Abstract
Many physicists have thought that absolute time became otiose with the introduction of Special Relativity. William Lane Craig disagrees. Craig argues that although relativity is empirically adequate within a domain of application, relativity is literally false and should be supplanted by a Neo-Lorentzian alternative that allows for absolute time. Meanwhile, Craig and co-author James Sinclair have argued that physical cosmology supports the conclusion that physical reality began to exist at a finite time in the past. However, on their view, the beginning of physical reality requires the objective passage of absolute time, so that the beginning of physical reality stands or falls with Craig’s Neo-Lorentzian metaphysics. Here, I raise doubts about whether, given Craig’s Neo-Lorentzian metaphysics, physical cosmology could adequately support a beginning of physical reality within the finite past. Craig and Sinclair’s conception of the beginning of the universe requires a past boundary to the universe. A past boundary to the universe cannot be directly observed and so must be inferred from the observed matter-energy distribution in conjunction with auxilary hypotheses drawn from a substantive physical theory. Craig’s brand of Neo-Lorentzian has not been sufficiently well specified so as to infer either that there is a past boundary or that the boundary is located in the finite past. Consequently, Neo-Lorentzian implicitly introduces a form of skepticism that removes the ability that we might have otherwise had to infer a beginning of the universe. Furthermore, in analyzing traditional big bang models, I develop criteria that Neo-Lorentzians should deploy in thinking about the direction and duration of time in cosmological models generally. For my last task, I apply the same criteria to bounce cosmologies and show that Craig and Sinclair have been wrong to interpret bounce cosmologies as including a beginning of physical reality.
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Notes
The case that relativity and the A-theory of time are not compatible has been presented in various places, but see Rietdijk (1966) and Putnam (1967), Penrose (1989, 201, 303-304), Petkov (2006), Romero & Perez (2014). For work by physicists discussing Neo-Lorentzian theories, see Builder (1958, Prokhovnik (1963, 1964a, 1964b, 1973, 1986), Bell (1976), Maciel & Tiomno (1985, 1989a, 1989b). Balashov and Janssen (2003) have offered a masterful reply to Craig’s Neo-Lorentzianism, to which Craig replies in his Unpublished. For a recent critical discussion of the view that absolute time is better accommodated by General Relativity than by Special Relativity because absolute time can be associated with cosmic time, as maintained by Craig and certain other A-theorists, see Read and Qureshi-Hurst (2020).
Huggett and Wüthrich (2018) likewise argued that a variety of bounce cosmologies, particularly those developed utilizing loop quantum gravity, should be interpreted to involve a double bang and not a bounce. However, Huggett and Wüthrich’s interpretation, as well as their argument for their interpretation, relies on the view that, in loop quantum gravity, time is explicable in terms of yet more fundamental physical entities. Craig and Sinclair’s view involves a distinct metaphysics of time in which time is absolute and cannot be explicated in terms of yet more fundamental physical entities. Moreover, given that non-fundamentality of time in quantum gravity plausibly commits one to some variety of eternalism (see, e.g., Bihan 2020), Huggett and Wüthrich’s interpretation is plausibly incompatible with the universe having a beginning in Craig and Sinclair’s sense.
Of course, there are tenseless theories of change and perhaps one could utilize a tenseless theory of change to construct a tenseless conception of the beginning of time. Whatever one might think of the attempt to develop an account of the beginning of time utilizing a tenseless theory of change, my point is only that A-theorists typically think objective change, and so the universe coming into being, requires the A-theory of time.
Moreover, I take it that the A-theoretical conception of a beginning is particularly salient for theology. On many versions of A-theory, part of what it means for time to pass is (roughly) that each moment (somehow) produces a successor moment, with caveats for the possibility that time is continuous. And on the view that each moment must be produced – either by another moment or by something else – we can ask what could have produced the first segment of time, since the first segment of time could not have been produced by another time. Barring backwards causation – which may not be possible on the A-theory anyway – only some entity external to the temporal order could have produced the first segment of time.
For a defense of the view that the universe beginning to exist does not require tensed facts, see Loke (2017).
Neo-Lorentzianism does not, in itself, provide a conclusive answer to the debate between substantivalists and relationalists. As Read & Qureshi-Hurst (2020, 1) explain, absolute time is “defined as enshrining a universal present moment, objective temporal passage, and tensed facts”. Consequently, the existence of absolute space and absolute time do not entail that time is substantival, but does entail that spatial and temporal relations are observer independent.
To be sure, Neo-Lorentzianism is one among a number of different strategies that A-theorists might pursue in reply and A-theory might still be true if Neo-Lorentzianism is false; for recent surveys of possible replies, see Gilmore et al. (2016) and Baron (2018). Nonetheless, Craig has argued against alternative A-theoretic strategies so that, on his view, the A-theorist has no plausible choice but to opt for Neo-Lorentzianism and so for ANL.
An anonymous reviewer has brought to my attention that teleparallel gravity may offer another approach to redescribing relativistic effects as the result of forces, e.g., Knox (2011).
There are some additional nuances in Craig’s view, since Craig denies the existence of instants. We might have expected Craig to endorse the existence of instants given his presentism, but Craig has long maintained that instants do not exist. For example, Craig argues that “only intervals of time are real or present and that the present interval (of arbitrarily designated length) may be such that there is no such time as ‘the present’ simpliciter; it is always ‘the present hour’, ‘the present second’, etc. The process of division is potentially infinite and never arrives at instants” (Craig, 1993a, 260); also see Craig (2000a, 179-180). Craig maintains that time is gunky, i.e., that every interval of time has proper sub-intervals, and he maintains that time cannot be decomposed into instants one of which is the present. I confess that I find the conjunction of presentism and gunky time difficult to understand. For example, if presentism is the thesis that the only things that exist simpliciter are present and that there is no present simpliciter – as Craig’s gunky time seems to entail – does nothing exist simpliciter?
