Craig bases his claim that time began with the big bang on the notion that the universe began as singularity-an infinitesimal region in space in which the mass and energy densities are infinite. This was believed to be the case. In 1970 cosmologist Stephen Hawking and mathematician Roger Penrose used Einstein's general theory of relativity to "prove" that our universe began with a singularity.?
However, over twenty years ago Hawking and Penrose realized that no such singularity marked the beginning of our universe. Indeed, Hawking explicitly says so in his phenomenal 1988 best seller, A Brief History of Time.8 The original proof of Hawking and Penrose was not in error as far as it went. General relativity does imply the singularity. However, the authors now admit that because of quantum mechanics, general relativity does not apply below a minimum distance equal to the Planck length and below a minimum time interval equal to the Planck time. In fact, as I argued above, these are the smallest definable time and distance intervals so the universe could never have been an infinitesimal point. In short, time (or space) need not have begun with the big bang. As we will see in chapter 16, modern cosmological scenarios call for a universe prior to ours and, very likely, many more as well.
So, the universe need not have had a beginning, refitting Craig's Kalam argument. But even if there was a beginning, it need not have had a cause. In his book, D'Souza ridicules me for making such a suggestion: "Physicist Victor Stenger says the universe may be `uncaused' and may have `emerged from nothing.' He quotes philosopher David Hume as saying, `I have never asserted so absurd a proposition as that anything might rise without cause."'
Well, Hume can be excused for not knowing about quantum mechanics. But D'Souza has no excuse for either not knowing or deliberately hiding the fact that quantum phenomena such as atomic transitions and nuclear disintegrations occur spontaneously without cause. Similarly, Craig has no excuse for continuing to use the singularity claim two decades after it was withdrawn by its authors.°
THE WAVE FUNCTION OF THE UNIVERSE
In 1983 James Hartle and Stephen Hawking proposed what they called the "no boundary" model of the origin of the universe.9 Following a review by David Atkatz,10 I have worked a version of this model out with complete mathematical rigor, although I managed, with some simplifications, to do this at about the level of a senior physics or mathematics major at an American university. The details can be found in my book The Comprehensible Cosmos11 and in my article in the philosophical journal Philo, available online.12 Let me just summarize the procedure, which I hope will sufficiently convince those theists who have expressed skepticism and even ridiculed the notion.13 Hartle, Hawking, and I are not just waving our arms but have a frilly developed mathematical and physical proposal for how the universe can have come about naturally.
Start with the conventional equation derived from general relativity called the Friedmann equation, which describes the evolution of a spherically symmetric universe. Assume the universe is empty, that is, has no matter, but still contains the energy stored in the curvature of space that Einstein associated with what he called the cosmological constant. Apply the standard "quantization" technique used in quantum mechanics to go from a classical equation to a quantum one. The result is an equation that allows you to calculate a wave function that describes the state of the universe. Since the universe is empty and spherically symmetrical, the only variable is its radius.
This equation is a simplified version of what is called the Wheeler DeWitt equation. Its form is mathematically identical to the nonrelativistic, time-independent, one-dimensional Schrodinger equation for a particle in a potential field familiar from elementary quantum theory. The particle has half the Planck mass,14 zero total energy, and a specific potential energy that is defined in the book and the article. This does not mean the universe is a particle of half the Planck mass, just that its wave function is mathematically equivalent to that of this particle.
Hartle and Hawking, and others who have played this game, call this the wave function of the universe. Their particular solution is shown in figure 16.2. When the radius of the universe is greater than a certain fixed value, the wave function oscillates like a real particle, just like the particle outside the barrier in figure 16.1. This gives the exponential inflation that, according to modern cosmology, takes place during the first tiny fraction of a second before the conventional big bang. When the radius is less than this value, the wave function of the universe is in a nonphysical region analogous to the region inside the barrier in figure 16.1. Only now, time is represented by an imaginary number.
The Hartle-Hawking model of the natural origin of our universe describes a larger universe that has no beginning or end of time. This is consistent with our discussion of time in chapter 5. Out of the limitless past in the time before our big bang, assuming the arrow of time for our universe, this prior universe deflates to the point where it becomes unphysical and time is imaginary. Its wave function then tunnels through the unphysical region and our universe appears on the other side.
Note, however, the entropy in the "prior" universe increases in the opposite direction to ours; thus, the arrow of time in that universe points the opposite way. So it is really a mirror universe to ours, though not an exact image because of randomness. Both universes can be seen as emerging from the same chaos, one expanding in one time direction and the other expanding in the opposite direction. They both have a beginning after all! But it is still a causeless beginning.
Of course, talking about time having two directions throws most theologians into a tizzy. All theological discussions about creation assume an absolute direction of time and causality that is fundamentally wrong.
Alexander Vilenkin has proposed an alternate scenario in which no prior universe exists, but our universe simply tunnels one way out of chaos.15 The same mathematical procedure applies in this case.
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