Section III summary

In his 2003 lecture at the Kavli Institute at UCSB, Guth acknowledges, “[Anthony]

Aguirre and [Steve] Gratton have proposed a model that evades our theorem, in which the arrow of time reverses at the t = –infi nity hypersurface, so the universe ‘expands’ in both halves of the full de Sitter space.”60 It is possible, then, to evade the BVG Theorem through a gross deconstruction of the notion of time. Suppose one asserts that in the past contracting phase the direction of time is reversed. Time then fl ows in both directions away from the singularity. Is this reasonable? We suggest not, for the Aguirre–Gratton scenario (Aguirre & Gratton 2002) denies the evolutionary continuity of the universe which is topologically prior to t and our universe. The other side of the de Sitter space is not our past.

For the moments of that time are not earlier than t or any of the moments later than t in our universe. There is no connection or temporal relation whatsoever of our universe to that other reality. Efforts to deconstruct time thus fundamentally reject the evolutionary paradigm.

Section III summary

Primarily, attempts to overcome the new singularity theorem of Borde, Vilenkin, and Guth center on generating universe models that do not feature average positive expansion in their past. This can be done by having average negative expansion (i.e. contraction) or by having zero average expansion (an asymptotically static model). Both attempts seem to encounter insurmountable diffi culties. The contraction model features acausal fi ne-tuning to its asymptotic past and BKL chaos as the contraction nears a singularity in its pre–Big 60. Alan Guth, speech to the Kavli Institute for Theoretical Physics, October 2003. Available at: http://online.kitp.

ucsb.edu/online/strings_c03/guth/.

158 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

Bang “bounce” into our present expanding reality. BKL chaos may, in fact, prove that it is impossible for a universe to pass through a singularity.

Zero average expansion models are usually constructed in two different ways. Either the expansion asymptotically approaches zero as time (looking backward) approaches negative infi nity. One can also consider an infi nite number of cycles where expansion and contraction exactly cancel for each cycle. The fi rst case has the dilemma that it must begin static and then transition to an expansion. Hence, the static phase is metastable, which implies that it is fi nite in lifetime. The universe begins to exist.

Cyclic models usually fail due to the necessary buildup of entropy from cycle to cycle.

If there were an infi nite number of cycles, why is the universe not in a state of “heat death”?

The entropy would also have the effect of making the amplitude of the cycles (the maximum size of the universe during a cycle) grow over time. Looking backward in time, then, this implies a fi rst cycle to the fi nite past. One can attempt to overcome these problems, as Baum and Frampton do, by claiming that a single universe fractionates into a multiverse of contractions. Most of the contracting “children” from the parent universe will have shed the entropy developed from the preceding phase and hence permit cycling.

But as we have seen, their mechanism appears to fail to fractionate. Even if it did fractionate into separate entropy-free domains, even an initially empty daughter universe would develop BKL chaos when approaching a contraction and disrupt the scenario!

The last gambit, that of claiming that time reverses its arrow prior to the Big Bang, fails because the other side of the Big Bang is not the past of our universe.

Hence, these models either have a beginning or are not viable.

IV. Quantum gravity

A fi nal, expected exception to the Hawking–Penrose theorems is a formulation known as “quantum gravity.” The two great pillars of twentieth-century physics, Einstein’s GR

(the science of the very large) and QM (the science of the very small), both enjoy overwhelming observational support. However, if the standard Big Bang theory were correct in its prediction that the universe must approach a singularity in its distant past, then QM must eventually govern it. But GR is a classical theory, not a quantum fi eld theory. For an extremely high-density early universe, where gravity acted both as the dominant force and as a quantum force, we must have a new theory – quantum gravity – to describe it. Further, in 2002,61 the fi rst observational evidence that gravity is indeed a quantum force was reported. One of the Hawking–Penrose assumptions for their singularity theorems, however, was that GR is a correct description of the universe. Since this is not true at the scale of singularities, perhaps singularities did not exist after all. Perhaps, extrapolating backward, the universe evolves smoothly through the Big Bang to an unknown past.

Here are three prominent candidates for a theory of quantum gravity (Figure 3.12). The main job of some quantum gravity models is to get one through the singularity to an (it is hoped) eternal past. Others will accept a “beginning” to the universe but will deconstruct the notions of time, nothingness, or causation.

61. Nesvizhevsky et al. (2001), see http://www.newscientist.com/article.ns?id = dn1801, or http://physicsworld.

com/cws/article/news/3525. The experiment was done by bouncing supercold neutrons and noticing that the height of the bounce was quantized.

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KA LA M C O S M O LO G I C A L A RG U M E N T 159

Quantum gravity classes

Quantum gravity

String

Semiclassical

Loop quantum

Figure 3.12 Families of quantum gravity cosmologies.

IVa. String models

String theory is by far the most popular method proposed so far to unify quantum theory with GR. Essentially, string theory proposes that the elementary entities of nature are not point particles (zero-dimensional objects) but are strings (one-dimensional objects). String theory eliminates many of the problems that occur in particle theories. Particle interactions can occur down to literally zero distance; where force laws blow up (recall, for example, that gravity’s dependence on distance is 1/ r 2; that is, the force becomes infi nite as range goes to zero) and predict infi nite (i.e. nonsensical) answers. String theory calms this behavior by introducing a minimum distance (the “Planck” distance) to interactions. By “spreading out” string interactions, infi nities are avoided.

Another advantage of string theory is that it can explain in a non– ad hoc manner the existence of different types of elementary “particles.” Differing “particle” properties could be merely different types of vibrations that occur on a string (similar to musical notes). It was hoped (and still is by some) that the theory would naturally predict the characteristics of the elementary particles that are otherwise free parameters in the earlier theory (which is called the “Standard model”).

The “minimum distance” feature of string theory is thought to be a desirable feature for cosmological models because, analogously to the case of particle interactions, the standard Big Bang model predicts that the scale factor of the universe shrinks to literally zero size. String theory could “calm” this feature of the model by suggesting a minimum size.

This could even overcome the Hawking–Penrose theorems and suggest that there was a

“before” to the singular condition. Perhaps the Big Bang was not an ultramundane event at which time itself came into being. If it was not, the door is open to a past eternal universe.

String theory has also given birth to “brane” cosmology, where the emphasis is on the background within which strings propagate rather than the strings themselves (Figure 3.13). These backgrounds, called n-branes, can be variable in the number of their dimensions. For example, it is normally proposed that our three-dimensional space is one of these

“three-branes” which may or may not be fl oating around in a higher-dimensional space (usually called “the bulk”).

160 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

Some string cosmologies

String

Pre–Big Bang inflation

Ekpyrotic/Cyclic

(Veneziano/Gasperini)

(Steinhardt/Turok)

Figure 3.13 String cosmology models and proponents.

IVa(i). Pre–Big Bang infl ation (PBBI)

There are two string models that can aspire to describe adequately a past infi nite pre–Big Bang environment. These are the PBBI scenario of Gabriele Veneziano and Maurizio Gasperini and the Ekpyrotic/cyclic model of Paul Steinhardt and Neil Turok. The PBBI scenario is a classic version of an asymptotically static model. Here is how one of its authors describes it:

According to the scenario, the pre-bang universe was almost a perfect mirror image of the post-bang one. If the universe is eternal into the future, its contents thinning to a meager gruel, it is also eternal into the past. Infi nitely long ago it was nearly empty, fi lled only with a tenuous, widely dispersed, chaotic gas of radiation and matter. The forces of nature, controlled by the dilaton fi eld, were so feeble that particles in this gas barely interacted. As time went on, the forces gained in strength and pulled matter together. (Veneziano 2004, p. 63)

Through gravitational contraction, regions of the pre–Big Bang universe turned into black holes. Due to quantum effects, once the density of a black hole reached a critical value, it underwent a “bounce” into a Big Bang. Our universe then persists within this otherwise closed surface (with respect to the ‘outer’ background space where everything began).

In his popularization in Scientifi c American, Veneziano seems to suggest that his beginning is an infi nitely distant but never reachable (i.e. ideal) point. The article implies that the model is to be interpreted realistically.62 But one must be wary in interpreting the infi nity of the past for this model, as it is easy to misuse the concept of an infi nite limit, as well to ignore the distinction between a realist and an instrumentalist interpretation of the model. The problems in interpreting this model are similar to those encountered when assessing the Emergent model class. It is worth noting that the coauthor of the PBBI model, Maurizio Gasperini, indicates that the entire asymptotic past (or future) should not be taken as real:

62. Or is it Scientifi c American that has inserted the realist interpretation?

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KA LA M C O S M O LO G I C A L A RG U M E N T 161

. . . I fi nd it misleading to talk of a ‘future of the PBB scenario,’ because the PBB scenario only (possibly) applies to describe some (more or less extended) portion of the past history of our cosmos, and is expected to smoothly join the standard cosmological scenario at an early enough epoch, so as to reproduce standard results on nucleosynthesis, baryogenesis, structure formation, and so on. In other words, the PBB scenario can be regarded as a model for explaining the initial conditions of our standard cosmological confi guration, in a way which is string-theory consistent, but it cannot be extrapolated towards the future without further assumptions, which at present have not been fully worked out (with the exception of the dilaton model of dark energy proposed by Piazza, Veneziano and myself on PRD 65, 023508 (2002)). (pers.

comm., January 10, 2006)

Can one build a realist interpretation of this model? It is interesting to contrast the depiction of PBBI as proving “the myth of the beginning of time” in a setting where sensational conclusions are encouraged ( Scientifi c American) with the characterization of PBBI as a “toy model” in a setting where scientists are naturally conservative (peer-reviewed academic journals).63

As described in the academic literature, the model appears to have an initial phase. The relevant phases are:

(1) A static (Milne) universe, or string perturbative vacuum (SPV) phase. This means that the universe is empty (energy and energy density is zero) and is static, that is, neither expanding nor contracting globally or locally.

(2) A quasi-Milne phase, which constitutes a “perturbed” SPV. Here “H is (small and) positive in the String frame, (small in modulus and) negative in the Einstein frame, and tends to zero as t goes to minus infi nity, and the Universe approaches the SPV

confi guration (where H is identically zero, since the spacetime is fl at)” (M. Gasperini, pers. comm., January 16, 2007).

(3) An

“infl ationary” phase. In one set of coordinates (the Einstein frame), matter collapses into trapped surfaces, or black holes. In another set of coordinates (the string frame), this can be viewed as a spatial expansion. This happens regionally rather than globally.

(4) A post–Big Bang FRW phase that is typical of the standard Hot Big Bang model.

The authors begin building the model at a fi nite time in the past where a condition called “asymptotic past triviality” (APT) obtains (Veneziano & Gasperini 2002, p. 54). APT

represents the boundary between phase (2) and phase (3). The period of contraction (infl ation in the string frame) is itself fi nite.

The authors then project this state into the future, and asymptotically evolve it into the past. Similar to the Maartens version of the Emergent model, one takes the APT past-directed duration of phase (2) to be infi nite (Figure 3.14).

Unlike the Emergent model, perturbed SPV lasts for a while and then individual patches that meet the Hawking–Penrose condition for a closed trapped surface begin regional 63. “The so-called ‘pre-big bang’ scenario described in this report has to be seen in the above perspective as a possible example, even just as a toy model of what cosmology can look like if we assume that the sought for standard model of gravity and cosmology is based on (some particular version of) superstring theory” (Veneziano

& Gasperini 2002, p. 4).

162 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

Penrose diagram for pre–Big Bang inflation

ϑ+ future null infinity

Today

ϑ +

Phase 4

FRW

(i.e. the observed universe)

Portion of model

described as

Big Bang

mathematically

Space

“Bounce” singularity

and observationally

Time

spatial

robust by Maurizio

Phase 3

infinity

Gasperini

inflation

APT

ϑ–

Phase 2

quasi-milne

Phase 1 (maybe an ideal point)

ϑ– past null infinity

string perturbative vacuum

Figure 3.14 Construction of the pre–Big Bang infl ation (PBBI) model is given at the “asymptotic past triviality” or APT point. From here, the model is projected forward in time to give the Big Bang universe. It is also projected backwards to past infi nity. Note that the APT data is given at a fi nite time in the past in the diagram. The proposed string perturbative vacuum era would be at “past null infi nity” or the lower point marked “ϑ−.” The past infi nite is “null” rather than “timelike” because the gravidilaton waves that embed it are massless. FRW = Friedmann–Robertson–Walker.

contraction (infl ation in string coordinates) (Figure 3.15). Should we treat SPV like ESS?

Gasperini observes that a signifi cant feature of SPV is that it is unstable:

. . . the SPV is unstable already at the classical level . . . it [decay of the SPV] can be described as a quantum transition, but it is a process which is also classically allowed. (pers. comm., January 4, 2007)

. . . the instability of the SPV is similar to the instability of a classical ball placed exactly at the top of a perfectly symmetric hill. In principle, if the system starts initially in the unique equilibrium confi guration, and there are no external perturbations, the system might remain static forever. In practice, however, there are physical perturbations removing the system from equilibrium, sooner or later, with a probability which is chaotically (or randomly) distributed. In the case of the SPV the perturbations removing it from equilibrium are the quantum fl uctuations of the background fi elds (in particular of the dilaton). In addition, the exact equilibrium confi guration can only be achieved as an asymptotic extrapolation, in the limit in which the cosmic time goes to minus infi nity: in practice, at any given fi nite physical time, the system is always displaced a bit from equilibrium. (pers. comm., January 9, 2007)

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KA LA M C O S M O LO G I C A L A RG U M E N T 163

Publisher's Note:

Permission to reproduce this image

online was not granted by the

requested to refer to the printed v ersion

of this chapter.

Figure 3.15 Rate of universe expansion versus time in the pre–Big Bang infl ation model. (source: Maurizio Gasperini, available at: http://www.ba.infn.it/~gasperin/)

I would say that the SPV is not a phase extended in time, it is only an asymptotic initial state which is approached, however, in an infi nite time. In practice, the physical description never starts “exactly” from that state, but from a state which represents an arbitrarily small perturbation of the SPV. (pers. comm., February 27, 2007)

. . . if I live in the initially collapsing portion of spacetime, then I have a chance to go through the bounce, at some epoch in the future. But this does not concern the entire spacetime. There are spacetime regions which are collapsing and eventually bouncing into a FRW like Universe, and others which do not. It is possible, in principle, to live in regions of spacetime never experiencing the bouncing nor the collapse, and staying for ever in a confi guration well described by the string perturbative vacuum (or by a quantum perturbation of it). (pers.

comm., January 9, 2006)

So if the SPV were real, it would be a state with a fi nite lifetime. Some time after decay, random portions will be suffi ciently dense to form closed trapped surfaces and begin gravitational contraction. Other regions could remain indefi nitely in the post-SPV state (i.e. already perturbed from an equilibrium condition).