For Gosse, the view that we cannot empirically determine whether – or when – the universe began was part of a strategy to render a literal reading of the Bible compatible with evidence from geology that the Earth is older than the Biblical narrative appears to indicate. Nonetheless, Gosse’s strategy has never enjoyed popularity – as Russell wrote, “nobody can believe it” (Russell, 1961, 68) – and, in any case, is straightforwwardly incompatible with any attempt to empirically determine the age of either the Earth or the universe.
A similar point was previously raised in, e.g., Weingard (1979).
A divergence in the various curvature parameters is neither necessary nor sufficient for space-time to be singular (Earman, 1995; Curiel, 1999, 2021, Joshi, 2014). For example, so-called conical singularities are well-known examples of singularities without associated curvature pathology. However, the singularity that represents the “Big Bang” in cosmologically relevant space-times is associated with a divergence in the Ricci scalar and the energy density.
While the predictions of a theory within a specific domain may provide some inductive evidence that the theory will apply to neighboring domains, no one should have confidence that the theory will apply to domains that are arbitrarily distant. Consider approaching a point p where the energy density diverges. As one approaches p, one encounters arbitrarily large energy densities and so one inevitably encounters energy densities which surpass the domain of applicability of General Relativity before one reaches p. For that reason, ceteris paribus, we should doubt the predictions made by General Relativity within the vicinity of curvature singularities.
An anonymous reviewer suggests that we may have reasons for trusting our memory that differ from the reasons we have for trusting other sorts of records of the past. For example, perhaps we have some reason to think that God would ensure our memory of the past is veridical. If so, we may have reason to avoid truncating the past during any period that any person remembers without invoking a general prohibition on truncated space-times, so that we may be able to avoid a skeptical catastrophe without invoking a prohibition on truncated space-times. Nonetheless, we ordinarily take our empirical access to the past to be based on more than memories. Importantly, successful cosmological science requires ampliative inferences to time periods no mere mortal could remember, e.g., the early universe. Perhaps we could once more invoke God to secure the veridicality of our records or of other ampliative inferences we might make to the past, but this begins to look like yet another prohibition on truncated space-times, albeit a prohibition invoking theological premises. Craig and Sinclair are unlikely to pursue this route, for they utilize cosmological science in defense of God’s existence, and naturalists are unlikely to find a theological defense of a truncation prohibition principle convincing.
Perhaps one can object that, in General Relativity, other mathematical relationships can describe the way that matter-energy couples to chronogeometry than the geodesic equation, for example, by the source term in the Einstein Field Equation or the Raychaudhuri equation. And, arguably, the Raychaudhuri equation is more important for inferring singular behavior from the matter-energy distribution. But analogous conclusions follow; whatever auxiliary hypothesis one uses, so long as the auxiliary hypothesis follows from General Relativity, an inference to the actual, and not merely apparent, chronogeometry requires a realistic construal of General Relativity.
The exact logical relationship between the Einstein Field Equations and the geodesic equation has been the matter of some dispute. For example, the Geroch-Jang theorem, as well as various related results, show that, at least for space-times and matter satisfying a small set of realistic conditions, the motion of small massive bodies (e.g., test masses) satisfies the geodesic equation. See Geroch & Jang (1975), Ehlers & Geroch (2004), Brown (2005), Weatherall (2011, 2019), Malament (2012). For my purposes, the point is that General Relativity provides us with a set of mathematical principles, whatever their interrelationship might be, which, when realistically construed, allow us to infer chronogeometric structure from the mass-energy distribution.
Craig provides us with another reason for thinking that the fundamental chronogeometric structure is decoupled from the motion of test masses. Though Craig does not endorse Prokovnik’s views about gravity, Craig does maintain an instrumentalist interpretation of the relationship between the distribution of matter-energy and chronogeometric structure. For example, Craig writes that the “geometrization of gravitation” is only “a heuristic device” (Craig, 2001c, 189). Elsewhere, Craig and Sinclair explicitly deny the “view that gravity just is the curvature of an objectively real space-time” (emphasis is Craig and Sinclair’s) and instead argue that gravity is a force that operates between bodies situated in space (Craig and Sinclair, 2012, 104). If, as they write, the “geometrization of gravity” is a mere “heuristic device” and gravity is instead a force operating between bodies, then the dynamics of the matter-energy distribution should ultimately be explained in terms of a force instead of the coupling of the matter-energy distribution to space-time curvature demanded by the Einstein Field Equation.
