The following is based on a comment I wrote in response to the post “The argument for god I had the hardest time with” by Christina on “What Would JT Do?”. Although my comment was about a week late for it to have mattered in any way.
2016 note: I wrote this when I was hip-deep in The Cult That Shall Not Be Named. As such, I use quite a bit more Sequences jargon than is healthy. Sorry. That said, I stand by the core of my argument.

Christina writes: “My main problem was not so much [the Cosmological argument] but… how DID the universe begin?”

As a refresher for those who know, or a quick primer for those who don’t, the Cosmological argument says:

  1. Every finite and contingent being has a cause.
    • “Finite” here is mostly concerned with “finite in time” — something that has a definite beginning and a definite end.
    • “Contingent” means “something you can’t prove or disprove from first principles” — that is, something that can only be learned by looking at the real world.
    • The definitions of “finite” and “cause” both involve time, which is not as simple as we once thought it was. That puts this assumption on shaky ground: physics might disprove it in the future.
  2. A causal loop cannot exist.
    • A causal loop is when A causes B, yet B causes A. (There can also be more intermediate steps, i.e. A causes B causes C causes… Z causes A.)
    • Most physicists think causal loops can’t actually exist, but we don’t yet see any reason why physics permits or forbids them. This assumption might also turn out to be a mistake.
  3. A causal chain cannot be of infinite length.
    • Now this is where the argument really starts to come off the rails for a lot of people. This assumption is saying outright “I assume that the Universe has a finite past with a beginning”, which is not obvious at all when we look at physics.
  4. Therefore, a First Cause (or something that is not an effect) must exist.
    • “Because the Universe began at some point in the finite past, there must have been a moment when it began.” Christian theologists add “Oh, and we’ve named that moment ‘God’ and decided it is a non-finite, non-contingent person, by the way.”

The Cosmological argument is frequently torn to pieces, and there are two popular ways to do it.

As you might have guessed from my running commentary, there’s another attack against the Cosmological argument that doesn’t get used as often: the whole thing hinges on ideas like “cause”, “effect”, “finite”, and “time”.

Julian Barbour’s The End of Time is a bit technical and isn’t the clearest writing style, but something like it is probably true. Just like chairs aren’t fundamental — none of the individual atoms in a given chair have “chair-ness” — Barbour argues that time isn’t fundamental either, when you dig down to the deepest levels of physics. He points out that when Schrödinger’s wave equation (the heart of Quantum Mechanics) was first discovered, the original form of the equation was timeless; the modern version with a time dimension had to be explicitly invented. Barbour also points out that Wheeler and DeWitt working in the 1960s discovered a timeless quantum formulation of General Relativity; the crisis of 20th century physics was the apparent impossibility of making GR obey quantum rules, yet the Wheeler-DeWitt equation does it (though it still leaves major questions unanswered and isn’t a complete Theory of Everything). As it turns out, time is the very thing that makes GR’s 4D spacetime incompatible with QM, but 4D spacetime isn’t as essential to GR as everyone believed. If physics itself is timeless at the bottom, and the deeper theory looks like the Wheeler-DeWitt equation, then the Many Worlds interpretation of QM is physically true: every possible world happens… with the oddity that some possible worlds “happen” more “strongly” than others, and the equation tells us how “strongly” each possible world happens. Unlike the common conception of Many Worlds, though, there is no “time” that separates possible worlds in the past from possible worlds in the future. The possible worlds all “happen” together, eternally and unchangingly.

With the Wheeler-DeWitt equation established as a model for how things really work, Barbour argues that likely worlds are related to each other, for tricky reasons. There’s a zero point in Barbour’s formulation, but it’s not the traditional Big Bang where space and time both spring into existence from vacuum fluctuations as a sort of Uncaused Cause. Instead Barbour’s zero point represents zero entropy: a world that contains no variations, that contains nothing “interesting”. This zero point skews the math so that likely worlds with high entropy (far from the zero point) bear strong similarities to other likely worlds with lower entropy (nearer the zero point). The evidence that science analyzes, the memories in our brains, the photons in mid-flight from the Andromeda Galaxy to our home planet, etc. all exist in this moment’s world, “Now”, but our memories of the past are also “time capsules” that reference other “Nows” that are closer to the zero point than our own present “Now”. We call this asymmetric relationship “past”.

This actually ties into some recent developments in more mainstream timeful physics. Barbour’s ideas can only be true if we ditch the pseudo-Newtonian framework of GR’s absolute spacetime, and we can only ditch absolute spacetime if the total energy of the universe is zero (gravity’s potential energy counts as negative, mass and energy count as positive, so zero is achievable). This zero-energy condition is exactly what Lawrence Krauss’s A Universe From Nothing lecture and book argue for, on completely unrelated cosmological grounds tied to the geometry of space and the Inflationary Big Bang model.

(I have an unsubstantiated hunch that the timeless physics stuff may even interplay with the Holographic principle and the somewhat related AdS/CFT correspondence. The former says that a volume of 3D space is equivalent to the entropy/information inscribed on the 2D surface of the sphere that encloses it, and the latter basically says that an N dimensional “Anti deSitter” spacetime with local particle/field physics (i.e. pretty similar to our universe) is mathematically equivalent to an N-1 dimensional “Conformal Field Theory” space with nonlocal “holomorphic” physics. Both strike me as similar to how the Wheeler-DeWitt equation carves 4D spacetime into a single 3D “Now” of your choice plus a deterministic rule for reconstructing 4D spacetime from that “Now”. But that’s just an interested layman’s wild guess.)

So… yeah.

TL;DR: we only have the vaguest idea of what the universe actually is, but it’s pretty clear that the “God is the Uncaused Cause” argument is just the same sort of kids-in-the-sandbox philosophy that made Euclid argue that space is flat by definition: namely, it brings in “intuitively correct” unstated assumptions that are mathematically equivalent to assuming the conclusion itself. Words like “time” and “cause” are dangerous in arguments like these: we intuitively treat those concepts as unopened black boxes, but they actually have deeper structure inside them that might invalidate our assumptions, depending on what’s in the box and what we’re trying to do with it. Whatever the universe is, it’s probably a “paradox” in the Twin Paradox sense (unintuitive), but it’s certainly not a paradox in the logical sense (a contradiction).