To misquote Arthur C. Clarke:
“Two possibilities exist: either the universe is infinite or it is not. Both are equally mind bending.”
I’ll reiterate my point. I don’t think there is even a useful definition of infinite in play. A big flat universe that goes on forever is probably the one least likely to be true. After that it comes down to philosophical differences. Like which is the least complicated, or involves the fewest assumptions. I don’t think there is even consensus about what assumptions we can usefully enumerate, let alone choose.
Geometers can construct you all manner of interesting infinite metrics on all sorts of spaces. Trying to shoe horn our current ideal Einsteinian 4D space-time into one is already making a lot of assumptions.
Whether you believe the time dimension is a fully fledged dimension with an extent and existence equivalent to the spatial ones is another question. Does the past exist? Does the future? How infinite would you like them?
If time has a start, maybe space does too. Does time end eventually? It started, we think. Does an end of time end space? Do we really claim that there was a universe of infinite extent into which time sprang into existence and began ticking? How did that happen? Moreover, what caused it, and how do we reason about causality here? How do we reason about causality anyway?
We don’t really have the tools to even usefully ask the questions, let alone provide answers.
Sorry to jump in here with what is probably an ignorant question, but nobody believes the universe started as finite in size, but is now infinite, right?
My understanding is that it is what fits our measurements best; we take measurements with increasing levels of precision and they all show no curvature. So the simplest explanation of what we have observed is a flat universe.
Stephen Hawking was an advocate of the “finite but unbounded” hypothesis. By mathematically rotating time into an imaginary metric, the model of spacetime using imaginary time becomes analogous to the surface of a sphere, finite but unbounded. The attraction of this model is that singularities disappear, resolving the paradox of their apparent physical impossibility. The Big Bang singularity becomes no more remarkable than the North Pole.
For some reason, terminology like “unbounded” is confusing me. Note that there exist spaces like the Clifton–Pohl torus that are compact Lorentzian manifolds but not geodesically complete.
The concept of a finite universe, a flat one, immediately makes me think “what is beyond the edge?”
Thinking of the steady-state model, imaging time running infinitely into the past literally makes my stomach feel like it is twisting. I can handle future infinities, but backwards infinties…ugh!
I believe in the infinite flat universe, because it is simpler.
My notion of the point of singularity (initial singularity) is that everything in the universe existed as a single point. Such as:
I, like you, don’t see how everything in an infinite universe could have existed as “single, dense point”. I realize that ‘common sense’ doesn’t apply here, but ISTM that if there was a Big Bang (current model), the universe must be finite.
Not the right thread to bring this up in, really, but though it’s a clever quote, I’ve never really been behind it. To me neither alternative is “terrifying”.
Concur. ‘Infinite’ is not the same category of thing as ‘very big’. I struggle to understand what the transition from ‘finite and very big’ to ‘actually infinite’ would even mean.
To use the Hilbert’s hotel concept of infinity, the only way you can convert a regular hotel to Hilbert’s is to add an infinite number of rooms, but that means the old hotel you had was meaninglessly small, regardless how big it was.
If one considers the universe to be limited by size, does that make it impossible to envision something that cannot exist because it is larger than that?
I can imagine something that is larger due to being infinitely large. What I can’t imagine is this.
How can something be both infinitely large and infinitely small both at the same time? Because if you can keep adding infinitely more rooms, presumably you can keep taking them away as well. And if you do that, where do you end up? With a non-sensical answer, at least according to my limited imagination because not only do you end up with infinitely many and infinitely few rooms, but you end up having both of those things at the same time.
An infinite number of ants is equal in size, number and weight to an infinite number of elephants. Would an infinite universe be larger, smaller or equal to either and/or both when it comes to holding them?
A good point to clarify. We know that we don’t have an infinitely long ago past. Which leaves unanswered the question of how long time will go into the future as well as the spatial dimensions. Is it possible to have one direction of one of the dimensions (the past) be finite while one or more of the other seven dimensional directions (the future, up, down, back, forward, left, and right) be infinite? How would that even work?
The Big Bang Theory may be in some trouble. We can now see galaxies that are 13 billion light years away. According to the BBT, that is less than a billion years from the origins of the universe, yet the galaxies we’re seeing are fully formed and mature galaxies. Something, theorized to be Dark Matter energy, is expanding the galaxies at speeds greater than the speed of light because space is literally being created at that pace so, even if there is a “border” to the universe, we could never move fast enough to even catch up to the expansion much less reach that “border”.
If you assume the definition of “universe” given by Roderick_Femm,
and if you assume there is an “edge” which bounds the universe, then it follows that nothing exists beyond the “edge”.
Some questions that popped into my head reading this thread:
If everything that exists refers to a finite quantity, and if the universe contains everything that exists, does that necessarily mean the universe has a finite boundary?
I don’t think it follows unless some other assumption is made. The set of numbers \{ 1, 4, 5 \} has three numbers, a finite quantity; and the set of all natural numbers \mathbb{N} contains \{ 1, 4, 5\}; yet the set of natural numbers \mathbb{N} is infinite.
If everything that exists refers to an infinite quantity, and if the universe contains everything that exists, does that necessarily mean the universe has no finite boundary?
I don’t think this follows, either. Imagine a number line from (-\infty, \infty). The line segment from [1, 2] contains an infinite number of points (such as 1.2 or 1.65), and the segment [0, 3] contains [1, 2]; yet the line segment [0, 3] has finite boundaries.
If everything that exists was once a singularity, and a singularity is a single point, does that mean everything that exists is finite in quantity?
I’m less confident here, but I don’t think this follows either. A singularity may be defined as a single point with infinite density, in which case because we’re dividing by zero, there could be an infinite quantity of things contained in the volume of the single point (though they can’t be differentiated, which is another definition of a singularity). If there is an infinite quantity of things in existence during the singularity, there may still be an infinite quantity of things afterwards.
Would it make sense to think of this as new space being created (rather than existing space being newly occupied) by the expansion of existing matter? (once again, my conceptual resources are in danger of collapsing.)
“Singularity” gets used to refer to a physical entity. It isn’t. It is a well defined mathematical term referring to “our model breaks here”. One thing we can be pretty sure of is that there are no such things as singularities in the real universe. What happens at those places where our current models break is going to be really interesting. When/if we get models that make sense at such extremes, one thing we won’t be calling them is singularities. (I fear that they will get called “dark manifolds” or “dark fuzzballs” and the like, as the current dearth of imagination reigns.)
It isn’t as if all current singularities are representing the same type of phenomenon. Same failure of the model perhaps.