Stephen Hawking was admitted to the hospital, April 20, 2009, with a chest infection. I hope he is recovering well. Like millions of others, Hawking first introduced me to cosmology. Health difficulties are nothing new to Hawking, he has spent most of his life in a wheelchair, and every day of life since 1963 has been a bonus for him. That year he was diagnosed with ALS and not expected to live more than a few years. During those bonus years he wrote A Brief History of Time: From The Big Bang to Black Holes. Published in 1988, A Brief History went on to become the largest selling science book of all time. In its “Acknowledgements” Hawking says that his book discusses the basic ideas about the origin and fate of the universe in language that people without a scientific education can understand. It is necessarily from that perspective that this essay is written, for I have no scientific education.
A Brief History of Time: From The Big Bang to Black Holes recounts that in 1929, Edwin Hubble made the observation that wherever you look, galaxies are moving rapidly away from us, just as the Russian physicist, Alexander Friedmann, had predicted they were. Friedmann took Einstein’s theory of relativity at face value and accurately described our universe as expanding evenly in every direction. Cosmologists concluded that if the universe is expanding, it must originally all have been in one place at one time, and then it banged.
“There was a time, called the big bang,” says Hawking “when the universe was infinitesimally small and infinitely dense.”i This, as he goes on to say, creates a big problem for science because mathematics cannot handle infinite numbers. “This means that the general theory of relativity…predicts that there is a point in the universe where the theory itself breaks down. Such a point is an example of what mathematicians call a singularity. In fact, all our theories of science…break down at the big bang singularity.” ii An answer to how that original “point” came into existence before time and space, and why it deployed into time and space, dissolves in a singularity for most scientists. Hawking, however, believes that if his no boundary theory—central to all his popular works—is ever worked out, it will avoid the singularity—that mysterious “point”–at the big bang and predict how the universe started off.
The breakdown of mathematics is but one of Hawkins’s theory’s problems. He says that in order to predict how the universe should have started off, one needs laws that hold at the beginning of time. The beginning of time, for Hawking, is the big bang. At the big bang, physical existence was minute, therefore Quantum mechanics—our best physical theory for describing laws for minute phenomena—would be needed to describe existence. Shortly after the big bang, as the universe became large, the theory of relativity—our best physical theory for describing laws for existence in the large—would be necessary. To be consistent the two must form a continuum such that any theory that reflects physical reality now, and predicts how it must have been at the big bang, would have to combine the theory of relativity with quantum mechanics. Unfortunately these two theories are not logically compatible with each other, and no unifying theory seems to be in the offing. Hawking says that even though we do not know what could unify these theories, “We are fairly certain of some features that such a unified theory should have.”iii
In order to see what Hawking says his theory would tell us, let’s avoid the details of these features and assume that everything is resolved. What then? He says his theory would then give us a history of a particle that represents the history of the whole universe.
There would be no singularities at which the laws of science break down and no edge of space-time at which one would have to appeal to God or some new law to set the boundary conditions for space-time. One could say: “The boundary conditions of the universe is that it has no boundary.” The universe would be completely self-contained and not affected by anything outside itself. It would neither be created nor destroyed. It would just BE. iv
What would this small dense particle, with which Hawking proposes to replace the singularity that gave rise to the big bang, and leave no place for a creator v be? If all other scientific theories fail at the infinite—a singularity—how is it that Hawking’s theory about an infinitely small, infinitely dense particle does not fail? Hawking never explains how his infinitely small, dense particle is less a singularity than the singularity it is intended to replace.
Moreover, he posits this particle–”point”–as existing before the big bang, therefore before the existence of time, space, and matter. But absent time, space, and matter, there could be no particle, no time for it to be in, no space for it to occupy, no matter for it to be. There would be nothing to see, no “large class of observations,” without which, according to Hawking’s own criteria, no good theory is possible. vi
For now, let’s again sidestep these problems so as to see with Hawking what he sees as the beginning of the universe, indeed, the very seed of a universe before it bangs and forms galaxies and stars that eventually house, what he calls, insignificant creatures like ourselves. “Using the no boundary condition, we find that the universe must in fact have started off with just the minimum possible nonuniformity allowed by the uncertainty principle.” vii Briefly stated, the uncertainty principle shows that a particle of the least possible size, the quantum, behaves in ways that the human mind cannot possibly understand. An example would be a single particle that seems to occupy two places at the same time. Hawking says that “Quantum mechanics … introduces an unavoidable element of unpredictability or randomness into science.” viii This unpredictability in its lowest allowable measure is what Hawking is referring to when he says that the universe started off with the minimum possible nonuniformity allowed by the uncertainty principle. We can’t be certain of what this non-uniformity is, but Hawking assures us that without it our universe would be a thin, cold soup rather than galaxies and stars.
