Abstract
The theory of relativity is often regarded as inhospitable to the idea that there is an objective passage of time in the world. In light of this, many philosophers and physicists embrace a “block universe” view, according to which change and temporal passage are merely a subjective appearance or illusion. My aim in this paper is to argue against such a view, and show that we can make sense of an objective passage of time in the setting of relativity theory by abandoning the assumption that the now must be global, and re-conceiving temporal passage as a purely local phenomenon. Various versions of local becoming have been proposed in the literature. Here I focus on the causal diamond theory proposed by Steven F. Savitt and Richard Arthur, which models the now in terms of a local structure called a causal diamond. After defending the reality of temporal passage and exploring its compatibility with relativity theory, I show how the causal diamond approach can be used to counter the argument for the ideality of time due to Kurt Gödel, based on his “rotating universe” solution to the Einstein field equations (the Gödel universe). I defend the second component of his argument, the modal step, against the consensus view that finds it wanting, and reject the first step, showing that the Gödel universe is compatible with an objective passage of time as long as the latter is construed locally, along the lines of the causal diamond approach.
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Notes
The arguments of C. W. Rietdijk (1966) and Hilary Putnam (1967) are often cited as the classic arguments defending this kind of view on the basis of relativity theory. It should be noted, however, that neither Rietdijk nor Putnam explicitly address the question of temporal passage in their papers. Rather, Rietdijk is concerned with the question of determinism, while Putnam asks whether future things (or events) are real, and whether contingent statements about future events have determinate truth values. The implications of their conclusions for questions about temporal passage, if any, are not spelled out. Another point that deserves mention is that Putnam later retracts a key element of his argument in response to the criticisms of Yuval Dolev, Mauro Dorato, and Steven Savitt, writing: “the question whether the past and the future are ‘real’ is a pseudo-question” (Putnam, 2008, p. 71).
In fact, this is the kind of world represented by John M. E. McTaggart’s B-series, where events are related by the two-place relations of “earlier than” or “later than,” but lack the determinations of “past,” “present,” or “future” (McTaggart, 1908). A world lacking both a past-future asymmetry and the passage of time is represented by McTaggart’s C-series, where there is only a three-place relation of “betweenness” among events.
This is what Arthur has called the “notorious sticking point” for static views of reality, namely: “how to account for the appearance of passage or temporal becoming without presupposing the becoming of the appearance” (Arthur, 2019, p. 14). See also the similar argument given by Abner Shimony (1998, pp. 164–65).
Of course, one might point out that the now depends on an observer’s temporal location, just as the here depends on an observer’s spatial location. But what distinguishes the now from the here (according to common sense) is that it makes perfect sense to say that only one of these temporal locations is the true now—there is only one moment that is actually taking place now, which is this very moment in which you happen to be reading this sentence—whereas it hardly makes sense to say that there is a single true here. When I say that the now is objective and shared by everyone, I am referring to this unique, distinguished now embodied in our common-sense conception of time.
More precisely, only the isotropy condition is necessary, because isotropy at every point (or even just two points) implies homogeneity (Peacock, 1999, pp. 65–66).
While a similar point is made by Callender (2017), he seems to hold that cosmic time presupposes not only Weyl’s Principle but also the Cosmological Principle. For example he writes: “FLRW time [i.e., cosmic time in the FLRW models] depends on elaborate averaging ... At most spatial scales the universe is not even close to being isotropic and homogeneous ... The standard model irons out these differences, as is only proper in a model. Yet why on earth should fundamental time, if it exists, march to that particular averaged scale?” (Callender, 2017, p. 75). But as we saw above, cosmic time does not depend on the Cosmological Principle, so Callender’s argument here misses the mark. Nonetheless, his general point—that cosmic time depends on elaborate averaging procedures—holds.
The condition that \({\mathscr{M}}\) be strongly causal means that \({\mathscr{M}}\) does not contain closed or almost-closed timelike curves (see Minguzzi & Sánchez (2008, Sec. 3.6) for a precise definition); this rules out spacetimes like the Gödel universe. As we will see later, our definition of a causal diamond will need to be slightly modified in order to extend it spacetimes that contain CTCs.
See (Malament, 2012, Sec. 3.1) for an excellent technical exposition of the Gödel universe.
An alternative kind of “modal argument” has also been suggested by Yourgrau (1999, pp. 47–48) and articulated by Savitt (1994). I set this argument aside here because, as pointed out by Gordon Belot (2005, p. 270fn), it is based on a passage where Gödel is dealing with an entirely different topic from the one we are concerned with here, namely, the implications of the existence of CTCs for the passage of time in the Gödel universe. Furthermore, I don’t see how one could justify in a non-question-begging way one of the premises of the argument as presented by Savitt, namely, that hypothetical inhabitants of the Gödel universe would have an experience of temporal passage just like ours (see Dorato (2002) for further discussion).
