As has become clear in the preceding chapters, special and general relativity theory pose a double challenge to the philosophy of science: on the one hand, we need to “save the phenomena” and account for the familiar and intuitively obvious features of time, in particular its irretrievable flow from the future via the present to the past, or at least explain how the overwhelming impression arises that time has these features. On the other hand, this objective must be met without invoking any implausible physics in order to defend flowing time and to rescue absolute simultaneity from relativity theory. In this chapter, we will consider in greater detail different answers to this problem. Of course, it is not possible to give a comprehensive overview of the relevant literature, so I will concentrate on a few authors representing the principal options for addressing the problem of time and relativity theory: cosmic A-theory, the block universe model, and proposals towards a third option which incorporates elements of the other two.

1 Cosmic A-theory—in Search of the True Present Hypersurface

A-theorists assume a mind-independent passage of time from the future via the present into the past. In the context of spacetime physics, it is therefore necessary to defend the existence of absolute simultaneity in such a way that, for every moment in time, there is a hypersurface—which need not necessarily be a hyperplane, that is, a flat hypersurface—containing all events occurring at that moment, whose content is independent of the frame of reference. In particular, one such hypersurface defines the worldwide “now” which separates the past from the future and which can be thought of as a global “wave” of becoming. On the crest of this wave, the open future turns into the fixed past. I will use the term “cosmic A-theory” to refer to this view of time. To identify the necessary privileged hypersurfaces, cosmic A-theorists need to posit additional spacetime structure than that afforded by relativity theory. Several scholars, whose work is cited below, have advanced detailed proposals to that end.

An argumentative cornerstone of cosmic A-theory is the passage of time as experienced, with its intuitively obvious distinction between past, present, and future. Since this cannot be simply dismissed as illusory, proponents of this theory argue that there must be a global present. To quote the physicist Lee Smolin:

We have direct experience of the world in the present moment … it is … an undeniable feature of the natural world that qualia are experienced in moments which are experienced one at a time. This gives a privileged status to each moment of time, associated with each experience … This means that we have direct access to a feature of the presently present moment … Any description of nature that does not allow now to be intrinsically defined is an incomplete description of nature.Footnote 1

In a similar vein, the philosopher Dean W. Zimmerman, in his paper “Presentism and the space-time manifold”,Footnote 2 has presented an argument which starts from the experience of the passage of time and concludes that global hypersurfaces of simultaneity must exist.Footnote 3

How does the global passage of time in cosmic A-theory square with the lack of a frame-independent simultaneity in spacetime physics? Proponents of the theory have come up with several ideas for finding a physical basis for global time in spite of relativity theory. These can be divided into three groups:

The first is to use the cosmic time functions which emerge from general relativity theory given the fact that we are living in a homogenous and isotropic universe, as discussed in detail in Chap. 4. Authors such as William L. Craig,Footnote 4 as well as Dean W. Zimmerman,Footnote 5 argue that cosmic time is suited to provide the privileged frame needed for the universal past-present-future distinction. On this basis, Craig advances the case that cosmic time coincides with metaphysical time, which is also the time which God experiences. He corroborates his case for a privileged frame of reference by identifying two further “modern equivalents of the aether” suited to define it: the microwave background radiation, and the quantum mechanical vacuum.Footnote 6 Roberto M. Unger and Lee Smolin likewise use cosmology as an argument for a time which is “non-emergent, global, irreversible, and continuous”—indeed, it is so basic that it remains “when everything else leaves”.Footnote 7 According to them, cosmic time constitutes a total order of all events, rather than only of large-scale stages of the universe: “any event, anywhere in the universe, fits on a single cosmological time line.”Footnote 8 Also, it is not just a B-series, but rather grounds mind-independent A-theoretical properties of states of the universe and of events: there is a present moment of the entire universe, as well as a concomitant global distinction between past and future.Footnote 9

The second strategy for obtaining absolute simultaneity and hence, global time, from physics is based on quantum mechanics , in particular from EPR-type experiments, as discussed in Sect. 4.4. This move is endorsed by Dean W. Zimmerman,Footnote 10 by William L. CraigFootnote 11 and—as we have seen in Sect. 2.2.5—by John R. Lucas. According to these accounts, the hypersurface along which the collapse of two spatially separated entangled particles occurs defines a privileged standard of simultaneity. In Craig’s thought, quantum mechanical simultaneity furthermore coincides with simultaneity as defined by the cosmic frame. He quotes the physicist Antony Valentini in support, according to whom

… the absolute 3-space along which subquantum nonlocality acts … will necessarily coincide with the observed rest-frame defined by the uniform microwave background. We therefore predict that, if the nonlocality ever becomes directly observable, it will be found to propagate along the hypersurface defined by the observed cosmological rest frame.Footnote 12

The third strategy is to use the Neo-Lorentzian interpretation of the special theory of relativity (SR) as a foundation for global simultaneity, a move endorsed by William L. CraigFootnote 13 as well as Michael Tooley.Footnote 14 This interpretation allows retaining absolute simultaneity in spacetime because, according to it, only the average round-trip speed of light is equal to c, but its instantaneous speed depends on the direction it is travelling in. Moreover, according to this account, Lorentz contraction is explained by motion of an object relative to the ether , and is thus accounted for dynamically rather than kinematically.

