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University of Pittsburgh

[This article was originally published in Philosophy of Science, Vol. 60, No. 4, December 1993, pp. 638-646.]

In Grünbaum (1989, 374, 390), I objected to Narlikar's (1977, 136-137) designation "event of 'creation'" for a supposed first cosmic instant t = 0, which he imports into the big bang cosmology of the general theory of relativity (GTR). Narlikar (1992, 361-362) does reject a theological construal of the creation." But, endeavoring to justify his secular creationism, he now points out that, in the GTR, the usual derivation of matter-energy conservation from Hilbert's stationary action principle cannot be extended to include the putative first instant t = 0. Narlikar reasons that this "breakdown" in the derivation of energy conservation at t = 0 qualifies the putative initial event as the "creation event." I argue that this inference is multiply fallacious.

1. Introduction. As I noted in Grünbaum (1989, 389-391), two sorts of big bang models--which I denominated as Case (i) and Case (ii)--have figured in discussions of creationist interpretations of the big bang. But, as I remarked, the first of these two classes is not countenanced by the classical general theory of relativity (GTR) (Torretti 1979, 328-329; 1983, 210-219; 1984, 197; Tipler 1987; Barrow and Tipler 1986, 442-443).

In the Case (i) model, the big bang is putatively the temporally first physical event of the spacetime, and is said to occur at the instant t = 0. But this scenario is not countenanced by GTR precisely because the big bang does not meet the requirements for being a physical event in the GTR. Instead, the big bang is a "singularity" in at least the sense that, as we approach it, the spacetime metric of the GTR becomes degenerate, and the scalar curvature as well as the density become infinite.

The view that this singular status robs the big bang of its event-status in the GTR has been carefully justified by J. Stachel (1993): As he showed, points of the theoretical manifold first acquire the physical significance of being events, when they stand in the chrono-geometric relations specified by the spacetime metric, which does double duty, of course, as the gravitational field in the GTR. As Stachel put it, "in general relativity, there is no structure on the differentiable manifold that is both independent of the metric tensor and able to serve as an individuating field-that is, to turn the [ideal] points of the manifold into points of [physical] space-time."

Thus, in the GTR it turns out that the notion of an event makes physical sense only when both manifold and metric structure are well defined around it. And in that theory, spacetime is taken to be the collection of all physical events. Thus, the big bang does not qualify as a physical event of the spacetime having three spatial coordinates and one time coordinate.

Case (i) features a cosmic time interval that is closed at the big bang instant t = 0, and furthermore, this instant had no temporal predecessor. In this relativistically illegitimate case, which nonetheless figures in the debate, t = 0 was a temporally first event of the physical spacetime at which all of the world-lines of the universe originated. Thus, there simply did not exist any instants of time before t = 0. But the relativistically bona fide big bang models under Case (ii) differ from those in the forbidden Case (i) by excluding the mathematical singularity at t = 0 as not being a physical event or an actual moment in time.

I nonetheless dealt with the relativistically spurious Case (i) as well, because J. Narlikar (1977, 136-137) and others have invoked it to give what I see as an ill-founded creationist twist to the question of the temporal origin, if any, of the universe. As Narlikar explains, "when one goes beyond the classical relativistic cosmology" (1992, 361), the inauthenticity of t = 0 as an instant of time "may disappear." Upon taking its authenticity for granted, he argues for its status as "the event of creation" in reply to my critique of his views (Grünbaum 1989).

I will now clarify and elaborate on my criticism of Narlikar (1977), then I will explain why I claim that Narlikar's (1992) defense of his secular creationism fails. But I must refer the interested reader to my new and most detailed critique of the doctrine of divine creation and conservation as being logically incompatible with the twentieth-century physical cosmologies (Grünbaum 1996).

2. Narlikar's Creationist Conception of the Most Basic Question of Cosmology. Narlikar complains that most cosmologists neglect the most basic cosmological question, which he transforms into a problem of creation:

The most fundamental question in cosmology is, 'Where did the matter we see around us originate in the first place?' This point has never been dealt with in big-bang cosmologies in which, at t = 0, there occurs a sudden and fantastic violation of the law of conservation of matter and energy. After t = 0 there is no such violation. By ignoring the primary creation event most cosmologists turn a blind eye to the above question. (Narlikar 1977, 136-137)

Narlikar had set the stage for this formulation of his question as follows:

So we have the following description of a big-bang Universe. At an epoch, which we may denote by t = 0, the Universe explodes into existence. . . .

The epoch t = 0 is taken as the event of 'creation.' Prior to this there existed no Universe, no observers, no physical laws. Everything suddenly appeared at t = 0. The 'age' of the Universe is defined as the cosmic time which has elapsed since this event. . . .