Veneziano and Gasperini’s language at times suggests treating SPV as an ultimately unrealized extrapolation similar to what is described in the Scientifi c American article. But here and elsewhere, they seem to suggest that the SPV is quite real (if the asymptotic past of the model were taken seriously):

The whole process may be seen as the slow, but eventually explosive, decay of the string perturbative vacuum (the fl at and interaction-free asymptotic initial state of the pre-big bang scenario), into a fi nal, radiation-dominated state typical of standard cosmology. (Veneziano

& Gasperini 2002, p. 21)

The PBBI model is described as a “decay” or a quantum “tunneling” event similar to the semiclassical models of Hawking–Hartle and Vilenkin (see section IVc) (Figure 3.16).

But:

164 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

Publisher's Note:

Permission to reproduce this image

online was not granted by the

requested to refer to the printed v ersion

of this chapter.

Figure 3.16 Pre–Big Bang infl ation as a string quantum transition. The fi gure contrasts “creation from nothing” models such as the Hawking–Hartle no-boundary approach or the Vilenkin “tunneling from nothing” (see section IVc) with a string approach. Here, a prior state quantum tunnels into our current Friedmann–Robertson–Walker universe. WDW = Wheeler–DeWitt equation, which is the basis for the semiclassical cosmologies to be discussed in section IVc (source: Maurizio Gasperini, available at: http://www.ba.infn.it/~gasperin/)

[PBBI] can also be interpreted as a tunneling process, not “from nothing”, however [which is how the Hawking–Hartle and Vilenkin models are interpreted; see section IVc], but “from the string perturbative vacuum.” (Veneziano & Gasperini 2002, p. 208)

It is reasonable to presume that if there is a physical transition from state “A” to state

“B,” and state “B” is ontologically real, then state “A” must be taken to be ontologically real.64

Signifi cant as well is that the state right after SPV decay (if SPV were a realized physical state) would obtain only a fi nite time ago to the past, given that Gasperini’s description of the decay product is identical to the following:

The generic regular solution thus approaches Milne as t [approaches negative infi nity] but, at any fi nite large [negative time] , also contains small dilatonic (and gravitational-wave) perturbations giving 0 < Ω << 1. As t→ −∞, Ω → 0. As time goes forward, instead, Ω tends to grow until, at some critical time –T0, Ω becomes O(1), in some region of space. From that moment on, in that “lucky” patch, the metric starts to deviate from Milne and dilaton-driven infl ation 64. If state “A” is unreal, then no transition at all takes place but rather an absolute “coming into being” of state

“B.” On this interpretation, the universe began to exist.

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KA LA M C O S M O LO G I C A L A RG U M E N T 165

sets in, pushing Ω extremely close to 1 in that patch. (Veneziano 1998, p. 10; emphasis added)65

So if the SPV state were real, there could only be a fi nite timeline from it to the present.

Only if the perturbation itself were unreal would the past eternal nature of the model survive. Is this realistic? As we look backward from the APT point, what would the signifi -

cance be of a real quantum perturbation to a state which was arbitrarily close to SPV?

Would not one have a situation that was virtually identical to simply starting with “real”

SPV? This is essentially a “pseudobeginning” scenario.

Vaas classifi es this cosmology as “soft bang/pseudobeginning” just as he does the Emergent models.66 Although the behavior of perturbed SPV is ultimately different from ESS (or perturbed ESS), the similarity with respect to classical (and quantum) instability should be the controlling one. The two models are mathematically similar with respect to the asymptotic approach to an infi nitely distant unstable state. Vaas argues that there is no obvious arrow of time and hence the asymptotic past is likely a mathematical artifact.

Perhaps the past infi nite timeline is only technical in nature: the duration from the APT

point extrapolated backward is infi nite, but that is to be understood instrumentally. In response to the question, “if the SPV is unstable, and within a fi nite time quantum fl uctuations of the dilaton will disturb its equilibrium, does that not imply that the past must be fi nite?” Gasperini answers:

From a physical point of view, a spacetime manifold has an infi nite (past) extension if its timelike or null geodesics can be (past) extended for infi nite values of their affi ne parameter, without ending into a singularity. This property is satisfi ed by the past extension of the pre-big bang solutions, so, in this sense, they are past eternal. (pers. comm., January 17, 2007) As Gasperini indicates, it is true that, in a sense, the solutions are past eternal. In pure GR, it is true that backward-directed geodesics will trace all the way to past infi nity. In fact, in pure GR, even if one assumed a real SPV state, it would still be the case that, technically speaking, backward-directed geodesics are past eternal for the same reason that a real ESS

is technically past eternal.

But the relevant question seems to be this: do all past-directed geodesics from a quasi-Milne state (or a quasi-ESS) intersect with a signifi cant system perturbation, or would 65. For clarifi cation, a Milne universe is a special state where the critical density parameter Ω is exactly equal to zero; the universe is empty. Recall that the critical density parameter Ω determines if an FRW cosmology will have a closed, fl at, or open geometry. It is closed if Ω < 1, fl at if Ω = 1, and open if Ω > 1. If the cosmological constant is zero, then a closed universe will recollapse, and a fl at or open universe will be ever-expanding.

66. Vaas elaborates:

A related problem refers to the pre-big bang model (Veneziano & Gasperini 2003). Here the string vacuum

– where a local collapse in the Einstein frame (which corresponds to a dilaton-driven infl ation in the string frame) before the big bang occurs – is quite simple, homogeneous, almost empty and does not have an overall arrow of time. But, mathematically, the origin of the pre-big bang – or, to be more precise, any pre-big bang, for the model does also imply a multiverse scenario – traces back to a maximally simple, static condition only in the infi nite past (principle of asymptotic past triviality). But this can also be interpreted just as a local predecessor of a big bang and not a feature characterizing the infi nite string vacuum as a whole. (Vaas 2004, pp. 18–9)

166 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

at least one geodesic trace, undisturbed, to past infi nity? Consider the following comparison:

A. Suppose that the SPV (or ESS) were viewed as ontologically real rather than just idealized points at past infi nity. Within a fi nite time, a quantum perturbation would disturb the state and the resultant timeline to the present would also be fi nite. The model would not be past infi nite.

B. Suppose, instead, that ESS or SPV are taken to be asymptotic ideal points. For analysis’

sake, start at the present and look backward. Within a fi nite time, one is arbitrarily close to the ideal condition. Now consider any (new) quantum fl uctuation that occurs to the quasi-SPV (or quasi-ESS) state while one is tracing the backward timeline. The probability of this is essentially 1.

What meaningful difference is there between the universe in case A and case B (at the

“new” fl uctuation point)? Looking backward, there will be an unbounded number of all types of fl uctuations of all sizes, any one of which will arrest the supposed asymptotic development of the SPV (or ESS). The proposed past infi nite extrapolation seems to be a mathematical artifact (or at least explanatorily vacuous). Even taken seriously (i.e. not as a “toy” model), the model does not predict that the past is infi nite.

IVa(ii). Ekpyrotic/cyclic

The Ekpyrotic model is a cyclic model, but not in the old sense of a universe that undergoes an eternal periodic sequence of expansion and collapse. The Ekpyrotic model makes use of the extradimensional nature of string theory to propose that cycling occurs, but in a higher dimension. Authors Paul Steinhardt and Neil Turok view the new model as preferable to the post–Big Bang infl ationary model because it has fewer ad hoc features. For example, (present-day) dark energy is an add-on to the earlier model but is a natural and necessary feature of their new cycling model. String theory allows entities called

“branes” that could be representative of what we would otherwise call our three (spatial)-

dimensional universe. String theory demands six extra dimensions of space in order to be self-consistent. It is thought that these extra dimensions are (usually) tightly curled up around the three macroscopic dimensions and hence usually unobservable. (Think of a soda straw versus a one-dimensional line. The circle formed by looking at the straw edge-on could be thought of as a second dimension curled around the fi rst.)

The Ekpyrotic model proposes that one of these extra dimensions (the “bulk” dimension) is of macroscopic size. Within this extra dimension lie two three-branes, either of which could represent our universe. These three-branes periodically collide, just as if they were connected by a spring. When they do so, the energy of the collision is transferred to the branes (Figure 3.17).

This energy is converted into the matter (and radiation) that ultimately gravitates into galaxies. The rest of the normal Big Bang sequence follows (stars, planets, and so on). As the branes separate from each other, the branes themselves are always expanding. (There are versions of the model where the branes undergo limited contraction, but always expand, on net, with each cycle.) Eventually, stars burn out, the galaxies recede beyond each galaxy’s visual horizon, and the universe enters a period of cold, burned-out cinders. Meanwhile, the branes cycle toward another collision.

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KA LA M C O S M O LO G I C A L A RG U M E N T 167

Ekpyroti/cyclic universe

Stage 2

branes collide

Stage 3

Stage 1

new galaxies

universe empty and cold

Stage 4

Stage 5

universe expands, cools

stars burn out

Figure 3.17 Pictorial description of the Ekpyrotic cycle.

The universe is then renewed with a new cycle. The energy that is released into the branes during each collision is replenished by an inexhaustible supply – gravitational potential energy. In this way, Ekpyrosis is an “open” system. There is always a limitless supply of free energy. This feature of cosmology as an open system (as opposed to the old

“heat death” scenario) is new but widespread in contemporary cosmology.

Despite avoiding the “heat death” scenario, however, there is now a new problem to solve. If new energy is dumped onto the brane for infi nite time, then either the entropy density or the energy density at each point must be infi nite. This would obviously be contrary to observation. The continual expansion of the infi nite-sized branes, however, keeps the entropy density constant. So (net) expansion is a critical model feature.

Steinhardt recognizes that his model of the universe is not truly beginningless. Here are the relevant comments from his Web site:

• Has the cyclic model been cycling forever?

• In principle, it is possible that the universe has undergone a semi-infi nite number of cycles in its past during which the volume increases from cycle to cycle. Even though this would take an infi nite time according to ordinary clocks, this cannot be the full story. This cycling regime would not cover all space-time. Something must have preceded the cycles.

• A similar issue arises in infl ationary cosmology. In both cases, this is an open question.

The issue is referred to as the problem of geodesic incompleteness referring to the fact

168 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

that a purely expanding phase does not span the entire space-time and one has to consider what happened before.67

Steinhardt’s website FAQ page indicates that the model is past geodesically incomplete.

Here the authors comment in their published work:

The most likely story is that cycling was preceded by some singular beginning. Consider a universe that settles into cycling beginning from some fl at slice in the distant past many bounces ago. Any particles produced before cycling must travel through an exponentially large number of bounces, each of which is a caustic surface with a high density of matter and radiation at rest with respect to the fl at spatial slices. Any particle attempting this trip will be scattered or annihilated and its information will be thermalized before reaching a present-day observer. Consequently, the observer is effectively insulated from what preceded the cycling phase, and there are no measurements that can be made to determine how many cycles have taken place. Even though the space is formally geodesically incomplete, it is as if, for all practical purposes, the universe has been cycling forever. (Steinhardt & Turok 2005, p. 5)

Steinhardt and Turok suggest the universe began in a singularity but that “for all practical purposes” it has been cycling forever. This claim is based on the fact that virtually no information as to the initial conditions of the universe could have survived to the present.

Steinhardt explains that photons carrying this information would be “semi-infi nitely redshifted” (pers. comm., January 27 and 30, 2004). There is a “semi-infi nite” number of cycles between that boundary and the present. How are we to understand this? The description of the model as “de Sitter like” and the associated “semi-infi nite” past timeline is nearly the same situation seen earlier with the discussion of the Misner “Mixmaster” universe (section IIIa). The key difference between Mixmaster and the Ekpyrotic model is that Mixmaster is intrinsically chaotic at its singularities (so not necessarily a good physical model of our universe), while the Ekpyrotic model avoids BKL chaos by having a positive equation of state (which is a unique feature of this cosmology) (pers. comm., January 17, 2006).68

Within the Ekpyrotic model an observer would see an infi nite number of bounces with roughly a trillion years per bounce. So on ordinary clocks, past time is infi nite (pers.

comm., January 27 and 30, 2004). Yet there is clearly a past boundary (an infi nitely distant beginning point?) preceding this behavior. One should note that the reason this model has a beginning is precisely because it falls under the previously mentioned BVG Theorem.

Borde et al. explicitly apply their theorem to the Ekpyrotic model of Steinhardt and Turok (Borde, Guth, & Vilenkin 2003).

That implies, among other things, that the “past boundary” must be reached in a fi nite amount of time. So Steinhardt seems to be mistaken in his prediction of a semi-infi nite number of cycles, unlike the Emergent and PBBI models, which evade the BVG Theorem (in proper time; i.e. if “an ordinary clock” is the most appropriate measure of physical time).

67. Cosmologist Paul Steinhardt’s internet site; FAQ section for the Ekpyrotic model http://wwwphy.princeton.

edu/~steinh/cyclicFAQS/index.html#eternal.

68. Recall that the equation of state is negative (for a cosmological constant pressure = minus density) for a typical infl ationary model. For Ekpyrosis, the collision singularity occurs in the “bulk” dimension between the two branes; not within the brane that we ourselves would live on.

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Some LQG cosmologies

LQG

Cyclic

Asymptotically static

(Bojowald)

(Ellis et al.)

Figure 3.18 Candidate loop quantum gravity (LQG) cosmologies.

Steinhardt indicated to us that measuring the distance between the present and the beginning is ambiguous. What is not ambiguous, however, is that there is a boundary. And are the infi nite cycles a necessary feature of the theory? In personal communication, he recognized that the theory does not require an infi nite number of cycles.

Steinhardt, similar to Maurizio Gasperini, suggested to us a pragmatic view of his model.

