Did Time Have a Beginning?

Abstract

By analyzing the meaning of time I argue, without endorsing operationalism, that time is necessarily related to physical systems which can serve as clocks. This leads to a version of relationism about time which entails that there is no time ‘before’ the universe. Three notions of metaphysical ‘time’ (associated, respectively, with time as a mathematical concept, substantivalism, and modal relationism) which might support the idea of time ‘before’ the universe are discussed. I argue that there are no good reasons to believe that metaphysical ‘time’ can be identified with what we ordinarily call time. I also briefly review and criticize the idea of time ‘before’ the big bang, associated with some recent speculative models in modern cosmology, and I argue that if the big bang model is a (roughly) correct description of our universe, then the best current answer to the question in the title is that time did have a beginning.

Acknowledgements

It is a pleasure to thank Svend E. Rugh for many discussions of the material presented here. I also thank María José García Encinas, Carl Hoefer, an anonymous referee, and the audiences during presentations in Seville and Valencia for constructive comments on earlier drafts. Financial support from the Spanish Ministry of Education and Science (project HUM2005‐07187‐C03‐03) is gratefully acknowledged.

Notes

[1] While the present work provides a systematic treatment and defence of this relation between time and clocks, it is discussed elsewhere as well. In Rugh and Zinkernagel (forthcoming) we examine (a slightly different formulation of) the time–clock relation in connection with a detailed critical discussion of the physical assumptions involved in setting up the standard model of cosmology. In Zinkernagel (in prep.) the time–clock relation, in conjunction with a relation between clocks and causality, is used in an argument against Hume’s scepticism about the future validity of causal laws and tomorrow’s sunrise.

[2] See also Weissman (1968, 56): ‘Indeed, if anyone is able to use the word correctly, in all sorts of contexts and on the right sort of occasion, he knows ‘what time is’ and no formula in the world can make him wiser’.

[3] As we shall discuss further below, the relevant modality here is physical—that is, a physical system serving as a clock (e.g. the Earth revolving around the Sun) is possible if its existence is allowed by physical laws.

[4] The notion of logical relations between concepts, which may be seen as a kind of implicit definitions, is inspired by Zinkernagel (1962).

[5] Since my interest here is in the time concept employed in ordinary practical language and physics, I shall (almost) disregard psychological, poetic or religious uses of the term. As concerns our psychological notion of time (associated with changes in mental states) I here assume that mental changes are somehow correlated with physical changes.

[6] Note that the concepts ‘constant or regular process’, and of course ‘equal time intervals’ refer to time—illustrating again that the concepts of ‘time’ and ‘clocks’ are interrelated but not reducible to one or the other. One may speak also of ‘order’—as opposed to ‘metric’—clocks which can only determine earlier/simultaneous/later relations, and in this sense the clocks need not necessarily be capable of determining equal time intervals. The clocks of ordinary life also include some kind of counter (e.g. a clock dial) to register the increments of time. I am here only interested in the first (core) component of a clock, namely the physical process in the clock’s interior (see also below and Rugh and Zinkernagel forthcoming).

[7] For instance, it makes sense to say ‘the amount of time given by the explosion’ or speak of ‘before or after the explosion’.

[8] In an influential paper, Shoemaker (1969) argued that time without change is possible, that is, that one can think of situations (e.g. a total freeze of some fantasy world) where the time concept can be meaningfully applied without referring to any change. Shoemaker’s argument may perhaps be seen as another instance of the second type of objection to the time–clock relation (since duration statements in Shoemaker’s fantasy world appear to be specified in terms of clocks: see Shoemaker 1969, 370). However, although I cannot here argue the point in detail, I think Shoemaker’s argument fails as no satisfactory account is given of what time, and specific time intervals like a year, means ‘during’ a putative total freeze in his fantasy world. Candidates would include ‘time is what a clock would have measured had the world not been frozen’. But since, by hypothesis, no clock can operate ‘during’ a total freeze, the only option for explicating this counterfactual definition seems to be to appeal to other (nearby) possible worlds in which no total freeze (but only, say, an almost total freeze) is taking place. However, as will be discussed in the section on ‘counterfactual time’ below, it is questionable whether times in different possible worlds can be identified (and thus, it is questionable whether one can say that time has passed ‘during’ a total freeze).

[9] Alternatively, or additionally, one may try to reinterpret ‘time’s flowing’. For instance, Earman (1989, 7–8) holds that time’s flow should be read as absolute simultaneity, absolute duration, and there being an intrinsic (e.g. independent of clocks) temporal metric.

[10] Both free particle motion and ephemeris time are connected to the idea of an implicit definition of (absolute) time via laws. As discussed in detail in Rugh and Zinkernagel (forthcoming, sec. 2.1), such implicit definitions of time via laws—as illustrated by ephemeris time—make essential reference to physical systems which can function as clocks and hence an implicit definition of time via laws is in conformity with the time–clock relation.

[11] In practice, there are more idealizations involved in the identification—e.g. connected to general relativistic corrections and limited observational accuracy of the positions of the solar system bodies; see e.g. Audoin and Guinot (2001, 46ff.) (ephemeris time actually served as the official astronomical time standard in the 1960s before the advent of atomic clocks).

