Something can be finite in extent without having a boundary. The trouble with trying to get one’s head around this is that we have a lot of difficulty moving away from our 3D flat model of the universe whenever we think about these things. We know space bends, and we know space bends to extremes in such things as black holes. So we already allow that space isn’t a simple rectilinear 3D thing.
There is no reason why the universe can’t be closed in the sense that if you set off travelling in a straight line (as you see straight) you eventually return to the place you started. The surface of a sphere has this property. We complain that it only manages this because it is a 3D object and thus the surface is a boundary, but that is simply imposing our 3D view of the universe. We might be in a 3D universe that behaves exactly like the 2D surface of a sphere does. And there are other options. On a sphere we return to our start coming from the other direction. We might live in a universe where the geometry returns us to our starting point from the direction we set out in. And there are many other possibilities. But you don’t require an edge.
The currently active thread on parallel lines meeting (or not) is pertinent.
Yes, so in that analogy the edge of the universe is right here, in fact it is everywhere, in some direction that isn’t up or down or left or right or backwards or forwards, but at right angles to all of them.
But there’s no edge in the way there would be an edge to a finite flat Earth.
Probably the right way to structure the question is: “where,* on the surface of the Earth*, is the edge of the Earth’s surface?” - because the answer is not ‘up’; the answer is null - there isn’t an edge.
Likewise the answer to “what’s beyond/outside the edge of the universe?” can be likened to “What’s north of the North Pole?”
Perhaps it’s better to ask where the edge of a map of the Earth’s surface is? Any flat map must have edges, but that’s just an artifact of trying to force something that isn’t actually flat onto flatness. There’s nothing special about “the edge of the map” on the Earth itself.
Except that the Universe is flat from what we can tell, in fact a spherical universe would require a negative energy potential just as a saddle shaped one would have a positive total energy.
One of the most amazing things about the entirety of the universe is that it, being flat is neutral on there and all of the “stuff” can be made literally from nothing.
Although when you start to talk about geometry vs topology the discussion gets a lot more complex. If the universe is the shape Mobius strips or Klein bottles, it’s on scales far, far larger than what we can observe. And thus those forms of connectivity are merely hypothesis.
Although, that’s not to say that the notion of an edge to a 3D space is an invalid notion, you do not have to go into a higher dimension to validate the concept.
In 2D space, we can have (say) the surface of a plate which has an edge; or the surface of a sphere, which does not.
In 3D space, we have (say) the observable universe, which is a ball with a spherical edge, and for which the shape is easy for us to imagine; or the entire universe, which does not have an edge, and which is much harder to imagine, and where the “what’s north of the north pole” notion kicks in.
I don’t think this is a conversation about the true shape of the universe. It’s more an effort to explore the best way to explain conceptually the notion that the universe does have an edge.
In any event, we can’t say definitively that the Universe is flat, just that if it does have an overall curvature, it’s on scales too big for us to be able to measure.
Yes, the point being is that really we don’t know…but for it to be connected as described above would be unlikely.
The best answer even to if the universe is infinite is we don’t know. We haven’t seen any interaction at the limits of our abilities to suggest that it has an edge or that it loops around.
Observing beyond a limited horizon will always be a problem, and we can infer that the Universe is at least 100 time larger than what we can see.
Planck space telescope can’t detect any distortion at all. The crazy part is that the universe had to be flat to 1 part within 1×10^57 parts at the big bang…that is true insanity or boring depending on personal tastes.
But I think you agree that none of the possibilities involves an edge, right?
And for most people that’s a really tough thing to conceive. Since some of the theoretically possible topologies are easier to imagine, I think it makes sense to describe them, whether or not they are consistent with current evidence. Only after it “clicks” for someone conceptually what “no edge” means can they really get to grips with considering the evidence for the true shape.
I have heard a few lectures that discuss the possibility, and if the universe is not infinite I don’t see why it couldn’t be as possible or more probable than a Mobius strip or Klein bottle connectedness.
Sorry I don’t take notes on those type of speculations but when I get home from work I’ll try and dig up a few papers that describe some those ideas.
That’s really not my point, although I’d be interested to read them.
My point is that if we’re talking through a certain topology, and whether it’s a good tool to help with visualizing “space without an edge”, pointing out that current evidence may rule out that topology is putting the cart before the horse.
My intent on bringing this up is that if someone is looking for answers on questions we simply don’t know the answer about it can lead to frustration and confusion, as there will always be lots of interesting and weird ideas on what is possible.
Some of us find this fun and engaging, but I think it is also important to be mindful of others who are looking for answers that we just do not have yet.
My point is that “space without an edge” is really a spherical cow
I did error and should have expanded on my post
Consider an ant that that can see in 2 dimensions, then envision this ant on a balloon that is being inflated and how the distances between two points seem to grow.
Sure, but in the case of a 2D plane surface that has an edge, there is space into which the edge could theoretically be extended - the idea if a finite, bounded space with nothing outside of it, is (I think) impossible.
Yes, the notion of an entire universe with a boundary doesn’t work sensibly in a mathematical sense. Our observable universe (with a boundary) is in something, the (presumed) entire universe. The entire universe is not “in” anything in the same sense, it’s not expanding into anything even though it’s getting bigger, it is the thing.
(Not intending to make that read like I’m explaining to you, btw, I know you understand this stuff probably better than me, just for the purposes of the thread in general.)