The model’s description of the approach to the past boundary (and the boundary) is not (yet) rigorous. The boundary referenced by the BVG Theorem could be the mark of something fundamental, such as a singularity, or instead be the marker for a transition to different physics. If one asserts that the boundary merely marks the transition to different physics, then the issue as to the age of the precycling confi guration asserts itself. Signifi -

cantly, Steinhardt argues the cyclic solution is a dynamic attractor (this is rigorous) (pers.

comm., January 27 and 30, 2004). What this means is that if one sets up the system with generic initial conditions within the twin-brane confi guration, it will automatically, within a fi nite time, converge to the cyclic solution. Thus, the precycling confi guration would have a fi nite lifetime. Thus, there is still an unexplained origin. So the Ekpyrotic universe (whether the boundary represents a genuine singularity of not) can safely be said to begin to exist.69

IVb. Loop Quantum Gravity (LQG)

Another theory of quantum gravity is the loop quantum approach (Figure 3.18). LQG takes the view that space-time itself is quantized; that is to say, space-time is divided into discrete constituent parts. It is a theory that aims to fi ll in the gap in standard GR by answering the question, what really happens at a singularity?

According to LQG, singularities do not really exist. As in string theory, there is a minimum size to nature that prevents microscopic mathematical infi nities. Hence, time and space do 69. Rüdiger Vaas has suggested that, while the cycling in the Ekpyrotic model had an origin, the brane components themselves could be past eternal. As we have seen, however, an explanation is necessary as to how they got into their initial noncycling state a fi nite time to the past. Vaas does not provide one (Vaas 2004, p. 17).

170 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

not come to an end as one comes to a “singularity.” There will be a past timeline. This leads to the conclusion of an asymptotically static past, or a true cyclic past.

Martin Bojowald is the foremost exponent of this approach. We may think of Bojowald’s model as a variation on the old Tolman cyclic model. There is only one universe. There are only three spatial dimensions. There is no “free” energy injected into the situation (such as there is in infl ationary or Ekpyrotic scenarios). The Tolman model had two problems which prevented its wide acceptance: (1) there is no known physical mechanism for producing a cyclic “bounce” and (2) thermodynamic considerations show that the universe of the present day should have achieved thermodynamic equilibrium (“heat death”). This suggests that the past is fi nite. Bojowald recognizes both problems and believes that he can solve them. His basic approach is the same to both issues; the problems will turn out to vanish upon the generalization of current “classical” theory into LQG.

With regard to the fi rst problem, the major diffi culty has been resolving a type of chaos predicted to occur near classical singularities70. This chaos, named “BKL” after its discoverer s (Belinsky, Khalatnikov, and Lifshitz) has been shown to be “calmed” by a loop quantum approach. As of 2007, some loop quantum theorists have been able to show that, for certain idealized models, a transition through a Big Bang condition is feasible (Ashtekar, Pawlowski, & Singh 2006). So, while a generalized proof is still lacking, the project seems promising.

The second condition is more daunting. How can there be truly cyclic behavior (one cycle looks pretty much like the last one, although there is not an event-by-event recurrence) when the second law of thermodynamics predicts that entropy must increase from cycle to cycle? Using a semiclassical approach to calculate entropy, Penrose fi nds that the end of our current cycle (the “Big Crunch”) should differ in entropy from the Big Bang singularity by the stupendous factor of 1022 (Penrose 2005, p. 730).71 Given no energy input from outside (and Bojowald argues that the system is truly closed), how can this outcome be avoided? There seem to be three possibilities:

1. The problem is epistemic only. In a 2004 paper, Bojowald and his colleagues appear to favor this solution:

While the effective dynamics is consistent with our expectations for both the beginning and the end of the universe, the apparent time reversal asymmetry remains. This is explained by the fact that the situation is, in fact, time asymmetric due to our own position in the universe.

We can see only some part of it, not the whole space-time, and in particular we see only a small part of the beginning. With the current understanding, the observable part of our universe can well be part of a classical space-time with a very inhomogeneous initial singularity.

70. This is the same type of chaos that Ellis mentioned as an obstacle to infi nite contraction models in section IIIa and is related to the problem mentioned by Banks for oscillating models (section IIIb).

71. Penrose considers that there are 1080 baryons in the observable universe. He then suggests that the maximum entropy for the universe is equivalent to a black hole with this mass. Should the fate of the universe be to ultimately collapse in a “Big Crunch,” this would be the entropy contributed by these 1080 baryons. Penrose uses the Hawking–Bekenstein formula for the entropy of a black hole, and in natural units (where constants of nature such as the speed of light are set to unity), fi nds that this entropy is approximately 10123. The entropy of our universe in the current day is far lower than this by about 22 orders of magnitude.

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KA LA M C O S M O LO G I C A L A RG U M E N T 171

Since most of the initial singularity is unobservable, however, it is not discussed further. The fi nal singularity, on the other hand, is completely unobservable until it is reached. If we compare only observable properties from within the universe, we simply cannot possibly know enough to tell whether past and future singularities are similar. If we compare the theoretical structure of a space-time from outside, then we conclude that in fact there is no conceptual difference between the beginning and the end of a generic spacetime.

Only if we compare the observable part of the initial singularity with the theoretical expectation for a fi nal singularity does the time asymmetry appear. (Bojowald & Hossain 2004, p. 38)72

2. Our current “classical” understanding of entropy is misleading. Bojowald suggested this possibility in personal communication:

The interpretation of entropy is as a measure for the lack of information an outside observer can obtain if he just knows macroscopic parameters such as the total mass or angular momentum.

The situation in non-equilibrium thermodynamics is more complicated, which would be relevant, e.g., for colliding black holes or violent stages of cosmology. For cosmology, it is also not so clear what the total entropy should be associated with mathematically, so a counting is diffi cult. For black holes, on the other hand, entropy refers to degrees of freedom in the black hole region, which can be identifi ed and counted within the theory.

Black hole entropy then describes the lack of information in classical stages of black holes (how many quantum states there are for given mass and other parameters). This is an absolute lack of knowledge in classical gravity because the black hole region is concealed from outside observers.

With quantum theory, however, black holes evaporate and thus reveal information at later stages (although it is still disputed to what degree this is realized). The lack of information is then only temporary and apparent because an outside observer is simply not patient enough to wait until he can recover all information. In other words, entropy in this context is observer dependent and not an absolute quantity. Since it includes only the black hole but not the observer or anything outside, it is also not the entropy relevant for cosmology.

The usual intuitive picture in cosmology is as follows: When there are many black holes, this apparent entropy is very high for outside observers. But if all degrees of freedom are considered, including those in the black holes which will re-emerge after evaporation, or one waits until after the black holes have evaporated one would obtain a smaller amount. This does not mean that entropy decreases; the accessibility of information by observers just changes. (pers.

comm., February 28, 2006; emphasis added)

3. Cycle by cycle, the entropy state is genuinely reversible. Again, this alternative emerges in personal communication:

Sinclair: ‘What it sounds to me you are saying in this last communication is that (with regard to the cyclic model) the same energy is endlessly recycled. This is a closed system, unlike some other cosmological proposals out there. Hence you are talking about a system that is fully reversible. This isn’t a case where there are dissipative, irreversible processes that build up over time and produce the “heat death” scenario.’

72. Note that the terms “initial” singularity and “fi nal” singularity refer to the states that begin and end our current cosmological cycle. Bojowald et al. are not referring to the beginning and end of time.

172 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

Bojowald: ‘At least in the cyclic version. If there is no recollapse at large volume, the universe would just have gone through a single bounce and will keep expanding. The end may be such a heat death, but since we don’t know the fi eld content of our universe (as evidenced by the dark matter and dark energy puzzles) the far future may be quite different from what it appears to be now’. (pers. comm., February 28, 2006)

It is important to note that Bojowald (and his colleagues) are not committed to a model with a past-infi nite number of cycles, as his last response shows. He is open to the possibility of an irreversible rise in entropy as a function of time. So the fact that entropy rises, cycle by cycle, and would trip up a proposed past infi nite cyclic model is not, per se, a test of the viability of the loop quantum approach as a candidate for quantum gravity. Instead our interest (in this section) is limited to beginningless cyclic models.

Considering the fi rst solution, Bojowald’s reply to Penrose would be that there is a large, unobservable part of the initial singularity that is a genuine generic manifold, that is, a state of maximum entropy featuring random inhomogeneity and anisotropy. Hence, the entropy of the initial and fi nal singularities would be similar. An infl ation mechanism (of a small patch of this manifold) would then produce the requisite homogeneity and isotropy of the current FRW universe. Penrose, however, had anticipated this objection. Using an anthropic observer selection argument, he argues that the size of the infl ationary patch we should expect to see should be much smaller based on thermodynamic criteria (by the factor 10(10∧123)) (Penrose 2005, p. 763).

Penrose suggests that life might need a universe only 1/10 the size of our current (visible) universe. He obtains the probability of an appropriately sized initial patch of a generic manifold using the Hawking–Bekenstein equation for the entropy of a black hole. The exponent “123” in Penrose’s formula is based on the square of the mass within the observable universe. So multiplying the radius of the universe by a tenth would have the following effect: the mass within this smaller sized universe would be reduced by a factor of 10−3

(since volume is proportional to r 3), and mass is squared in the entropy formula. Hence, the exponent is reduced by 6; so the overall entropy is reduced from (10123) to (10117). The probability of fi nding ourselves in either state would be approximately 10 raised to the appropriate power.73

How many more infl ationary events in a multiverse, then, would produce a life amenable but smaller universe? This is obtained from dividing out the probabilities: E =

−( ∧

10 117)

−( ∧

10 123)

Take the logarithm of both sides and simplify:

LOG( E) = −10117 +10123 = 10123.

Here −10117 is negligible compared with the larger 10123. Hence, E = 10(10∧123). The reciprocal of this represents the likelihood of fi nding ourselves in a big universe versus a small one.

73. The entropy is related to the number of possible confi gurations of a system of particles. The number of confi gurations is approximately equal to the exponential of the entropy. Given the size of the numbers involved, there is essentially no difference between ex and 10 x. So Penrose uses base 10 for convenience.

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KA LA M C O S M O LO G I C A L A RG U M E N T 173

So it is exceedingly improbable to fi nd ourselves as the product of an infl ationary event of a generic manifold, as Bojowald et al. originally proposed. Hence, Penrose argues, the entropy of the initial manifold must be exceedingly low.

Aside from this, the epistemic argument takes no account of entropy generation during the cycle. Over infi nite time, this would have to be a factor, although it may be negligible for a single cycle. Eggs break, people get old, stars burn out. This entropy may be negligible compared to black hole formation. But over infi nite cycles, it would add up.

The second solution – that the “classical” understanding of entropy is misleading –

mitigates the problem of entropy growth but does not resolve it. While entropy as classically calculated may be too high (i.e. Penrose’s estimation overestimates entropy due to contex-tual lack of information), the quantum approach still recognizes entropy (and entropy growth) as a genuine physical quantity. Black holes are still highly entropic. So their formation during a cycle, especially if one lands in a Big Crunch, would still cause a fi nal manifold to have more entropy than an initial manifold. One would still expect that this situation would imply a beginning, since it implies a heat death given infi nite cycles. Hence, Bojowald is only being realistic in opting for the third solution, that the cyclic LQG model does, indeed, need to be fully reversible.

But opposing the second law of thermodynamics is a formidable task; one recalls the words of early twentieth-century cosmologist Sir Arthur Eddington:

If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations – then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation – well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. (Eddington 1948, p. 74) So the question is, can LQG really prove reversibility? We must await further developments in the fi eld. It is fair to say that the prevailing view in cosmological community at large disagrees with Bojowald. As Bojowald himself admits, the jury is still out: Sinclair: ‘Is the assumption of entropy reversal: a) an initial assumption around which a self-consistent LQG model is built, or b) a natural fallout of LQG models?’

Bojowald: ‘It is defi nitely b), as far as we can see it currently. Many details have to be fi lled in, but we do not make any a priori assumptions about entropy. Since entropy is not a fundamental object but a measure for our ignorance of what is happening microscopically, it is not even possible to make such an assumption in a theory like loop quantum gravity. We can only make assumptions on microscopic objects, and then see what this implies for more common quantities. What we don’t know yet is how entropy changes balance out exactly. So we are not sure if entropy does not increase from cycle to cycle. We can only say that the usual black hole arguments are not as strong as usually assumed’. (pers. comm., March 29, 2006; emphasis added)

To his credit, Bojowald has not simply assumed zero net entropy in his model. He is using the right approach; allowing the physics to predict entropy accrual over time. So far, however, the only reliable conclusion is that LQG may show that Penrose’s entropy arguments must be modifi ed from their semiclassical orientation (what we have called option 2). This has failed to show, however, that universe entropy does not increase cumulatively

174 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

cycle-by-cycle. The force of Penrose’s argument remains intact even if his quantitative assessment of entropy must change.

Aside from the entropy issue, there remains the issue of dark energy, which may have the potential to stop cycling and induce an open-ended expansion. The current empirically observed dark energy effect, for example, appears adequate to produce an open-ended accelerated expansion. This result would be defi nitive if the dark energy were of the form of a cosmological constant (i.e. its value were independent of space and time; see Barrow

& Dabrowski 1995).74 As related earlier (Overbye 2006), this does appear to be the fate of the present day universe. But if an entropy gain (cycle-to-cycle) is denied, one can never have more than one “cycle.” The cosmological constant would have led to open-ended expansion the fi rst time. Hence, the initial singularity (our Big Bang) represents an absolute beginning.

If the dark energy were of the form of “quintessence” (i.e. had a value that is dependent on space and/or time), however, then it would be possible that its value could reverse and be consistent with a collapse phase, even given the current observational evidence.