I’m not sure what sort of forces Craig and Sinclair would put in place of space-time curvature; they never offer a fully worked out and mathematically precise alternative to General Relativity. Craig (2001c, 189) cites (Weinberg, 1972, vii), but Weinberg alternately states that his focus on geometry is a pedagogical strategy instead of a denial that gravity is the curvature of space-time (Weinberg 1972, viii) and that he is otherwise ambivalent concerning the metaphysical upshot of General Relativity: “The important thing is to be able to make predictions on the astronomers’ photographic plates, frequencies of spectral lines, and so on, and it simply doesn’t matter whether we ascribe these predictions to the effects of gravitational fields on the motion of planets and photons or to a curvature of space and time.” In other words, Weinberg’s attitude – at least as of 1972 – was that, instead of trying to determine the metaphysics of space-time, we should “shut up and calculate”. This is obviously not an attitude that friends of ANL can adopt. Moreover, Weinberg is no friend of Craig’s approach to relativity. Weinberg’s anti-metaphysical interpretation of relativity is likely the result of a wholesale anti-metaphysical attitude that would reject appeals to absolute time and absolute space. Elsewhere, Weinberg has argued that we should “score” physical theories against whether they satisfy Lorentz invariance (Weinberg 2003, 85) – whereas ANL only appears to, but does not actually, satisfy Lorentz invariance - and that we should think Einstein was rightly victorious in his debate with Lorentz (2003).
Perhaps I’ve moved too quickly here. As an anonymous reviewer points out, while Craig and Sinclair cannot infer that the Ricci scalar, or other curvature parameters, qua curvature of space-time, was arbitrarily large in the past, they may be able to infer that the Ricci scalar, or other curvature parameters, construed as some mixture of geometry and universal forces, was arbitrarily large.
Two comments can be made in reply. First, any argument from curvature pathology to singular behavior is weak because curvature pathology does not ensure a space-time singularity. Part of what matters for a boundary to space-time is that there is some “location” beyond which paths cannot be reasonably extended and yet “[...] no species of curvature pathology we know how to define is either necessary or sufficient for the existence of incomplete paths” (Curiel, 2021). For this reason, space-time singularities are now typically understood in terms of geodesic incompleteness and not in terms of curvature pathology. Second, a physical field can exhibit singular behavior without a corresponding boundary to time. For example, in classical electrodynamics, electric charges are singularities in the electric field. Classical electrodynamics is well-defined on Minkowski space-time, for which there is no past boundary. If we understand gμν as a physical field defined on a background absolute space and time, then, instead of attributing curvature pathology to an objectively real temporal boundary, curvature pathology can be attributed to a divergence in a physical field. In that case, we come to the analogy that I construct between ANL and the theory considered by Feynman, Pitts, and Schieve.
Or some other pathology in virtue of which space-time is not further extendable to the past in whatever sense turns out to be appropriate.
An anonymous reviewer objects that the CMC foliation might not be the foliation picked out by the cosmic microwave background, as stipulated by Craig and other authors. As the reviewer notes, the CMB picks out a foliation for which the density of a scalar field – representing the CMB – is roughly spatially homogeneous, whereas a CMC foliation picks out a time-slicing so that the Hubble expansion is spatially homogeneous. Consequently, the two procedures could pick out distinct foliations. Supposing the two procedures did pick out distinct foliations, we would have yet another criticism of Craig’s arguments and therefore further support to my own case against Craig’s ANL. Nonetheless, I can see two reasons to think that the two procedures do pick out the same – or approximately the same – foliation.
First, we are discussing FLRW space-times, that is, space-times that are exactly homogenous and isotropic. Suppose that there were a space-time in which the CMB were not isotropic so that an observer co-moving with the universe’s expansion would observe the CMB as being significantly “hotter” in one direction as compared with other directions. If the CMB were hotter in one direction than in another, then this would presumably be the result of an anisotropy in the matter-energy distribution. And if the matter-energy distribution is anisotropic, then the universe is not an FLRW space-time. So, while I agree that one could have had a CMB density that did not pick out a CMC foliation, I don’t see how that would have been possible in an FLRW space-time. And given that the universe we inhabit is well approximated by the FLRW ansatz on cosmological scales, if everything else I’ve said in this paragraph is correct, we have that the CMB density picks out a foliation that is at least well approximated by the CMC foliation.
Second, in the case of FLRW space-times, space-time is “naturally” foliated in a way that locally corresponds to observers at rest with respect to the universe’s expansion. This is the foliation that can be labeled with the cosmic time. And, as it turns out, at least in FLRW space-times, the surfaces of constant cosmic time are also surfaces of constant extrinsic scalar curvature. That is, the surfaces labeled by the cosmic time just are the CMC surfaces (Callender, 2017, 75). But then the surfaces labeled by the cosmic time are just those that are uniform with respect to the CMB.
As Roser describes,
[...] the initial data can only be given on a a slice of constant scalar extrinsic curvature [that is, a CMC hypersurface], or equivalently of constant T. If we take the idea of a theory of gravity described by three-dimensional space whose geometry evolves through time (rather than the four-covariant ‘spacetime’ picture) seriously, then the [fact that the initial data can only be given on a CMC hypersurface] strongly suggests that slices of constant T are slices of constant time, so that the foliation on which the initial-value problem can be solved is indeed the foliation that corresponds to stacking of spaces at consecutive instances. For if physical time corresponded to a different time variable, that is, if the reconstruction of spacetime from the space-through-time theory were not a reconstruction from a constant-mean-curvature foliation, then as a consequence initial data could not be specified at a single instance in time. This would pose a major conundrum for the notion of what determines the dynamics of a physical system (Roser, 2016, 49).
A cut-off scale does not necessarily imply Lorentz invariance violation; see, e.g., (Rovelli & Speziale, 2003).
