Stephen Hawking’s Model of Cosmic Origins*
Because it is well-accepted that the Standard Big Bang model cannot describe the origin of the universe, there have been many proposals which attempt to explain cosmic origins. One of these ideas which has garnered much discussion is Stephen 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 their recent book The Grand Design (pg. 134-135),
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.
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.”
Now, 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, it seems to me that any honest person will admit that it’s at least an intriguing idea. Craig, on the other hand, seems to reject the idea of “imaginary time” outright.
*Note: This post is an edited version of my post on the Tuesday Afternoon blog.
Debunking William Lane Craig 
Complex numbers form a field whose mathematical properties actually correspond to real-world operations. The label ‘imaginary’ is just a vestige from the past, as is ‘irrational.’ That said, *no* number exists in the same way a physical object exist; they “exist” in the sense it is logically possible for some state of affairs to instantiate their mathematical meaning. Presumably Craig hasn’t made arguments against the standard model of particle physics on grounds the Lie groups describing the symmetries are just abstract ‘devices’ and hence can’t reflect how reality works – thus this recent defensive maneuver sounds like incredibly contrived and hasty apologetics on his part.
Also, seems silly of him to claim no one understands complex numbers. Is he projecting, or what?
I so agree with your comment. Craig is so wrong on this point…among so many more.
Imaginary time does not render the need for a “God! Poof! Magic!” explanation superfluous, the B-theory of time already does that. All imaginary time does is help avoid singularities in the past, which are entangled webs of mathematical and logical contradictions.
There are a large number of problems with this. We have factually examined the universe expanding, this isn’t open for debate. On top of that we can look into the past of the universe. We can see what the early universe is like. An expanding universe in which we can look into the past and in which the movement of space basically is the movement of time as well is completely incompatible with Hawking’s model. Hawking’s model requires space to have no beginning, yet we can look back towards a beginning. His model would not allow us to do that since he is trying to make space look like what we perceive as time, yet we can trace space back to a beginning. Changing what we consider time to a direction of space doesn’t solve any problems, since space can be traced backwards.
The ultimate killer of Hawking’s proposition though, is black holes. Singularity’s are at the core of black holes and these break the laws of physics. So, if there are no singularities in imaginary time as Hawking proposes then his position is effectively refuted.
You misunderstand Hawking’s theory. It doesn’t deny the Big-Bang as the creation of the Universe. It simply says that the Big-Bang doesn’t need a cause.
This is easy to explain, yet hard to envision. Imagine a video that replays when it’s finished.
The video itself isn’t infinite; it’s finite in size (it may be an hour long). But it continues to play over and over again. Our Universe is a replaying video. If you travelled all the way back in time to the Big Bang, and then tried to go more back… you would actually end up in the future, then back to your current time period, then back to the Big-Bang ad infinitum. Therefore, “time” is a property of the Universe, and is NOT independent of it.
Atheist scientists cannot escape the fact that there has always been something.
So, it is always ultimately just a sleight of hand to make people think that the universe came from nothing, and that is intellectual dishonesty altogether whatever many abstruse math and words you use: there has always been something, wherefore the universe did not come from nothing.
Now, if you insist that the universe has always existed, then you have to face the fact that there are things in the universe that have a beginning, and these things depend on causes to come to existence: wherefore there is ultimately the final cause within the universe which final cause has always existed.