2 The Block Universe

The fact that relativity theory undermines the concepts of a uniquely defined present, past, and future of the universe has led several thinkers to conclude that “everything is written”, that the four-dimensional block constituting the entire history of the universe is in a sense “already there” and that therefore the notion of true becoming is illusory. This idea is well illustrated by a quote from Kurt Gödel, who held that relativity of simultaneity leads to a fundamentally changeless world:

It seems that one obtains an unequivocal proof for the view of those philosophers who, like Parmenides, Kant, and the modern idealists, deny the objectivity of change and consider change as an illusion or an appearance due to our special mode of perception. The argument runs as follows: Change becomes possible only through the lapse of time. The lapse of time, however, means (or at least, is equivalent to the fact) that reality consists of an infinity of layers of “now” which come into existence successively. But, if simultaneity is something relative … reality cannot be split up into such layers in an objectively determined way. Each observer has his own set of “nows”, and none of these various systems of layers can claim the prerogative of representing the objective lapse of time.Footnote 15

The same train of thought appears in the definition of the block universe given by John C. Polkinghorne and Christopher J. Isham:

The central thesis of those who support the idea of a block universe is that (i) the notion of a set of spacetime points is meaningful; and (ii) all such points have an equal ontological status. In particular, no fundamental meaning is to be ascribed to the concepts of “past”, “present”, and “future”. Thus the notion of an ephemeral “now”—a moving barrier that continuously travels into the future, leaving behind an unchangeable past—is regarded as being a construct of the human mind that has no reference to reality as understood in the framework of modern physics. A secondary implication is that our perception of a genuine openness of future events is essentially illusory or, at the very least, needs to be understood within this framework of an “eternally existing” spacetime. Such a view of spatial and temporal relationships can raise serious difficulties for any theological or philosophical position in which the concept of human freedom plays a significant role.Footnote 16

We have already considered the argument for temporal determinism advanced by Wim Rietdijk and Hilary Putnam, according to whom the transitivity of the relation “being present” between events renders the entire content of spacetime fixed and unchangeable. But the block universe model also enjoys the support of some of the founders of modern spacetime physics themselves. For example, as is well known, Albert Einstein believed that the distinction between present, past, and future is illusory, as is illustrated in his writing of condolence to the widow of his friend Michele Besso: “People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.”Footnote 17 As Rudolf Carnap recounts, Einstein was deeply interested in the “now” of human experience, but held that the difference between past, present, and future “does not and cannot occur within physics”.Footnote 18 Einstein was furthermore a determinist, ruling out the possibility of an open future:

Everything is determined, the beginning as well as the end, by forces over which we have no control. It is determined for the insect as well as the star. Human beings, vegetables, or cosmic dust, we all dance to a mysterious tune, intoned in the distance by an invisible piper.Footnote 19

While Einstein’s views on time and causality imply a block universe where “everything is written”, it is important to note that Einstein’s determinism, as is apparent from the last quote, is causal rather than temporal.

The view that future events are “already there” has also been endorsed by the early relativist Arthur Eddington, who famously stated:

The division into past and future (a feature of time-order which has no analogy in space-order) is closely associated with our ideas of causation and free will. In a perfectly determinate scheme the past and future may be regarded as lying mapped out—as much available to present exploration as the distant parts of space. Events do not happen; they are just there, and we come across them. “The formality of taking place” is merely the indication that the observer has on his voyage of exploration passed into the absolute future of the event in question.