An anonymous reviewer suggested a problem for the argument from IMPAPT. The argument from IMPAPT supposed that we could parallel transport, with respect to the Levi-Cevita connection, future directed tangent vectors from one space-time location to another. But, given the ANL proponent’s interpretation of the Levi-Cevita connection, we might have reason to doubt the veridicality of results drawn from parallel transporting, with respect to the Levi-Cevita connection, vectors to arbitrary space-time points. To put the point another way, the argument from IMPAPT assumed that General Relativity is empirically adequate for a sufficiently broad class of potential (and not necessarily actual) observers. But if General Relativity is not empirically adequate for a sufficiently broad class of potential observers, the argument from IMPAPT would not establish the global direction of time. Similar worries may likewise endanger the cogency of the argument from empirical adequacy. Nonetheless, without a mathematically and empirically sufficient formulation of a Neo-Lorentzian successor to General Relativity, I have difficulty seeing how friends of ANL could establish the global direction of time in any other way. In order to be generous to Craig and Sinclair, I will assume that General Relativity is empirically adequate for a sufficiently broad class of potential observers, so that the size of the class of observers for whom General Relativity is empirically adequate is no problem for establishing a global direction of time using the arguments from empirical adequacy and IMPAPT.
Caveats apply since, for example, for FLRW space-times, the CMC foliation is unique only for closed universes.
For example, on page 220 of Craig’s (2001a), Craig cites Qadir & Wheeler (1985) in support of Craig’s comments on cosmic time. While Qadir and Wheeler use the phrase ‘cosmic time’ in their paper, Qadir and Wheeler’s ‘cosmic time’ is York time. Despite Qadir and Wheeler’s placement of the Big Bang at past time-like infinity, Craig states – on the same page! – that cosmic time places the Big Bang at approximately fifteen billion years ago.
There may be worries about quantum indeterminacy. For example, perhaps there is no precise matter-energy distribution, with the consequence that the York time becomes ambiguous on small scales and so that no labeling could be exact. If so, we would be unable to define any candidate for the absolute time based on chronogeometric structure on sufficiently small spatio-temporal scales. Nonetheless, this would be an objection that applies equally to all possible candidates for absolute time and not to any specific candidate.
George Ellis and Rituparno Goswami have promoted a generalization of the cosmic time – the proper time co-moving gauge – as a candidate for the absolute time (Ellis & Goswami, 2014, 250). Ellis and Goswami’s proposal would apply to inhomogenous or anisotropic space-times. However, Ellis and Goswami’s proposal labels a distinct foliation from the CMC foliation. Moreover, while one might have expected that any surface in the foliation labeled by absolute time is a space-like surface, Ellis’s proposal has the bizarre consequence that, in inhomogenous space-times, some surfaces in the foliation Ellis’s proposal picks out may be time-like surfaces. Therefore, if the proper time co-moving gaugage corresponds to absolute time, some moments of time are time-like surfaces, which is implausible. For this reason, the York time parametrization of the CMC foliation is arguably superior or at least not inferior.
Craig Callendar and Casey McCoy object that in the de Sitter phase of an inflationary multiverse, all CMC surfaces have the same value of the York time (Callender & McCoy, 2021). If all of the CMC surfaces in the de Sitter phase have the same value of the York time, and the York time is identified with absolute time, then the awkward consequence follows that all of the CMC surfaces in the de Sitter phase are (somehow) simultaneous with one another. Nonetheless, Roser points out that an actual inflationary phase is only approximately de Sitter and that the York time really is “increasing during this cosmological period” (Roser, 2016, 50); also see Roser (2016, 76-79).
For example, Craig has considered a thought experiment in which the universe is a vast equilibrium gas with small, localized fluctuations from equilibrium. As Craig notes, for his reductionist interlocutors, there may be no sense in which a fluctuation at one time is either before or after a fluctuation at another distinct time. Craig thinks that an advantage of his anti-reductionism is that there would be a fact about which fluctuation is first regardless of how the universe’s entropy changes in the interim (Craig, 1999, 354). As Craig (1999) writes, “The fact that entropy states of a process range in value between higher and lower numbers tells us nothing about which values exist later”.
As I argued in my (2020a), not all bounce cosmologies do include a global reversal of the entropic arrow of the sort that would be undermined by an inductive inference of this kind.
Kristie Miller (2017) has recently offered a related argument. Miller argues that, independent of the supervenience of mental states on brain states, all versions of A-theory on offer suggest that the passage of time can make no relevant difference to our phenomenal experience. If she is right, then our experience of temporal passage does not provide a reliable guide to the direction in which time passes.
References
Afshordi, N. (2009). Cuscuton and low-energy limit of hořava-lifshitz gravity. Phys. Rev. D, 80, 081502. https://doi.org/10.1103/PhysRevD.80.081502.
Agullo, I., & Singh, P. (2017). Loop Quantum Cosmology. In A. Ashtekar J. Pullin (Eds.) Loop Quantum Gravity: The First 30 Years (pp. 183–240). World Scientific.
Albert, D. (1992). Quantum mechanics and experience. Harvard University Press.
Albert, D. (2000). Time and Chance. Harvard University Press.
Albert, D. (2015). After physics. Harvard University Press.
Ashtekar, A., & Singh, P. (2011). Loop quantum cosmology: a status report. Classical and Quantum Gravity, 28(21), 1–122.
Balashov, Y., & Janssen, M. (2003). Presentism and relativity. The British Journal for the Philosophy of Science, 54(2), 327–346.
Baron, S. (2017). Feel the flow. Synthese, 194, 609–630.
Baron, S. (2018). Time, physics, and philosophy: It’s all relative. Philosophy Compass 13(1).
Bastin, J. A. (1960). An extension of the newtonian law of gravitation. Mathematical Proceedings of the Cambridge Philosophical Society, 56(4), 401–409. https://doi.org/10.1017/S030500410003471X.