But then a new problem could intrude. Bojowald recognizes that after the bounce and the following energy transfer, different modes of the matter fi elds will become excited such that the next bounce will differ from the preceding one. But if the quintessence term changes, then perhaps the most generic model of LQG would be a hybrid

between the cyclic and single-bounce models. On some particular cycle a value for the quintessence term would be such that it would lead to an open-ended expansion. Bojowald responds,

If there is just a cosmological constant, it would be fi xed for all cycles and not change. But if there is some kind of quintessence, you are right that its initial conditions for the classical phase would be affected by the bounce transition. So your scenario can be realized in suitable quintessence models. However, what people usually prefer are quintessence models which have an attractor behavior at late times, or the so-called tracking solutions. This allows one to avoid too much fi ne-tuning, and it makes the dynamics less sensitive to changes in initial values. For such models one thus does not generically expect big changes between cycles. On the other hand, since the effect would be quite dramatic if open-ended expansion can be realized, even a non-generic possibility can be important. (pers. comm., March 9, 2006)

Given an infi nite number of rolls of the dice, any nonzero probability that quintessence could produce an open-ended expansion would be suffi cient to do so. An open-ended expansion implies that that the overall number of cycles has been fi nite, and hence, the model would not be beginningless.75

In general, LQG looks like a promising alternative to string theory as a candidate for quantum gravity. But building a genuinely beginningless cyclic LQG model seems to be a far more diffi cult challenge.76

74. According to the National Aeronautics and Space Administration (NASA) (http://map.gsfc.nasa.gov/m_mm/

mr_limits.html), their current data tends to favor the cosmological constant theory for dark energy as opposed to quintessence, although the latter is not ruled out.

75. Barrow and Dabrowski do indicate that if the dark energy were of the type to decay away into matter and radiation; that is, if it is impermanent, then cycling would recommence after the decay.

76. We note that there are other LQG models that feature Vaas-type pseudobeginnings and seem to us to be viable.

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KA LA M C O S M O LO G I C A L A RG U M E N T 175

Creation ex nihilo scenarios

Semiclassical quantum gravity

“Tunneling from nothing”

“No boundary”

(Vilenkin)

(Hawking–Hartle)

Figure 3.19 Quantum models with an explicit beginning to the fi nite past.

IVc. Semiclassical creation ex nihilo models

When infl ation was fi rst explored as a concept, it was understood to be a phase in the history of our universe that occurred sometime after the origin event and ended long ago. This naturally led to the question: “How could infl ation itself have started?”

(Figure 3.19).

That understanding has changed with the work of cosmologists such as Andrei Linde (chaotic infl ation) and the recent work on the String Landscape by pioneers such as Suss-kind, Bousso, and Polchinski (and many others). Here, infl ation is not viewed just as a phase in development but instead as the dominant feature of a larger multiverse, within which our “universe” is just a regional phenomenon. Nevertheless, given the singularity theorems developed by Borde, Vilenkin, and Guth, infl ation itself is viewed as not past eternal.77 Hence, the old question still persists: How did infl ation get started? Vilenkin (1982) explains an approach he initiated to address this question:

Many people suspected that in order to understand what actually happened in the beginning, we should treat the universe quantum-mechanically and describe it by a wave function rather than by a classical spacetime. This quantum approach to cosmology was initiated by DeWitt and Misner, and after a somewhat slow start received wide recognition in the last two decades or so. The picture that has emerged from this line of development is that a small closed universe can spontaneously nucleate out of nothing, where by ‘nothing’ I mean a state with no classical space and time. The cosmological wave function can be used to calculate the probability distribution for the initial confi gurations of the nucleating universes. Once the universe nucleates, it is expected to go through a period of infl ation, driven by the energy of a false vacuum. The vacuum energy is eventually thermalized, infl ation ends, and from then on the universe follows the standard hot cosmological scenario. (Vilenkin 2002, p. 2; emphasis added)

Vilenkin uses quantum tunneling of a particle through a potential well as an analogy for the whole universe. In Figure 3.20, the ‘ E > 0’ line represents an ordinary, closed FRW

77. One remembers, of course, exceptions such as asymptotically static models and Linde’s objection that the behavior of the whole may not be the same as its parts.

176 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

Energy diagram for the “tunneling from nothing” scenario

Energy of a small, finite-

Quantum mechanically,

sized universe of energy

there is a probability

“E”. Universe oscillates

that the universe could

The universe now

between size zero and

tunnel through this

commences an open-

classically forbidden

ended de Sitter

1 as, classically, it is

“trapped” by the height

region to radius a

expansion.

of the potential.

E > 0

(potential) U

Energy = 0

a 1

a 2

a 0

a (scale factor)

In the limit as the energy of

Even from “nothing”, there

universe goes to zero, the

A de Sitter universe of initial

is a finite probability of a

radius also goes to zero.

radius a

universe creating tunneling

0 is formed as a

Out of this point, where

creation ex nihilo event.

event through the classically

there is no space, time,

forbidden region.

matter, or energy, a universe

emerges.

Figure 3.20 Creation ex nihilo of a universe.

universe, which (classically) does not have enough energy to escape into an open-ended expansion. Hence, it goes through continued Big Bang/Big Crunch cycles. In classical physics (GR), this state of affairs would persist forever.78 But quantum gravity provides a way out. There is a fi nite probability that, instead of a recollapse, the universe will “tunnel”

through the energy barrier and commence an infl ationary expansion instead.

This approach still does not solve the problem of creation; rather it has moved the question back one step: to the initial, tiny, closed, and metastable universe. This universe state can have existed for only a fi nite time. Where did it come from?

Vilenkin’s solution was to consider what happens in the limit as the energy of this initial closed universe becomes zero. The scale factor of the universe becomes zero as well. This is the genesis of the claim that the universe is created from “nothing.” There is no space, time, matter, or energy. This constitutes a topological transformation: “Creation of a universe from nothing . . . is a transition from the null topological sector containing no universes at all to the sector with one universe of topology S3” (Vilenkin 1994, p. 23). Vilenkin grants that nothingness so conceived is not the same as the absence of being: 78. Assuming, of course, that the problems of cyclic cosmologies (entropy buildup, bounce physics, etc.) were solvable.

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KA LA M C O S M O LO G I C A L A RG U M E N T 177

Hawking–Hartle geometry

Lorentzian metric: time

and evolution behave

normally

Age of universe

Size of universe

Euclidean metric: universe

“is neither created nor

destroyed”

Figure 3.21 Transition to “normal” time in a Hartle–Hawking approach. This is really just a mathematical technique called analytic continuation, which is useful for problems with “badly behaved”

functions, but which does not imply ontological commitment.

I understand that a universe of zero radius is not necessarily the same thing as no universe at all. But mathematically my quantum tunneling from nothing is described by the same “shuttlecock” geometry as Hartle and Hawking [NB Figure 3.21]. (In fact, the shuttlecock fi rst appeared in my 1982 paper.) This geometry is certainly not past-eternal, and there is no point on the Euclidean sphere which you can identify as the initial universe of zero size. So, if the Hartle-Hawking approach avoids the “paradoxes of creation”, I don’t see why my mine doesn’t. (pers.

comm., October 23, 2006)

The mathematical description of a tunneling universe suggests that time, space and matter came into being a fi nite time ago. “Nothing” refers to the “prior” state. (pers. comm., October 30, 2006)

The universe clearly has a beginning in this approach. But the claim seems to go beyond this: the universe “came into being” from a “prior” state of “nothing.” This latter claim (that the universe comes into being) is signifi cant because the notion of time becomes ill defi ned in these models near the beginning.

A similar approach to Vilenkin’s is the “no-boundary proposal” of James Hartle and Stephen Hawking. Hartle and Hawking make use of Richard Feynman’s approach to QM.

Feynman’s (1985) approach is to fi nd the probability for a certain fi nal quantum state by a path integral, a “sum over histories.” In quantum terms, this is a superposition of states.

Every possible universe history is part of the wave function; each possible end state has an associated probability of realization (alternatively, one can view all the possible states as existing “somewhere” in a realized multiverse). The path integral of the universe, as one might imagine, presents an intractable problem; hence, Hartle and Hawking make an educated guess as to a subset of possible universes that are expected to dominate the calculation and assert compact spaces only in order to solve the problem that path (or contour) integrals often are badly behaved. They tend to diverge and give nonsense answers (such as “infi nity” for a probability).

To rectify the divergence problem, Hartle and Hawking make use of Euclidean metrics to describe the earliest phases of the universe’s existence. This is a mathematical technique called analytic continuation (or more specifi cally, a Wick rotation), which allows one to analyze a better behaved function in the domain of interest. A “normal” or “Lorentzian”

178 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

metric has signature (–,+,+,+), indicating a special character to the time dimension. A Euclidean metric (+,+,+,+) treats time the same as it does the space dimensions. The Wick rotation takes the real time variable “T” and replaces it with the imaginary quantity “I ×

T”. Here “i” is the square root of negative one. Thus, Hartle and Hawking are said to employ

“imaginary time” in their model.

The use of a Euclidean metric has the effect of removing the initial singularity predicted by “pure” GR – hence the term “no boundary proposal.” There is, in general, no ontological commitment associated with this change in metric signature. But Hawking, in his popular writings, appears to assert the physical reality of the Euclidean signature. This is the genesis of Hawking’s claim that “[the universe] would neither be created nor destroyed. It would just BE” (Hawking 1988, p. 141). Hawking goes on to ask “What place, then, for a creator?”

Yet, curiously, Hartle and Hawking also claim their universe can be interpreted to have come into being out of “nothing”:

One can interpret the functional integral over all compact four-geometries bounded by a given three-geometry as giving the amplitude for that three-geometry to arise from a zero three-geometry; that is, a single point. In other words, the ground state is the probability for the Universe to appear from nothing. (Hawking & Hartle, 1983, p. 2961) [They then refer to Vilenkin’s “tunneling from nothing” paper.]79

A third interpretation of these results exists as well. Recall that Gott and Li have criticized the creation ex nihilo approach on two grounds. (1) Transitions in QM are always between allowed classical states (Vilenkin and Hartle–Hawking’s approach has a transition from a classically forbidden region to a classically allowed region). (2) The Vilenkin and Hartle–Hawking approaches should contain realistic energy fi elds (something closer to what we actually see in nature). If they did, then Heisenberg’s uncertainty principle would require that the initial state of their models have a fi nite and nonzero energy. It that is the case, then semiclassical quantum models actually start in a classically allowed metastable state, rather than “nothing.” Gott and Li elaborate:

The problem with this model [Vilenkin and Hawking–Hartle] is that it ignores the “zero-point energy.” If there is a conformal scalar fi eld φ, then the “energy” levels should be En = n + 1/2.

Even for n = 0 there is a “zero-point-energy.” The potential makes the system behave like a harmonic oscillator in the potential well near a = 0. A harmonic oscillator cannot sit at the bottom of the potential well – the uncertainty principle would not allow it. There must be some zero-point-energy and the particle must have some momentum, as it oscillates within the potential well when the fi eld φ is included. Thus, when the “zero point-energy” is considered, we see that the initial state is not a point but a tiny oscillating (0 < a < a 1) big bang universe, that oscillates between big bangs and big crunches (though the singularities at the big bangs and big crunches might be smeared by quantum effects). This is the initial classical state from which the tunneling occurs. It is metastable, so this oscillating universe could not have existed forever: after a fi nite half-life, it is likely to decay. It reaches maximum radius a 1, and then tunnels to a classical de Sitter state at minimum radius a 2 where a 2 < a 0. (Gott & Li 1998, p. 38; emphasis added)

79. Note that in Vilenkin’s comment (above), he indicates that the geometry of his model can be understood in terms of an initial Euclidean metric (which would represent the “forbidden” region of the energy diagram (Figure 3.20).

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KA LA M C O S M O LO G I C A L A RG U M E N T 179

The relevant question for the interpretation of these models, then, is: Is the universe (i) created from nothing, (ii) neither created not destroyed but, in effect, timelessly subsistent, or (iii) left ultimately unexplained, since the existence of the initial, metastable, closed, Planck-sized universe out of which our universe was born is not itself accounted for?

Option (i), if adopted, clearly implies that the universe began to exist. Nonetheless, as even Vilenkin himself recognizes, “nothing” as he describes it is not the same as absence of being. Whatever reality underlies the laws of QM must exist at least, so as to transform the null topological sector into an FRW universe. The laws themselves, if they exist, are mere abstract objects of a propositional nature and so do not stand in causal relations to anything. As such they are irrelevant to what happens in the world; it is the reality that corresponds to them that distinguishes merely logical from real possibility. As Heinz Pagels once remarked: “This unthinkable void converts itself into the plenum of existence–a necessary consequence of physical laws. Where are these laws written into that void? What “tells” the void that it is pregnant with a possible universe? It would seem that even the void is subject to law, a logic that exists prior to space and time” (Pagels 1985, p. 347). Option (i), then, is mistaken, being based upon an idiosyncratic use of the word “nothing.” That initial state is clearly not nothing, but something.

As for option (ii), Hawking himself seems to give good grounds for treating their proposal as an instrumental approach only. In his collaboration with Roger Penrose, The Nature of Space and Time (Hawking & Penrose 1996), he demonstrates the same mathematical approach (analytic continuation) to describe pair production of electron–positron pairs in a strong electric fi eld. This is a standard mathematical technique sometimes used when complex analytic functions are better behaved in a certain domain than their real counterparts. It does not imply ontological commitment to the alternative description, however. It seems to us that given the unintelligibility of the “imaginary time” region in these models, it is most reasonable to treat this approach as nonrealist in character.

As for option (iii), we seem to have the same sort of situation that we encountered with the Emergent and PBBI models with their associated metastable ESS and SPV states. The universe cannot be past eternal because the initial metastable state can have had only a fi nite lifetime. This seems to us to be the most reasonable option to take for a realist interpretation of these models. It employs known, meaningful interpretations of physical phenomena from “classical” quantum theory and extends them to the quantum gravity models.

One avoids the problems associated with the novelty of asserting a zero-energy condition for the initial state (denied by the Heisenberg uncertainty principle), the novelty of asserting a quantum transition from a forbidden to a classically allowed state (normal quantum theory only includes transitions over or through forbidden regions from one allowed state to another), and it is consistent with more realistic energy fi elds. Option (iii) is also consistent with the second premise of the kalam cosmological argument.

2.34. Summary

Taking as a springboard challenges to the Hawking–Penrose singularity theorems, we have surveyed the historical development of three research programs each pursuing known exceptions to the theorems:80 (1) CTCs; (2) violation of strong energy condition (eternal 80. The fourth and fi fth conditions, viz., satisfaction of a generic energy condition and the existence of a closed trapped surface in our past are easily met.

