Paper I
ABSTRACT. In paper I, I adopted the strategy of assuming that God is not timeless, and seeking to describe the nature of God’s time before going on to deal with physical time in the present paper. Physical time is treated as an independent variable derived from God’s unmeasured time by a ‘program for becoming’, using the tree of actualizable worlds. The program actualizes physical time as a growing sequence of ‘chronons’, or intervals of little happening. This gives a universe awaiting scientific investigation. The result is thus a kind of low-level theory of a world with an objective, advancing, universal present, as in the A-theory of time. It is shown how the content of the present may appear in a spacelike hypersurface. The model is independent of many theological and philosophical positions, and it resolves several questions about time. In this version of the paper the terminology has been modified to speak of the present as unique.* The content of the present is called a juncture, and is variable.
1 Introduction. 2 God’s time. 3 Physical time. 4 Theoretical present. 5 Applications. 6 Concluding remarks. 7 Notes and references.
1 Introduction
On the assumption that God is not wholly atemporal, a number of writers have produced models of God’s time in its relation to physical time[1].
J. R. Lucas argues that God’s omniscience must involve a “divinely preferred frame of reference”, without doing any damage to the Special Theory of Relativity (STR)[2].
William Lane Craig suggests that cosmic time in the General Theory of Relativity (GTR) coincides with God’s metaphysical time since creation[3]. Craig has more recently suggested that the identification of cosmic time in GTR with Newtonian absolute time, as God’s time, is strengthened by the following interesting fact. The relativistic expansion of the universe in the simple case of the Robertson-Walker metric with no pressure, is reproduced by Newtonian gravitation and fluid mechanics, when applied to a Euclidean space containing a spatially homogeneous fluid (with an additional force to bring in the cosmological constant)[4]. I do not accept this argument, for reasons such as (i) the universe is not a smoothed-out fluid, as the equations require. Physicists love approximations, but God sees every detail; (ii) for other than the case of flat space, GTR deals with a different configuration of matter; (iii) Einstein formulated his field equations to give Newtonian gravitation in the classical limit, so the coincidence is best seen as a mathematical quirk in a special case. In my model, Newtonian absolute time - which “flows equably”[5] - simply does not exist.
In Alan Padgett’s model, “God ... is not measured by our time”[6], but “every moment of our time is simultaneous with a moment of God’s time”[7].
Garrett DeWeese holds that after creation, God’s time, or metaphysical time, is the ground of physical time, and they are in one-to-one correspondence. He argues that time coordinates in the Special Theory of Relativity (STR) might not measure metaphysical time, or absolute simultaneity might be found in the Lorentz interpretation of STR, or it might be given by cosmic time in GTR[8].
In all these models, there is a direct connection between God's time and physical time (or the theoretical cosmic time). In my model things are more complicated, as explained in section 3. Also, the above suggestions explicitly or implicitly take God’s time to have the structure of an interval of the real numbers. My model avoids that as unwarranted speculation. I have used many of the main concepts of this paper in earlier papers[9; Time]. Here they are used in a different way in order to eliminate unnecessary speculation and apply a slightly different terminology. This paper presents the essence of the model.
2 God’s time
God’s time was defined in paper I as a growing sequence of what will be called God’s junctures (or ‘divine junctures’, for a simpler singular form). No metric applies to divine junctures, so God’s time is unmeasured (cf. Table 1). The advance of junctures in the present enables us to say that “the present is advancing”. The structure of the class of God’s junctures is unknowable, but we can talk about God’s time as follows. In the abstract, God’s time at any stage exists partitioned into arbitrary intervals of little happening, called kairons. Any such partition provides a growing sequence of kairons. Starting from some chosen kairon, a sequence may be indexed by ordinals.
In an earlier paper[9], I suggested that pressure of time for agents in a non-physical world would be avoided if time were partially ordered and each agent had their own time line. This, however, makes it difficult to understand communication between such beings. Having too little or too much time, and the problems of a metric of time, are avoided by postulating that God’s time is ordered and unmeasured.
| Table 1. God’s time and physical time |
 |
3 Physical time
There is only one time, God’s time, and all other forms and aspects of time derive from it. In the model of this paper, God’s advancing present is the source of an objective, advancing, universal present in the physical world - but not in a simple way. By ‘physical time’ I do not mean anything like Greenwich Mean Time, or any time variable in a scientific theory. I mean the temporality of the physical world, prior to any scientific theory. As the world is actualized, the content of the present is a sequence of sets of events, the physical junctures (or simply, junctures). Just as for God’s time, the structure of the class of junctures is unknowable. So, as before, we may think of a growing sequence of intervals of little happening, called chronons (Table 1). The connection between God’s time and physical time is through a program for becoming. The definition of a chronon here is different from the familiar one of ‘a least interval of time’, although that could be a chronon in my sense. In the model, each chronon is specified during the running of the program for becoming, which will now be described.