Beisbart, C. (2009). Can we justifiably assume the cosmological principle in order to break model underdetermination in cosmology?. Journal for General Philosophy of Science, 40(2), 175–205.
Bell, J. (1976). How to teach special relativity. Progress in Scientific Culture, 2(1), 1–13.
Bihan, B. L. (2020). String theory, loop quantum gravity and eternalism. European Journal for Philosophy of Science, 10(17), 1–22.
Borde, A., Guth, A. H., & Vilenkin, A. (2003). Inflationary Spacetimes Are Incomplete in Past Directions. Physical Review Letters, 90, 1–4.
Brandenberger, R., & Peter, P. (2017). Bouncing Cosmologies: Progress and Problems. Foundations of Physics, 47(6), 797–850.
Brown, H. (2005). Physical relativity: Space-time structure from a dynamical perspective. Clarendon Press.
Builder, G. (1958). The Constancy of the Velocity of Light. Australian Journal of Physics, 11, 457–480.
Butterfield, J. (2014). On under-determination in cosmology. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 46(A), 57–69.
Cai, Y.-F., & Wilson-Ewing, E. (2015). A ΛCDM bounce scenario. Journal of Cosmology and Astroparticle Physics, 1503, 006. https://doi.org/10.1088/1475-7516/2015/03/006, 1412.2914.
Callender, C. (2017). What makes time special?. Oxford University Press.
Callender, C., & McCoy, C. (2021). Time in Cosmology. In E. Knox A. Wilson (Eds.) The Routledge Companion to Philosophy of Physics. Routledge.
Carroll, S. (2021). Why Boltzmann Brains Are Bad. In S. Dasgupta, B. Weslake, & R. Dotan (Eds.) Current Controversies in Philosophy of Science (pp. 7–20). Routledge.
Carroll, S., & Craig, W. L. (2016). God and Cosmology: The Existence of God in Light of Contemporary Cosmology. In R. Stewart (Ed.) God and Cosmology: William Lane Craig and Sean Carroll in Dialogue (pp. 19–106). Fortress Press.
Castagnino, M., Lombardi, O., & Lara, L. (2003). The global arrow of time as a geometrical property of the universe. Foundations of Physics, 33 (6), 877–912.
Corda, C., & Cuesta, H. M. (February 2011). Inflation from R2 gravity: A new approach using nonlinear electrodynamics. Astroparticle Physics, 34, 587–590. https://doi.org/10.1016/j.astropartphys.2010.12.002, arXiv:1011.4801.
Craig, W. L. (1979). The Kalām Cosmological Argument. Macmillan Press.
Craig, W.L.s (1990). God and Real Time. Religious Studies, 26, 335–347.
Craig, W. L. (1992). God and the Initial Cosmological Singularity: A Reply to Quentin Smith. Faith and Philosophy, 9(2), 238–48.
Craig, W. L. (1993). A Criticism of the Cosmological Argument for God’s Non-Existence. In W.L. Craig Q. Smith (Eds.) Theism, Atheism, and Big Bang Cosmology (pp. 256–276). Oxford University Press.
Craig, W. L. (1993). The Finitude of the Past and God’s Existence. In W.L. Craig Q. Smith (Eds.) Theism, Atheism, and Big Bang Cosmology (pp. 3–76). Oxford University Press.
Craig, W. L. (1999). Temporal becoming and the direction of time. Philosophy & Theology, 11(2), 349–366.
Craig, W. L. (2000). The extent of the present. International Studies in the Philosophy of Science, 14(2), 165–185.
Craig, W. L. (2000). The Tensed Theory of Time: A Critical Examination. Springer.
Craig, W. L. (2001). God, Time, and Eternity. Springer.
Craig, W. L. (2001). Time and Eternity: Exploring God’s Relationship to Time. Crossway Books.
Craig, W. L. (2001). Time and the metaphysics of relativity. Springer.
Craig, W. L. (2002). Must The Beginning of the Universe Have a Personal Cause?: A Rejoinder. Faith and Philosophy, 19(1), 94–105.
Craig, W. L. (2007). Creation and Divine Action. In Routledge Companion to Philosophy of Religion (pp. 318–328). Routledge.
Craig, W. L. (2008). The metaphysics of special relativity: three views. In W.L. Craig Q. Smith (Eds.) Einstein, Relativity and Absolute Simultaneity (pp. 11–49). Routledge.
Craig, W. L. (2017). Bergson Was Right about Relativity (well, partly)!. In S. Gerogiorgakis (Ed.) Time and Tense: Unifying the Old and the New. Philosophia Verlag.
Craig, W. L. (a Unpublished). Response to McCall and Balashov. https://www.reasonablefaith.org/writings/scholarly-writings/divine-eternity/response-to-mccall-and-balashov/. Comments given at the Philosophy of Time group meeting at the September 2001 meeting of the American Philosophical Association.
Craig, W. L., & Sinclair, J. (2009). The Kalām cosmological argument. In W. L. Craig J. P. Moreland (Eds.) The Blackwell Companion to Natural Theology (pp. 101–201). Wiley-Blackwell.
Craig, W. L., & Sinclair, J. (2012). On Non-Singular Space-times and the Beginning of the Universe. In Y. Nagasawa (Ed.) Scientific Approaches to the Philosophy of Religion (pp. 95–142). Palgrave Macmillan.
