GUEST BLOGGER: Quentin Smith's Atheist Cosmology - Response

Interestingly enough, I had mentioned in the nether regions of the comments section that I was going to post a response to Quentin Smith in the near future. Well, that future was not near enough as unbeknownst to me IrishFarmer stopped gathering his potatoes long enough to post his response to Quentin Smith.

However, I, and as it turns out he, was responding to the first of Quentin Smith's "Two Ways to Prove Atheism." I will still post my response in the near future since we did have different takes.

Meanwhile, along came our guest blogger Andrew T who wrote a response to the second way to prove atheism. Andrew does not, as of yet, have a website or blog but perhaps his inauguration here will prompt him to get'er'done; or else he can just come back as a guest any 'ol time-yes, this is your official invitation Andrew.

And now, without further delay is Andrew T's essay:

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Quentin Smith has relatively recently promoted an atheist argument from cosmology based on James Hartle's and Stephen Hawking's wave function model for the existence of the universe. This argument is succinctly addressed in the first part of the following article: Quentin Smith, Two Ways to Prove Atheism (1996). This post will criticise the argument in the form put forward in the above link and other publications, based on work performed by William Lane Craig, Robert Deltete and Reed Guy.

Quentin Smith in the above article is attempting to refute the Kalam Cosmological argument, as contemporaneously put forward by William Lane Craig. As Quentin Smith correctly points out, the form of the argument is:

1. Whatever begins to exist has a cause.2. The universe began to exist.3. Therefore, the universe has a cause.

Quentin Smith first attacks premise 1, stating that it is not self-evidently true and can't be deduced in any way from other self-evident premises. I think there are problems in his analysis here, but the main concern of this post will be to examine his attack on premise 2, i.e. that the universe began to exist. From a cursory examination of big bang cosmology, it is clear that a somewhat unassailable case can be made for the big bang hypothesis, a hypothesis which states that the universe began in a cataclysmic rapid expansion from a seeming singularity of incredible energy density. This incredible event stemming from an essentially dimensionless point seems to intuitively confirm the creation of the universe ex nihilo, out of nothing, at least to theists. This also seems to imply an absolute beginning to the universe, at the moment of the big bang inflation from the singularity.
However, research performed by James Hartle and Stephen Hawking (hereinafter H&H)1 claims to offer evidence to reject this understanding of a beginning, stating that the universe had a high probability of existing and coming into being "naturally" from nothing (Atheism is Dead has recently posted on two views of cosmology: here and here).

In order to understand Quentin Smith's argument, it is also necessary to understand to some extent the research in question by H&H. This research is an exercise of quantum cosmology, or in other words, using the scientific theories of quantum mechanics and quantum field theory to examine the very beginning of the universe and the associated inflationary period. For those who aren't aware, quantum theories are used to examine the behaviour of the very small, which, oddly enough, is the realm of the very beginning of our universe. Big bang theory posits a singularity of unfathomably high density which is small enough to be examined in terms of quantum mechanics (along with special relativity).

H&H aim to determine the wave function of the universe. The wave function of a particle in quantum mechanics is a probability amplitude of a certain state of said particle at a certain location and time. The wave function amplitude of a state can be calculated using Richard Feynman's path integral approach, which is an interesting method. The wave function amplitude of, say, a particle at a certain time and position can be calculated by summing the paths of all possible histories of that particle, with each path having its own phase determined by something called the action S.

Essentially, most of these unusual paths will have phases such that they cancel each other out, so we are left with the classical path being the most probable. However (and this will be important later) in order to determine all the possible histories, these paths must be bounded by a previous well defined state of the particle (i.e. a well defined position or momentum of the particle at a previous time). The square of the wave function gives the actual conditional probability of the particle being in that state at a certain location and time.

The part of the research which is pertinent to this post (and Quentin Smith's position) pertains to the predicted probability of the Universe to "appear from nothing". Without trying to get too technical, the paper examines the transition of the universe from a "zero three geometry" to a non-zero three geometry, namely the three geometry of the universe we experience. A zero three geometry is a interesting state, in which the extent of the three spatial dimensions are zero and we are left with a single point, or singularity. H&H make the controversial statement that the ground-state wave function (which determines this transition from zero three geometry to non-zero three geometry) "is the amplitude for the universe to appear from nothing" [my emphasis]. In other words, H&H are controversially interpreting the zero three geometry as being metaphysically nothing. This has been challenged by a number of philosophers [see endnotes 2-4]. Yet, Quentin Smith is quick to jump on this to create an anti-theistic argument.

However, this jump is unfounded. It is now time to examine the aforementioned article by Quentin Smith. He first claims that, speaking of the wave function of the universe:

"Their theory is that there is a scientific law of nature called the Wave Function of the Universe that implies that it is highly probable that a universe with our characteristics will come into existence without a cause."

Note the phrase "come into existence". By this coming into existence, Quentin Smith actually means the transition from the zero three geometry mentioned above into a non-zero three geometry which describes the Universe. In other words, he takes the theory to state that it is highly probable that the universe comes into existence from nothing. This is understandable, for H&H do actually claim this as can be seen in the quote above. However, this interpretation is very problematic and Quentin Smith should have perhaps been more careful in taking H&H's word for it. I will address some of the problems following:

1. Quentin Smith, in another paper2, states that the probability of the ground state of the universe is an unconditional probability. In other words, it is a kind of a priori probability in that it relies on no other "given that" information and therefore can be properly said to emerge from nothing. To quote Smith, an unconditional probability is:

"a probability that is not dependent upon the existence of any concrete thing or event."