This means that determinate events, linked by deterministic causal laws, are spread out throughout spacetime:

A detached observer contemplating our world would see some events apparently causing events in their future, others apparently causing events in their past—the truth being that all are linked by determinate laws, the so-called causal events being merely conspicuous foci from which the links radiate.Footnote 20

A particularly clear statement in favour of a block universe model is given by Olivier C. de Beauregard in his paper “Time in relativity theory: Arguments for a philosophy of being”Footnote 21:

There can no longer be any objective and essential (that is, not arbitrary) division of spacetime between “events which have already occurred” and “events which have not yet occurred”. There is inherent in this fact a small philosophical revolution… If matter has spatial extension, it follows … that it has also extension in time. This is why first Minkowski, then Einstein, Weyl, Fantappiè, Feynman, and many others have imagined spacetime and its material contents as spread out in four dimensions. For those authors, of whom I am one, who take seriously the requirement of covariance, relativity is a theory in which everything is “written” and where change is only relative to the perceptual mode of living beings. Humans and other living creatures, for reasons which one can try to explain, are compelled to explore little by little the content of the fourth dimension, as each one traverses, without stopping or turning back, a time-like trajectory in spacetime…

There are writers who affirm that the future contains elements which are undetermined by the past and the present, and that the future light cone in the diagram must therefore be left blank. The answer is that there is a future. Nature “will take” one of the alternatives open to her, and it is this that we must imagine inscribed, even though we do not know what it “will be”.Footnote 22

Beauregard is of course aware that this picture conflicts with the intuitions whereby time is a one-way street, and whereby furthermore we can act freely to influence the future. He explains the former phenomenon in terms of irreversible processes in nature, such as increase of entropy at macroscopic levels, and emission of radiation by charged particles, phenomena which are themselves probabilistic in nature: “the irreversible evolution of the universe imposes, via probability, its dissymmetry even on the microscopic scale.”Footnote 23

While Beauregard denies the possibility of an indeterminate future light cone, because its content is “written”,Footnote 24 he does not therefore squarely deny free will, but rather argues for a compatibilist picture, whereby the history of the universe can be recounted in two ways: First, in terms of the “psi-function of the entire universe”, which

denotes which possible states are occupied and which are not. In the Heisenberg picture the occupation numbers of the states never change: nothing happens. This picture is a reformulation in quantum terms of the classical and deterministic conception of nature in which everything is written once and for all.

The other way is the “interaction picture” for which there is some indeterminacy. However, according to Beauregard, the effect of this indeterminacy consists in the fact that

our successive sense impressions cannot in general be put in exact causal relation with each other … in this sense, a four-dimensional diagram of an observer’s sensory experience will not consist of causally related events.Footnote 25

In the picture drawn by Beauregard, these two views are complementary rather than mutually exclusive. However, the indeterminacy in the second view applies only to experience, not to action, so that there is no notion of a “branching” future which would enable choices by agents to actually change the content of spacetime. In this sense, Beauregard’s view is similar to the compatibilism about free will advanced by Immanuel Kant.

3 Why Neither Cosmic A-theory nor the Block Universe Works

Neither cosmic A-theory nor the block universe lead to a satisfactory account of the passage of time in the context of relativity theory. Cosmic A-theorists rightly emphasize that a viable theory of time must account for its passage and its asymmetric character, for the irretrievability of the past and the openness of the future, rather than simply declaring these features to be unreal by spatializing the time axis, and by appealing to the relativity of simultaneity. However, proponents of the theory assume that true becoming is possible only if there is an absolute flow of time with a global present , and in this way, extrapolate from an indeed central feature of our experience to the structure of the world as a whole. This leads essentially to a doubling of temporal dimensions, since an absolute time existing over and above the time measured by local clocks is postulated in order to save the global past-present-future distinction. In this picture, time is in general not what the clock measures, unless the clock happens to be carried by a privileged observer. Thus, while the cosmic hyper-time is meant to save experienced temporal asymmetry, it only leads to the additional problem of how it is that the past-present-future distinction which we experience locally happens to coincide with the cosmic one.

The three proposals advanced by cosmic A-theorists in order to provide a foundation for the global wave of becoming suffer from their sheer physical implausibility:

First, cosmic time functions cannot provide a foundation for a global “now”, as can be seen from a simple argument: A global “now” would consist of a particular set comprising all events happening simultaneously. For such a set to exist, a total order of events is necessary, so that for any two events x and y, either x is before y, or the converse, or they are simultaneous. But, as we have seen in Chap. 4, cosmic time functions do not permit all events to be so ordered—unlike maintained by Unger and Smolin—but only large-scale states of the cosmos. Therefore, they do not deliver what the cosmic A-theorist needs.

Second, quantum mechanical simultaneity does not corroborate the case for cosmic simultaneity, as contended by Craig and Zimmerman, but rather weakens it, since there is no reason to suppose that simultaneity as defined through cosmic time functions coincides with that occurring in quantum mechanics. If it did so coincide, violations of the predictions of quantum mechanics would result, for reasons given in Sect. 4.4.