Crisp, T. (2008). Presentism, eternalism and relativity physics. In W. L. Craig Q. Smith (Eds.) Einstein, Relativity and Absolute Simultaneity (pp. 262–278). Routledge.
Crisp, T. (2012). Temporal Passage: A Shape-Dynamic Account. Magyar Filozófiai Szemle, 56(4), 19–32.
Curiel, E. (1999). The analysis of singular spacetimes. Philosophy of Science, 66, S119–S145.
Curiel, E. (2021). Singularities and Black Holes. In E. N. Zalta (Ed.) The Stanford Encyclopedia of Philosophy. Spring 2021. Metaphysics Research Lab, Stanford University.
Dowker, F. (2020). Being and becoming on the road to quantum gravity; or, the birth of a baby is not a baby. In N. Huggett, K. Matsubara, & C. Wthrich (Eds.) Beyond Spacetime: The Foundations of Quantum Gravity (pp. 133–142). Cambridge University Press.
Earman, J. (1977). Till the End of Time. In J. Earman, C. Glymour, & J. Stachel (Eds.) Foundations of Space-Time Theories (pp. 109–133). University of Minnesota Press.
Earman, J. (1995). Bangs, Crunches, Whimpers, and Shrieks. Oxford University Press.
Ehlers, J., & Geroch, R. (2004). Equation of motion of small bodies in relativity. Annals of Physics, 309(1), 232–236.
Ellis, G., & Goswami, R. (2014). Spacetime and the passage of time. In A. Ashtekar V. Petkov (Eds.) Springer Handbook of Spacetime (pp. 243–264). Springer.
Feynman, R., Moringo, F., & Wagner, W. (2003). Feynman Lectures on Gravitation. CRC Press. Edited by Brian Hatfield.
Friedman, M. (1983). Foundations of space-time theories. Princeton University Press.
Geroch, R., & Jang, P. S. (1975). Motion of a body in general relativity. Journal of Mathematical Physics, 16(1), 65–67.
Gilmore, C., Costa, D., & Calosi, C. (2016). Relativity and Three Fourdimensionalisms. Philosophy Compass, 11(2), 102–.f120.
Godfrey-Smith, W. (1977). Beginning and Ceasing to Exist. Philosophical Studies, 32(4), 393–402.
Gosse, P. H. (1857). Omphalos: An attempt to untie the geological knot. John Von Voorst.
Halvorson, H., & Kragh, H. (2019). Cosmology and Theology. In E. N. Zalta (Ed.) The Stanford Encyclopedia of Philosophy. Spring 2019. Metaphysics Research Lab, Stanford University.
Hor̆ava, P. (2009). Quantum gravity at a Lifshitz point. Physical Review D, 79, 084008. https://doi.org/10.1103/PhysRevD.79.084008.
Huggett, N., & Wüthrich, C. (2018). The (A)temporal Emergence of Spacetime. Philosophy of Science, 85(5), 1190–1203.
Ijjas, A., & Steinhardt, P. (2017). Fully stable cosmological solutions with a non-singular classical bounce. Physics Letters B, 764(10), 289–294.
Ijjas, A., & Steinhardt, P. (2018). Bouncing cosmology made simple. Classical and Quantum Gravity, 35(13), 135004.
Ijjas, A., & Steinhardt, P. (2019). A new kind of cyclic universe. Physics Letters B, 795, 666–672.
Joshi, P. (2014). Spacetime Singularities. In A. Ashtekar V. Petkov (Eds.) Springer Handbook of Spacetime (pp. 409–436). Springer.
Knox, E. (2011). Newton-cartan theory and teleparallel gravity: The force of a formulation. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 42(4), 264–275.
Koperski, J. (2015). The physics of theism: God, physics, and the philosophy of science. Wiley Blackwell.
Leon, F. (2019). On Finitude, Topology, and Arbitrariness. In Is God the Best Explanation of Things? A Dialogue (pp. 53–70). Palgrave Macmillan.
Linford, D. (2020). Big Bounce or Double Bang? A Reply to Craig and Sinclair on the Interpretation of Bounce Cosmologies. Erkenntnis. https://doi.org/10.1007/s10670-020-00278-5.
Linford, D. (2020). The Kalōm Cosmological Argument Meets the Mentaculus. The British Journal for the Philosophy of Science. https://doi.org/10.1093/bjps/axaa005.
Lockwood, M. (2007). The Labyrinth of Time: Introducing the Universe. Oxford University Press.
Loewer, B. (2007). Counterfactuals and the Second Law. In H.s Price R. Corry (Eds.) Causation, Physics, and the Constitution of Reality: Russell’s Republic Revisited (pp. 293–326). Oxford University Press.
Loewer, B. (2012). The emergence of time’s arrows and special science laws from physics. Interface Focus, 2(1), 13–19.
Loewer, B. (Forthcoming). The mentaculus vision. In V. Allori (Ed.) Statistical mechanics and scientific explanation: Determinism, indeterminism and laws of nature. World Scientific.
Loke, A.T.sE. (2017). God and ultimate origins: A novel cosmological argument. Palgrave.
Maciel, A. K. A., & Tiomnio, J. (1985). Experiments to detect possible weak violations of special relativity. Physical Review Letters, 55(2), 143–146.
Maciel, A. K. A., & Tiomnio, J. (1989). Analysis of Absolute Space-Time Lorentz Theories. Foundations of Physics, 19(5), 505–519.
Maciel, A. K. A., & Tiomnio, J. (1989). Experimental Analysis of Absolute Space-Time Lorentz Theories. Foundations of Physics, 19(5), 521–530.
