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The Big Bang model, or atleast versions of it to my knowledge, posit that time itself started at the singularity. Time is proposed to come into existence at the moment of the singularity of the cosmos.

Now, in what sense is it sensible for time to start at a point? The notion of “starting” or “coming into existence” usually requires the notion of time atleast in one’s imagination. When we say that X starts somewhere, we usually mean that X starts at some time t.

But to say that time “started” at t = 0 seems nonsensical if t = 0 requires time to already exist as a reference point. How does one resolve this? It seems that the notion is either illogical or is simply meaningless/vacuous. Is there a third option I’m missing here?

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    All you need is ∃x¬∃y(y≺x), which being an existential statement is not analytical, hence not falsifiable on grounds of contradictoriness. QED, it seems. Nov 11, 2023 at 14:52
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    Asking questions about the beginning of time seems like going to the north pole and asking: Where is the direction pointing north?
    – Jo Wehler
    Nov 11, 2023 at 15:15
  • "Everything that has a beginning has an ending. Make your peace with that, and all will be well." - The Buddha
    – Scott Rowe
    Nov 11, 2023 at 15:34
  • The axioms that General Relativity runs on stop being good approximations of reality a (very) short time before General Relativity predicts singularity, so nothing at all is posited in mainstream physics for the moment of singularity, including whether there even was a moment of singularity. Physicists like to speculate as much as anyone, of course, and bring the tools and rigor of physics to their speculations in search of testable hypotheses, but at this point speculation is all any of it is.
    – g s
    Nov 12, 2023 at 8:14

2 Answers 2

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The culprit in the appearance of a self-defeating proposition is an ambiguity in the expression "t = 0." When taken as a sort of absolutely free-standing term, "t = 0" still presupposes a temporal grid with an origin, something isomorphic to the natural or positive real number lines (say). But the temporal grid as a whole is not reducible to its null intervals (0, 0) or [0, 0] (or even [0, 0) and (0, 0]), and of the grid itself it is unclear how to speak of it "beginning to exist," since all beginnings as we experience them are relative to timelines inscribed within (or wherefrom) the grid.

Still, the linear grid itself might be thought to be an effect of a cause that has no coordinates interior to the linear grid. The general timeline is embedded in a higher-dimensional manifold of temporal possibility, and in abstracto there is no finite limit to how many higher dimensions of time we can (dimly) imagine. If the concept of cause-and-effect requires temporal intuition to be substantiated, however, then in the infinite delimitation of temporal dimensionality, there will be no external substantive cause that we can identify; the infinite-dimensional hypergrid will not seem to have (nor, to be sure, clearly lack) a cause or "beginning." The obscure possibility of the hypergrid's being caused at the beginning of yet another linear timeline unfolding from the eternal duration of a divine will, say, might be admitted for speculative purposes.

For all that, yet it does not follow that a beginning of time is contradictory, if we mean that individual timelines or other temporal manifolds can be embedded as having initial intervals or points-of-departure in other temporal or, ultimately, pure causal manifolds.

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Kristian Berry gives a good answer assuming some sort of embedding dimension/manifold.

If we stick with the observable universe, we can think of t=0 not as a point in a pre-existing timeline, but as the "right hand limit" of reality as we go backwards in time. This limit point isn't a when or a where - it's every-when and every-where -- it is the point that separates static timelessness from the dynamic world we inhabit.

Mathematically, we can think of cosmic time as existing on the set (0, τ], where τ is the current cosmic time coordinate. The point [0] isn't really part of our world, but it represents the boundary of reality.

One could view the project of cosmology as exploring limτ → 0+ S(τ) where S is some property of the universe.

Extending this analogy, we can view cosmic history as having a discontinuity at τ=0, so that the view looking backwards in time will not give us access to τ=0 because that actual point is just beyond the boundary of time, it is the inf but not the min, so to speak.

In this view, we cannot say time began at τ=0 but time approaches a limit point as we go backwards approx. 13 billion years from today. It is really a unique situation that doesn't have analogs in our experience of the world or our intuition.

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