It’s been a while, but I’ve finally gotten around to jotting down a few thoughts about the Sean Carroll vs. William Lane Craig debate. I previewed the debate here (part one, two, three, four). I thoroughly enjoyed the debate. Future posts will discuss a few of the philosophical questions raised by the debate, but I’ll briefly discuss some of the science in this point. (I didn’t manage to record my talk a few weeks ago, but this post summarises it.)
Firstly, I want to refer you to the much greater expertise of Aron Wall of UC Santa Barbara. I’ll list them all because they’re great.
- Did the Universe Begin? I: Big Bang Cosmology
- Did the Universe Begin? II: Singularity Theorems
- Did the Universe Begin? III: BGV Theorem
- Did the Universe Begin? IV: Quantum Eternity Theorem
- Did the Universe Begin? V: The Ordinary Second Law
- Did the Universe Begin? VI: The Generalized Second Law
- Did the Universe Begin? VII: More about Zero Energy
- Did the Universe Begin? VIII: The No Boundary Proposal
- Did the Universe Begin? IX: More about Imaginary Time
- Fuzzing into existence
(I’m on the “astrophysics” end of cosmology. The beginning of the universe probes the “particle and plasma and quantum gravity and beyond” end of cosmology. I know the field, but not as well as someone like Wall or Carroll.)
No one expects the beginning of the universe!
Regarding the scientific question of the beginning of the universe, here is how I see the state of play. Cosmologist don’t try to put a beginning into their models. For the longest time, even theists who believed that the universe had a beginning acknowledged that the universe shows no sign of such a beginning. We see cycles in nature – the stars go round, the sun goes round, the planets go round, the seasons go around, generations come and go. “There is nothing new under the sun”, says the Teacher in Ecclesiastes. Aristotle argued that the universe is eternal. Aquinas argued that we cannot know that the world had a beginning from the appearance of the universe, but only by revelation.
So when a cosmic beginning first raised its head in cosmology, it was a shock to the system. Interestingly, theists didn’t immediately jump on the beginning as an argument for God. Lemaître, one of the fathers of the Big Bang theory and a priest, said:
“As far as I can see, such a theory [big bang] remains entirely outside any metaphysical or religious question.”
In 1951, Pope Pius XII declared that Lemaître’s theory provided a scientific validation for existence of God and Catholicism. However, Lemaître resented the Pope’s proclamation. He persuaded the Pope to stop making proclamations about cosmology.
The philosophical defence of the argument from the beginning of the universe to God (the Kalam cosmological argument) starts essentially with Craig himself in 1979, half a century after the Big Bang theory is born.
In fact, the more immediate response came from atheist cosmologists, who were keen to remove the beginning. Fred Hoyle devised the steady state theory to try to remove the beginning from cosmology, noting that:
“… big bang theory requires a recent origin of the Universe that openly invites the concept of creation”. His steady-state theory was attacked “because we were touching on issues that threatened the theological culture on which western civilisation was founded.” (quoted in Holder).
Tipping the Scales
But what of the beginning in the Big Bang model? Singularities in general relativity weren’t taken seriously at first. Einstein never believed in the singularities in black holes. Singularities were believed to be the result of an unphysical assumption of perfect spherical symmetry. In Newtonian gravity, a perfectly spherical, pressure-free static sphere will collapse to a singularity of infinite density. However, this is avoided by the slightest perturbation of the sphere, or by the presence of pressure. A realistic Newtonian ball of gas won’t form a singularity, and the same was assumed of Einstein’s theory of gravity (General Relativity).
The next 80 years of cosmology sees the scales tipping back and forth, for and against the beginning.
For: The Friedman-Lemaitre-Robertson-Walker (FLRW) model for the universe has a beginning. Spacetime cannot be extended through that boundary. A beginning is there for a wide range of universes, including ours.
Against: Bouncing cosmology. Perhaps the pressure of matter will prevent the universe from collapsing to zero size, causing the size of the universe to bounce. As we look back in time, the universe’s current expansion is preceeded by one or more bouncing eras.
For (Tolman, 1930’s): the second law of thermodynamics says that entropy will continue to increase through the bounce. Each bounce will be bigger than the last, and there must have been a first bounce.
Against: The FLRW model is perfectly (and hence unrealistically) symmetric. Inhomogeneities will prevent the universe from collapsing to a point. A Universe with lumps and bumps will collapse to a non-zero size, before which it was contracting.
For (Hawking and Penrose, 1960-70’s): the existence of an initial singularity is not prevented by inhomogeneities. In fact, singularities exist under a surprisingly broad range of conditions. In particular, gravity must be attractive and general relativity must continue to hold.
Against (Guth, et al. 1980’s): Gravity is not always attractive. The theory of inflation (and particle physics models) shows that there are forms of energy with repulsive gravity, which can avoid the singularity theorems. In particular, evidence for inflation is evidence that such forms of energy were relevant to the early universe.
For (Borde, Guth and Vilenkin [BGV] 2003): a stronger singularity theorem that inflation alone doesn’t seem to be able to avoid. In particular, a classical spacetime which is expanding on average must have a beginning.