Malament, D. (1977). Observationally Indistinguishable Space-times. In J. Earman, C. Glymour, & J. Stachel (Eds.) Foundations of Space Time Theories (pp. 61–80). University of Minnesota Press.
Malament, D. (2012). A Remark About the Geodesic Principle in General Relativity. In Analysis and Interpretation in the Exact Sciences: Essays in Honour of William Demopoulos (pp. 245–252). Springer.
Manchak, J. (2009). Can We Know the Global Structure of Spacetime?. Studies in History and Philosophy of Modern Physics, 40, 53–56.
Manchak, J. (2011). What Is a Physically Reasonable Space-Time?. Philosophy of Science, 78(3), 410–420.
Manchak, J. (2021). General relativity as a collection of collections of models. In J. Madarász G. Székely (Eds.) Hajnal Andréka and István Németi on unity of science: from computing to relativity theory through algebraic logic. Springer.
Matthews, G. (1979). Time’s Arrow and the Structure of Space-time. Philosophy of Science, 46(1), 82–97.
Miller, K. (2017). Time Passages. Journal of Consciousness Studies, 24(3-4), 149–176.
Milne, E. (1948). Kinematic Relativity. Oxford University Press.
Misner, C. (1969). Absolute Zero of Time. Physical Review, 186 (5), 1328–1333.
Misner, C., Thorne, K., & Wheeler, J. (1973). Gravitation. Princeton University Press.
Monton, B. (2006). Presentism and Quantum Gravity. Philosophy and Foundations of Physics, 1, 263–280.
Monton, B. (2009). Seeking god in science: An atheist defends intelligent design. Broadview Press.
Mullins, R. (2011). Time and the Everlasting God. Pittsburgh Theological Journal, 3, 38–56.
Mullins, R. (2016). The end of the timeless god. Oxford University Press.
Newton, I. (1974). Mathematical principles of natural philosophy and his system of the world. University of California Press, translated by Motte, A., & Cajori, F.
Nilsson, N. A., & Czuchry, E. (2019). Hořava-lifshitz cosmology in light of new data. Physics of the Dark Universe, 23, 100253. https://doi.org/10.1016/j.dark.2018.100253, http://www.sciencedirect.com/science/article/pii/S2212686418300943.
Norton, J. (2011). Observationally indistinguishable spacetimes: A challenge for any inductivist. In G. Morgan (Ed.) Philosophy of Science Matters: The Philosophy of Peter Achinstein. Oxford University Press.
Norton, J. (2020). Philosophical Significance of the General Theory of Relativity or What does it all mean, again? Geometric Morals. Nullarbor Press. http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/significance_GR_geometry/significance_GR_geometry.html.
Oderberg, D. (2003). The Beginning of Existence. International Philosophical Quarterly, 43(2), 145–158.
Odintsov, S., & Oikonomou, V. (2015). ΛCDM bounce cosmology without ΛCDM: The case of modified gravity. Physical Review D, 91, 064036. https://doi.org/10.1103/PhysRevD.91.064036.
Oikonomou, V. (2015). Superbounce and loop quantum cosmology ekpyrosis from modified gravity. Astrophysics and Space Science, 359.
Penrose, R. (1989). The Emporer’s New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford University Press.
Petkov, V. (2006). Is There an Alternative to the Block Universe View?. Philosophy and Foundations of Physics, 1, 207–228.
Pitts, J. B. (2004). Some thoughts on relativity and the flow of time: Einstein’s equations given absolute simultaneity. http://philsci-archive.pitt.edu/2760/. Chronos: The Annual Proceedings of the Philosophy of Time Society 6 (2003-4). Paper from Philosophy of Time Society meeting, April 2004, at American Philosophical Association, Central Division meeting, Chicago.
Pitts, J. B. (2008). Why the Big Bang Singularity Does Not Help the Kalām Cosmological Argument for Theism. The British Journal for the Philosophy of Science, 59(4), 675–708.
Pitts, J. B. (2019). Space-time constructivism vs. modal provincialism: Or, how special relativistic theories needn’t show Minkowski chronogeometry. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 67, 191–198.
Pitts, J. B., & Schieve, W. C. (2003). Nonsingularity of Flat Robertson-Walker Models in the Special Relativistic Approach to Einstein’s Equations. Foundations of Physics, 33(9), 1315–1321.
Pitts, J. B., & Schieve, W. C. (2004). Null Cones and Einstein’s Equations in Minkowski Spacetime. Foundations of Physics, 34(2), 211–238.
Pitts, J. B., & Schieve, W. C. (2007). Universally coupled massive gravity. Theoretical and Mathematical Physics, 151(2), 700–717.
Poincaré, H. (2001). Science and Hypothesis. In S.J. Gould (Ed.) The Value of Science: Essential Writings of Henri Poincaré. Originally published in 1905. (pp. 2–178). Random House.
Poincaré, H. (2001). The Value of Science. In S.J. Gould (Ed.) The Value of Science: Essential Writings of Henri Poincaré. Originally published in 1913. (pp. 180–353). Random House.
Price, H. (1997). Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time. Oxford University Press.
Prokhovnik, S. J. (1963). The Case for an Aether. The British Journal for the Philosophy of Science, 14(55), 195–207.
Prokhovnik, S. J. (1964). A cosmological model of light propagation. Mathematical Proceedings of the Cambridge Philosophical Society, 60(2), 265–271.