Although scientists are not in the habit of discussing the creation event or the situation prior to it, a lot of research has gone into the discussion of what the Universe was like immediately after its creation. (Ibid., 125)

Note immediately a significant ambiguity in Narlikar's sentence, "Prior to this [i.e., prior to the big bang] there existed no Universe." It could have either of two meanings: (i) there existed moments of time before the big bang, but the physical universe did not yet exist at those prior times, or (ii) not even moments of time existed prior to the big bang, let alone a physical universe. Narlikar's wording suggests, and his 1992 article confirms, that he opts for the existence of prior times: "scientists are not in the habit of discussing the creation event or the situation prior to it" (emphasis added).

This assumption of the existence of prior times shows how Narlikar construes his fundamental cosmological question, "Where did the matter we see around us originate in the first place?" He presumably takes it to be asking how the presumed event at t = 0, which he calls "the primary creation event," came about temporally. By the same token, it is this reading of the question he has in mind in his complaint that "by ignoring the primary creation event most cosmologists turn a blind eye to the above question."

In Narlikar's view, "as a physical theory, the classical big bang cosmology is less than complete [temporally] on the issue of origin of the universe" (1992, 362). But until and unless his envisioned modification of the big bang model can come up with an integrated account of moments of time existing prior to t = 0, his invocation of them renders his question ill-founded and indeed question-begging, because the pertinent big bang model simply rules out their very existence.

By the same token, it was misguided on the part of Pius XII (1952) to insist on asking "how matter reached this [big bang] state . . . and . .what went before it" (p.190). Unaware of the cogent reason for the absence of a scientific answer to this Munchausen question, he opined, "In vain would he [the questioner] seek an answer in natural science, which declares honestly that it finds itself face to face with an insoluble enigma" (ibid.). Yet Pius XII assures us that philosophy and theology can do better. Elsewhere (Grünbaum 1996), I have argued extensively against the various underpinnings of that thesis. And as Barrow and Tipler (1986, 442) point out correctly, in the context of the big bang model under discussion, the question "what happened before t = 0?" makes just as little sense as to ask, in the case of a universe featuring an unbounded past of infinite duration, "what happened before the Universe began?"

3.Narlikar's Secular Creationist Argument from the "Breakdown" of Energy Conservation. In a very recent response to my 1989 article Narlikar (1992) has offered a defense of his account against my criticism of his views. He presented the following arguments.

1. Speaking of the "law of conservation of energy and momentum," he says, "I may term an event as a 'creation event' if it involves a breakdown of the above conservation law. In using the word 'creation' I may still be open to Grünbaum's criticism of the word in the philosophical context. However, I will go by the dictionary meaning [of the transitive verb 'to create,' which means] 'bring into existence' (see Pocket Oxford Dictionary)" (1992, 362). Thus, in Narlikar's parlance, the verb "to create" calls for both the subject or agency that does the creating, and an object, which is the product of the creative activity. Yet he agrees with me that current cosmology does not support biblical creation ex nihilo (ibid., 361, 362).

It is important to note that an event of bringing energy into existence is much more than an event involving the mere breakdown of the energy conservation law. Yet Narlikar had first made it sound as if the mere breakdown was sufficient for creation.

2. Turning to the deduction of the energy conservation law from a global symmetry principle, Narlikar says that "in special relativity . . . the temporal translation invariance results in the global law of conservation of energy" (ibid., 363). He then infers, "If there were a finite end to the time axis [such as a first or last moment of time], then necessarily the law would break down at the end. This is the reason why we may associate a creation or annihilation event with the [beginning or] end" (ibid.; emphasis added).

As for the situation in the general theory of relativity (GTR) and a big bang model embedded in it, Narlikar points out that "[t]he global translational invariance of special relativity is replaced in general relativity by the coordinate covariance locally" (ibid.). And the corresponding conservation law is "the local law of conservation of the energy-momentum tensor Tik, given by the vanishing of its covariant divergence" (ibid.). But, as J. Stachel has pointed out to me, W. B. Bonnor (1969) has shown that this condition on the covariant divergence is only necessary but not sufficient for conservation. Nevertheless, for argument's sake, let it be granted that the condition is also sufficient, since I wish to contend that, even then, Narlikar's reasoning is not sound.

Narlikar points out that if one is to derive this conservation law from Hilbert's principle of stationary action, it is necessary to consider a small spacetime 4-volume surrounding the point P(xi). However, as Narlikar explains, "The crux of the argument is that this procedure cannot be carried out if P is a boundary point of the manifold. Green's theorem cannot be applied to the boundary point" (1992, 363).