A possible world is a possible total course of events, in the abstract. At each juncture, he past is fixed, but there are many possible futures. Hence the possible worlds at a particular juncture form a tree, as in Fig. 1, where the future may have many branches. An actualizable world is a possible world that God might choose to actualize. The actual world is the world developing as a result of these choices. At some stage before creation, God made the following preliminary decisions (PD):
PD. God creates the abstract tree of all possible worlds (hence God knows all that is possible);
God selects the subtree of actualizable worlds (hence all God’s purposes will be fulfilled in this model, whatever world may be actualized). Each actualizable world has its own sequence of junctures.
First chronon. In the schematic diagrams of Fig. 2, p(0) is either the first juncture (i.e., at creation) or the earlier limit of all junctures. p(1) denotes the juncture chosen for the actual world at the [later] end of the chronon with ordinal number 1 (i.e. ‘chronon 1’). This is in fact the first chronon in the physical world. Between p(0) and any p(1) there might be many junctures, and there can be many branchings of the tree of actualizable worlds; but there is only one world connecting p(0) to p(1). The first chronon may be represented schematically as a half-open interval of junctures (p(0), p(1)].
There are two ways in which this chronon may be actualized. Either the content of the present changes through a subinterval of junctures, or it changes according to the AB-theory of time (giving an ‘AB-chronon’, which does not have that sequence of junctures. Note that each chronon will contain at least one juncture, and ends with a juncture.
General chronon. Similarly, p(χ) is the juncture in the actual world at the end of chronon χ, and p(χ + 1) is to be chosen from the actualizable junctures as the end of the next chronon. As before, only one world connects p(χ) to p(χ + 1). Chronon χ + 1 is the half-open interval (p(χ), p(χ + 1)], and it is actualized in one of the two ways already described.
The program for becoming models the temporal progress of the actual world by analogy to a computer program with external input, where the program has a loop The program runs in God’s time, and is executed by God. A simple phenomenological[a] form of the program, with notes, looks like this:
1. Put χ = 0, p = p(0) (as initial juncture, or lower limit of junctures if there is an initial singularity)
2. Consider all agents’ choices and wishes, and any relevant laws of nature (see discussion below)
3. Choose a juncture p(χ + 1) in an actualizable world (this juncture is to be the end of chronon χ + 1)
4. Actualize chronon χ + 1 (as explained above)
5. Put χ = χ + 1
6. Go to 2
Whatever input comes at statement 2, the program leaves God free to make a choice at statement 3, and to allow secondary causes and relevant laws of nature as God wishes. Statement 3 applies even if there is only one actualizable world, as in Calvinism, Molinism in its third moment, and physical determinism. Hence the model admits a very wide variety of theologies and philosophies, with all possible degrees of involvement by God and created agents.
God’s sovereignty and human freedom is not the subject of this paper, but it may be mentioned that the concept of actualizable worlds allows a precise and powerful definition of ‘strong freedom for an agent at a juncture’, as the existence at that juncture of two or more actualizable worlds in which the agent’s life differs. If God knew what the agent would do, only one world would be actualizable. Hence any employment of strong freedom requires God’s input at the time. Strong freedom need not obtain for all agents at all times, and could be unexceptionable if, for instance, it involves actions which are inconsequential, or which represent different routes to God’s final purposes. Actions which could be inconsequential include standing at two very close locations, or thinking two slightly different thoughts. If God is atemporal, there is no ‘strong freedom’.
Between each execution of statement 4, there is a sequence of God’s junctures during which there is no lapse of physical time. How can this start-stop unmeasured sequence of chronons in God’s time produce continual happening in the physical world? The answer lies in the concept of an independent variable. In physics, a point particle moving with constant velocity v travels a distance vt in time t. The distance is a dependent variable, depending on the independent variable t. Hence I postulate that physical time is an independent variable for all processes in the created world.