Prokhovnik, S. J. (1964). Neo-Lorentzian Relativity. Journal of the Australian Mathematical Society, 5(2), 273–284.
Prokhovnik, S. J. (1973). Cosmology Versus Relativity – The Reference Frame Paradox. Foundations of Physics, 3(3), 351–358.
Prokhovnik, S. J. (1986). Light in einstein’s universe. D. Reidel Publishing Company.
Prosser, S. (2000). A new problem for the a-theory of time. Philosophical Quarterly, 50, 494–498.
Prosser, S. (2007). Could we experience the passage of time?. Ratio, 20, 75–90.
Prosser, S. (2013). Passage and perception. Nous, 47, 69–84.
Putnam, H. (1967). Time and Physical Geometry. Journal of Philosophy, 64, 240–247.
Qadir, A., & Wheeler, J. (1985). York’s Cosmic Time Versus Proper Time as Relevant to Changes in the Dimensionless “Constants”, K-Meson Decay, and the Unity of Black Holes and Big Crunch. In E. Gotsman G. Tauber (Eds.) From Su(3) To Gravity (pp. 383–394). Cambridge University Press.
Read, J., & Qureshi-Hurst, E. (2020). Getting tense about relativity. Synthese.
Reichenbach, H., Reichenbach, M., & Freund, J. (1958). The philosophy of space and time. Dover.
Reichenbach, H. (1971). The direction of time. University of California Press M. Reichenbach (Ed.).
Rietdijk, C. W. (1966). A rigorous proof of determinism derived from the special theory of relativity. Philosophy of Science, 4(33), 341–344.
Romero, G.s, & Pérez, D. (2014). Presentism meets black holes. European Journal for Philosophy of Science, 4, 293–308.
Roser, P. (2016). Gravitation and cosmology with York time. Doctoral dissertation from Clemson University.
Roser, P., & Valentini, A. (2017). Cosmological history in York time: inflation and perturbations. General Relativity and Gravitation 49(13).
Rovelli, C., & Speziale, S. (2003). Reconcile Planck scale discreteness and the Lorentz-Fitzgerald contraction. Physical Review D 67. https://doi.org/10.1103/PhysRevD.67.064019.
Russell, B. (1961). Religion and Science. Oxford University Press.
Saudek, D. (2020). Change, the Arrow of Time, and Divine Eternity in Light of Relativity Theory. Palgrave Macmillan.
Saunders, S. (2002). How Relativity Contradicts Presentism. Royal Institute of Philosophy Supplements, 50, 277–292.
Shtanov, Y., & Sahni, V. (2003). Bouncing braneworlds. Physics Letters B, 557(1-2), 1–6.
Smith, Q. (1985). On the Beginning of Time. Nous, 19(4), 579–584.
Steinhardt, P., & Turok, N.s. (2007). Endless Universe: Beyond the Big Bang – Rewriting Cosmic History. Broadway Books.
Steinhardt, P. J., & Turok, N. (2002). Cosmic evolution in a cyclic universe. Physical Review D, 65(12), 1–20.
Tawfik, A., & Dahab, E. A. E. (2017). FLRW Cosmology with Horava-Lifshitz Gravity: Impacts of Equations of State. International Journal of Theoretical Physics, 56, 2122–2139.
Valentini, A. (1996). Pilot-Wave Theory of Fields, Gravitation and Cosmology. In J. Cushing, A. Fine, & Sheldon Goldstein (Eds.) Bohmian Mechanics and Quantum Theory: An Appraisal. Springer.
Weatherall, J. O. (2011). On the status of the geodesic principle in Newtonian and relativistic physics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 42(4), 276–281.
Weatherall, J. O. (2019). Conservation, inertia, and spacetime geometry. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 67, 144–159.
Weatherall, J. O., & Manchak, J. B. (2014). The Geometry of Conventionality. Philosophy of Science, 81(2), 233–247.
Weinberg, S. (1972). Gravitation and cosmology: Principles and applications of the general theory of relativity. Wiley.
Weinberg, S. (2003). Facing up: Science and its cultural adversaries. Harvard University Press.
Weingard, R.s (1979). General Relativity and the Length of the Past. The British Journal for the Philosophy of Science, 30(2), 170–172.
Whitrow, G. (1961). The Natural Philosophy of Time.Thomas Nelson and Sons Ltd.
Wüthrich, C. (2010). No Presentism in Quantum Gravity. In V. Petkov (Ed.) Space, Time, and Spacetime: Physical and Philosophical Implications of Minkowski’s Unification of Space and Time. Springer.
Wüthrich, C. (2013). The fate of presentism in modern physics. In R. Ciunti, K. Miller, & G. Torrengo (Eds.) New Papers on the Present: Focus on Presentism. Philosophia.
York, J. Jr. (1972). Role of conformal three geometry in the dynamics of gravitation. Physical Review Letters, 28, 1082–1085. https://doi.org/10.1103/PhysRevLett.28.1082.
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Thanks to Levi Greenwood, Philipp Roser, George Gale, Felipe Leon, Jeffrey Brower, Martin Curd, and Jacqueline Mariña’s dissertation seminar for helpful discussions or feedback on this article.
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This paper is dedicated to my father, Paul Linford, who unfortunately passed away when this paper was accepted for publication. I love you, dad.
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Linford, D. Neo-Lorentzian relativity and the beginning of the universe. Euro Jnl Phil Sci 11, 111 (2021). https://doi.org/10.1007/s13194-021-00417-x
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DOI: https://doi.org/10.1007/s13194-021-00417-x