Quentin Smith is mistaken to use such a probability here however, as Robert Deltete and Reed Guy point out.3 As stated previously, in the paper H&H use quantum mechanical theory in order to determine the transition probability, or ground state wave function amplitude analogously. The problem however, is that probabilities described in QM theory are conditional probabilities.
For instance, the probability amplitude of, say, the particle being in a certain location at a certain time can be calculated by performing a Feynman path integral over all possible paths between the current state and a previous definite state. In other words, the probability can be stated as: "the probability of a particle being in position x at time t given that the particle was in state x-1 at t-1". In order to use QM theory to determine the probability amplitude of a certain state, a prior real state is needed. To quote Robert Deltete and Reed Guy:

"Even their ground-state wave function for the universe implies a transition between two states, where the initial state is a 'zero three-geometry'"

So clearly, it is erroneous to assume that the probability amplitude of the ground-state of the universe is unconditional while using conditional, dynamical (i.e. transitions between real states) QM theory. This point of view is further supported by work done by Wim Drees.4

2. The other problem that Quentin Smith encounters is a dubious definition of the zero three space as being metaphysically nothing. As stated in 1, this clearly cannot be the case as the QM theory used in the paper requires a real boundary condition to sum the paths over. Therefore, the zero three space must be something real in a sense otherwise the whole exercise of H&H is meaningless.
As Robert Deltete and Reed Guy point out, another author Alexander Vilenkin, who has retreated from his strong statements about the universe emerging from literally nothing, calls this zero three space "a pure space-time foam, without any classical space-time substrate". Whatever this is, it is certainly not a metaphysical nothing. Also, the high probability of the universe evolving into the life-permitting state that we now experience is critically dependent on this zero three space, so it is an initial condition in the real sense of the word, that not surprisingly lacks a natural explanation. This is all assuming that this mathematical speculation can be taken in a realist sense, which is what will be addressed in the next point.

3. Quentin Smith (and Stephen Hawking it seems) take a stridently realist approach to the H&H model. In other words, Quentin Smith seems to take the H&H model as describing things as they really are instead of just seeing the model as precisely that, that is, a mathematical formulation which attempts to describe the operation of something. This view is also problematic. In their paper, H&H rotate the time dimension into "imaginary time", so that non-Euclidean four space becomes a Euclidean four space. This is essentially a mathematical trick to, as Stephen Hawking puts it "avoid the technical difficulties in actually performing the sum over histories".5
This trick essentially causes the boundary, or singularity of the big bang to "disappear", instead one is left with a boundary-less early universe. With this manipulation of the time variable, it is now possible to state such problematic things as the universe arising from nothing. However, does this actually really mean anything? There is no convincing reason to take this mathematical trick as having any ontological status, as William Lane Craig describes.6 In addition to this, there are serious problems with the quantum gravity model as described in H&H and as yet has no firm footing as a viable theory.

Therefore, taking 1, 2 and 3, I believe it is clear that Quentin Smith's use of H&H's quantum gravity theory for the origin of the universe is fatally flawed, and therefore his anti-theist arguments based around this theory should not cause the theist to lose any sleep.

Finally, before finishing up this (very long) post, what should we make of Quentin Smith's bold assertions that this theory has "predicted" things like the isotropy of the universe and the structure of the COBE background radiation, and therefore that rational persons will take this as evidence for the theory and yield to subsequent anti-theist arguments? Well, I think this is a little misleading. These sorts of properties are predicted not by H&H's model per se, but rather by the earlier theories regarding the inflationary regime of the universe. The H&H model has been "grafted" onto the beginning of this inflationary regime and while consistent with the isotropy and radiation predictions, it has not made any successful predictions on its own that have not already been made by inflationary theories of the big bang, as William Lane Craig points out.7 Therefore rest assured fellow theists, one can certainly still be rational while rejecting this flawed and somewhat misleading argument.

1. 1. Hartle, J. and S. W. Hawking. 1983, "Wavefunction of the universe," Physical Review, D28: 2960-75.
   
2. 2. Smith, Q. 1997, "Quantum cosmology's Implication of Atheism," Analysis, 57: 295-304.
   
3. 3. Deltete, R.T. and Guy R.A. 1991, "Hartle-Hawking Cosmology and Unconditional Probabilities," Analysis, 57: 304-315.
   
4. 4. Drees, W. B. 1987, "Interpretation of the 'wave function of the universe,' International Journal of Theoretical Physics, 26: 939-42.
   
5. 5. Hawking, S. W., A Brief History of Time (New York: Bantam Books, 1988).
   
6. 6. Craig, W.L. 1990, "'What Place, Then, for a Creator?': Hawking on God and Creation," The British Journal for the Philosophy of Science, Vol. 41, No. 4 (Dec., 1990), pp. 473- 491.
   
7. 7. Craig, W. L. 1997, "Hartle-Hawking Cosmology and Atheism," Analysis, 57: 291-95.