Incidentally, flat earth theory has not fared well the past week.
https://twitter.com/i/moments/961009927618674720?ref_src=twsrc^tfw
If there is a finite size and scale to the “bubble” in which inflation ended there may be a large number of such bubbles contained within the larger, inflating spacetime.
Unless inflation went on for a infinite amount of time, the Universe must be finite in extent, although it may be in a larger structure often called a multiverse.
I don’t know how we would develop the mathematical models for this without some form of observation, but if the universe is flat, and thus all matter and energy can arise from nothing it is quite possible that some form of situation like an edge where, when crossed, there is no arrow of time, or matter and/or energy exists.
I hope someone is clever enough to consider the possibilities, but my (probably incorrect) understanding of the current models point to a finite size and scale to the “bubble” produced by our inflation event.
Some forms of ideas explaining multiverses try to explain this multiple inflation bubble idea. I will need to verify my assumptions but if anything is infinite it is inflating spacetime but the edge of our inflation bubble could be described as an edge in several possible scenarios.
We do not know if the rules that we hold as fundamental carry across that finite boundary.
But the “bubbles” are an analogy. They are not bubbles in the sense of a normal 3D bubbles with edges expanding into a larger 3D space. That’s the fundamental issue that got this thread started.
And we know that how?
If the constants in our universe held across the expansion horizon and the larger space time multiverse kept the arrow of time why not?
The curved effects of spacetime are insignificant compared to the observations pointing to flatness.
We don’t have enough information to rule these possibilities out and it could be the arrow of time that is expanding which could still be described as an edge.
Geometrically (mathematically), you can embed smooth manifolds (with or without boundary) in a higher-dimensional space as in the Whitney embedding theorem, but there is no problem considering a manifold as a space by itself; it is certainly not impossible. And physically, it seems like that is the only way to think about it; otherwise, the spacetime of the universe would be embedded in— what? A bigger universe with twice as many dimensions?
To quote the OP:
I would note that what got this thread started is the miss-understanding that the expansion relates to the velocity of matter or other features that are limited by the speed of causality.
That initial question is answerable by the fact that space is expanding and the causal distance is growing, but that doesn’t preclude the possibility of an edge.
As inflation did stop, and expansion is far slower this bubble should be finite under current theories, we just don’t know what that limit should be. Right now we know it through inference that it needs to be at least 100 times larger than our observed universe, but there is no evidence to point that inflation/expansion is infinite at this time, and our models infer it is finite.
Why not a 4 dimensional space, where time is not temporal? When one passes through the event horizon on a black hole, radially outward becomes the inaccessible dimension as spacetime collapses faster than the speed of light. So it is not that we don’t have theories that may possibly suggest this option.
I should note that spacetime is not simply connected, which appears to be required for the Whitney embedding theorem. (unless I am wrong which is very likely)
We can only make that inference if we assume a trivial topology. With a nontrivial topology like a 3-torus, all we can say is that the size of the unit scale is bigger than what we can see, but we can’t say by how much. It’s possible that we would see some matches, due to seeing the same region of space from two different directions, if we could see just a little bit further. Or, of course, it’s possible that those matches really are a hundred or a billion or a googol times further out, or that they don’t exist at all and the Universe really is infinite.
EDIT: It’s possible that spacetime is not simply connected (that would mean a nontrivial topology), but we have no evidence to suggest that that’s the case.
I agree,
To clarify, we do not know if spacetime is simply connected and to clarify my position further,
We do not know whether the Universe is finite or not.
Isn’t that unknowable though? How do you test if the current or previous universe had a spatial bound? I think a truly infinite universe is a fascinating possibility as that means there is more than one me, but how could you know?
I suppose in a truly infinite universe some life forms know since they’d be witnessing exceedingly improbable events that perhaps only an infinite universe could explain.
I am not sure if this is the case but don’t confuse the multi-worlds use of Multiverse with this subjects use of the term.
It is quite possible that other possible Universes are so different and matter doesn’t exist or it may not exist in a way that would support life.
I’m not. It’s that in an infinite universe there are only so many permutations of matter in any given finite volume. Therefore, it seems that each permutation exist should exist multiple if not infinite times.