Narlikar's defense of his views prompts several corresponding sets of critical comments.

1. According to his avowed use of the term "creation event" and "creation" (ibid., 362), the event at t = 0 qualifies as the "creation" of the energy of the universe for the following reason: The energy conservation law "breaks down" at t = 0 such that the energy existing conservatively at all later times is first "brought into existence" at t = 0. Let me add that the complete text of The Oxford English Dictionary defines the passive "created" as "brought into being by an agent or cause."

However, in the context of his plea for earlier times, Narlikar's notion of bringing energy into existence at t = 0 is elliptical for two presuppositions: (i) there exist times t < 0 at which the energy did not exist yet, and (ii) its coming into existence at t = 0 is brought about by the operation of a prior cause or agency. After t = 0, the energy existed and exists conservatively.

Therefore, we must ask whether Narlikar's characterization of t = 0 as the "creation event" in the stated sense is licensed by his argument that the energy conservation law "breaks down" at t = 0, because its derivation from Hilbert's principle of stationary action cannot be extended so as to include the bounding instant t = 0.

2. One immediate, though incomplete, answer to our question is given, in effect, by Barrow and Tipler (1986):

At every [bona fide] instant of time in the Friedman universe the general relativity stress-energy conservation law . . . holds. The law does not hold at the singularity [t = 0], but the singularity is not in time. . . . [T]he conservation law would not hold on the boundary, but the boundary is not in time. . . .Mass-energy is never created or destroyed... . (P.443)

We can answer our question further on the basis of some very telling observations offered by A. Janis (private communication).

(a) In the context of the special theory of relativity, Narlikar (1992, 363) points out that the global law of energy conservation is derived from the invariance of temporal translation (via Noether's theorem). He then claims, "If there were a finite end to the time-axis, then necessarily the [conservation] law would break down at the end" (emphasis added).

But his assertion of such a necessary breakdown at the temporal termini is apparently based on his assumption that the conservation law can be legitimated in the theory only by the particular derivation he mentions. Evidently, he relies on just this assumption to infer that at whatever times the given derivation does not hold, notably at temporal endpoints, the energy conservation law itself also does not hold. This inference, in turn, serves as Narlikar's basis for his further animadversion that at t = 0, "there occurs a sudden and fantastic violation of the law of conservation of matter and energy" such that energy was first brought into existence at this "creation event" (1977, 125, 136-137).

For argument's sake, let it be granted that the legitimation of this law does require the stated derivation. Then, as Janis remarked, the assumed categorical breakdown of its derivability so as to exclude t = 0 would show that the energy attribute is not defined at t = 0. But it does not license Narlikar's conclusion that at t = 0 there is a "sudden and fantastic violation of the law of conservation" such that (i) there were earlier times t < 0 after all at which no energy existed, and (ii) energy first came into existence at t = 0. The mere breakdown of derivability at t = 0 allows, for example, that even if there were earlier times t < 0, the same quantity of energy did exist at those prior times.

A fortiori, Narlikar is apparently not entitled to his contention that t = 0 constitutes a creation event at which energy is first brought into existence by a cause or agency. Thus, he apparently reasoned fallaciously when he explicitly offered the breakdown of the given derivation of energy conservation at t = 0 as "the reason why we may associate a creation . . .event" (1992, 363) with that instant.

To this, I add the decisive objection that Narlikar himself entirely undermines his own argument for a "creation event" at t = 0. By insisting that there exist instants t < 0 after all, he clearly retracts his initial pivotal assumption that t = 0 is a bounding instant of the past. But he had rested his case for the breakdown of energy-conservation at t = 0 on just that assumption. Having subverted his argument for such a breakdown by his retraction, he likewise sabotaged his claim that t = 0 qualifies as a "creation event," which is predicated on the inferred breakdown.

(b) Mutatis mutandis the same objections to Narlikar apply in the context of the GTR: The nonderivability of energy conservation from Hilbert's principle for time periods including t = 0 does not suffice to justify Narlikar's claim that, as a matter of fact, no energy whatever exists at his putative though incoherent times t < 0, but only thereafter.

As shown by Janis's criticisms of Narlikar's nonderivability argument, Narlikar has not even warranted the contention that energy came into existence at t = 0. A fortiori he has not licensed his secular creationist claim that before or at t = 0 the energy was caused to exist thereafter by being "brought into existence." And, as I have just shown decisively, Narlikar's assertion of the existence of times t < 0 (1992, 365) simply destroys his own case for a "creation event" at t = 0. These formulations of objections against Narlikar supersede some of the ones I offered earlier before he had clarified his position (Grünbaum 1989, 390; 1991, 240).