Here then is how Hawking’s theory describes the incipient universe: an infinitesimally small, infinitely dense particle with the smallest nonuniformity allowable under the uncertainty principle.
Hawking describes this particle as a sphere, and as a sphere, it has no singularity or edge. He uses the earth as an analogy of it, saying that he traveled round the earth without ever having run into a singularity or an edge. ix We have granted Hawking’s theory a lot of leeway, but here we must object. Because the earth is in the shape of a sphere, and one traveling around it will never run into a singularity or edge, one cannot conclude that the earth is infinite, at least not in its existence. Nothing in its shape proves that the earth cannot have had a beginning in time, and shall have an end.
Moreover, until this “infinitesimally small, infinitely dense” particle explodes, it does not exist in any physical sense of the word exist. No model can describe something beyond time and space, and time and space, as Hawking and all cosmologists have told us time and again, did not exist beyond fourteen billion years ago. Until the big bang, nothing existed. Hawking makes no sense when he describes this tiny particle as if it existed before the big bang. Nor does he make sense when he says that life and intelligence are insignificant, and that because the earth is a sphere that a person could walk forever around and never fall off, the earth is infinite. Hawking’s particle, if it is to replace the need for a creator, is going to have to make more sense than Hawking here describes it.
HAWKING’S INFINITE PARADOX
If we are not careful Hawking will roll that particle into an infinitesimally small, infinitely dense ball and sneak it by us without our seeing it and asking that haunting metaphysical question, “Where’d that come from?” If something is infinitely small, it follows that there is an infinite number of divisions that are smaller than it, and an infinite number of divisions larger. If it is infinitely dense, there are an infinite number of divisions that are denser than it and an infinite number of divisions less dense. That’s what infinite means.
No one illustrates better the breakdown of mathematics when it meets with the infinite than the fifth-century B.C.E. Greek philosopher, Zeno of Elea. Here is one of his paradoxes: Two runners are racing around a track; the second runner is gaining on the first. He halves the distance between himself and the lead runner, then halves the distance again, then halves that distance and so forth. It is mathematically impossible for the second runner to overtake the lead runner because however many times the second runner halves the distance between himself and the lead runner, there will forever be another mathematical number to halve—divide two and you get one; divide one and you get one-half; divide one-half and you get one-fourth. You can divide forever and never arrive at a last division between the two runners.
Zeno used that paradox to show some illustrious Pythagorean mathematicians of his day that their theories and formulas, divorced from the physical world, can lead to absurdities. It’s a lesson that has escaped Stephen Hawking. Laymen like me avoid the problem by simply pointing out to the Pythagoreans of Zeno’s scorn that the second runner did indeed overtake the first. The problem lies with the primacy the Pythagoreans place on mathematics. For centuries, mathematics was a religion to the Pythagoreans. They are something of an historical allegory of a tendency in humanity to put too much faith in scientific systems, the blessings of science not withstanding.
But Zeno’s paradox is less a problem than Hawking’s paradox. The failure of mathematics to describe one runner overtaking the other is not a denial that in reality the second runner overtakes the first runner, but an illustration that mathematics can neither avoid nor explain infinity. Zeno’s “infinite” is not a difficulty in reality but in mathematics. Stephen Hawking’s difficulty is not in mathematics but in reality—how does one describe something as either existing before time and space, or describe something as coming from nothing?
THE UNCERTAINTY PRINCIPLE
Remember those nonuniformities at the big bang that Hawking characterized, “as small as they could be, consistent with the uncertainty principle.”x Without these minute imbalances, he has no theory, but more importantly, he has no starry universe about which to theorize, for if the big bang were perfectly balanced, the universe would now be a thin, cold soup and Stephen Hawking would not exist.
