The Fire in the Equations

The Fire in the Equations: Science, Religion, and the Search for God
By Kitty Ferguson
Eerrdmans, 308 pages, $25

There has been a recent proliferation of books on science and religion, and this one is among the most absorbing and vivacious. Kitty Ferguson has a gift for explaining abstruse scientific ideas with homely analogies, and her accounts are on the whole quite accurate, in spite of the fact that she is not trained as a scientist.

She is not as sure-footed, however, when it comes to the implications of scientific theories. She declares, for example, that “on the quantum level of the universe the objective truth seems to be that we lose objective reality,” which is, to say the least, debatable. She says of chaos theory and complexity theory that they “can be seen to demolish the concept of a completely deterministic, mechanistic universe,” which is untrue. The phenomenon of chaos (unlike quantum mechanics) implies nothing whatsoever about determinism. (To be fair to Ferguson, others make these mistakes as well.)

Like a number of recent authors, Ferguson treats science and religion as alternative paths in the “search for God.” She appears to wish to end the war between science and religion with a negotiated settlement, and so her public stance is that of a mediator rather than a partisan. “This is not,” she writes, “a book designed to pit science against religion and come up with a winner.” Of course, in that conflict we should not want a winner (unless we are talking about a false religion), for we are confident that any such conflict will disappear with better understanding. However, the actual contest is, for the most part, between scientific atheism and religion.

Ferguson’s irenic intentions perhaps explain a strange and somewhat irritating feature of her book. More than once she points out a fatal fallacy in some atheist idea only to trot out the same idea in a later chapter as something considerable and weighty. For whatever reason, Ferguson takes the pet philosophical ideas of some physicists far more seriously than they deserve”though she is right that these ideas, though philosophically bogus, have great currency among both physicists and popular writers on “science and religion.”

One theme of Ferguson’s book is a search for the First Cause of the universe. She presents three contenders for this role: God, Logical or Mathematical Consistency, and the Universe itself. The latter two are the popular choices of scientific atheists. As Ferguson explains it, the First Cause must be something necessary, or else it would itself require a cause. Something can be said to be necessary if logical or mathematical consistency requires it. To many scientists the laws of physics are the ultimate “cause” of everything. And some have suggested that there is a unique set of laws that is mathematically and logically self-consistent. Thus the second candidate on Ferguson’s list.

This notion presents a problem even at the level of physics, which is that the complete specification of any physical system (including the universe as a whole) includes not only the general laws of its evolution but also either initial conditions that tell how it started off, or some other boundary conditions. However, in some quarters there is hope that the laws of physics will ultimately be seen to determine the initial conditions of the universe uniquely. The celebrated Hartle-Hawking “no-boundary boundary condition” is a suggestion along these lines.

The more serious problem with this idea of the laws of physics as the necessary First Cause is that it is based on an elementary confusion. At most, the laws of physics could be said to be the “formal cause” of the physical universe, whereas by “the First Cause” is meant the efficient cause of the universe, the cause of its very existence. Hawking himself asked precisely the right question when he wrote, “Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the question of why there should be a universe for the model to describe.” That is absolutely decisive-crushing. And yet Ferguson, having quoted this and indeed taken the title of her book from it, quite unaccountably says in a later chapter, “We do have a genuine standoff between two First Cause candidates-God and Mathematical and Logical Consistency.”

Aside from all this, the idea of uniquely self-consistent physical laws has (to reverse Henry Kissinger’s phrase) the added disadvantage of being false. There are an infinite number of perfectly self-consistent sets of “rules and equations” that could be laws of physics for some hypothetical universe. The literature of physics is filled with such “models.” There are all sorts of mechanical systems, and “field theories” (both classical and quantum, “free” and “interacting,” “exactly soluble” and otherwise, in various number of dimensions), and sophisticated things like “string theories,” which are either known to be perfectly mathematically consistent or are in all probability so. What seems to be in the minds of those who speak about “unique laws” is that it is hard to come up with mathematically self-consistent theories combining certain specific features; in particular there may only be one consistent theory of quantum gravity. But gravity and quantum mechanics are not logically necessary. They are just empirical facts about the world in which we find ourselves.

What then of the idea of the Universe as First Cause? So as not to put a premature end to the discussion, let us not inquire too closely how a thing can be the cause of itself. Instead, we shall look at some of the popular versions of this idea.

The evidence that our universe has a temporal beginning is now enormously strong. In the “classical” description of the Big Bang (i.e., one that leaves quantum effects out of account) the universe has a first instant of time, which we may call t = 0 . As one goes back toward this first instant, various physical quantities (such as temperature) grow without limit. At the point t = 0 itself, if it existed, these quantities would have been infinite, and one could no longer make sense of the equations.

Such “singular points” are generally regarded with suspicion by physicists, for a number of reasons. But the point t = 0 also looks unpleasantly like a “moment of creation.” Indeed, it is often called that in popular writing on the subject. Aside, then, from purely technical motivations, there is a belief among some scientists that by banishing this point they will have struck a blow against religion. Some attempts to do this try to revive the idea, which prevailed before the discovery of the Big Bang, of a universe of infinite age. For example, there is the “Bouncing Universe” idea, and the idea of an infinite succession of parent and “baby” universes. But some recent proposals assume that the universe indeed has a finite age and seek only to get rid of that nettlesome point at t = 0 . The attitude seems to be that if there has to be a Beginning at least we do not want it to happen at an identifiable instant.

Many scientists suspect, for good reasons, that this “singularity” at t = 0 will get washed out when proper account is taken of quantum effects (which is not yet feasible). Hartle and Hawking have a speculation about this, which has been advanced not only in technical papers but in the enormously popular book A Brief History of Time .

