whose values are measurable in the dimensions.
Even the question of what counts as spacetime in GTR models, and the assumption or rejection of the so-called ”metrical essentialism” (relativistic spacetime is not only the manifold, but the manifold plus the metric), which could be recalled by Oriti’s text, are not crucial problems for thesis (Primacy).
Hartmann writes about the possibility of discrete spacetime elsewhere (Hartmann 1950, 95–96). Apparently he has read Heisenberg on the idea of fundamental length [Elementarlänge], and believed the issue could be decided empirically in the future.
These are specifically determined by the particular dimension in which they are used (e.g., rod for space, clock for time).
As I mentioned at the end of Section 2, the authors of Huggett and Wüthrich (2013) propose a different meaning of ”physical salience” for – at least – QG theories. Different from Hartmann’s account, of course. Indeed, according to them physical salience is a theory-laden notion that should not be inherently spatiotemporal, and the only requirement for a theory to be physically salient is to provide a model from which one can recover the features of general relativistic spacetime at low-energies. Clearly, such an epistemological position is compatible with the (ontological) claim that the fundamental, physical reality described by QG (the high energy limit) does not need to be spatiotemporal in any sense, and relativistic spacetime can be only an ”emergent” (i.e., non-fundamental) structure.
For a similar argument about time see Hartmann (1950, 156–157).
References
Hagar, A. (2014). Discrete or Continuous? The Quest for Fundamental Length in Modern Physics. Cambridge: Cambridge University Press. Final draft in http://philpapers.org/rec/HAGLMT-2.
Smolin, L. (2010). Generic Predictions of Quantum Theories of Gravity In Oriti, D. (Ed.), Approaches to Quantum Gravity, pp. 548–570. Cambridge: Cambridge University Press.
Huggett, N., & Wüthrich, C. (2013). Emergent spacetime and empirical (in)coherence. Studies in the History and Philosophy of Modern Physics, 44, 276–285.
Oriti, D. (2012). Disappearance and emergence of space and time in quantum gravity. Preprint.
Wüthrich, C. (2014). Raiders of the lost spacetime In Lehmkuhl, D. (Ed.), Towards a Theory of Spacetime Theories. Berlin: Birkhäuser.
Hagar, A., & Hemmo, M. (2013). The Primacy of Geometry. Studies in the History and Philosophy of Modern Physics, 44(3), 357–364.
Rovelli, C. (1993). A Generally Covariant Quantum Field Theory and a Prediction on Quantum Measurements of Geometry. Nuclear Physics B, 405, 797–815.
Dittrich, B., & Thiemann, T. (2009). Are the Spectra of Geometrical Operators in Loop Quantum Gravity Really Discrete? Journal of Mathematical Physics, 50(1), 012503–11.
Nicolai, H., & Peeters, K. (2007). Loop and spin foam quantum gravity: A brief guide for beginners In Stamatescu, I.-O., & Seiler, E. (Eds.), Approaches to Fundamental Physics, pp. 151–184. Berlin Heidelberg: Springer.
Rickles, D. (2005). A new spin on the hole argument. Studies in the History and Philosophy of Modern Physics, 36, 415–434.
Rovelli, C. (2004). Quantum Gravity. Cambridge: Cambridge University press.
Feynman, R., & Hibbs, A.R. (1965). Quantum Mechanics and Path Integrals. New York: Dover Publications.
Hartmann, N. (1950). Philosophie der Natur. Berlin: De Gruyter.
Bombelli, L., Lee, J., Meyer, D., Sorkin, R. (1987). Spacetime As a Causal Set. Physical Review Letters, 59, 521–524.
Acknowledgments
I am grateful – first of all – to Prof. Amit Hagar for the fundamental support, and for letting me read the manuscript of his new book. Special thanks to prof. Sander Gliboff for the English translation of Hartmann’s text in Section 4.3, and to the entire Department of History and Philosophy of Science of the Indiana University at Bloomington, which sponsored my research project in the USA. I am particularly indebted to prof. Marco Giunti and the ALOPHIS society, and to prof. Annamaria Loche and the Scuola di Dottorato in Filosofia ed Epistemologia, who approved my project, and to the Regione Autonoma della Sardegna and the Università di Cagliari, which supported it. Of course, I am grateful to my three anonymous referees for their critical comments. Finally, I wish to thank my tutor, prof. PierLuigi Lecis, who, years ago, drove me to study Hartmann’s philosophy. A different version of this article is present in my Ph.D. thesis: Time in Nicolai Hartmann’s philosophy, Università di Cagliari, 2014 (partly published by Lambert Academic Publishing with the title: Problems of time in Nicolai Hartmann’s philosophy).
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Pinna, S. The philosophy of quantum gravity – lessons from Nicolai Hartmann. Euro Jnl Phil Sci 5, 279–296 (2015). https://doi.org/10.1007/s13194-014-0103-8
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DOI: https://doi.org/10.1007/s13194-014-0103-8