The situation is somewhat similar to a television drama with commercial breaks. The commercial break is like going round the loop in God’s time to the next execution of statement 4, and the drama advancing in its own time is like the actualization (i.e., happening) of the chronon. As described here, the connection between God’s time and physical time is fuzzy, as indicated in Fig. 3.
The program does not allow a one-to-one correspondence between the physical junctures and God’s junctures. This shows that even if physical time has a measure, this does not provide a measure for God’s time in the model.
An independent variable has no need of a rate of change. Consequently, the teasing question “How fast does time flow?”, has no meaning. The model depicts a dynamic observable world, not a scientific theory of it. The history of science shows how time is measured and how it is used in theories.
4 Theoretical present
Applying the model to physical theories involves theoretical junctures having the cardinality of the real numbers (unless discrete time is used). The time in these theories may be termed ‘theoretical time’. Our observations and theories are coarse-grained, and there is no guarantee that the events in any theoretical juncture would map into those happening in the physical present. It is something like the motion of a model car compared to the motion of the real car: if the model car is not to scale, no changes in position and configuration agree exactly[b].
To avoid an obvious objection, I shall now show how, even in the theory of relativity, it is perfectly possible for the physical world to have the familiar past, present, and future that are objective and universal. To start with a particular example, traditional models of the expanding universe in GTR use simple forms of curved three-dimensional space and a universal ‘cosmic time’ that measures the expansion of this space. Craig argues that this cosmic time is a measure of God’s time (see section 1). Hence simultaneity in cosmic time conveniently characterizes both space and a theoretical present. In this cosmology, three-dimensional space is a particular spacelike hypersurface in the relativistic manifold. As Craig also allows, many families of spacelike hypersurfaces provide different choices for cosmic time, and hence for the family of theoretical junctures. There is a natural tendency to deprecate any choice for an absolute time other than cosmic time, because of its simplicity[10]. However, consider the following situation:
In a small region of space-time there is an inertial frame with cosmic time as its time coordinate.
After a Lorentz transformation from this frame to the frame of some observer, many pairs of events in the theoretical present have different time coordinates.
This separation of time measure from happening is something Einstein never considered.
The relativity of simultaneity is a perfectly good part of STR, but what it proves is merely that the present is not characterized locally by simultaneity in each frame.
I therefore claim that any suitable family of spacelike hypersurfaces is a genuine candidate for the family of theoretical junctures[11]. This means that the present need not be characterized by simultaneity in any time coordinate whatsoever. The ordering of a sequence of junctures, whether ‘theoretical’ or ‘physical’, is logically independent of the ordering of any time coordinate. Hence we retain results like the relativity of simultaneity in different time coordinates. The proposal that the present is characterized by simultaneity in cosmic time is a reasonable hypothesis for use with the cosmological models available to us, but is not the only possible hypothesis. In any case, it is clear that current theory is perfectly able to include a theoretical present. The exact location of any juncture is an empirical matter, and is as yet unknown.[12]
When GTR is used, the actualizable worlds in a branching future can be modelled by a tree of actualizable space-times, branching at junctures[9a].
5 Applications
A few applications involving physics, some with reference to God:
(1) Traditional QM treats time as a parameter, while other variables become operators. The existence of an objective past, present, and future makes it possible to locate the collapse of the wave-function in a juncture (i.e., collapse is in the present)[9a], but how far the model can be applied to QM remains to be seen.
(2)The model removes the strangeness from Feynman’s time reversal[9a]. G. J. Whitrow has given a non-technical description of this[13]. A photon turns into an electron and a positron. The positron and another electron collide and become a second photon. Quantum Mechanics (QM) allows the world-lines of the positron and two electrons to be interpreted as the world-line of a single electron moving backwards and forwards, respectively, in the time coordinate of an inertial frame. However, all the particles move forward in the time shown by a laboratory clock, and my model makes this the reality of the situation. It is also clear that under an A-theory of physical time, time reversal can describe only processes that are in the past or merely postulated. It may be noted that a particular relativistic space-time does not undergo any change in itself. The four-dimensional space-time manifold exists in the abstract world of mathematics as a sophisticated graph of space against time, from which changes can be read off[14].