Some idea of what is involved can be had by the analogy of a mathematical cone. Such a cone has a singular point at the sharp end, where its curvature is infinite. We can call that point “ t = 0 ” and imagine “time” as running down the cone from the smaller to the larger end. Hartle and Hawking’s idea has the effect of smoothing out that sharp point. One might imagine that, smooth or not, there still has to be an “earliest” point on the cone. But it turns out that in the Hartle-Hawking scheme time radically changes its character near “the beginning” and becomes like space. Instead of three spatial and one temporal dimensions, there are four space dimensions. It becomes impossible, then, to talk about which point is really “first.” (It should be noted that all these remarkable things would happen in the first ten-millionth of a billionth of a billionth of a billionth of a billionth of a second of the universe’s history.)

As a physics idea this is elegant and highly interesting. But does it have philosophical or theological implications? I think not. The idea does achieve the goal of getting rid of the “first moment in time,” which is why it is called the “no boundary” proposal. It may be of some comfort to those who are awed and consternated by the mathematics of “imaginary time” and quantum cosmology that the same effect of removing the “first moment” may be accomplished much more straightforwardly even in the simple and intuitively graspable classical picture-namely, just by saying that the point t = 0 is not there.

The net effect of this infinitesimal alteration is that there is no longer a first instant of time. (Just as, if we exclude the precise instant of Noon itself, there is no “first moment of the afternoon.” Each and every moment of the afternoon lies a finite time after Noon, and so has some of the afternoon preceding it.) But who could possibly care about such a quibble? How can anything of consequence depend on whether that one geometrical point, t = 0 , is or is not there? It would appear that some cosmologists like their angels to dance on the point of the pin.

The Hartle-Hawking scheme has a potentially more significant effect, in apparently eliminating the need for specifying the “initial conditions” of the universe (which some suppose to be God’s only job). In fact, however, the requirement that there be no boundary is itself just a special kind of boundary condition among many others that are logically possible. As the Harvard physicist Sidney Coleman pungently remarked in the introduction of one of his technical papers, “Although the ‘no-boundary’ boundary condition may be pretty, it is not divinely ordained, and thus [we shall also] investigate alternative boundary conditions.”

The sufficient answer to the no-boundary boundary condition as an argument against God has been well expressed by the physicist Don Page, a friend and collaborator of Stephen Hawking and, as it happens, a born-again Christian: “God creates and sustains the entire universe rather than just the beginning. Whether or not the Universe has a beginning has no relevance to the question of its creation, just as whether an artist’s line has a beginning and an end, or instead forms a circle with no end, has no relevance to the question of its being drawn.” Though Ferguson quotes this, she ends that chapter still declaring a standoff.

Another class of ideas involve explaining the Big Bang as a quantum event. In quantum mechanics one can have particles being “created out of the vacuum.” That is, there can be transitions from a state with no particles to a state with one or more particles. By analogy it has been suggested that spontaneous transitions can occur from a state with “no universes” to a state with one (or more) universes.

Whether this makes sense as physics is not yet clear. But if it does, will it give us creation ex nihilo without God? Only if one equivocates about what “nothing” and “universe” mean. A quantum state without any particles or even without any “universes” is not nothing-it is a quantum state.

Perhaps the distinction can be illustrated with an analogy. There is a difference (if not a spendable one) between a bank account with no dollars in it and no bank account at all. To have a bank account, even one with a momentarily zero (or negative) balance, requires having a bank, an agreement with that bank, a monetary system, a currency, and banking laws. Similarly, to talk about states with various numbers of “universes” requires having a quantum system with different possible “states,” and laws determining the character of those states and governing the transitions among them. The term “the universe” should really be applied to this whole system with its laws, and not, as is misleadingly done in such discussions, to “space-times” that are coming into and going out of existence.

Hawking had it right: having equations that describe a “universe” (or anything else) coming into being does not mean that these equations must be describing anything real. Having a story about fairies does not mean there are fairies.

Pascal found the “god of the philosophers” a poor thing; we can only imagine what he would have said about the gods of the physicists. What we should say is that these speculations are pretty, and some may even turn out to be true, but they leave the argument about a First Cause just where it was. There either is a First Cause and it is God, or there is no need of a First Cause. Physics can shed no light on that issue.

Does modern physics, then, have anything at all of importance to say to philosophy? It does, but paradoxically its main contribution is in supporting old ideas-religious ideas, indeed-that had been challenged on the basis of earlier science. In that earlier science matter and energy, which could “neither be created nor destroyed,” evolved according to an iron determinism against the static backdrop of an infinite space and time. There was no hint of a Beginning and no possibility of genuine freedom. But the Big Bang has brought us back to a Beginning, and quantum theory has pushed determinism out of the saddle. The discoveries of Copernicus, Darwin, and modern astronomy had, it seemed to many, relegated man to marginality and insignificance. But the growing awareness of the so-called “anthropic coincidences”-numerous fortunate features of the laws of physics that made possible the emergence of life-has led even some scientists of agnostic tendency to embrace the idea that there might be a purpose after all, and man a part of it.

The Latin apologist Minucius Felix, writing around 200 a.d. , said, “If upon entering some home you saw that everything there was well-tended, neat, and decorative, you would believe that some master was in charge of it, and that he himself was superior to those good things. So too in the home of this world, when you see providence, order, and law in the heavens and on earth, believe there is a Lord and Author of the universe, more beautiful than the stars themselves and the various parts of the whole world.” The greatest contribution of science to the “search of God” has been to bring into fuller view the grandeur of this providence, order, and law.

Stephen M. Barr is Associate Professor of Physics at the Bartol Institute, University of Delaware.