Against: quantum gravity is expected to take over from classical gravity in the very early universe. In particular, we expect spacetime to be an approximation to something else, something which behaves according to quantum laws (and in particular, the uncertainty principle) but behaves like classical spacetime on large scales. We don’t have a theory of quantum gravity, so we don’t know whether the singularity theorems hold.
For: the second law of thermodynamics states that entropy increases with time, as physical systems tend towards thermal equilibrium. If the universe were infinitely old, then it would have reached thermal equilibrium by now. Thus, it must be finitely old.
Against: The Ekpyrotic model of the history of the universe shows how, in an infinite universe, the entropy can keep increasing but never reach a maximum, being continuously diluted by the expansion. (Wall calls this “shell games with infinity”).
For: The BGV theorem also applies to the Ekpyrotic model, showing that it too must have a beginning.
Against: other models which propose a collapsing or “boring” (static) phase prior to the current expansion of the universe avoid the BGV theorem and permit an eternal universe.
For: Quantum instabilities might not allow the universe to remain still for all of eternity, and may cause a collapsing universe to crunch rather than bounce while avoiding the ordinary second law of thermodynamics. (I won’t even pretend to understand the generalised second law. See Wall.) For example, Aguirre and Kehayias say:
Although we have analyzed only one version of the emergent universe, we would argue that our analysis is pointing to a more general problem: it is very difficult to devise a system—especially a quantum one—that does nothing ‘‘forever,’’ then evolves. A truly stationary or periodic quantum state, which would last forever, would never evolve, whereas one with any instability will not endure for an indefinite time.
See also Vilenkin and Zhang. There can be singularities in quantum gravity (e.g. string) models, but in the absence of a complete theory of quantum gravity, we don’t know the physics of the bounce.
Against: the quantum eternity theorem shows that beginnings cannot be found in quantum mechanics as we know it, unless the universe has zero energy. When we wonder “what will quantum gravity – the uniting of quantum mechanics and general relativity – say about the beginning?”, the two pieces suggest opposite answers. General relativity suggests a beginning (with loopholes). Quantum mechanics suggests no beginning (with loopholes). What happens when these two wacky characters share an apartment? We don’t know.
??? Beginning in the middle. There are a number of models, including one by Carroll, that have a universe with an infinitely long time dimension. However, the “beginning of time” in the thermodynamic sense (the minimum of entropy) is in the middle. There are an infinite number of one-second-long intervals, but “half” of them are not in the past of the other half. Is this an eternal universe, or just two universes, each with a beginning? There is no “edge” in the model (so to speak), like a singularity, where our picture of earlier states causing later states breaks down. And yet, the first half of the universe does not “give rise” to the second half in any meaningful sense.
???: Hartle-Hawking “No boundary condition” and Vilenkin’s “tunnelling from nothing“. Again, read Wall on these ideas. Popular images of the Hartle-Hawking cosmology seem to suggest that the universe has a finite age, without having a beginning point. However, these pictures come with significant caveats:
quantum cosmologists have made proposals that postulate a ‘framework’ (as we have seen it may well not deserve the name ‘spacetime’!), which replaces the Big Bang singularity of classical general relativistic cosmology, and from which classical spacetime somehow ‘emerges’. Probably the best-known example is the Hartle-Hawking no-boundary proposal. But this ‘emergence’ is not a process in time: Hartle and Hawking’s proposed ‘framework’, and others such as Vilenkin’s, stands in no temporal relation to classical spacetime, or any of its parts (regions or points), even very early ones.
… one often sees a picture in which a cone-like spacetime structure (representing a cosmological solution of classical general relativity) is attached to a spherical shape that represents a Euclidean 4-manifold. This erroneously suggests that the bottom sphere is straightforwardly earlier than the classical cosmology represented by the open cone in the top half of the figure. But the 4-manifold is not earlier: there is no temporal relation between the two halves represented in the figure (or their parts)! (Butterfield & Isham, 1999)
Similarly, “tunnelling from nothing” is a metaphor, a cute nickname that shouldn’t be taken too seriously. Vilenkin says:
I have recently [in 1982] suggested a cosmological model in which the Universe is created by quantum tunnelling from “nothing” to de Sittter space, where by “nothing” I mean a state with no classical space-time.
It’s not “non-being”, and has no relevance whatsoever to the question of why anything at all exists. It’s tempting to think that this describes the transition from a quantum-gravity regime to a classical regime, except that this would suggest that at one time, there was no such thing as time and then at a later time – hey presto! – there’s time. Which is incoherent. If some sense can be made of this scenario, we might be faced with time-as-we-know-it having a beginning, like a smooth line emerging from a fractal. There wouldn’t be a classical universe with a singular boundary as a beginning point, but neither would there be an eternal universe.
Conclusion
It’s a bit of a mess. There are enough surprising hints for the beginning of the universe to be taken very seriously, but enough unknowns to keep us busy. If offered even money, I’d bet on the proposition that there has only been a finite amount of classical time in the history of the universe.
Filed under: Astronomy, cosmology, Science, The Universe Image may be NSFW.
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