The Whitney embedding theorem, Nash embedding theorem, and generalizations to pseudo-Riemannian manifolds do not require the space to be simply connected, but, again, these are results in pure geometry that have nothing obviously to do with the universe.
A shapeless object would be have to be something with no stable structure, that is an entity with a dynamic geometry where faces, vertices and holes would appear and disappear so that no constant shape could be ascribed to it.
This thread is about the characteristics of the matter/energy and the spacetime containing it at the periphery of the Universe. The OP calls it the ‘edge’, but I prefer ‘periphery’. To discuss that, one has to determine/decide on the shape of the Universe, something which I understand is tremendously tricky.
To clarify that, some people here refer to Earth and the way its inhabitants perceive its geometry. I want to point out that Earth is roughly speaking a sphere, with a center and a face. The Earth surface is its periphery, which can be observed by astronauts leaving the planet or orbiting it and which can be analyzed in terms of crust and atmosphere. There is a reason why the crust and atmosphere are situated at the periphery. There are differences between the planet’s center and its periphery. A high energy neutrino can be detected if it goes through a region at Earth’s periphery whereas it may never be detected if it goes through the Earth’s core, with which it is likely to react.
Now the question is, regardless of the Universe’s shape, whether the Universe can be compared with Earth in terms of core and periphery. Let me mention two aspects. First, Earth is not a homogeneous body: temperature, viscosity and gravity, at Earth’s core are different from those at Earth’s surface. Second, there is an exterior environment that influences the nature of Earth’s periphery. Thus, my minute level of understanding causes me to think (1) given the Universe’s observable homogeneity and lack of center of expansion, the Universe is likely to have no center and hence no periphery; and (2) the fact that there is no exterior environment in which the Universe is expanding rules out any influence that such exterior environment may exert on the Universe.
This is the reason why we should regard the place we’re at right now as the wavefront of the expanding Universe the OP mentions because whatever should happen at the ‘edge of the Universe’ is happening right here right now.
But where is the periphery of the surface of the Earth? Where on the surface can we find the center?
The first answer is a bit hard, but the second is easy.
In light of the OP, where the question is about the periphery of a three-dimensional object, I think the comparison to Earth applies as long as we refer to our planet in its entirety. Unless they’re infinite or shapeless, I think three-dimensional objects should generally have an identifiable periphery.
The Universe, as commonly understood, has a size but has no edges. If you could travel at light speed (you cannot, because you have mass, but let’s pretend) you could go towards the “edges” but space itself is curved, so, in a long enough time you will end at your starting point.
The Universe has a definite size. Some people believe that it must be 13.000 million years in radius, but, one of the marvelous things we have learned relatively recently is that space itself is expanding, so, in the 13.000 million light-years since its creation, the Universe has reached a size of around 46.000 million light-years in radius (or a total size, or diameter of 91.000 million light-years).
*The Big Bang is not an explosion like in ordinary life: the size of the space is changing. You could say that space is being created. If you measure the distance between things, you find that is always growing, as this graphic shows.
*
Link to image here
As you can see, the Universe had the size of the distance from Earth to Sun when it was 10^-18 years (which is around 0,00000000003 seconds).
When a second had passed since Big Bang, the Universe was around 10 light-years in diameter, which is the distance to the nearest stars.
When a year has passed since Big Bang, the Universe was around 10.000 light-years, give or take, which is comparable to the size of a galaxy.
At none of these moments you could “pass the edge”: the space is where you are, there is no way out. You can go in circles around the Universe, but it has no edges.
I often say to my kids that space is a property of matter: there can be no space but between things. Time, as it must be measured by oscillations, cannot exist outside of things.
This means that space and time have no meaning “outside” our Universe. The are as created as particles, leaves of grass and yourself.
But if your three-dimensional space is, say, a 3-sphere, then it is finite but has no boundary, so your thought turns out to be incorrect. The Earth in its entirety is three-dimensional and has a periphery but is shaped like a ball, not a sphere. (Two-dimensional analogue: a closed disc versus a 2-sphere.) In short, there is no geometric or topological reason for the universe to have any edges.