[12] Note that there are mathematically trivial ways of changing a representation from that of the positive real line to that of the whole real line, e.g. by using the transformation t → log(t). Such transformations, however, cannot in any relevant sense be used to address times ‘before’ the big bang.

[13] See also the algebraist Cayley in his Presidential Address to the British Association in 1883: ‘It appears to me that we do not have in Mathematics the notion of time until we bring it there’ (quoted from Withrow 1980, 176).

[14] Underdetermination‐type arguments have also been put forth within the context of the general theory of relativity: As noted e.g. by Hoefer (1996, 11) there is nothing inherent in a mathematical manifold which distinguishes space and time (and so it is unclear how the pure manifold could somehow be the ‘representator’ of time). Grünbaum (1977, 356–357) has argued that the formal properties of the g_µν (gravitational) field in general relativity are insufficient to determine that this g_µν field is also the metric tensor of space‐time (rather, Grünbaum suggests, this role is only secured by making reference to the behaviour of external metrical standards like rods and clocks).

[15] By contrast, within the context of general relativity, modern substantivalists may well agree, insofar as they assign the metric tensor a role in representing (space and) time, that there can be no time ‘before’ the universe (before the big bang). This is so since physically interesting space‐times (metric tensors) are confined to those—like the one underlying big bang cosmology—which satisfy Einstein’s equations, and since the metric of the big bang model cannot be extrapolated back (there is no container) ‘before’ the beginning of the universe; see e.g. Earman (1977) and below. I shall not here take issue with this kind of substantivalism (see however the discussion in Rugh and Zinkernagel forthcoming, sec. 2).

[16] Kant’s theory of time—which is not substantivalist—is too complex to be considered here in any detail. I should note, however, that Kant’s central claim that ‘time is nothing but the inner sense [… and] the formal a priori condition of all appearances’ cannot allow for time before the universe (even though this is a presupposition of both horns of Kant’s first antinomy, see e.g. Newton‐Smith 1980, 101) if we assume that minds (and their accompanying bodies) appeared after the universe came into existence—since, on Kant’s account, there cannot be time without minds (and hence not before minds).

[17] It is a matter of debate whether relationism is compatible with an empty universe without any actual physical objects or events (or whether, rather, such a universe would make substantivalism and relationism indistinguishable, see e.g Earman 1989, 135). In the context of big bang cosmology we can sidestep this question since—as pointed out in note 15 above—there is no container ‘before’ the beginning (and thus there is no empty universe waiting to be populated ‘before’ the big bang).

[18] Again, this assumption might be denied on dualistic and/or theological grounds, e.g. by holding that minds (or some supreme mind) are independent of bodies and eternal. But this would—at least—require a convincing account of how minds and/or God exist, and how this existence relates to our usual notion of time.

[19] A similar idea about time before a first event was formulated already by Locke in 1689—see e.g. van Fraassen (1970, 27). Another example of using counterfactuals to address time before the big bang can be found in Lucas (1999, 15).

[20] This is even a physically possible world, since no laws necessarily have to be changed: a rough estimate of the age of the universe is given by the present value of the inverse Hubble parameter (see e.g. Peacock 1999, 127). This parameter is a measure of the rate of the universal expansion, and its value is determined observationally. The value of the Hubble parameter can be taken to be part of the (contingent) boundary or initial conditions for the physical laws in our universe, and it takes no great leap of imagination to think of this value as being different from what it actually is.

[21] This subsection is based on Rugh and Zinkernagel (forthcoming).

[22] The Hubble law supports the idea of the expansion of the universe through a relation between the t parameter and the cosmic scale factor (which, for a closed Friedmann model, is equal to the radius of the universe). The change in the scale factor (the clock), in turn, is given physical significance via redshifted light (i.e. frequency changes in electromagnetic radiation monitor the expansion). The light nuclei abundances in the universe are compatible with a hot primordial origin of these elements when seen in the light of a relation between t and temperature (thus, temperature here acts as a clock). Similarly, the microwave background radiation is thought to be a consequence of a drop in temperature at an early time allowing for a decoupling between matter and radiation.

[23] In fact, the necessity of (possible) rods and clocks for setting up the FLRW model suggests that it might not even be possible to extrapolate the t ↔ time interpretation all the way back to the Planck scale (unless speculative physics is invoked): current theories (the standard model of particle physics) indicate that the physical conditions no longer allow for (metric) rods and clocks when the FLRW model is extrapolated back to 10¹¹ seconds, corresponding to the so‐called Higgs transition before which the universe might become scale invariant (Rugh and Zinkernagel forthcoming, sec. 5).

[24] According to these ideas, the big bang is identified with the beginning of the expansion at the Planck scale. For a popular overview of pre‐big bang cosmology (and the so‐called ekpyrotic scenario—which is a modern string theory inspired version of the cyclic model) see e.g. Veneziano (2004).

[25] Providing such an account is not made easier by the fact that chaotic inflation relies on Planck scale physics (see e.g. Peacock 1999, 336–337)—and the scenario may therefore be susceptible also to the problems mentioned above concerning time in quantum gravity.

[26] In a similar manner, Rugh (pers. commun.) has emphasized the difficulties in extrapolating physical concepts from our universe to other parts of the multiverse.