Gödel explicitly makes this point in one of his working drafts for the article quoted above: “A lapse of time [...] would have to be founded, one should think, in the laws of nature” (Gödel, 1946/49, p. 238).
Of course, one might suppose that there is some yet unknown law that causes time to flow whenever a given spacetime satisfies the necessary geometric features. But we can’t just postulate such a law; at present there are simply no reasons for supposing such a law to exist.
As an example of a spacetime that is not temporally orientable, consider defining a direction of time on a Möbius strip: transport the “arrow” of time continuously along the strip, and it will have reversed its direction when it returns to its original position (Maudlin, 2012, pp. 156–57). Hence we cannot define a direction of time consistently on the entire strip.
References
Arthur, R. (2006). Minkowski spacetime and the dimensions of the present. In D. Dieks (Ed.), The ontology of spacetime. Elsevier.
Arthur, R. (2019). The reality of time flow: Local becoming in modern physics. Springer.
Belot, G. (2005). Dust, time and symmetry. The British Journal for the Philosophy of Science, 56(2), 255–91.
Boltzmann, L. (1964). Lectures on gas theory (trans: Brush, S.G.) Dover. [1896–1898].
Bourne, C. (2004). Becoming inflated. The British Journal for the Philosophy of Science, 55(1), 107–19.
Callender, C. (2017). What makes time special? Oxford University Press.
Clifton, R., & Hogarth, M. (1995). The definability of objective becoming in Minkowski spacetime. Synthese, 103(3), 355–87.
Craig, W.L. (1990). What Place, then, for a creator?: Hawking on god and creation. The British Journal for the Philosophy of Science, 41(4), 473–91.
Davies, P. (1995). About time: Einstein’s unfinished revolution. Simon & Schuster.
Dieks, D. (2006). Becoming, relativity and locality. In D. Dieks (Ed.), The ontology of spacetime. Elsevier.
Dorato, M. (2002). On becoming, cosmic time and rotating universes. In C. Callender (Ed.), Time, reality and experience. Cambridge University Press.
Dowe, P. (2017). A and b theories of closed time. Manuscrito, 40 (1), 183–96.
Dowker, F. (2013). Introduction to causal sets and their phenomenology. General Relativity and Gravitation, 45, 1651–67.
Dowker, F. (2014). The birth of spacetime atoms as the passage of time. Annals of the New York Academy of Sciences, 1326, 18–25.
Earman, J. (1995). Bangs, crunches, whimpers, and shrieks: Singularities and acausalities in relativistic spacetimes. Oxford University Press.
Gibbons, G.W., & Solodukhin, S.N. (2007). The geometry of small causal diamonds. Physics Letters B, 649(4), 317–324.
Gödel, K. (1946/49). Some observations about the relationship between theory of relativity and kantian philosophy. In: (Gödel, 1995).
Gödel, K. (1949a). An example of a new type of cosmological solutions of Einstein’s field equations of gravitation. Reviews of Modern Physics, 21, 447–50. Reprinted in (Gödel, 1990).
Gödel, K. (1949b). A remark about the relationship between relativity theory and idealistic philosophy. Albert Einstein: Philosopher-Scientist. ed. Paul Arthur Schilpp. Open Court. Reprinted in (Gödel, 1990).
Gödel, K. (1949c). Lecture on rotating universes. In (Gödel, 1995).
Gödel, K. (1990). In S. Feferman, et al. (Eds.), Collected works, Vol. II: Publications 19381974. Oxford University Press.
Gödel, K. (1995). In S. Feferman, et al. (Eds.), Collected works, Vol. III: Unpublished essays and lectures. Oxford University Press.
Jeans, J. (1936). Man and the universe. In Scientific Progress. George Allen & Unwin Ltd.
Lucas, J.R. (1999). A century of time. In J. Butterfield (Ed.), The arguments of time. Oxford University Press.
Malament, D.B. (1977). The class of continuous timelike curves determines the topology of spacetime. Journal of Mathematical Physics, 18, 1399–1404.
Malament, D.B. (2012). Topics in the foundations of general relativity and Newtonian gravitation theory. University of Chicago Press.
Manchak, J.B. (2016). On Gödel and the ideality of time. Philosophy of Science, 83(5), 1050–58.
Maudlin, T. (2007). On the passing of time. In The metaphysics within physics. Oxford University Press.
Maudlin, T. (2012). Philosophy of physics: Space and time. Princeton University Press.
McTaggart, J.E. (1908). The unreality of time. Mind: A Quarterly Review of Psychology and Philosophy, 17(68), 457–74.