180 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

infl ation); and (3) falsity of GR (quantum gravity). Major theoretical developments concerning options (2) and (3) were infl ationary theory (repulsive gravity) and semiclassical quantum gravity.

CTCs, while interesting, seem to fail given the CPC. Counterexamples to the conjecture can be found, but they seem to be unphysical and/or infi nitely fi ne-tuned toy models.

As for infl ation, an exotic type of energy fi eld possesses the bizarre property of negative pressure. This energy wants to collapse in on itself due to pressure, yet according to Einstein’s equations, pressure also produces a gravitational force. If the pressure is negative, the gravitational force is repulsive. It turns out that the repulsion is the stronger of the two tendencies; greatly so. The universe can expand many orders of magnitude in a fraction of a second; from invisibly small to bigger than the entire observable sky. This development permitted a reappraisal of the question of origins that lasted two decades. Finally, a new singularity theorem, developed by Arvind Borde, Alexander Vilenkin, and Alan Guth showed that this model – the infl ationary universe – still had a beginning in the fi nite past.

It is fascinating to note that the recent history of cosmology can be mapped by attempts to overcome these singularity theorems. Following the BVG Theorem in 2003, attempts to build models have been based on exceptions to that theorem. These were (1) average past expansion of universe is negative (contraction-bounce), (2) average past expansion is zero (asymptotically static universe), (3) average past expansion is zero (cyclic universe), and (4) exotic space-time.

The fi rst, somewhat akin to the de Sitter universe, featured an infi nite contraction into a bounce at the singularity, followed by our current expansion. But it featured a Hobson’s choice between an acausally fi ne-tuned contraction or an infi nitely distant beginning point.

In either case, the bounce was predicted to be chaotic (due to BKL oscillations), and hence its “Big Bang” would look nothing like the one we actually measure.

The second case, exemplifi ed by the Emergent model class, features an unstable or metastable initial state followed by an infl ationary expansion. But an unstable state (ESS) or a metastable state (the LQG addition to the Emergent model) has a fi nite lifetime. So the beginning of the universe reasserts itself.

The third case has long been known, since the original models of Richard Tolman, to be problematic on entropy grounds. Baum and Frampton have sought to solve this problem through an approach dubbed “the phantom bounce.” Here, the universe undergoes a superexpansion aided by the effects of “phantom” energy, which accelerates the expansion with effects similar to infl ation. The universe would then fractionate into a multiverse, with almost all of the daughter universes having jettisoned their entropy given the initial expansion. Could this work? It does not appear so, the chief diffi culty being that causal reconnection of universe likely occurs at the “turnaround” point (when expansion goes over to contraction) leading to one contraction, rather than to many. A more certain conclusion is that, even given an “empty” universe81 undergoing contraction, chaotic fl uctuations as the contraction nears a singularity would create matter, thereby leading to a chaotic crunch, which would prevent cycling.

The fourth case features a deconstruction of time itself. It postulates two mirror-image, infl ationary expansions, where the arrows of time lead away from a past boundary. Thus, 81. That is, except for the zero entropy phantom energy.

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the mirror universe is not our past. This is just a case of a double Big Bang. Hence, the universe still has an origin.

What about the attempts at quantum gravity models (many of which overlap with those previously discussed)? They include (1) string models, (3) LQG models, and (3) semiclassical quantum gravity models.82

The most popular new fi eld is the class of string models. Two prominent approaches are the Ekpyrotic/cyclic and PBBI models. But the fi rst is subject to the BVG singularity theorem and hence has a beginning. The second is probably to be interpreted instrumentally only and seems in any case to have the characteristics of the Emergent class with respect to the initial state. Hence, it has a metastable beginning phase, called the SPV, which cannot be eternal in the past. The most popular string model is the generalization of infl ationary theory known as the String Landscape. This scenario, however, is known to have a beginning to the fi nite past due to the same BVG Theorem.

LQG is a competitor to string theory. We saw one such application when LQG was

incorporated into the Emergent model class. Another LQG approach is to try to build a viable cyclic model. LQG seems a promising approach to address the issue of BKL chaos, hence, perhaps, providing a justifi cation for a bouncing model. But the cyclic LQG still seems to fail to account for the entropy effects that usually doom infi nite cyclicity. Even if it did, current observations show that our universe is in an open-ended expansion rather than a Big Bang/Big Crunch cycle. So current LQG attempts do not appear to support a past eternal universe.

The semiclassical quantum gravity models have, in their very approach, a beginning to the fi nite past. The beginning has been described in three possible (and not consistent) ways. Either:

1. The universe came into being from a prior state of null topology (but somehow containing the laws of physics themselves) to a Lorentzian metric (the normal universe).

Hence, the universe “tunneled from nothing” into existence.

2. The initial state of the universe is uncreated. This is due to the nature of time in a Euclidean metric. It is equivalent to a spatial dimension.

3. Because the initial state of the geometry must have a zero point energy, it is in a classical state with a Lorentzian metric. It is a metastable closed universe. Hence, this state could not have existed forever and, in a manner unexplained by the model, began to exist.

The second description seems to be purely instrumental in character. The fi rst and third imply that the universe began to exist. Hence, semiclassical models are supportive of the universe’s having a beginning.

Our survey shows that contemporary cosmology is quite supportive of the second

premise of the kalam cosmological argument. Further, this conclusion is not reached through ferreting out elaborate and unique failure conditions for scores of individual 82. In interests of economy, we have not discussed earlier attempts to postulate a regional, immanent status for the Big Bang which leave the origin of the initial space in question. It would seem that this space cannot contract, expand, or be static without violating criteria mentioned earlier (singularity theorems, chaotic bounces, metastable beginnings, etc.). Thus, these models proved to be untenable.

182 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

Table 3.1 Effective principles in ruling out a beginningless model

Model average expansion history

Condition requiring a beginning

1) Expanding models

Singularity theorems

2) Asymptotically static models

Metastability

3) Cyclic models

Second law of thermodynamics

4) Contracting models

Acausal fi ne-tuning

models. Rather, the repeated application of simple principles seems effective in ruling out a beginningless model.83 They are found in Table 3.1.

It seems that the fi eld of cosmology, therefore, yields good evidence that the universe began to exist.

1.0. Everything That Begins to Exist Has a Cause

To return, then, at length to the fi rst premise of the kalam cosmological argument 1.0. Everything that begins to exist has a cause,

we take (1.0) to be obviously true – at the least, more plausibly true than its negation. Three reasons can be given in its support.

1.1. Ex nihilo nihil fi t

First and foremost, the principle is rooted in the metaphysical intuition that something cannot come into being from nothing. For to come into existence without a cause of any sort is to come into being from nothing.84 To suggest that things could just pop into being uncaused out of nothing is to quit doing serious metaphysics and to resort to magic. Nobody sincerely believes that things, say, a horse or an Eskimo village, can just pop into being without a cause. But if we make the universe an exception to (1.0), we have got to think that the whole universe just appeared at some point in the past for no reason whatsoever.

Sometimes it is said that quantum physics furnishes an exception to the claim that something cannot come into being uncaused out of nothing, since on the subatomic level, 83. This does not exhaust the list of possible model formulations. Different types of mosaic models are likely to be the next thing to come down the pike. Nor did we survey every model that exists in the present (nor could we). There is also the complaint of philosopher James Brian Pitts: “What rights do unborn theories possess?”

84. See Oppy’s suggestion that we construe the fi rst premise to assert that everything that begins to exist has a cause of some sort, whether effi cient or material (Oppy 2006b, p. 153). His protest that the cause of the universe could then be a material cause is not troubling because the incorporeality of the First Cause plausibly follows from a conceptual analysis of what it is to be a cause of the space-time universe, on which see further discussion below.

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so-called “virtual particles” come into being from nothing. In the same way, certain cosmogonic theories are interpreted as showing that the universe could have sprung into being out of the quantum vacuum or even out of nothingness. Thus, the universe is said to be the proverbial “free lunch.”

This objection, however, is based on misunderstanding. In the fi rst place, wholly apart from the disputed question of whether virtual particles really exist at all,85 not all physicists agree that subatomic events are uncaused. A great many physicists today are quite dissatisfi ed with the traditional Copenhagen interpretation of quantum physics and are exploring deterministic theories like that of David Bohm.86 Indeed, most of the available interpretations of the mathematical formalism of QM are fully deterministic. Quantum cosmologists are especially averse to Copenhagen, since that interpretation in a cosmological context will require an ultramundane observer to collapse the wave function of the universe. Thus, quantum physics hardly furnishes a proven exception to (1.0). Second, even on the indeterministic interpretation, particles do not come into being out of nothing. They arise as spontaneous fl uctuations of the energy contained in the subatomic vacuum, which constitutes an indeterministic cause of their origination. Third, the same point can be made about theories of the origin of the universe out of a primordial vacuum. Popularizers touting such theories as getting “something from nothing” apparently do not understand that the vacuum is not nothing but is a sea of fl uctuating energy endowed with a rich structure and subject to physical laws. Such models do not, therefore, involve a true origination ex nihilo.87

Neither do theories such as Vilenkin’s quantum creation model. Vilenkin invites us to envision a small, closed, spherical universe fi lled with a so-called false vacuum and containing some ordinary matter. If the radius of such a universe is small, classical physics predicts that it will collapse to a point; but quantum physics permits it to “tunnel” into a state of infl ationary expansion. If we allow the radius to shrink all the way to zero, there still remains some positive probability of the universe’s tunneling to infl ation. As we have seen, Vilenkin equates the initial state of the universe explanatorily prior to tunneling with nothingness. But postulating such an equivalence is grossly misleading. As Vilenkin’s own diagram illustrates (Vilenkin 2006, p. 180), quantum tunneling is at every point a function from something to something (Figure 3.22). For quantum tunneling to be truly from nothing, the function would have to have only one term, the posterior term.

Another way of seeing the point is to refl ect on the fact that to have no radius (as is the case with nothingness) is not to have a radius, whose measure is zero. Thus, there is no basis for the claim that quantum physics proves that things can begin to exist without a cause, much less that universe could have sprung into being uncaused from literally nothing.

A more pertinent objection to the justifi cation of (1.0) on the basis of the metaphysical principle that something cannot come from nothing issues from the partisans of the B-Theory of time (Grünbaum 1967, p. 153; 2000, p.16). For B-Theorists deny that in beginning to exist the universe came into being or became actual. They thereby focus attention on the theory of time underlying the kalam cosmological argument. From start to fi nish, the kalam cosmological argument is predicated upon the A-Theory of time. On a B-Theory 85. See Weingard (1982) for doubts.

86. See Cushing (1994) and Cushing (1998).

87. See remarks by Kanitscheider (1990).

184 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

Publisher's Note:

Permission to reproduce this image

online was not granted by the

requested to refer to the printed v ersion

of this chapter.

Figure 3.22 Quantum tunneling of the universe to an infl ationary condition. Note that the tunneling is at every point from something to something; the origin of the initial point remains unexplained.

(source: Vilenkin 2006)

of time, the universe does not in fact come into being or become actual at the Big Bang; it just exists tenselessly as a four-dimensional space-time block that is fi nitely extended in the earlier than direction. If time is tenseless, then the universe never really comes into being, and, therefore, the quest for a cause of its coming into being is misconceived.

Although G. W. F. Leibniz’s question, Why is there (tenselessly) something rather than nothing? , should still rightly be asked, there would be no reason to look for a cause of the universe’s beginning to exist, since on tenseless theories of time the universe did not begin to exist in virtue of its having a fi rst event anymore than a meter stick begins to exist in virtue of having a fi rst centimeter. In affi rming that things which begin to exist need a cause, the mutakallim assumes the following understanding of that notion, where “x”

ranges over any entity and “t” ranges over times, whether instants or moments of nonzero fi nite duration:

A. x begins to exist at t iff x comes into being at t.

x comes into being at t iff (i) x exists at t, and the actual world includes no state of affairs in which x exists timelessly, (ii) t is either the fi rst time at which x exists or is separated from any t′ < t at which x existed by an interval during which x does not exist, and (iii) x’s existing at t is a tensed fact.

By presupposing an A-Theory of time, according to which temporal becoming is real, the mutakallim justifi ably assumes that the universe’s existing at a fi rst moment of time represents the moment at which the universe came into being. Thus, the real issue separating the proponent of the kalam cosmological argument and critics of the fi rst premise is the objectivity of tense and temporal becoming.

It is worth recalling that having a beginning does not entail having a beginning point, lest someone should essay to avert the beginning of the universe by asserting that the series of past states of the universe might converge toward t = 0 in the metrically fi nite past as a

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merely ideal limit.88 On such a proposal, it is alleged, the universe lacks a beginning point and can therefore be said to have no earliest time of its existence. Hence, it does not, despite its past temporal fi nitude, begin to exist, and so no cause of the universe’s origin need be postulated.

It is not clear that such a proposal is even physically possible;89 but let that pass. The fundamental philosophical shortcoming of this proposal is its gratuitous assumption that having a beginning entails having a beginning point. This is not, in fact, how the locution

“begins to exist” is typically understood.90 Contemporary cosmologists frequently “cut out”

the initial cosmological singularity as a merely ideal point on the boundary of space-time, so that the universe has no fi rst instant of its existence; but they do not therefore think that the universe no longer begins to exist or that the mystery of the origin of the universe has thereby been solved.

Granted a tensed theory of time, the key criterion for determining if something has a beginning is its past metrical fi nitude.91 Something has a beginning just in case the time during which it has existed is fi nite. Time itself may be said to begin to exist just in case for any nonzero, fi nite interval of time that one picks, there are only a fi nite number of congruent intervals earlier than it. Or, alternatively, time begins to exist just in case for some specifi ed nonzero, fi nite interval of time, there are no congruent intervals earlier than it. In either case beginning to exist does not entail having a beginning point.

So understood, deleting the beginning point of a thing’s existence does not imply that that thing no longer begins to exist and therefore came into being uncaused. As mentioned, cosmologists continue to puzzle over the origin of the universe out of nothing, whether or not it had an initial instant of its existence. One is reminded in this connection of the ancient sorites-style problems of starting and stopping.92 If there is a last instant at which some object is at rest, then when does it begin to move? The answer can only be 88. Quentin Smith suggested as much on the occasion of the forum “Science and Religion,” University of California, Santa Barbara, January 30, 2004, featuring William Lane Craig, Richard Gale, Alvin Plantinga, and Quentin Smith, available in DVD format through www.veritas-ucsb.org. See also Grünbaum (2000, pp. 16–7).