(3) In connection with quantum gravity and the Hartle-Hawking no-boundary condition, the use of imaginary time gives the impression that the universe has no beginning in physical time. A paper from Stephen Hawking’s university department puts it like this, where an ‘instanton’ is 4-dimensional but Euclidean:
“Note that the concept of time does not arise in this process” [i.e., the quantum process of universe creation]. “Universe creation is not something that takes place inside some bigger spacetime arena - the instanton describes the spontaneous appearance of a universe from literally nothing. Once the universe exists, quantum cosmology can be approximated by general relativity so time appears”[15].
There may not be a bigger space-time arena, but the model provides a transcendental arena, with the advance of God’s time. I have given a rough sketch of this approach in an earlier paper. Hence initially an puzzling concepts like imaginary time and Feynman’s time reversal are no more than neat mathematical manipulations.
(4) The distinction between physical time and God’s time in the model also dissolves a technical problem raised by Quentin Smith about the relation between God and the world. Quentin Smith has argued that if God exists in time, and time branches, then God cannot exist in more than one branch, because God is a particular. He points out that this may be a real problem, since some cosmogonies use branching time, and may allow some branches to reconverge[16]. First of all, the model does not make God exist in physical time, but God’s time exists in God.
Secondly, such theoretical branches form a partially ordered set of instants, with the cardinality of the continuum. Suppose there really is branching time, with a physical present in each branch. In the model, God’s time is totally ordered time. Now, any partially ordered set of junctures is contained in a totally ordered set, by Szpilrajn’s theorem[17]. (Fig. 3 shows two elementary cases, but Szpilrajn covered the general case.) Then the program for becoming could generate this totally ordered set as easily as it can produce totally ordered physical time. As God’s time advanced, the totally ordered junctures would be actualized in their appropriate branches, and in this way generate partially ordered physical time.
Some other applications:
(5)The objective reality of the present is important for tense logic, including its use of possible worlds[18].
(6) The existence of two forms of time makes for some useful linguistic distinctions. It is proper to say ‘before the foundation of the world’[19], referring to God’s time, but saying that the world was created ‘not in time, but with time’, refers to physical time[20].
6 Concluding remarks
The model developed here shares several properties with the models of earlier writers. It provides an A-theory of physical time, derived from an A-theory of God’s time. It shows once again that the concept of God's time as different from physical time gives us a different and helpful perspective on many matters. It explains why time advances at all: its dynamic is in God’s life. This also explains the arrow of time. The model gives an explanation of how God can have completed a beginningless past, but has an endless future. . The model does suggest that our possible comprehension of the physical world is limited. I hope the model will stimulate further thought.
I am grateful to Brian Pitts, Mogens Wegener, and two early correspondents whose names I have regretfully mislaid, for helpful discussions. Any remaining errors are my own.
7 Notes and references
* I owe this point to Mogens Wegener.
[a] ‘Phenomenological’ in the sense used in theoretical physics for a phenomenological theory which “saves the phenomena”.
[b] Let a car of length l travel a distance d (in units of its length) when its wheels of radius r turn through θ radians. Then d = (r/l)θ, and for θ ≠ 0 the pair (d, θ) is always different for the car and the toy that is not to scale. I take this to be an analogy of the relation between a scientific theory and reality.
[1] Reasons for taking this stance are conveniently expounded in Alan G. Padgett, God, Eternity and the Nature of Time (New York: St Martin’s Press, 1992; repr., Eugene, OR: Wipf and Stock, 2000); and William Lane Craig, Time and Eternity: Exploring God’s Relationship to Time (Wheaton, IL: Crossway, 2001); see also Craig’s papers at http://www.leaderu.com/offices/billcraig/menus/eternity.html (accessed 2 May, 2008).
[2] J. R. Lucas, The Future: An Essay on God, Temporality and Truth (Oxford: Blackwell, 1989}, p. 220.
[3] William Lane Craig, “Divine Eternity and the General Theory of Relativity,” Faith and Philosophy 22 (2005), pp. 543-557 (at p. 552); cf. Time and Eternity, p.66; “The Elimination of Absolute Time by the Special Theory of Relativity,” in Gregory E. Ganssle and David M. Woodruff, eds., God and Time: Essays on the Divine Nature (Oxford: O. U. P., 2002), pp. 129-152 (at p. 147).