Auto mechanics call such nearness, “clearances.” For instance, “clearance” specifies the space between a rod bearing and the crankshaft throw in an engine. Those in my 1986 Ford Ranger, four-thousands of an inch, allow a thin layer of oil to cushion the transfer of power from the up and down motion of the pistons to torque that turns the crankshaft. Too close and the bearings melt. Too wide and the rods hammer the engine to junk iron. These clearances were designed not just to convey oil, but ultimately to convey people. Designed well it seems, the old four cylinder has gone half a million miles and never had the pan pulled. It is illogical to attribute the clearances in my Ford to accident, and illogical to attribute to accident the far, far closer clearances that brought our universe to exist and persist.
Hawking says that the uncertainty principle, which I have described above as unfathomable to the human mind, “is a fundamental, inescapable property of the world,” because of which “one cannot measure the present state of the universe precisely.”xi And yet it is this very unexplainable principle that Hawking uses to explain his theory. This goes against logic. One cannot logically explain something by using in his explanation something that is unexplainable. In the case of the uncertainty principle, how the smallest particle behaves is not only unexplained, it is uncertain. And yet this uncertain particle Hawking uses to predict how the universe started off, a prediction—or theory—that he says leaves no place for a creator.
Until Hawking can predict what the quantum particle will do and why it does it he cannot justify his prediction that when it bangs it will eventuate in that just-right-billion-upon-billion-to-one imbalance that becomes stars and galaxies and his own being. A creator with a design in mind is more logical.
COCA-COLA VERSUS THE SECOND LAW OF THERMODYNAMICS
Another difficulty Mathematics has is in describing the big bang as the beginning of time. Mathematics cannot distinguish between the past and the future. Hawking’s theory sidesteps this impossible mathematical situation by relying on the 2nd law of thermodynamics to describe a universe that moves toward the future rather than the past. The 2nd law says that things that are hot now, if left unattended, will become cold in the future; buildings left unattended will grow dilapidated.
One can’t argue with this. In our experience time does indeed move toward the future rather than toward the past, much as Hawking describes it. The objection is with the idea that, because of the 2nd law, time inevitably will eventuate in chaos. I must warn people like me who have no scientific education: to object to the inevitability of the 2nd law is to be seen as a fool. Our consolation is that the exceptions to the 2nd law which these same scientist accept without question—and there is a world of them—appear far more foolish than our objection.
The cosmologist, Brian Greene, gives as such an exception the return of gas back into a soda bottle after it has wheezed out. “Don’t hold your breath waiting for this outcome…” says Greene, “but it can happen.”xii This means that the bottling of soda is itself an exception to the 2nd law. Here’s how: ingredients that, under the 2nd law, would go to entropy—disorder—are stopped on their trek to chaos, picked, cooked and put into a precise, orderly design and bottled. Even if only to satisfy our taste and quench our thirst, these ingredients are given meaning, a property not possible under an insentient 2nd law. In fact the Coca-Cola Bottling Company has been bottling and capping order in defiance of the 2nd law since 1886 .
When one opens a bottle of Coke, he opens order, he opens design. Experience compels us to reject any odds that say that once a Coke bottle is opened, it is possible that the ingredients, on their own or by some quirk of nature may return to the bottle in the same proportions they left. They were put in by the Coca-Cola Bottling Company and should they return by some quirk of nature we would call it miracle.
The objection to my Coke example is that in the bottling of Coke, energy is expended and adds to the total entropy of the universe. It does, but in no definable proportions. The physical act of concocting and bottling cola requires planning and calculating. And planning and calculating presupposes a living being with nonphysical intelligence (thoughts are not physical; they have no extension in time and space). The driving force responsible for creating intellect may not be physical energy at all, as we think of energy. Force itself is a mystery, but to complicate the Coke mystery, until we know what kind of force creates intelligence we can’t know the total amount of energy expended in creating a non-material intellect that can bottle soda, and thus cannot know the amount of energy expended in the bottling of soda. We cannot use that force in a one-for-one calculation with physical energy. We may be dealing with two different currencies here, one like the pre-Second World War Deutsch Mark and the other a 1956 dollar.
