gmalivuk wrote:Nobody believes that space is bounded, and the fact that you say both small and closed suggests to me that you're not using "closed" the same way as a topologist or cosmologist.
Hmm, perhaps "compact" is a better word? Not sure. What I mean to say is that "all points in space are no more than some maximum distance from one another", either because there's a boundary or because space is "cyclic" (dang, what the heck's the right word for "cyclic" in topology??). If the universe is much larger than the visible universe, it could have almost any topology and it would be unlikely we'd have direct evidence of which. However, if the universe is smaller than the visible universe, we can know.
If the universe is "small" (smaller than the most distant visible object), and bounded, then it could only be a simulation because it sure doesn't look that way. I suspect we could eventually discover if we were in a simulation, but that's a different thread.
However, if the universe is "small" and "cyclic", then there will be evidence in the CMBR. There is a whole group of topological cosmologists who have cataloged a vast array of possible ways the universe could be "cyclic", with each sort of curvature and many different kinds of "tiling" (more than I would have ever imagined), and what the CMBR would look like in each case. From what I hear, there was no obvious match to anything in the CMBR, but they haven't given up hope yet and analysis is ongoing.
gmalivuk wrote:Even if space may be cyclic and time may be cyclic, it's still really obviously not in the same way. According to every going theory, the Big Bang was still a thing that definitely happened, more or less. Like, maybe it was a Big Bounce or something more exotic, but there was still a time when everything we currently observe was all super close together. There is at least something like an endpoint for time, and there is something like an arrow of time, with causality and a past that's separate from the future in a way that cannot happen with three spatial dimensions. Time is objectively distinct from space, and there's no reason to suppose that therefore general principles that hold for space should also hold for time..
Well, I don't completely agree. There is an interesting event in time and space
that we call the "big bang", to be sure. There's some evidence the 4D topology of spacetime has a boundary there, or at least narrows to a point or nearly so if it's cyclic, or if it extends past infinitely in both directions. But AFAIK the universe could still have the topology of a 4-sphere, with the big bang being just a spot on the sphere that everyone can agree on. Sure, the topology could
be different along the time axis than the space axes, but that's not necessarily
Sure, you can assign a "direction" to time in a way that distant observers can agree on, as long as they're not separated by an event horizon, and that's interesting. But event horizons (and singularities) are also interesting, and if you don't consider the universe as bounded by event horizons, then I'm not sure the direction of time or even the axis in spacetime we call "time"
is universal. I think everyone locally
can agree that one axis is special and assign it the negative sign in Minkowski space, sure, but approach a singularity and not so much. I also believe that if time exists "before" the big bang, then the arrow of time point uniformly away form the big bang, not in a consistent direction "through" it (hmm, I should start a thread about that - I'd love to discuss that in more depth).
gmalivuk wrote:In addition, as previously mentioned there are already *plenty* of things that are only true now which weren't true in the early universe and won't be in the late universe. We are a life form that could only have evolved in the presence of heavy elements and a particular type of star, and those aren't things that have always existed or will always exist. On top of that are all the additional coincidences like the previously mentioned two-kinds-of-eclipse and visible-non-local-group-galaxies that weren't true in the distant past and won't be again in the distant future.
There are plenty
of things that are true if your location is in the core of a star that aren't true here as well. We are a life form that could only have evolved at the appropriate distance from a star, and that's a rare set of locations. But that's not really what the Copernican Principle is about, is it? It's the rules
that are the same everywhere/when, not e.g. the temperature. So, yes, it was stretching things a bit to suggest that the universe is "just that special size", that it's a very specific level of tired
, but it's not the time
aspect that makes it a stretch. BUt it would still be, like the size of the Moon, one heck of a coincidence to be so exact.