Third, the Neo-Lorentzian view of spacetime rests on implausible physical assumptions: the existence of an ether, and an anisotropy in the speed of light. It is ontologically simpler to do without the former, and to assume that the laws of nature are the same in every frame of reference, so that speed of light is everywhere equal to the fixed value resulting from Maxwell’s equations. However, it is also important to note that Neo-Lorentzian theory cannot be conclusively disproved experimentally: to do so would require measuring the one-way speed, as opposed to the round-trip speed, of light. This, however, can only be done by using two spatially separated clocks assumed to be synchronized, an assumption which cannot be taken for granted, because clock transport involves time dilation both in standard relativity theory and in the Neo-Lorentzian theory, according to which moving clocks interact with the ether. Notwithstanding this experimentally open issue, it is preferable to account for time’s passage with a less cumbersome ontology, compatible with standard relativity theory, than that proposed by the Neo-Lorentzians. A proposal to this end is offered in Chap. 9.

In sum, cosmic A-theory takes our experience of the passage of time seriously but extrapolates the structure of this experience to the universe as a whole, and thus essentially has the universe comply to our deep-seated pre-relativistic intuitions.

The evaluation of the block universe model is simpler: This model incurs no conflicts with physics in the way in which cosmic A-theory does. Its principal problem is its failure to account for the passage of time as experienced. A fully satisfactory model would need to save the phenomena in some way. If it declares them to be illusory, it would at least need to be shown how the illusion arises. We have seen, in the context of the Rietdijk-Putnam argument discussed in Sect. 3.2, that the characteristic temporal determinism of the block universe fails, principally because the content of the future light cone of a spacetime point depends on what is happening at that point, and can therefore be influenced. Furthermore, the very notion of temporal determinism over and above causation was seen to arise from the confusion between necessitas consequentis and necessitas consequentiae . By the same token, the lack of a frame-independent past-present-future distinction in relativity cannot be cited in support of the view whereby the four-dimensional spacetime block constituting the universe is “already there” so that “everything is written”. Indeed, like the A-theoretic models discussed earlier, this notion itself clandestinely introduces a kind of hyper-time existing externally to the manifold, as has been well put by Huw Price:

In an attempt to highlight the contrast with the dynamic character of the “moving present” view of time, people sometimes say that the block universe is static. This is rather misleading, however, as it suggests that there is a time frame in which the four-dimensional block universe stays the same. There isn’t of course. Time is supposed to be included in the block, so it is just as wrong to call it static as it is to call it dynamic or changeable. It isn’t any of these things, because it isn’t the right sort of entity—it isn’t an entity in time, in other words.Footnote 26

The block universe model thus likewise extrapolates a pre-relativistic notion onto spacetime as a whole, which in this case is the ontological status of the past. Why, one may ask, shouldn’t the ontological status of the future, by parity of reasoning, be extrapolated in this way, landing us in a fuzzy block?

The failure of temporal determinism is of course of no avail against Einstein’s block universe, since the determinism in it is causal. However, as we will see in the next chapter, it is questionable whether a causally deterministic universe can evolve at all, so that Einstein’s block seems to conflict with evolutionary cosmology. Of course, the downfall of determinism in physics furthermore weakens the case for such a universe.

4 A Third Way?

At this point, readers may well wonder whether some third way is available which overcomes the dichotomy between cosmic A-theory and the block universe, an alternative which posits no implausible physics but yet is able to save the phenomena of the passage of time as experienced. Some proposals pointing in this direction are indeed available. A brief overview of this literature follows, where I will limit myself to describing some of the key points therein:

First, Robert J. Russell puts forward a “relational and inhomogenous spacetime ontology”,Footnote 27 compatible with spacetime physics and yet hospitable to flowing time. Russell’s crucial move to arrive at such an ontology is to propose that relations between events, rather than properties of events, ground the distinction between past, present, and future. In this way, events are never assigned contradictory properties, so that McTaggart’s paradox does not arise. At the same time, the difference between past, present, and future is not merely subjective, being grounded in relations which truly hold between events. The relational structure by which events are connected leads to a complex, fractal structure, whose topology Russell explores in detail.Footnote 28

A further contemporary author who argues that true becoming does not demand a total and global temporal ordering is Steven F. Savitt, who rejects the argument against the passage of time and true becoming advanced by Beauregard by emphasizing two important distinctions: First, that between coordinate time and proper time measured along a world line. And second, between becoming, understood as the “mere occurrence of events at various serially ordered clock times” on the one hand, and tense, with its distinction between present, past, and future on the other. Savitt, citing the support of Adolf Grünbaum, proposes that, while change is mind-independent, tense is mind-dependent. The reason is that the tensed predicates “now”, “past”, and “future”, are indexical terms, and therefore depend on there being language-users to employ them. Furthermore, such predicates do not represent any “physical attribute” in their referents. This distinction between change and tense means that Gödel’s argument, whereby relativity of simultaneity and the downfall of a global present also entail a world without temporal passage, is invalid. In Savitt’s own words:

