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I don't know if this is more a question for mathematicians or physicists (or even philosophers), but what would be the difference between time having a beginning infinitely long ago and time having no beginning (apart from the obvious, one had a beginning and the other didn't)? How could we tell whether it has always existed or began infinitely long ago?

In other words, did time have a beginning or did it begin an infinitely long time ago? How could we tell?

It appears, from Ryder Rude's answer and the embedded link, that the problem is addressed in questions about the shape of the universe.

Michael Greaney
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  • "an observer in time" As opposed to what? – D. Halsey Nov 15 '22 at 13:32
  • Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. – Community Nov 15 '22 at 14:52
  • @Michael welcome to physics stack exchange! is this a known "thing"? that is, if you can provide any links or elaborate further; as you state too (..)"or physicists (or even philosophers), " this doesn't seem to be mainstream physics (correct me if I am wrong!) :) – William Martens Nov 15 '22 at 15:50
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    There is no difference in math. Flip it the other way: What is the difference between ending infinitely into the future vs having no end? That can be reframed as what is the last number when counting to infinite which is more obvious to think about. Honestly, "beginning infinitely long ago" sounds more like poetry to me than anything else. – DKNguyen Nov 15 '22 at 16:25
  • What does "infinitely long ago" mean? – WillO Nov 15 '22 at 19:01
  • Also look up "topological censorship theorem" and https://physics.stackexchange.com/questions/127590/is-topology-of-universe-observable – Ryder Rude Nov 17 '22 at 12:07

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According to general relativity, spacetime is a four dimensional manifold. The most trivial topology of spacetime would be that of an infinite $R^4$ space. This sort of universe has no beginning. The geodesics can be extended in the past infinitely far. There are other interesting topologies too. You can read about them here in the Global Universe Structure section.

"Having a beginning infinitely long ago" is an oxymoron. There can be no beginning if something has existed for infinitely long.

About the space dimensions, it is hypothesized that they might be compact, like some 3D equivalent of the 2D surface of a cylinder or a torus. I don't know if a similar claim can be taken seriously for the time dimension. Nevertheless, if you hypothetically consider that time is like that, then time doesn't have a beginning but it didn't exist infinitely far back.

Ryder Rude
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