89. It will depend crucially on one’s theory of quantum gravity. A typical approach to marrying quantum theory to GR involves describing the evolution of space-time as a path integral (a sum over all possible paths) in superspace, which is a space of points representing three-dimensional confi gurations of the universe. The points of this confi guration space can be regarded as instantaneous states or even as instants, but the fact that in the quantum theory one has a path integral, rather than a single path, makes it impossible to “stack” these instants into a unique history constituting a space-time. So, eventually, the dividing process becomes ill-defi ned in the theory. The fact that the fi rst split second of the universe’s existence as measured in cosmic time is not resolvable into a unique sequence of ever briefer states is not inconsistent with there being a fi rst second of its existence.

90. We might mention as well that the proposal commits us to the reality of points, which surely overloads the expression “begins to exist” with unintended ontological commitments. Such metaphysical issues should be decided by argument, not defi nition.

91. Oppy seems ready to concede that the second premise of the kalam cosmological argument is true if we accept that something begins to exist iff it is fi nite in the past (Oppy 2006b, p. 147). Given a tensed theory of time, we think that that biconditional holds for wholly temporal entities. So the remaining question, as Oppy says, is whether everything that begins to exist in this sense has a cause. While not denying the causal principle, Oppy denies that that premise is either obviously true or supported by experience (Oppy 2006b, pp. 150–3).

92. See Sorabji (1983, pp. 403–21).

186 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

that there is no fi rst instant of its motion. Nonetheless, the object does begin to move and plausibly requires a cause to set it in motion. Similarly, if a thing has not always existed, then it is plausible that that thing began to exist and requires a cause to bring it into being, whether or not there was a fi rst instant at which it existed.

In view of the seemingly evident metaphysical absurdity of something’s coming into being without a cause, one would not anticipate that naturalists would deny the fi rst premise of the kalam cosmological argument and assert that the universe sprang into existence uncaused out of nothing. It is therefore surprising how many nontheists, confronted with the evidence of the universe’s beginning, have taken this route. For example, Quentin Smith, commenting that philosophers are too often adversely affected by Hei-degger’s dread of “the nothing,” concludes that the most reasonable belief is that we came

“from nothing, by nothing, and for nothing”(Craig & Smith 1993, p. 135)93 – a nice ending to a sort of Gettysburg address of atheism, perhaps. Such a confession merely expresses the faith of an atheist. For it is, we repeat, literally worse than magic.

1.2. Why only universes?

Second, if things really could come into being uncaused out of nothing, then it becomes inexplicable why just anything or everything does not come into existence uncaused from nothing. Why do bicycles and Beethoven and root beer not pop into being from nothing? Why is it only universes that can come into being from nothing? What makes nothingness so discriminatory? There cannot be anything about nothingness that favors universes, for nothingness does not have any properties. Nothingness is the absence of anything whatsoever. As such, nothingness can have no properties, since there literally is not anything to have any properties. Nor can anything constrain nothingness, for there is not anything to be constrained. How silly, then, when popularizers say things such as

“Nothingness is unstable to quantum fl uctuations” or “The universe tunneled into being out of nothing”!

Some critics have responded to this problem by asserting that while (1.0) is true with respect to things in the universe, it is not true of the universe itself. But this proposed differentiation misconstrues the nature of the Causal Principle. Premise (1.0) does not state a merely physical law such as Boyle’s law or the second law of thermodynamics, which are contingent laws of nature. Premise (1.0) is not a physical principle. Rather, it is a metaphysical principle: being cannot come from nonbeing; something cannot come into existence uncaused from nothing. Such claims are not contingent upon the properties, causal powers, and dispositions of the natural kinds of substances which happen to exist.

Critics have given no good reason for construing such claims as merely physical rather 93. Smith’s most recent criticism of the kalam cosmological argument is also a denial of the fi rst premise, despite Smith’s avowal that he now accepts the conclusion that the universe has a cause of its existence (Smith 2007, pp.

182–98). Smith’s most recent published position is that the initial singular point of the universe is not real and that, therefore, the sequence of instantaneous states of the universe is a beginningless series converging toward zero as a limit. Each state is caused by its prior states and there is no fi rst state. Any nonzero interval or state, such as the fi rst second of the universe’s existence, “is not caused by any or all of its instantaneous states and is not caused by any external cause” (Smith 2007, p. 189). Smith takes “the beginning of the universe” to refer to the Planck era, that state which lasts until 10−43 seconds after the singularity. As a state of nonzero duration, the beginning of the universe therefore has no cause of any sort. The universe therefore comes into being uncaused out of nothing.

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than as metaphysical claims. The Causal Principle plausibly applies to all of reality, and it is thus metaphysically absurd that the universe should pop into being uncaused out of nothing.

Second, why think in any case that the universe is an exception to the rule? As Arthur Schopenhauer once remarked, the Causal Principle is not something we can dismiss like a cab once we have arrived at our desired destination. Sometimes critics will say that while it is impossible for things to come into being uncaused in time, things can come into being uncaused with time, that is, at a fi rst moment of time. But until the premise’s detractors are able to explain the relevant difference between embedded moments of time and a fi rst moment of time, there seems to be no reason to think it more plausible that things can come into being uncaused at a fi rst moment than at a later moment of time. If something cannot come into existence uncaused at t, where t is preceded by earlier moments of time, why think that if we were to annihilate all moments earlier than t, then that thing could come into existence uncaused at t? How could the existence of moments earlier than an uncaused event be of any possible relevance to the occurrence of that event?

Indeed, given a pure A-Theory of time, according to which only the present exists, every moment of time is a fresh beginning, qualitatively indistinguishable from a fi rst moment of time, for when any moment is present, earlier moments have passed away and do not exist. Thus, if the universe could exist uncaused at a fi rst moment of time, it could exist uncaused at any moment of time. There just does not seem to be any relevant difference.

It follows that if the latter is metaphysically impossible, so is the former.

Third, the objection stifl es scientifi c exploration of cosmological questions. The absolute beginning of time predicted by the standard Friedmann–Lemaître model was the crucial factor in provoking not only the formulation of the Steady-State model of continuous creation, but a whole series of subsequent models all aimed at avoiding the origin ex nihilo of our universe predicted by the standard model. Both philosophers and physicists have been deeply disturbed at the prospect of a beginning of time and an absolute origination of the universe and so have felt constrained to posit the existence of causally prior entities such as quantum vacuum states, infl ationary domains, imaginary time regimes, and even timelike causal loops. The history of twentieth-century astrophysical cosmology would be considerably different if there were thought to be no need of a causal explanation of the origin of time and the universe.

By contrast, the mutakallim cannot be similarly accused of stifl ing science because it is only with the conceptual analysis of the argument’s conclusion that he is able to identify the cause of the universe as a being of religious signifi cance, and the mutakallim will in any case welcome attempts to falsify his theistic hypothesis in hopes of corroboration of his preferred hypothesis by the failure of such naturalistic explanations.

1.3. Experiential confi rmation

Finally, (1.0) is constantly confi rmed in our experience. Scientifi c naturalists thus have the strongest of motivations to accept it. It is precisely on the strength of the role played by the Causal Principle in science that the naturalist philosopher of science Bernulf Kanitscheider warns, “If taken seriously, the initial singularity is in head-on collision with the most successful ontological commitment that was a guiding line of research since Epicurus and Lucretius,” namely, out of nothing nothing comes, which Kanitscheider

188 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

calls “a metaphysical hypothesis which has proved so fruitful in every corner of science that we are surely well-advised to try as hard as we can to eschew processes of absolute origin” (Kanitscheider 1990, p. 344). Doubtless, as mentioned earlier, this same conviction inspired many of the efforts to craft cosmological models aimed at averting the absolute beginning of the universe. If we do have good reasons for accepting the fact of the universe’s absolute origin, that fact in no way entails that the Causal Principle is false. Qua physicists, we may refuse to draw the inference implied by the two premises on the quite reasonable grounds that one thereby crosses the threshold of science into the realm of metaphysics, but qua philosophers, we are free to draw whatever inferences the premises logically imply.

Wesley Morriston opposes two other empirical generalizations to the Causal Principle which he thinks enjoy comparable support but are allegedly incompatible with the kalam argument, to wit, (i) everything that begins to exist has a material cause and (ii) causes always stand in temporal relations to their effects (Morriston 2002, p. 162). Notice, however, that neither of these principles is incompatible with the Causal Principle enunciated in (1.0).

They form a consistent triad. Morriston, in truth, offers no defeater at all for the argument’s causal premise, taken as an empirical generalization.

What is true is that the conjunction of (1.0) and (2.0) will imply the falsity of at least (i), if not (ii). As putative defeaters of the conclusion (3.0) of the kalam argument, however, (i) and (ii) are not compelling. The evidence for (i) is, indeed, impressive. But it is not unequivocal or universal.94 More importantly, (i) may be simply overridden by the arguments for the fi nitude of the past. For if it is impossible that there be an infi nite regress of past events, it is impossible that the First Cause be a material object, since matter/energy is never quiescent.95 If (2.0) commends itself to us, then, we must reject (i), and it would 94. Morriston himself takes our own power to control our actions to be the paradigm of causality. But, as J. P. Moreland argues, such control plausibly requires some sort of dualism (Moreland 1998b, pp. 68–91), in which case we have a clear counterexample to the claim that every effect has a material cause. For not only do I cause effects in my physical body, but my mental states are causally connected.

Again, many philosophers believe that immaterial, abstract objects such as numbers, sets, propositions, and so on exist necessarily and eternally. But there are also many abstract objects which seem to exist contingently and noneternally, for example, the equator, the center of mass of the solar system, Beethoven’s Fifth Symphony, Leo Tolstoy’s Anna Karenina, and so forth. None of these is a material object. Tolstoy’s novel, for example, is not identical to any of its printed exemplars, for these could all be destroyed and replaced by new books. Nor can Beethoven’s Fifth be identifi ed with any particular series of ink marks or any performance of the symphony. Now these things all began to exist: the equator, for example, did not exist before the earth did. But if they began to exist, did they have a cause or did they come into being out of just nothing? (Notice that it makes sense to ask this question even though these entities are immaterial and so have no material cause.) Many philosophers would say that these objects did indeed have causes: it was Tolstoy, for example, who created Anna Karenina. So in cases such as these (and they are legion), we do, indeed, have instances of effi cient causation without material causation.

We may not agree that such abstract objects really exist; but charity demands that we say that the view defended by our philosophical colleagues is a coherent one.

Moreover, in the realm of physics itself, we have already alluded to the creation of space in the expanding universe as a case of the effi cient causation of something real in the absence of any material cause. Moreover, some physicists have taken background fl uctuation models to be a counterexample to (i), since if the total energy of the universe is on balance zero, the universe did not borrow any energy from the vacuum and so has no material cause, even though it was spawned by the vacuum as its effi cient cause. (See Craig 1998, pp. 332–59).

95. See Craig (1991, pp. 104–8).

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be the height of folly then to go on to reject (1.0) as well. For if coming into being without a material cause seems impossible, coming into being with neither a material nor an effi -

cient cause is doubly absurd.

As for (ii), it appears to be merely an accidental generalization, akin to Human beings have always lived on the Earth, which was true until 1968. There does not seem to be anything inherently temporal about a causal relationship. More importantly, however, (ii) is not at all incompatible with the kalam argument’s conclusion, since its defender may hold that God exists timelessly sans creation and temporally at and subsequent to the moment of creation, so that His act of causing the beginning of the universe is simultaneous with the universe’s beginning to exist.96

1.4. Objections

J. L. Mackie, in response to the kalam cosmological argument, reserved his chief criticism for its fi rst premise. He complains, “there is a priori no good reason why a sheer origination of things, not determined by anything, should be unacceptable, whereas the existence of a god [ sic] with the power to create something out of nothing is acceptable” (Mackie 1982, p. 94). Indeed, he believes creatio ex nihilo raises problems: (i) If God began to exist at a point in time, then this is as great a puzzle as the beginning of the universe. (ii) Or if God existed for infi nite time, then the same arguments would apply to his existence as would apply to the infi nite duration of the universe. (iii) If it be said that God is timeless, then this, says Mackie, is a complete mystery.

Now it is noteworthy that Mackie never refutes the principle that whatever begins to exist has a cause. Rather, he simply demands what good reason there is a priori to accept it. He writes, “As Hume pointed out, we can certainly conceive an uncaused beginning-to-be of an object; if what we can thus conceive is nevertheless in some way impossible, this still requires to be shown” (Mackie 1982, p. 89; cf. Oppy 2006b, p. 151). But, as many philosophers have pointed out, Hume’s argument in no way makes it plausible to think that something could really come into being without a cause. Just because I can imagine an object, say a horse, coming into existence from nothing, that in no way proves that a horse really could come into existence that way. The mutakallim plausibly claims that it is ontologically impossible for something to come uncaused from nothing. Does anyone really believe that, however vivid his imagination of such an event, a raging tiger, say, could suddenly come into existence uncaused, out of nothing, in the room right now?

The same applies to the universe: if there was absolutely nothing prior to the existence of the universe – no God, no space, no time – how could the universe possibly have come to exist?97

96. Craig (2001, pp. 275–80).

97. Elsewhere, Mackie reveals his true sentiments: “I myself fi nd it hard to accept the notion of self-creation from nothing, even given unrestricted chance. And how can this be given, if there really is nothing?” (Mackie 1982, p. 126). It seems inconceivable that the space-time universe could have come into being without a cause, for in that case there was not even the potentiality of the universe’s existence prior to the beginning (since there was no “prior”). But how could the universe become actual if there was not even the potentiality of its existence? It seems more plausible to hold that its potentiality lay in the power of its cause to create it.