Yet I welcome, of course, Narlikar's disclaimer of the further theological attribution of energy creation to external divine intervention at or before t = 0. But I have criticized those atheists who have imposed an ideological straitjacket on the scientific legitimacy of any big bang model that features a finite age of the universe (Grünbaum 1990). I object to them on two counts: (i) As I have argued (Grünbaum 1989; 1991; 1996), there is no basis at all for their fear that any such model actually lends cogent support to religious creationism; but (ii) even if the model were to abet creationism, sound scientific practice makes it methodologically unacceptable to reject the model solely on antireligious grounds. If a model of the universe does command empirical support, then one must let its philosophical chips fall where they may.

3. Narlikar talks completely at cross purposes with me when he objects that "the way the [energy conservation] law is deduced in theoretical physics from a global symmetry principle" (1992, 363) is "at variance" with the following caveat of mine:

But let us note that even an unrestricted conservation principle does not rule out a cosmological model featuring a first moment of time, that is, a model featuring an instant that has no temporal predecessor. Why not? Because the [unrestricted] conservation of matter or energy requires only that at all existing times, the amount of matter-energy has to be the same. Such conservation does not require that every instant have a temporal predecessor. (Grünbaum 1989, 380)

Narlikar quotes this passage but not my immediately preceding sentence:

Indeed, if the principle of conservation of energy or mass-energy were to have unrestricted validity [for all times and for the universe as a whole], there could not have been any temporal process of creation out of nothing, since there could then not have been any time at which the amount of matter-energy was less than now. (Ibid.)

I issued this two-fold caveat in Grünbaum (1989, sec. 2), which was devoted to "The Traditional [Theological] Creation Argument" (Pius XII 1952), before dealing systematically with the big bang theory later in section 3, which is entitled "The New Creation Argument."

Narlikar apparently overlooked my subjunctive conditional clause "if the principle of conservation of energy or mass-energy were to have [temporally and cosmologically unrestricted] validity." Clearly, I was merely calling attention to the incompatibility of the putatively unrestricted conservation principle with creation ex nihilo, and to its own logical compatibility with a bounded finite past. These logical relations are hardly gainsaid, as Narlikar claims, by his explanation that, within the context of the GTR, Hilbert's principle does not permit the deduction of such a temporally unrestricted conservation law if t = 0 is taken as a bona fide instant of time.

4. Narlikar proposes to banish t = 0 as a singularity at which the time axis is terminated by considering it "as a defect of the classical gravity theory" (1992, 365), arising from "an incomplete understanding of how gravity operates when matter is in an extremely dense state" (1988, 67; 1992, 370). Hence he concludes, "A more satisfactory interpretation seems to me to regard the time axis as from - infinity to + infinity, whatever the solution [of Einstein's field equations]" (1992, 365).

In this vein, Narlikar explains that the classical big bang cosmology is an incomplete theory, "There exist ways of making a more complete physical theory that justifies and answers" (ibid., 370) the question "what existed prior to the big bang event at t = 0" (ibid.). In an oblique allusion to my 1989 critique of his treatment of the Case (i) models, Narlikar concludes, "To summarize then, it is not a symptom of 'confusion' to ask what existed prior to the big bang event at t = 0" (1992, 370).

But in the very 1989 paper at which he directed his 1992 reply, I had written:

If Narlikar and Lovell take the given big bang model [Case (i)] to be physically true, then the questions they have addressed to it are illegitimate, because then these questions are based on a false presupposition. Of course, they are indeed entitled to reject the model by giving cogent reasons for postulating the existence of times before t = 0. But, failing that, it is altogether wrong-headed for them to complain that-even when taken to be physically adequate-this model fails to answer questions based on assumptions which it denies as false. (pp. 389-390)

More generally, I argued in my 1989 article that questions in cosmology, no less than in other areas of inquiry, are theory-relative or theory-driven: A question that is ill-posed in the context of a given theory may well be highly appropriate within the framework of one of its rivals. Thus I hardly blocked the road to further inquiry. Indeed, I allow that there may always be unfinished business in science and that any theory whatever may be incomplete.

Narlikar's "creation" of the big bang universe would seem to be a mere origination after all if we grant that t = 0 is an authentic first instant of time. So much then for his treatment of Case (i).

Importantly, the question of initial creation--either secular or divine--does not even arise in the context of the bona fide Case (ii) models of the classical GTR, because they are temporally unbounded in the past, although the age of that big bang universe in years (circa 15 billion years) is only finite. Nor, I have argued (Grünbaum 1996), is there well-conceived scope for the operation of divine conservation in the Case (ii) models. Indeed, I have shown that divine creatio continuans is logically incompatible with them.


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Copyright © 1993 by the Philosophy of Science Association.