So I have had the infinite universe explained to me as:
I am in my ever lasting space ship, I travel in a straight time for how ever long it takes, eventually I end up where I started.
Okay, I kind of understand how this works, the whole curvature of space thing.
But where do they keep the other universes?
Perhaps there won’t be an explanation simple enough for me to grasp, but I find the whole multiple universe hypothesis fascinating and just get a bit overwhelmed by the physics and math that usually comes with the explanation.
Please assume I know nothing, I have tried my hardest to give ‘A Brief History of Time’ and the like a go and would love to have a greater understanding of these concepts, my head just swims a bit!
That seems an odd definition of Infinity to me–if you’re starting with the idea tha the universe is infinite and you travel forever in a straight line, why would you end up where you started? You have to throw in the second point that, in addition to being infinite, it’s also circular. One without the other just has you an infinite distance from where you started.
Also, starting from the idea that the universe is infinite has nothing to say about other, or multiple, universes, just that this one is infinite.
I doubt there’s going to be a definitive answer to this question.
I don’t mean to hijack this, but I think this question is related. If you (OP) don’t agree, please feel free to ask for discussion to be limited to the original question.
If the universe is everything, and the universe is constantly expanding… what is it expanding into if it already contains everything?
First, I agree that if you go in a straight line and end up where you started, you have good grounds for suspecting that your universe might not be circular,just like an ant on a beach ball - or us on the surface of the earth, for instance.
In terms of ‘where the other universes are’, perhaps try considering a flat little guy living in an endless sheet of paper. No matter what direction he heads out in within the plane of that paper, (the only dimensions that he can relate to,) he can keep going without ever having to stop, or ending up someplace that he’s been before. That, to me, is a better definition of infinity.
But there might be another sheet of paper touching his own ‘universe’ just above or below it, or both. The fact that his sheet is infinite and boundless on its own terms does not mean that it is ‘everything’ in its own frame of reference.
As a nitpick, it’s also possible to carve a piece out of an infinite universe so that it is also infinite in extent, but has boundaries. For instance, the cone of our universe starting from the sun and extending out in the general direction of the constellation Ursa Minor. If our whole universe is an infinite three-dimensional space, then that ‘slice’ of it would also be infinite in extent, and you could travel on endlessly without leaving the cone - as long as you keep going in that general direction.
That’s like asking, if all the odd numbers are an infinity where do they keep the infinite even numbers?
Infinity does not mean “everything.” It merely means unending. The two are logically different concepts.
You can have an infinity in a very small space. If you take 0.99999~ you can add an infinite number of 9’s to the end. You’ll wind up with a number that is the same as the number 1. Unending, but confined.
You can have an infinite universe. You can have another infinite universe in another “place” unseen by and invisible to the first, just as the even numbers are unseen by the odd numbers. You can have an infinite number of infinite universes, just as you can have an infinite number of mathematical infinities.
What you can’t have is a circular infinite universe. That concept is something you misunderstood.
Infinite means (Gods and little fishies forgive me) “without limit” or “without end” It doesn’t mean “all-inclusive”
There are an infinite number of even integers and an infinite number of odd integers yet, never the twain shall meet. You could further further subdivide those infinities into negative and nonegative subgroups, each of which is still infinite.
Perhaps more viscerally relevant, there are an infinite number of rational (or irrational) numbers between 1 and 2; and an equal infinity between 2 and 3, 3 and 4, etc. Each of these ranges can be seen as an “infinite universe” of its own (you could visit a billion numbers a second until the end of eternity, and never visit the same number twice). Moreover, each would appear continuous to an observer inside the range: while there are “holes” in the rational numbers – namely the irrational numbers-- and vice versa, an observer might never see them: between any two members of the set is another (actually an infinity of) member of the set, so no matter where you poke your stick, or how pointy the stick is, there seems to be a suitable number filling the hole.
This is completely non-rigorous, but I hope it paints a picture.
That would be a finite, not an infinite universe. In an infinite universe, in at least some directions, no matter how far you go, you will never end up where you started.*
Assuming you are assuming the universe is finite (since that’s how you describe it above, even though you call it infinite) the answer to the question is, in other finite spaces. Perhaps our own (spherical) universe is embedded in a higher order space like a raisen in a muffin, and perhaps there are other raisens.
If you really meant to ask where other universes are given ours is infinite then the answer is a little harder to visualize. Imagine an infinite plane (i.e., infinite two dimensional universe). There might still be other planes parallel to it–each plane infinite in itself. An inhabitant of one of those planes might ask “Where are the other infinite universes?” And the answer to him would be “right above and below you.” The problem is–that inhabitant would find it difficult to understand what “above” and “below” mean since it has only had to deal with directions like left right forward and backward, living, as it does, on a plane. But the answer would be right, nonetheless. And we could, for all we know, have a similar relation to a series of three dimensional universes that we are similarly unequipped to deal with.
That’s not the only way there could be mutliple infinite universes, but it’s one way.
-FrL-
*Question for others: Could you have a universe which is finite but in which, going in a single direction for an arbitrary amount of time, you never go back to where you started, and you never hit an edge? I am visualizing a plane where “straight” ends up looking more like a spiral. Can you have a space like this?