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In fact, Mackie’s appeal to Hume at this point is counterproductive. For Hume himself clearly believed in the Causal Principle. In 1754, he wrote to John Stewart, “But allow me to tell you that I never asserted so absurd a Proposition as that anything might arise without a cause: I only maintain’d, that our Certainty of the Falsehood of that Proposition proceeded neither from Intuition nor Demonstration, but from another source” (Grieg 1932, 1: p. 187). Even Mackie confesses, “Still this [causal] principle has some plausibility, in that it is constantly confi rmed in our experience (and also used, reasonably, in interpreting our experience)” (Mackie 1982, p. 89). So why not accept the truth of the Causal Principle as plausible and reasonable – at the very least more so than its denial?

Because, Mackie thinks, in this particular case the theism implied by affi rming the principle is even more unintelligible than the denial of the principle. It makes more sense to believe that the universe came into being uncaused out of nothing than to believe that God created the universe out of nothing.

But is this really the case? Consider the three problems Mackie raises with creatio ex nihilo. Certainly, the mutakallim will not hold (i) that God began to exist or (ii) that God has existed for an infi nite number of, say, hours, or any other unit of time prior to creation.

But what is wrong with (iii), that God is, without creation, timeless? This may be “mysterious” in the sense of “wonderful” or “awe inspiring,” but it is not, so far as we can see, unintelligible; and Mackie gives us no reason to think that it is.

Moreover, there is also an alternative that Mackie failed to consider, namely, (iv) prior to creation God existed in an undifferentiated time in which hours, seconds, days, and so forth simply do not exist.98 Because this time is undifferentiated, it is not incompatible with the kalam arguments against an infi nite regress of events. This alternative would require us to distinguish between time as it plays a role in physics and time as a metaphysical reality, a distinction famously defended by Isaac Newton on the basis of God’s eternal duration independent of any physical measures thereof (Newton 1966, I: p. 6). Even apart from theism, the distinction between time and our physical measures thereof is one that is quite plausible and intuitive, and, given theism, it becomes nearly incumbent, since God could experience a temporal succession of contents of consciousness in the absence of any physical world at all. Mackie, then, is quite unjustifi ed in rejecting the fi rst premise of the argument as not being intuitively obvious, plausible, and reasonable.

So it seems that the Causal Principle enunciated in (1.0) has considerable warrant for us and that putative defeaters of the principle can be undercut or rebutted.

3.0. The Cause of the Universe

From the two premises, it follows logically that the universe has a cause. This is a staggering conclusion, for it implies that the universe was brought into existence by a transcendent reality.

Or does it? As we have seen, Gott and Li have sought to avoid this conclusion by defending the extraordinary hypothesis that the universe created itself. Noting that GR allows for the possibility of CTCs, they hypothesize that as we trace the history of the universe back through an original infl ationary state, we encounter a region of CTCs prior to infl ation (Figure 3.4). According to one possible scenario, a metastable vacuum infl ates, producing 98. Such a view is defended by Padgett (1992).

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an infi nite number of (Big Bang type) bubble universes. In many of these a number of bubbles of metastable vacuum are created at late times by high-energy events. These bubbles usually collapse and form black holes, but occasionally one will tunnel to create an expanding, metastable vacuum or baby universe. One of these expanding, metastable vacuum baby universes “turns out to be the original infl ating metastable vacuum we began with.” Gott and Li conclude that “the laws of physics may allow the universe to be its own mother” (Gott & Li 1998, p. 023501–1).

We have seen that even on the physical level Gott and Li’s model is probably not a plausible account of the universe’s origin. But the Gott–Li hypothesis raises even more fundamental metaphysical issues about the nature of time which render their hypothesis either metaphysically impossible or else superfl uous. For all instances of causal infl uence over the past which have been suggested – whether we are talking about CTCs, time travel, tachyonic antitelephones, or whatever – presuppose the truth of the B-Theory of time. For on the A-Theory, at the time at which the effect is present, the cause is future and therefore literally nonexistent. Thus, the effect just comes into being from nothing. Not only is this scenario metaphysically absurd, but it also defeats the claim that the universe is self-caused.

Rather the universe just came uncaused from nothing.

Thus, the Gott–Li hypothesis presupposes the B-Theory of time. But if one presupposes such a view of time, then Gott and Li’s hypothesis becomes superfl uous. For, as we have seen, on a B-Theory of time the universe never truly comes into being at all.99 The whole four-dimensional space-time manifold just exists tenselessly, and the universe has a beginning only in the sense that a meter stick has a beginning prior to the fi rst centimeter. Although the space-time manifold is intrinsically temporal in that one of its four dimensions is time, nonetheless it is extrinsically timeless, in that it does not exist in an embedding hypertime but exists tenselessly, neither coming into nor going out of being.

The four-dimensional space-time manifold is in this latter sense eternal. Thus, there is no need for the device of causal loops or CTCs at the beginning to explain how it came into being.

Given the truth of the A-Theory of time, the idea that the universe is self-created, that is to say, that it brought itself into being via CTCs, is metaphysically impossible because it reduces to the notion that the universe sprang into existence uncaused out of nothing. The universe, then, must have an ultramundane cause.

Properties of the First Cause

Conceptual analysis of what it is to be a cause of the universe enables us to recover a number of striking properties which this ultramundane cause must possess and which are of theological signifi cance. For example, the cause must be uncaused, since, as we have seen, an 99. This is the salient point of Grünbaum’s most recent salvo against the inference to a First Cause of the origin of the universe (Grünbaum 2000). As a B-Theorist, Grünbaum does not believe that the universe ever came into being, even if it had a fi rst temporal interval. As he elsewhere writes, “coming into being (or ‘becoming’) is not a property of physical events themselves but only of human or conscious awareness of these events” (Grünbaum 1967, p. 153). What Grünbaum fails to see, however, is that the claim that an absolute beginning of the universe entails that the universe came into being is rooted, not in the presupposition of the so-called Spontaneity of Nothingness, but in an A-Theory of time.

192 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

infi nite regress of causes is impossible. One could, of course, arbitrarily posit a plurality of causes in some sense prior to the origin of the universe, but ultimately, if the philosophical kalam arguments are sound, this causal chain must terminate in a cause which is absolutely fi rst and uncaused. There being no reason to perpetuate the series of events beyond the origin of the universe, Ockham’s Razor, which enjoins us not to posit causes beyond necessity, strikes such further causes in favor of an immediate First Cause of the origin of the universe. The same principle dictates that we are warranted in ignoring the possibility of a plurality of uncaused causes in favor of assuming the unicity of the First Cause.

This First Cause must also be beginningless, since by contraposition of Premise (1.0), whatever is uncaused does not begin to exist. Moreover, this cause must be changeless, since, once more, an infi nite temporal regress of changes cannot exist. We should not be warranted, however, in inferring the immutability of the First Cause, since immutability is a modal property, and from the Cause’s changelessness we cannot infer that it is incapable of change. But we can know that the First Cause is changeless, at least insofar as it exists sans the universe. From the changelessness of the First Cause, its immateriality follows. For whatever is material involves incessant change on at least the molecular and atomic levels, but the uncaused First Cause exists in a state of absolute changelessness. Given some relational theory of time, the Uncaused Cause must therefore also be timeless, at least sans the universe, since in the utter absence of events time would not exist. It is true that some philosophers have argued persuasively that time could continue to exist even if all events were to cease (Shoemaker 1969; Forbes 1993), but such arguments are inapplicable in the case at hand, where we are envisioning, not the cessation of events, but the utter absence of any events whatsoever. In any case, the timelessness of the First Cause sans the universe can be more directly inferred from the fi nitude of the past. Given that time had a beginning, the cause of the beginning of time must be timeless.100 It follows that this Cause must also be spaceless, since it is both immaterial and timeless, and no spatial entity can be both immaterial and timeless. If an entity is immaterial, it could exist in space only in virtue of being related to material things in space; but then it could not be timeless, since it undergoes extrinsic change in its relations to material things. Hence, the uncaused First Cause must transcend both time and space and be the cause of their origination. Such a being must be, moreover, enormously powerful, since it brought the entirety of physical reality, including all matter and energy and space-time itself, into being without any material cause.

Finally, and most remarkably, such a transcendent cause is plausibly taken to be personal. Three reasons can be given for this conclusion. First, as Richard Swinburne (1991, pp. 32–48) points out, there are two types of causal explanation: scientifi c explanations in terms of laws and initial conditions and personal explanations in terms of agents and their volitions. For example, in answer to the question, “Why is the kettle boiling?” we might be told, “The heat of the fl ame is being conducted via the copper bottom of the kettle to the water, increasing the kinetic energy of the water molecules, such that they vibrate so violently that they break the surface tension of the water and are thrown off in the form of steam.” Or alternatively, we might be told, “I put it on to make a cup of tea. Would you like some?” The fi rst provides a scientifi c explanation, the second a personal explanation. Each 100. This needs some qualifi cation, since the kalam argument strictly demonstrates only that metric time had a beginning. Perhaps the cause exists changelessly in an undifferentiated time in which temporal intervals cannot be distinguished. On this view, God existed literally before creation, but there was no moment, say, 1 hour or 1

million years before creation.

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is a perfectly legitimate form of explanation; indeed, in certain contexts it would be wholly inappropriate to give one rather than the other. Now a fi rst state of the universe cannot have a scientifi c explanation, since there is nothing before it, and therefore, it cannot be accounted for in terms of laws operating on initial conditions. It can only be accounted for in terms of an agent and his volitions, a personal explanation.

Second, the personhood of the First Cause is already powerfully suggested by the properties which have been deduced by means of our conceptual analysis. For there appear to be only two candidates which can be described as immaterial, beginningless, uncaused, timeless, and spaceless beings: either abstract objects or an unembodied mind. Abstract objects such as numbers, sets, propositions, and properties are very typically construed by philosophers who include such things in their ontology as being precisely the sort of entities which exist necessarily, timelessly, and spacelessly. Similarly, philosophers who hold to the possibility of disembodied mind would describe such mental substances as immaterial and spaceless, and there seems no reason to think that a Cosmic Mind might not also be beginningless and uncaused. No other candidates which could be suitably described as immaterial, beginningless, uncaused, timeless, and spaceless beings come to mind. Nor has anyone else, to our knowledge, suggested any other such candidates. But no sort of abstract object can be the cause of the origin of the universe, for abstract objects are not involved in causal relations. Even if they were, since they are not agents, they cannot volitionally exercise a causal power to do anything. If they were causes, they would be so, not as agents, but as mindless events or states. But they cannot be event-causes, since they do not exist in time and space. Even if we allow that some abstract objects exist in time (e.g. propositions which change their truth-value in virtue of the tense of the sentences which express them), still, in view of their abstract nature, it remains utterly mysterious how they could be causally related to concrete objects so as to bring about events, including the origin of the universe.

Nor can they be state-causes of states involving concrete objects, for the same reason, not to mention the fact that in the case at hand we are not talking about state-state causation (i.e. the causal dependence of one state on another), but what would amount to state-event causation (namely, the universe’s coming into being because of the state of some abstract object(s)), which seems impossible. Thus, the cause of the universe must be an unembodied mind.

Third, this same conclusion is also implied by the fact that only personal, free agency can account for the origin of a fi rst temporal effect from a changeless cause. We have concluded that the beginning of the universe was the effect of a First Cause. By the nature of the case, that cause cannot have any beginning of its existence nor any prior cause. Nor can there have been any changes in this cause, either in its nature or operations, prior to the beginning of the universe. It just exists changelessly without beginning, and a fi nite time ago it brought the universe into existence. Now this is exceedingly odd. The cause is in some sense eternal, and yet the effect which it produced is not eternal but began to exist a fi nite time ago. How can this be? If the necessary and suffi cient conditions for the production of the effect are eternal, then why is not the effect eternal? How can all the causal conditions suffi cient for the production of the effect be changelessly existent and yet the effect not also be existent along with the cause? How can the cause exist without the effect?

One might say that the cause came to exist or changed in some way just prior to the fi rst event. But then the cause’s beginning or changing would be the fi rst event, and we must ask all over again for its cause. And this cannot go on forever, for we know that a beginningless series of events cannot exist. There must be an absolutely fi rst event, before

194 WILLIAM LANE CRAIG AND JAMES D. SINCLAIR

which there was no change, no previous event. We know that this fi rst event must have been caused. The question is: How can a fi rst event come to exist if the cause of that event exists changelessly and eternally? Why is the effect not coeternal with its cause?

The best way out of this dilemma is agent causation, whereby the agent freely brings about some event in the absence of prior determining conditions. Because the agent is free, he can initiate new effects by freely bringing about conditions which were not previously present. For example, a man sitting changelessly from eternity could freely will to stand up; thus, a temporal effect arises from an eternally existing agent. Similarly, a fi nite time ago a Creator endowed with free will could have freely brought the world into being at that moment. In this way, the Creator could exist changelessly and eternally but choose to create the world in time. By “choose” one need not mean that the Creator changes his mind about the decision to create but that he freely and eternally intends to create a world with a beginning. By exercising his causal power, he therefore brings it about that a world with a beginning comes to exist.101 So the cause is eternal, but the effect is not. In this way, then, it is possible for the temporal universe to have come to exist from an eternal cause: through the free will of a personal Creator.

A conceptual analysis of what properties must be possessed by an ultramundane First Cause thus enables us to recover a striking number of the traditional divine attributes. An analysis of what it is to be cause of the universe reveals that:

4.0. If the universe has a cause, then an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful.

From (3.0) and (4.0), it follows that:

5.0. Therefore, an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful.

This, as Thomas Aquinas was wont to remark, is what everybody means by “God.”

101. Such an exercise of causal power plausibly brings God into time, if He was not temporal already. As Moreland explains, in the case of personal causal explanations, the salient factors are the existence of an agent with his relevant properties and powers, the agent’s intention to bring about some result, an exercise of the agent’s causal powers, and in some cases a description of the relevant action plan. So “a personal explanation (divine or otherwise) of some basic result R brought about intentionally by person P where this bringing about of R is a basic action A will cite the intention I of P that R occur and the basic power B that P exercised to bring about R” (Moreland 1998b, p. 75; see further Moreland 1998a). Notice that it is insuffi cient for P to have merely the intention and power to bring about R. There must also be a basic action on the part of P, an undertaking or endeavoring or exercise of P’s causal powers. Thus, it is insuffi cient to account for the origin of the universe by citing simply God, His timeless intention to create a world with a beginning, and His power to produce such a result. There must be an exercise of His causal power in order for the universe to be created. That entails, of course, an intrinsic change on God’s part which brings Him into time at the moment of creation. For that reason He must be temporal since creation, even if He is timeless sans creation.

