This is the weekly Q & A blog post by our Research Professor in Philosophy, Dr. William Lane Craig.
I listened to your debate with Sean Carroll, read your post-debate threads, interacted with Aron Wall and Luke Barnes, and have determined that you haven't yet responded to Carroll's Quantum Eternity point against premise 2 of the kalam, "under conventional quantum mechanics, any universe with a non-zero energy and a time-independent Hamiltonian will necessarily last forever toward both the past and the future." Aron Wall confirmed that this point is independent of one's stance towards an A or B theory of time. Wall mentions on his blog that one could try to argue that the total energy of the universe is zero, but Barnes and others don't think this is the case. Do you have any response yet to Carroll on this? Even better would be a response that presupposes that the net energy of the universe is non-zero.
Dr. William Lane Craig’s Response
I encountered the point you mentioned, Kevin, in Carroll’s published work during the course of my debate preparations. I suspect that you, too, have been reading Carroll's work, since the quotation you cite above is not, in fact, to be found in our debate. Rather what Carroll says in his opening speech is
If you have a universe that obeys the conventional rules of quantum mechanics, has a non-zero energy, and the individual laws of physics are themselves not changing with time, that universe is necessarily eternal. The time parameter in Schrödinger’s equation, telling you how the universe evolves, goes from minus infinity to infinity. Now this might not be the definitive answer to the real world because you could always violate the assumptions of the theorem but because it takes quantum mechanics seriously it’s a much more likely starting point for analyzing the history of the universe.
Carroll expresses his point more fully in his 2008 article “What if Time Really Exists?” and in his 2012 blog “A Universe from Nothing?” He explains,
Let’s be clear about the scenario we are envisioning to be the case. Just as in ordinary quantum mechanics, the state of the universe is described by a wave function |Ψ〉, a ray in a Hilbert space with some number of dimensions. There exists a Hamiltonian operator H^ defined on this Hilbert space; we assume that the Hamiltonian is itself independent of time. The wave function evolves with time according to the Schrödinger equation,
H^|Ψ〉 = i∂t|Ψ〉.
. . . Assuming the validity of the Schrödinger equation has a deep, if somewhat obvious, consequence: time stretches for all of eternity. In classical mechanics, singularities in phase space can disrupt the evolution, causing time to grind to a halt. But in quantum mechanics, unitary evolution ensures that there there [sic] is no boundary to time; the variable t runs from −∞ to +∞.
I was puzzled by the significance Carroll seems to ascribe to this point, for it is a wholly theoretical claim in abstraction from any physical evidence. Saying that the time variable t runs from −∞ to +∞ just implies that quantum time evolution is information-preserving: “given the current quantum state, we can reliably reconstruct the past just as well as the future.” In other words, we can extrapolate from the present indefinitely into the past or future. This allows us to describe a moment prior to a given moment if there is such a moment; but in order to know whether there is such a moment we must look to empirical evidence.
What we want to know is whether the universe actually is extended infinitely into the past, and to answer that question one must look at the evidence. When we do that, then the theoretical scenario Carroll describes is, as he recognizes, on a collision course with observation. Namely, we run into the thermodynamic problem of our universe’s low entropy condition in the past which points to a beginning. So Carroll asks, “Can the observed arrow of time be explained by the apparently reversible physics embodied in the Schrödinger equation?” Here he discusses the famous Boltzmann Brain problem that featured so centrally in our debate. Carroll notes that Boltzmann’s model of the universe was founded on essentially the same assumptions as the quantum theoretical scenario he has described. “So the problems of this model are not simply a matter of academic or historical curiosity; they represent severe problems for any theory of the universe founded on these principles.” Carroll then describes the Carroll-Chen model as his best shot at avoiding those problems. We saw in our debate, however, some of the obstacles confronting that model.
Carroll says that in order to reconcile the thermodynamic arrow of time with his theoretical assumptions (viz., a quantum state evolving in time according to the conventional Schrödinger equation with a time-independent Hamiltonian),
we are led to conclude that the Hilbert space must be infinite-dimensional, with at least one accumulation point for the set of energy eigenvalues, and to the suggestions that the de Sitter phase toward which our current universe is evolving is somehow an unstable configuration, and that the very far past of our universe could be experiencing an arrow of time directed in the opposite sense to our own. That is a great deal of output from a rather small amount of input.
Indeed! Wouldn’t it be far simpler to question whether all of his theoretical assumptions hold? In fact, given the implausibility of Carroll’s results (e.g., a reversal of the arrow of time at some point in the past), it seems to me that we are virtually compelled to question whether the real universe conforms to all of those assumptions. For more on this, take a look atAron Wall’s blog.
For example, maybe the Hamiltonian operator H^ does have a zero value. The physicists I’ve consulted tell me that the evidence is fairly weak that there is a time-independent Hamiltonian with non-zero energies and that most quantum cosmologists think it is zero or undefined. In his blog Carroll notes that
This kind of scenario is exactly what quantum cosmologists like James Hartle, Stephen Hawking, Alex Vilenkin, Andrei Linde and others have in mind when they are talking about the ‘creation of the universe from nothing.’ In this kind of picture, there is literally a moment in the history of the universe prior to which there weren’t any other moments. There is a boundary of time (presumably at the Big Bang), prior to which there was . . . nothing. No stuff, not even a quantum wave function; there was no prior thing, because there is no sensible notion of ‘prior.’
Here we confront the evidence of big bang cosmogeny for the past finitude of the universe to which I appealed in the debate. As I argued, postulating a quantum gravity era from which our classical spacetime “emerged” does not subvert but actually supports the conclusion that the universe began to exist. Moreover, such a scenario does not imply a tenseless, static, so-called B-theory of time, since the Hilbert space in which spacetime is described is not a real space but merely a mathematical space.
In sum, we shouldn’t be misled by appeals to purely theoretical claims in abstraction from what the physical evidence indicates is actually the case. I also observe that if George Ellis is correct that we have reached the physical and observational limits possible for human beings, then these conclusions will not and cannot be overturned by any future scientific discoveries.
This post and other resources are available on Dr. William Lane Craig's website: www.reasonablefaith.org
 Ibid., p. 4.
 Ibid., p. 5.
 Ibid., p. 9.
 Sean Carroll, “A Universe from Nothing?” <http://www.preposterousuniverse.com/blog/2012/04/28/a-universe-from-nothing/>.
 I want to thank physicists Stephen Barr, Donald Page, James Sinclair, and Aron Wall for comments of the first draft of this response.