Minguzzi, E., & Sánchez, M. (2008). The causal hierachy of spacetimes. In D. V. Alekseevsky, & H. Baum (Eds.), Recent developments in pseudo-Riemannian geometry. European Mathematical Society. arXiv:gr-qc/0609119.
Muller, R.A. (2016). Now: The physics of time. W. W. Norton & Co.
Muller, R.A., & Maguire, S. (2016). Now, and the flow of time. arXiv:1606.07975.
Narlikar, J.V. (2002). An introduction to cosmology, 3rd edn. Cambridge University Press.
Norton, J.D. (2010). Time really passes. Humana.Mente: Journal of Philosophical Studies, 13, 23–34.
Peacock, J.A. (1999). Cosmological physics. Cambridge University Press.
Popper, K. (2002). Unended quest: An intellectual autobiography. Routledge.
Prigogine, I. (1980). From being to becoming: Time and complexity in the physical sciences. W. H. Freeman & Co.
Putnam, H. (1967). Time and physical geometry. The Journal of Philosophy, 64(8), 240–47.
Putnam, H. (2008). Reply to Mauro Dorato. European Journal of Analytic Philosophy, 4(2), 71–73.
Reichenbach, H. (1999). In M. Reichenbach (Ed.), The direction of time. Dover. [1956].
Rietdijk, C.W. (1966). A rigorous proof of determinism derived from the special theory of relativity. Philosophy of Science, 33, 341–44.
Rovelli, C. (2019). Neither presentism nor eternalism. Foundations of Physics, 49, 1325–35.
Rugh, S.E., & Zinkernagel, H. (2011). Weyl’s principle, cosmic, time, and quantum fundamentalism. In D, Dieks, et al. (Eds.), Explanation, prediction, and confirmation. Springer. arXiv:1006.5848.
Savitt, S.F. (1994). The replacement of time. Australasian Journal of Philosophy, 72(4), 463–74.
Savitt, S.F. (2005). Time travel and becoming. The Monist, 88 (3), 413–22.
Savitt, S.F. (2009). The transient nows. In W.C. Myrvold & J. Christian (Eds.), Quantum reality, relativistic causality, and closing the epistemic circle: Essays in Honour of Abner Shimony. Springer.
Savitt, S.F. (2015). I ♡♢ s. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 50, 19–24.
Savitt, S.F. (2017). Closed time and local time: A reply to Dowe. Manuscrito, 40(1), 197–207.
Savitt, S.F. (2018). Review of Craig callender, what makes time special? BJPS review of books. http://www.thebsps.org/reviewofbooks/craig-callender-what-makes-time-special/. Accessed 5 Oct 2021.
Shimony, A. (1998). Implications of transience for spacetime structure. In S. A. Huggett, et al. (Eds.), The geometric universe: Science, geometry, and the work of Roger Penrose. Oxford University Press.
Smeenk, C., & Wüthrich, C. (2011). Time travel and time machines. In C. Callender (Ed.), The Oxford Handbook of Philosophy of Time. Oxford University Press.
Smolin, L., & Verde, C. (2021). The quantum mechanics of the present. arXiv:2104.09945.
Sorkin, R. (2006). Geometry from order: Causal sets. Einstein Online, 02, 1007.
Stein, H. (1968). On Einstein-Minkowski spacetime. The Journal of Philosophy, 65(1), 5–23.
Stein, H. (1970). On the paradoxical time-structures of Gödel. Philosophy of Science, 37(4), 589–601.
Stein, H. (1991). On relativity theory and the openness of the future. Philosophy of Science, 58(2), 147–67.
Wald, R.M. (1984). General relativity. University of Chicago Press.
Weyl, H. (2009). Philosophie der Mathematik und Naturwissenschaft. 8. Auflage. Oldenbourg. [1966].
Yourgrau, P. (1999). Gödel meets Einstein: Time travel in the Gödel universe. Open Court.
Acknowledgements
I wish to express my deepest gratitude to Satsuki Matsuno, who was kind enough to read through my manuscript and offer his expertise in the technical aspects of relativity theory. I have also benefited greatly from the probing comments and criticisms I received from Steven Savitt and an anonymous reviewer: this paper has been much improved thanks to their help. The main ideas in this paper were presented at the Kochi University of Technology, School of Environmental Science and Engineering Colloquium “Frontiers of Science and Engineering” (Nov. 30, 2021), and the 22nd Meeting of the Singularity Research Group (Dec. 28–30, 2021), both held online. I want to thank Taksu Cheon and Tsuyoshi Houri for inviting me to give these lectures, and the participants of both sessions for their incisive questions and feedback.
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Aames, J. Temporal becoming in a relativistic universe: causal diamonds and Gödel’s philosophy of time. Euro Jnl Phil Sci 12, 44 (2022). https://doi.org/10.1007/s13194-022-00471-z
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DOI: https://doi.org/10.1007/s13194-022-00471-z