We should not say that in agent causation the agent causes his causing of some effect. Partisans of agent causation typically say that the agent’s causing some effect is not an event requiring a cause, either because it is not itself an event, but just a way of describing an agent’s causing an event, or if it is an event, then it is not further caused (O’Connor 2000, chap. 3). Neither alternative requires revision of Premise (1.0), which concerns, not events, but substances which come into being.

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Objections

Certain thinkers have objected to the intelligibility of this conclusion. For example, Adolf Grünbaum has marshaled a whole troop of objections against inferring God as the Creator of the universe (Grünbaum 1990b). As these are very typical, a brief review of his objections should be quite helpful.

Grünbaum’s objections fall into three groups. Group I seeks to cast doubt upon the concept of “cause” in the argument: (1) When we say that everything has a cause, we use the word “cause” to mean something that transforms previously existing materials from one state to another. But when we infer that the universe has a cause, we must mean by “cause”

something that creates its effect out of nothing. Since these two meanings of “cause” are not the same, the argument is guilty of equivocation and is thus invalid. (2) It does not follow from the necessity of there being a cause that the cause of the universe is a conscious agent.

(3) It is logically fallacious to infer that there is a single conscious agent who created the universe.

But these objections do not seem to present any insuperable diffi culties: (1) The univocal concept of “cause” employed throughout the argument is the concept of something which brings about or produces its effects.102 Whether this production involves transformation of already existing materials or creation out of nothing is an incidental question. Thus, the charge of equivocation is groundless. (2) The personhood of the cause does not follow from the two premises of the cosmological argument proper, but rather from a conceptual analysis of the notion of a First Cause of the beginning of the universe, as we have seen. (3) The inference to a single cause of the origin of the universe seems justifi ed in light of the principle, commonly accepted in science, that one should not multiply causes beyond necessity. One is justifi ed in inferring only causes such as are necessary to explain the effect in question; positing any more would be gratuitous.

The objections of Group II relate the notion of causality to the temporal series of events: (1) Causality is logically compatible with an infi nite, beginningless series of events. (2) If everything has a cause of its existence, then the cause of the universe must also have a cause of its existence.

Both of these objections, however, seem to be based on misunderstandings. (1) It is not the concept of causality which is incompatible with an infi nite series of past events. Rather the incompatibility, as we have seen, is between the notion of an actually infi nite number of things and the series of past events. The fact that causality has nothing to do with it may be seen by refl ecting on the fact that the philosophical arguments for the beginning of the universe would work even if the events were all spontaneous, causally unconnected events. (2) The argument does not presuppose that everything has a cause. Rather the operative Causal Principle is that whatever begins to exist has a cause. Something that exists eternally and, hence, without a beginning would not need to have a cause. This is not special pleading for God, since the atheist has always maintained the same thing about the universe: it is beginningless and uncaused.

Group III objections are aimed at the alleged claim that creation from nothing surpasses all understanding: (1) If creation out of nothing is incomprehensible, then it is irrational to believe in such a doctrine. (2) An incomprehensible doctrine cannot explain anything.

102. That is to say, an effi cient cause. Alternatively, we could leave the question of material causation open by taking “cause” to mean either an effi cient or a material cause. Then our conceptual analysis of what it is to be a cause of the universe will eliminate the alternative that the cause is a material cause, leaving us with an ultramundane effi cient cause.

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But with regard to (1), creation from nothing is not incomprehensible in Grünbaum’s sense. By “incomprehensible,” Grünbaum appears to mean “unintelligible” or “meaningless.” But the statement that a fi nite time ago a transcendent cause brought the universe into being out of nothing is clearly a meaningful statement, not mere gibberish, as is evident from the very fact that we are debating it. We may not understand how the cause brought the universe into being out of nothing, but such effi cient causation without material causation is not unprecedented, as we have seen, and it is even more incomprehensible, in this sense, how the universe could have popped into being out of nothing without any cause, material or effi cient. One cannot avert the necessity of a cause by positing an absurdity. (2) The doctrine, being an intelligible statement, obviously does constitute a purported explanation of the origin of the universe. It may be a metaphysical rather than a scientifi c explanation, but it is no less an explanation for that.

Grünbaum has one fi nal objection against inferring a cause of the origin of the universe: the cause of the Big Bang can be neither after the Big Bang (since backward causation is impossible) nor before the Big Bang (since time begins at or after the Big Bang). Therefore, the universe’s beginning to exist cannot have a cause (Grünbaum 1990a, 1991; cf. Craig 1994a). But this argument pretty clearly confronts us with a false dilemma. For why could not God’s creating the universe be simultaneous (or coincident) with the Big Bang?

God may be conceived to exist timelessly (or in an undifferentiated time) without the universe and in time from the moment of creation. Perhaps an analogy from physical cosmology will be illuminating. The initial Big Bang singularity is not considered to be part of physical time, but to constitute a boundary to time. Nevertheless, it is causally connected to the universe. In an analogous way, we could say that God’s timeless eternity is, as it were, a boundary of time which is causally, but not temporally, prior to the origin of the universe. It seems, therefore, that it is not only coherent but also plausible in light of the kalam cosmological argument that God existing changelessly alone without creation is timeless and that He enters time at the moment of creation in virtue of His causal relation to the temporal universe. The time of the fi rst event would be not only the fi rst time at which the universe exists but also, technically, the fi rst time at which God exists, since sans the universe God exists timelessly.103 The moment of creation is, as it were, the moment at which God enters time. His act of creation is thus simultaneous with the origination of the universe.

Conclusion

The fi rst premise of the kalam cosmological argument is obviously more plausibly true than its contradictory. Similarly, in light of both philosophical argument and scientifi c evidence, its second premise, although more controversial, is again more plausibly true than its negation. The conclusion of the argument involves no demonstrable incoherence and, when subjected to conceptual analysis, is rich in theological implications. On the basis of the kalam cosmological argument, it is therefore plausible that an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful.

103. Leftow (1991, p. 269, cf. p. 201) captures this idea nicely. Senor has dubbed such a model of divine eternity

“accidental temporalism” (Senor 1993, p. 88). See further Craig (2001, pp. 256–80).

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The Teleological Argument:

An Exploration of the

Fine-Tuning of the Universe

ROBIN COLLINS

1. Introduction: Setting Up the Argument

1.1. Nature of project and summary of sections

Historically, the argument from design probably has been the most widely cited argument for the existence of God, both in the West and the East (such as in theistic schools of Hinduism). Modern scientifi c discoveries, particularly the discovery beginning around the 1950s that the fundamental structure of the universe is “balanced on a razor’s edge” for the existence of life, have given this argument signifi cant new force in the last 30 years, with several books and many essays written on it.1 This precise setting of the structure of the universe for life is called the “fi ne-tuning of the cosmos.” This fi ne-tuning falls into three major categories: that of the laws of nature, that of the constants of physics, and that of the initial conditions of the universe, each of which we shall explore in Section 2. As will become clear in Section 5.2, the sort of life that is most signifi cant for the argument is that of embodied moral agents, of which humans are one example.

This chapter is a highly abridged version of an in-process book-length project in which I argue for the existence of God based on this fi ne-tuning of the cosmos for life along with the beauty and intelligibility of the laws of nature. The main purpose of the book is to put this argument on as rigorous as possible scientifi c and philosophical foundation. Although this chapter has the same purpose, it will focus solely on the argument based on the fi ne-tuning for life, although in my judgment the argument based on beauty and intelligibility is as strong.

The sections of this chapter are arranged as follows. In Section 1.2, I present some key terms and defi nitions for easy reference. In Section 1.3, I present the basic form of what I call the core fi ne-tuning argument for the existence of God. This argument is explicated in terms of what I call the restricted version of the Likelihood Principle. In Section 1.4, I present an alternative way of formulating the argument using what I call the method of probabilistic 1. For shorter versions of the fi ne-tuning argument appropriate for undergraduates, see Collins (2002, 2007, 2008), Leslie (1988, 1998), and Collins (www.fi ne-tuning.org). For other book-length treatments of the fi ne-tuning argument, see Leslie (1989) and Holder (2004).

The Blackwell Companion to Natural Theology Edited William Lane Craig and J. P. Moreland

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tension. In Sections 2.1–2.6, I present the evidence for fi ne-tuning and consider some of the main criticisms of this evidence.

Since I shall formulate the argument in Sections 1.3 and 1.4 in terms of certain conditional epistemic probabilities, I need to develop an account of conditional epistemic probability and a general method for determining the degree of conditional epistemic probability that one proposition has on another. I do this in Sections 3.1–3.3. In Sections 4.1–4.5, I address some further critical issues for my formulation of the fi ne-tuning argument, namely, the appropriate background information to use in the argument and the appropriate comparison range of values for the constants of physics. In Sections 5.1 and 5.2, I complete the core fi ne-tuning argument by using the results of the previous sections to derive the premises of the main argument presented in Sections 1.3 and 1.4.

In Sections 6.1–6.3, I address the so-called multiverse hypothesis as an alternative explanation of the fi ne-tuning, or at least as a way of undermining the fi ne-tuning argument for theism. The multiverse hypothesis is widely considered the leading alternative to a theistic explanation. In Sections 7.1–7.5, I reply to various miscellaneous objections to the fi ne-tuning argument, such as the so-called “who designed God?” objection. Finally, in Section 8, I conclude the entire argument.

My overall approach will be to present a version of the fi ne-tuning argument that is more rigorous than its predecessors by presenting the argument in a step-by-step fashion and then justifying each step using widely used principles of reasoning. This way of developing the argument will not only show that the argument can be developed in a philosophically principled way, but it automatically will answer many of the criticisms that have been raised against it; it also will help us go beyond a mere “battle of intuitions” between advocates and critics of the argument. Further, as much as possible, I shall avoid using theories of confi rmation that attempt to account for everyday and scientifi c forms of reasoning but whose claims go signifi cantly beyond what these forms of reasoning demand. Thus, for instance, I will avoid appealing to prior probabilities and to notions of purely logical probability that claim that relations of probability exist completely independently of human cognizers (see e.g. Sections 1.3 and 3.2).

1.2. Some key defi nitions, terminologies, and abbreviations

In this section, I shall defi ne some key terminologies and abbreviations that are used in more than one section. This will help the reader keep track of my terms and symbolisms.

1 Embodied moral agents. An “embodied moral agent” will be defi ned as an embodied conscious being that can make morally signifi cant choices, without prejudging the status of moral truths. Our main concern, however, will be with embodied beings that are relevantly similar to humans – that is, who exist in a world with fi xed laws and who can signifi cantly affect each other for good or ill. Thus, whenever I talk about embodied moral agents, this is the type of agent I shall have in mind.

2 The existence of a life-permitting universe (LPU). This will always mean the existence of a material spatiotemporal reality that can support embodied moral agents, not merely life of some sort. Indeed, in every case where I use the word “life,” I shall have in mind embodied moral agents as the relevant kind of life. The reason that embodied moral agents are the relevant kind of life will become clear in Section 5.2, where I argue that LPU is not improbable under theism. Throughout, it will be

204 ROBIN COLLINS

assumed that the existence of such beings requires a high degree of organized material complexity, such as we fi nd in the brains of higher-order animals.

3 Fine-tuning of the universe; existence of a fi ne-tuned universe; fi ne-tuning evidence; fi ne-tuning data. To stay in conformity with the literature, I shall mean by the

“fi ne-tuning of the universe” or the “existence of a fi ne-tuned universe” the conjunction of the following two claims: (i) the claim that the laws and values of the constants of physics, and the initial conditions of any universe with the same laws as our universe, must be set in a seemingly very precise way for the universe to support life; and (ii) the claim that such a universe exists, or when the background information includes the information that there is only one universe, the claim that this universe is life-permitting, where this is an indexical that picks out the one universe that actually exists. When I speak of the “fi ne-tuning evidence (data),” or “the evidence (data) of fi ne-tuning,” or variations of these, I shall be referring only to claim (i). The reason for this is that “evidence” and “data” implicitly refer to what physicists have discovered. Clearly, physicists have not discovered that the laws, constants, and initial conditions are life-permitting since we always knew that based on our existence. Rather, they have discovered claim (i). When I attempt rigorously to formulate the argument, the distinction between claim (i) and claim (ii), and the distinction between the “fi ne-tuning of the universe” and the “fi ne-tuning evidence (or data)” should be kept in mind.

4 Fine-tuning of a constant C of physics. When discussing a constant C of physics (see Sections 2.3 and 4.2), I shall use the term “fi ne-tuning” specifi cally to refer to the claim that the life-permitting range of C – that is, the range of values that allows for life – is very small compared with the some properly chosen “comparison range” for that constant.

(For how to choose this comparison range, see Sections 4.3 and 4.4.) In connection with a constant C, the term “fi ne-tuning” will never be used to include the claim that it has a life-permitting value.

5 Constant C has a life-permitting value (Lpc). This denotes the claim that the value of a constant C is such that, given the laws of nature, the initial conditions of the universe, and the values of the other constants, the universe would allow for the existence of the relevant type of life – namely, embodied moral agents.

6 The Theistic hypothesis (T). According to this hypothesis, there exists an omnipotent, omniscient, everlasting or eternal, perfectly free creator of the universe whose existence does not depend on anything outside itself.

7 The naturalistic single-universe hypothesis (NSU). This is the hypothesis that there is only one universe, the existence of which is an unexplained, brute given, and that within that universe the laws and constants of physics do not signifi cantly vary from one space-time region to another. NSU does not build in any hypothesis about the structure of the universe that does exist, other than that it is some sort of material, spatiotemporal reality that obeys physical laws; it also excludes any transcendent explanation of the universe, be that explanation theistic or nontheistic.

8 Multiverse hypothesis. This is the hypothesis that there are many universes or regions of space-time in which the constants and initial conditions of the universe, and in some versions the laws themselves, vary from universe to universe. The naturalistic multiverse hypothesis is the hypothesis that there is no transcendent explanation for such a multiverse.

9 P(A|B) and conditional epistemic probability. P(A|B) represents the conditional epistemic probability of a Proposition A on another Proposition B. See Sections 3.1

and 3.2 for details.

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