… time qua passage is a local phenomenon, tied to a world line. For eons we have tied passage to an advancing global now , and this idea is buried deep in our worldview. It is an idea that we must transcend.Footnote 29

James Harrington likewise argues that a robust difference between a determinate past and an open future can be upheld in a spacetime which lacks such a distinction globally.Footnote 30 His approach is based on the notion of relational indeterminacy—or, conversely, determinacy—which holds between regions of spacetime. In his own words: “One region of space-time P is relationally indeterminate relative to another region Q when the causal past of Q fails to determine the state of P.”Footnote 31 Thus, spacetime itself comes with a structure which accommodates a modal distinction: “[T]he past null-cone and its interior of each point of Einstein-Minkowski space-time is closed and the rest of the space-time is open relative to that point.”Footnote 32 Harrington’s investigations lead him, like Savitt, to emphasize the priority of proper time measured locally along a world line. Succinctly put: “proper time just is time.”Footnote 33

I concur with the proposals outlined above and believe that they point in the right direction in that they emphasize the relational character of temporal asymmetry, and are based on local events and regions in spacetime, rather than the universe as whole. What is still lacking, however, is an answer to the question of the origin of temporal asymmetry: Why is there a relation of precedence—the relation “before”—between events in the first place? Why does passage from the past to the future occur, and how can we account for the fact—or, at least, the impression—that the future is open and the past fixed? These features of time, as the authors cited above rightly argue, are not in conflict with spacetime physics, but they still remain to be explained.

In addition to the above, recent years have seen contributions to the literature on time and relativity theory emerge which fully embrace spacetime physics and its lack of a global past-present-future distinction, but try to bridge the physics with time’s passage as experienced. Michael Silberstein, W. M. Stuckey and Timothy McDevitt propose that this should be done through overcoming traditional divides between materialism and dualism concerning the problem of mind and matter, and instead embracing a “neutral monism”.Footnote 34 In this way, the authors hope to overcome one-sidedly subjectivist or objectivist accounts of the relation between the subject and the outside world. Instead, something which they call “Presence”, a concept taken to be fundamental and not capable of further definition, serves as the desired bridge. The upshot is that, if said dichotomies are overcome, that between time as described by physics versus time as experienced is so likewise.Footnote 35 As for the direction of time, the authors contend that, since time lacks an intrinsic, objective direction, no explanation needs to be found for it.Footnote 36

Craig Callender, whose work on time and quantum mechanics we already encountered in Sect. 4.4, provides an in-depth survey of experimental work on the psychology of temporal asymmetry, in particular on how our attitudes and emotions, both positive and negative, vary depending on whether an event is past or future. He combines these psychological considerations with an evolutionary account, whereby living beings which respond differently to past and future events have a survival advantage and are selected for. Callender is hopeful that an explanation for time’s experienced asymmetric structure may be attained in this way, although he concedes that work remains to be done to that end.Footnote 37

I am sceptical of the approach proposed by Silberstein, Stuckey and McDevitt. While there is nothing to be said against an account of the relationship between mind and matter which goes beyond materialist reductionism and substance dualism, the question remains: how does this yield time as experienced? How do we get from their undifferentiated “Presence”, designed to mediate between the subjective and the objective, to the structure of time with its ordering, metric properties, and characteristic asymmetries? A big, unexplained gap remains. It also seems rather facile to claim that time has no direction to be explained since, while there is indeed no preferred direction in the spacetime manifold considered as whole, individual world lines do exhibit direction. Callender, on the other hand, in my view rightly attempts to bridge experimental psychological knowledge on the rich structure of time as experienced with the philosophy of its modal structure, an intersection of research areas which may well prove fruitful. I would object, however, that different affective attitudes to future and past presuppose that distinction, so that it is hard to see how they could explain it. Similarly, evolution can only select for living beings with such different affective attitudes—as, indeed, it may well have done—if that which those attitudes refer to is already given. Thus, while a deeper understanding of the experience of time may well be attained through such interdisciplinary research, I doubt that it will be able to yield an explanation of the arrow of time itself.

In sum, then, a satisfactory theory able to account for the arrow of time is lacking in the present state of research. In Chap. 9, I will set out a derivation of the relation “before”, and from there on, of the difference between the fixed past and the open future, all in purely local terms, in order to fill this gap. But before doing so, some further building blocks will need to be assembled in the following chapters.