William Lane Craig vs. Stephen Hawking

With the recent release of Stephen Hawking and Leonard Mlodinow’s new book The Grand Design, a slew of news outlets published stories with provocative titles such as CNN‘s “God Didn’t Create the Universe” and ABC‘s “Science Makes God Unnecessary.”  Coincidentally, William Lane Craig, our favorite Christian apologist, has been releasing podcasts concerning his cosmological argument which happen to briefly criticize Hawking’s cosmology.

So, what does Craig have to say about Hawking? And are his criticisms valid? Well, first let’s get a bit of background on what Hawking is actually proposing.

AN ALTERNATIVE TO THE STANDARD

Contrary to what William Lane Craig often argues, the problems with using the Standard Big Bang model to describe the origin of the universe are well-accepted among contemporary physicists and cosmologists.  Rather than elaborating on the details (as I’ve done here and here), I’ll simply state that, among other issues, the singularity predicted by the Standard model is contradicted by what we know about quantum mechanics.

Indeed, Hawking and Mlodinow make this point bluntly in The Grand Design (pg. 128) where they write, ”although one can think of the big bang picture as a valid description of early times, it is wrong to take the big bang literally, that is, to think of Einstein’s theory [general relativity] as providing a true picture of the origin of the universe. That is because general relativity predicts there to be a point in time at which the temperature, density, and curvature of the universe are all infinite, a situation mathematicians call a singularity. To a physicist this means that Einstein’s theory breaks down at that point and therefore cannot be used to predict how the universe began, only how it evolved afterward.”

For this reason, physicists have proposed a number of ideas to avoid this breakdown of general relativity in order to explain the origin of the universe.  One of these ideas which has garnered much discussion is Hawking’s “no-boundary proposal,” first popularly articulated in his 1988 best-seller A Brief History of Time.  Hawking’s proposal is fairly easy to understand yet very difficult to imagine.  He describes time as being finite but without a boundary. Just think of time as being analogous to a sphere: it has a finite amount of surface area but no “beginning” or “end.”

As Hawking and Mlodinow explain, ”In the early universe — when the universe was small enough to be governed by both general relativity and quantum theory — there were effectively four dimensions of space and none of time.  … The realization that time can behave like another direction of space means that one can get rid of the problem of time having a beginning … when one combines the general theory of relativity with quantum theory, the question of what happened before the beginning of the universe is rendered meaningless” (The Grand Design, pg. 134-135).

Craig’s main criticism of this proposal focuses on the way in which Hawking converts the time dimension to a fourth spacial dimension using imaginary numbers.  As Craig explained in a recent Reasonable Faith podcast, ”Now, the interesting thing about this is that Hawking was able to achieve this result only by using imaginary numbers for the time variable.  Now, imaginary numbers are numbers which are the products of the square root of negative one. Now, there’s no real number that is the square root of a negative number … And the problem is that although these are useful tools in computations, nobody has any idea what it would mean to talk about imaginary time anymore than talking about the imaginary volume of this room … The use of imaginary numbers is just a mathematical device to make the equations easier to solve … when you reconvert to real numbers in [Hawking's] model, presto, the singularity reappears.”  Craig then goes on to claim outright that imaginary time “has no physical significance.”

IMAGINARY TIME VS REAL TIME

It should first be pointed out that imaginary numbers aren’t any more “imaginary” than most real numbers.  As mathematicians John Conway and Richard Guy write, imaginary numbers “turn out to be invaluable in many applications of mathematics to engineering, physics, and almost every other science.  Moreover, these numbers obey all the rules which you already know for ‘real’ numbers” (The Book of Numbers, pg. 212).

Conway and Guy go on to explain that irrational numbers (which are a subset of “real” numbers) , such as √2 or pi, don’t truly exist in the physical sense, yet these numbers certainly go a long way in helping us to understand reality.   A similar conclusion can be drawn about negative numbers.  For example, does negative money make sense in the real world?  Well, “negative dollars” certainly don’t exist, but they still go a long way in helping us to describe the (very real) concept of debt.

So, can imaginary numbers be used to describe the concept of time in the very early universe?  Luckily, this is discussed at length in A Brief History of Time (pg. 139).  ”If the universe really is in such a quantum state, there would be no singularities in the history of the universe in imaginary time.  … In real time, the universe has a beginning and end at singularities that form a boundary to space-time and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries.  So maybe what we call imaginary time is really more basic, and what we call real time is just an idea that we invent to help us describe what we think the universe is like.”  Hawking then suggests that asking the question “which is real” might be irrelevant, “It is simply a matter of which is the more useful description.”

While I personally have no idea whether “imaginary time” exists or not, any honest person will admit that it’s an intriguing possibility.  Craig, on the other hand, seems to reject the idea of “imaginary time” outright, the motivation for which should be obvious:  As long as the origin of the universe remains completely mysterious to science, it creates a nice gap which Craig can fill with God via the Kalam Cosmological Argument.

But maybe I’m being a bit too critical. Maybe Craig truly believes that the idea of an all-powerful, disembodied mind creating the entire universe for the benefit of a single species of mammals is simply more plausible than the idea that time could be accurately described using imaginary numbers.  The world may never know.