[4] Craig, Time and Eternity, pp. 64-65; “Divine Eternity”, p. 554; H. Bondi, Cosmology (Cambridge: University Press, 1952), p. 104.
[5] Isaac Newton, Scholium to the definitions in Philosophiae Naturalis Principia Mathematica, Bk. 1 (1689); trans. Andrew Motte (1729), rev. Florian Cajori (Berkeley: University of California Press, 1934), quoted in Arthur Danto and Sidney Morgenbesser, Philosophy of Science (Cleveland, OH: Meridian, 7th printing 1967), p. 322.
[6] Alan G. Padgett, God, Eternity, p. 127.
[7] Padgett, “Response to Critics,” in Gregory E. Ganssle, ed., God & Time: Four Views (Downers Grove, IL: InterVarsity, 2001), pp. 124-128 (at p. 126). Perhaps Padgett means that, conversely, every moment of an interval of God’s time is simultaneous with a moment of our time. If not, then his concept is similar to mine (see section 3 of this paper).
[8] DeWeese, God and the Nature of Time (Aldershot, England: Ashgate, 2004), pp. 60, 68-69, 252-253. DeWeese also gives a detailed account of other writers’ views.
[9][9a] Anthony P. Stone, “A Program Model of Becoming,” Physics Essays 10 (1997), pp. 150-163. There is a very brief further explanation: “Erratum: A Program Model of Becoming,” ibid., 11 (1998), p. 180, [add: clarifying that RP always means reinterpretation principle, and that the idea of the [subjective] present as a spacelike hypersurface was used by Fred & G. Hoyle in a science fiction novel Fifth Planet (London: Heinemann, 1963), p. vii]. This paper includes a detailed discussion of an objective universal present in relativity. It refers to the “highest agent”.
[10] Cf. Craig, “Divine Eternity,” n.14, pp. 555-556.
[11] Provided each such juncture divides space-time into past and future. Other space-times may be regarded as non-physical. For more details see Stone, “Program Model.” In the Preface to their 1963 science fiction novel Fifth Planet (London: Heinemann, 1963), p. vii, Fred Hoyle and Geoffrey Hoyle suggested that spacelike hypersufaces could give the subjective (and perhaps merely local) present, but the idea works equally well in a wider context.
[12] There is some work on GTR with absolute simultaneity, e.g., J. Brian Pitts, “Some Thoughts on Relativity and the Flow of Time: Einstein's Equations given Absolute Simultaneity,” (Philosophy of Time Society meeting at APA Central Chicago, April 2004), http://philsci-archive.pitt.edu/archive/00002760/01/ReaTimePTS.pdf, July 26, 2004 (accessed 2 May, 2008).
[13] G. J. Whitrow, The Natural Philosophy of Time, 2nd ed. (Oxford: Clarendon Press, 1980, repr. 1990), pp. 332-335.
[14] Or, as Richard Swinburne says, space-time is “a mere convenient calculating device.” Swinburne, Space and Time, 2nd ed. (New York, NY: St. Martin’s Press, 1981), p. 237.
[15] Cambridge Relativity: Quantum Gravity. “Quantum Cosmology,” http://www.damtp.cam.ac.uk/user/gr/public/qg_qc.html (accessed 2 May, 2008).
[16] Quentin Smith, “A New Typology of Atemporal Permanence,” Noûs 23 (1989), pp. 307-30 (at pp. 311-312). Also at http://www.qsmithwmu.com/a_new_typology_of_temporal_and_atemporal_permanence.htm (accessed 2 May, 2008).
[17] E. Szpilrajn, “Sur l’extension de l’ordre partiel,” Fundamenta Mathematicae 16 (1930), pp. 386-389.
[18] See A. N. Prior, “The Syntax of Time Distinctions,” Franciscan Studies 18 (1958), pp. 105-120, on the need for the present in tense logic; and, in contrast, D. H. Mellor, “Special Relativity and Present Truth,” Analysis 34 (1974), pp. 74-77, for a statement of the view (which I deny) that STR does not allow this. Lucas, Future, for instance, uses trees of possible worlds (p. 135 and passim).
[19] Ephesians 1:4.
[20] Augustine, The City of God, 11.6.
Version 2.1 (with new text in red) Copyright (C) Anthony P. Stone 2008. This material may be freely used, provided the author is acknowledged.
Last updated: 25 November 2008