The way I understand it, you can have a circular (closed) universe that is unbounded, but it isn’t infinite–possibly the OP is confusing these two concepts. Imagine a flatlander who lives on the two-dimensional surface of a universe shaped like an enormous beachball. If he travels far enough, he’ll come back around to his starting point, and his universe won’t be infinite, it will have some finite (though possibly very large) extent; but it also won’t have an “edge” that our 2D astronaut could possibly sail off of. For him, with his two-dimensional brain, trying to imagine exactly in what direction his universe is curved will likely be as headache-inducing as contemplations of higher-than-three spatial dimensions are to us, and he’ll probably have to deal with them by analogy, imagining his universe to be like a 2D circle, but extending into that freaky unimaginable third dimension.
(OK, it looks like no less than Albert Einstein said all this back in 1920, so at least I’m not just making it up.)
Imagine a balloon. The rubber surface of the balloon is a 2 dimensional surface that exists within a 3 dimensional volume. As the balloon inflates, every point on the balloon gets further apart in a 2 dimensional sense as it expands through 3 dimensions.
Our universe is like that, only it is (at least) 3 dimensional, expanding through a fourth higher dimension (that we cannot even comprehend) - we see the effect of the expansion in the 3 dimensions we understand, but find it hard to visualise the fourth dimensional expansion.
As for the multiverse, additional universes exist (like ours) in the fourth dimensional space. Imagine a book. If you are constrained to the 2 dimensions of the page (i.e. you cannot look up or down) you can have another universe (page) pressed right up next to your own, and you will not be aware of it. Alternative universes could occupy the same volume, or different volumes in 4 dimensional space. However, because they do not share any of the same dimensions as us, those universes cannot interact with ours at all - we cannot even prove that they exist.
As I said this was how it was explained to me, I am more than happy to be corrected.
I have a hard time getting my head around the concept that if something doesn’t end in all directions it isn’t everything. But I guess the 2D man give me a bit of an idea of what I am up against.
These seem to eventually come up in every thread where the “infinite” is mentioned, but outside of a certain narrow context, they rarely have anything much to do with the particular topic being discussed, or, at least, do not help analyze it. There is more than one concept in the web of instances of the infinite; the very particular one formalized by isomorphism types of discrete sets (using arbitrary pairings) is not always relevant or apt. [E.g., a 1 inch line and an infinitely wide plane both have 2^{aleph_0} many points, as usually formulated, yet are clearly very different as regards the OP’s concerns]
Not a slam on your mention; just pointing out that thinking about aleph numbers is not the way to go in addressing the OP. Though they may, I suppose, end up being worth discussing in addressing future questions that arise in this thread, wandering as I suspect it will be.
I don’t know from physics (to use an apt construction not really native to my speech), but there’s nothing mathematically incoherent about this (in itself, though everything depends, of course, on what other principles of geometry you wish to impose alongside it). E.g., consider an Asteroids-style universe: a finite square screen whose sides wrap-around in the familiar way. Movement in any constant direction will eventually bring you back to where you started if and only if the “slope” of that direction is a rational number; thus, with probability 1, picking a random direction and moving in it will never bring you back where you started (though you will come arbitrarily close).
“Your theory of a donut-shaped universe is intriguing. I may have to stealit.”
On the other hand, if we assume that our traveller occupies a finite volume and specify the criterion as ‘never overlapping a space that they’ve been again after they’ve left it,’ then you’re probably stuck with universes that do actually contain infinite volume, since every second you’re ‘using up’ space that you don’t get to reuse again.
I was actually wondering about a case in which there is no direction that gets you back where you started. Rereading my post, I see it could be interpreted to be asking about case in which there is just some direction that fails to get you back where you started.
There are an infinite number of even numbers.
There are an infinite number of odd numbers.
There are an infinite number of numbers divisible by 19.
There are an infinite number of numbers that contain the word “hundred.”
There are an infinite number of numbers divisible by negative pi.
How could all of these infinities coexist in the same set of numbers?
In that case, no, it’s not possible (or at least, if it is, it wouldn’t look like anything we’d call a “universe”). As chrisk says, for any small distance you care to name, you’re guaranteed to get within that distance of your starting point, because you’re using up volume whenever you move. If spacetime is smooth on any scale, you could just pick the scale on which it’s smooth as your distance, and since it’s smooth on that scale, you could adjust your initial trajectory to bring you exactly to that point, instead of just near it.
And the donut-shaped universe is not a novel idea: Non-simply-connected universes like that are subject to serious scientific consideration lately. The problem is that, since such universes are not necessarily curved, the only way to determine if the Universe has such a topology is to see the same thing wrapped around in multiple directions, and if the identification scale is large enough, there’d be no way to detect it at all. So we can never rule out the possibility of a finite universe.
With apologies, I don’t understand what you mean by “using up volume.”
This sounds like you’re saying that in any two points in a space, there is always a straight line between those two points. Is that what you’re saying? If so, I don’t understand the relevance.
I was wondering whether there could be a space which is finite, but which is such that no matter what direction you go in a straight line in, you’ll never end up back where you started.
