Abstract
This chapter discusses the relevance of so-called cosmic time functions for the philosophy of time. After an introduction to how these functions arise in general relativity given the homogenous and isotropic universe in which we live, there follows an analysis of what follows from their existence, and what does not. In particular, it will turn out that cosmic time functions are not suited to restore a global “now”. Finally, a further candidate often advanced as an argument for a privileged notion of simultaneity is discussed: the collapse of entangled wave functions in quantum mechanics. Again, however, a close look at this phenomenon reveals that it undermines, rather than saves, such privileged simultaneity.
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Notes
- 1.
On this term, cf. footnote 1 in the introduction.
- 2.
Cf. G. F. R. Ellis, “Issues in the Philosophy of Cosmology” (2008), p. 1. http://arxiv.org/pdf/astro-ph/0602280v2.pdf.
- 3.
See Kritik der reinen Vernunft, 2nd edn (1787), AA 57–8.
- 4.
Cf. M. Dorato, Time and Reality (1995), p. 191.
- 5.
R. A. Mould, Basic Relativity (1994), p. 393.
- 6.
Ellis (2008), pp. 24–25.
- 7.
Observational evidence indicates that space is homogenous from a scale of about 100 Mega-parsecs. For comparison , the Andromeda galaxy is located at a distance of about 0.75 Mega-parsecs.
- 8.
More precisely, if any point is chosen as the origin of a spacetime coordinate system, space is flat at that point, up to the second derivative of the metric tensor.
- 9.
T. P. Cheng, Relativity, Gravitation and Cosmology, 2nd edn (2010), p. 231.
- 10.
See the end of Appendix B for an explanation of the symbols.
- 11.
Mould (1994), p. 407.
- 12.
That is, roughly speaking, velocity through spacetime.
- 13.
The Natural Philosophy of Time (1963), p. 246.
- 14.
Whitrow (1963), pp. 183–192.
- 15.
pp. 248–250, which see also for the quote from Eddington. Whitrow uses the variable r also for what is here termed ρ.
- 16.
Dorato (1995), p. 200, emphasis in the original. Alternatively, particle horizons can be described as “the limit of matter that we can have had any causal contact with since the start of the universe” (Ellis [2008], p. 14).
- 17.
Ellis (2008), pp. 14–15 and pp. 26–27.
- 18.
Spatial infinity is often assumed for flat and open universes (i.e. for κ equal to zero or −1). The notion of physical infinities is of course beset with difficult problems. For a discussion, see Ellis (2008), pp. 47–48, and R. Rucker, Infinity and the Mind (1982), pp. 9–35.
- 19.
L. Bergström, A. Goobar, Cosmology and Particle Physics (1999), p. 65.
- 20.
Ellis (2008), pp. 15–16.
- 21.
See, for example, Mould (1994), pp. 349–377; G. F. R. Ellis, R. M. Williams, Flat and Curved Space-Times (2000), ch. 6.
- 22.
“An example of a new type of cosmological solutions of Einstein’s field equations of gravitation” (1990). Cf. also S. W. Hawking, G. F. R. Ellis, The Large Scale Structure of Space-Time (1973), pp. 168–170. For a discussion of the philosophical implications of the Gödel universe, see especially M. Dorato, “On becoming, cosmic time and rotating universes ”, in C. Callender (ed.) Time, Reality and Experience (2002); P. Yourgrau, The Disappearance of Time: Kurt Gödel and the Idealistic Tradition in Philosophy (1991); and B. Dainton, Time and Space, 2nd edn (2010), pp. 381–386.
- 23.
Cf. M. Tooley, Time, Tense, and Causation (1997), pp. 290–291. See also Dorato (1995), p. 191, footnote 9 for references.
- 24.
K. Gödel, “A remark about the relationship between relativity theory and idealistic philosophy” (1949).
- 25.
On the question of whether time travel can be causally harmless, cf. Dainton (2010), ch. 8.
- 26.
Dorato (2002), pp. 259–260.
- 27.
Cf. Sect. 1.1 on the notion of “strong” substantivalism about time.
- 28.
D. W. Zimmerman, “Presentism and the space-time manifold” (2013), p. 110.
- 29.
That is, the fractional contribution of matter and cosmological constant, respectively, to the total mass-energy of the universe.
- 30.
Including that of a comoving observer, since it is not her hyperplane of simultaneity which defines the universe at cosmic time t = constant, but rather the atlas consisting of the hyperplanes of simultaneity of all comoving observers.
- 31.
Cheng (2010), p. 264.
- 32.
For a more detailed discussion, see S. E. Rugh, H. Zinkernagel, “On the physical basis of cosmic time”.
- 33.
Dorato (1995), p. 208, emphases in the original. However, Dorato does not commit himself to an A-theoretic reading of cosmic time.
- 34.
For a critique of attempts to reconstruct a worldwide now from cosmology, see also R. J. Russell, Time in Eternity (2012), pp. 309–313.
- 35.
See, for example, M. A. Morrison, Understanding Quantum Physics (1990), pp. 18–96; D. Z. Albert, Quantum Mechanics and Experience (1992), pp. 1–72.
- 36.
Morrison (1990), pp. 468–472. Some observables have continuous, rather than discrete eigenvalues, so that the state vector can also be written as an integral of the eigenstates of such an observable, with each one multiplied by its respective probability amplitude.
- 37.
As is well known, other interpretations than the Copenhagen interpretation, which I am assuming here, have been advanced. I will leave these aside in the current discussion, since the “orthodox” interpretation, for all we currently know, best agrees with experiment.
- 38.
It can rightly be questioned whether we are really faced with two events here, rather than a single one, namely the collapse of the joint wave function describing the state of both entangled particles. I am using the talk of two events merely because this is necessary in order to present the argument from entangled states to absolute simultaneity between spacelike-separated events.
- 39.
“On relativity theory and openness of the future”, Philosophy of Science (1991), here p. 165.
- 40.
“Finding ‘real’ time in quantum mechanics” (2007), p. 13. http://philsci-archive.pitt.edu/4262/. Emphases in the original.
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Saudek, D. (2020). Cosmic Time. In: Change, the Arrow of Time, and Divine Eternity in Light of Relativity Theory. Palgrave Frontiers in Philosophy of Religion. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-38411-1_4
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