On earth, existence is not always on a one-way track to chaos, but often to order. That gas escapes from opened bottles and temperatures level out is no proof that overall disorder will prevail. Every living organism is an example of nature assembling itself into an orderly construction. Scientist are quick to point out that this exception to the 2nd law is only temporary and that shortly the organism will die and continue on its way to chaos. But the exceptions are so numerous—every living plant or animal—that reason makes one wonder if there is some rule at foot that the 2nd law is not accounting for, and which science is reluctant to consider.
In any other than a scientific context such claims as gas returning to soda bottles or dead matter assembling into living matter would be considered outrageous, especially if the one claiming it cannot explain why or how it can happen other than to say that it is an exception to the usual way things happen. Hawking not only accepts the 2nd law—outrageous exceptions and all—as inevitable, he basis a key component of his unbound theory on it. Were any one but a scientist to place such faith on a law with such supposed exceptions he would be considered a religious crackpot. The concept of design for the universe is not not nearly as outrageous as the exceptions to the 2nd law.
WHAT BREATHES FIRE INTO THE EQUATIONS?
I would like to trace back one of those billions of particles speeding away from the big bang, trace it back to that tiny speck in which all such specks were fused before they exploded. Then trace that speck back as gravity shrinks it ever smaller and denser until it arrives at a point that Stephen Hawking in the twentieth century would describe as “infinitesimally” small, “infinitely” dense. But I would like to go further back, because if this speck really is infinitely small and dense there are an infinite number of smallers and densers to trace back. Eventually my pursuit tires me and I finally ask the question that’s bugging me, “Does this speck get so small that it finally ceases to exist?”
If it doesn’t arrive at a point where it exists one second, and a second beyond ceases to exist, then it must have existed always. The other alternatives are that it materialized out of nothing (absurd), or that something already in existence caused it to exist. If the universe did not exist before the big bang, what was the big bang that caused it to exist, and why did it bang? If the universe somehow existed infinitely before time, I want to know that. If it exists now, in infinite space, or if it has finite dimensions as my house does, I want to know. These questions that deal with physical reality I would hope a scientific theory could answer for me. They are what philosophers call ontological questions.
Roger Penrose, under whom Hawking received his PhD, calls Hawking one of those “‘positivists’ who have no truck with ‘wishy-washy’ issues of ontology in any case, claiming to believe that they have no concern with what is ‘real’ and what is ‘not real.’” He quotes Hawking: “I don’t demand that a theory correspond to reality because I don’t know what it is. Reality is not a quality you can test with a litmus paper. All I’m concerned with is that the theory should predict the results of measurements.”xiii
Penrose asks, “What is the physical justification in allowing oneself to be carried along by the elegance of some mathematical description and then trying to regard that description as describing a ‘reality’?”xiv
Mathematics is real, but in no physical sense. “Two plus two equals four” is a formula that may describe physical reality, but it is not itself physical. Hawking’s theory, if ever proven, may give an accurate mathematical formula for how the universe began, but describe nothing that is or ever was materially real. Hawking closes his book with precisely this point: “Even if there is 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?”xv
The humility of this closing statement is absent from most of A Brief History of Time. He opens his Brief History by requiring that a theory of cosmology conform to close rules of science. He closes with a confession that mathematics does not answer the crucial question of physical existence. Between the opening and closing he claims that his mathematical model, the no boundary little ball, displaces any need for a creator, a hefty ambition for “just a set of rules and equations.” If his theory displaces a need for a creator, one would at least expect him to know what creation is, what reality is. This, however, he says he does not know.
Give Hawking his due. His Brief History of Time is precisely that—a good brief history of cosmology. His no boundary theory that attempts to displace a creator, however, remains with those that Brian Greene characterizes as valiant but non-conclusive.xvi Were it worked out it would not tell how the universe started off. It would simply affirm, mathematically, that the little ball has existed eternally. It would be our present universe, reduced to a tiny ball the why of whose existence and whose bang forever a mystery.
i Stephen W. Hawking, A Brief History of Time (New York: Bantam Books, 1988), 8.
xii Brian Greene, The Fabric of the Cosmos (New York: Random House, 2004), 156.
xiiiRoger Penrose, The Road To Reality (New York: Alfred A. Knopf, 2004), 785.
xivPenrose, Road, 631–32.
xvHawking, A Brief History, 174.
xviBrian Greene, The Elegant Universe (New York: W. W. Norton, 1999), 366.