Well, this is akin to the idea that our universe is a nested black hole inside another universe that’s a black hole inside another and so on.
The question, assuming that our universe was created this way, or at least shares attributes with being inside an event horizon, is: is there a finite resolution or granularity to space itself? Does it cease at the planck length, and if so, might this prevent infinitely nested universes as the quanta of action within space becomes untenable.
Or might it mean that the resolution of space is reset upon each nested universe, like burrowing down into a fractal; or perhaps the resolution of space is infinite, and only the quanta lengths are reset, etc.
By definition the two-dimensional surface of the balloon is all there is, mathematically. As I said earlier, there is no inside and there is no outside. From the point of view of a two-dimensional being on that surface, there is no getting off of it to look at it. You only think so because you’re used to living in a 3-D world. But from our pov, a three-dimensional curved universe is also all there is, finite, with no inside and no outside. You can’t stand outside the universe and look at it because there is no fourth spatial dimension from which to do so. (String theory multiple dimensions don’t change this for the purposes of this discussion.)
Inside of a black hole is a singularity. Our current physics do not explain it, although many have suggested explanations.
In the balloon analogy (which is great, BTW) would there be a way of knowing that “space” was growing? I.e., is there a ruler that would not also be expanding that one could compare to a physical feature such as your foot? Could you just measure how long it took for light to travel that distance?
I believe that’s exactly what the red-shifting of galaxies is showing us. That since almost all of these distant galaxies are red-shifting in accordance to what a universe undergoing spatial-expansion would predict, it means just that; Space itself is ever-growing, and like boats on an ocean whose “shores” are ever expanding, because the water keeps pouring in, we’re all drifting apart from each other (despite any local movement relative to each other).
Using the balloon model, are you saying our universe is on the surface of the balloon?
This does seem to be in line with black hole theory and the law of conservation of information. Information supposedly can not be lost in a black hole and a ‘image’ of this is recorded on the event horizon according to a model. If the universe is inside a BH, then the balloon theory would be the 2d image of our 3d universe. So while the balloon model would be valid in this model it would only be half the story as the model does continue into the BH according to that model, so there would be the balloon and also a inside extra dimensional model that works together.
That’s the thing about reducing dimensions, you loose some of the accuracy in exchange for a clearer way of imaging what’s going on.
In so far as experimental evidence goes, we only have proof of 3 dimensions of space (which can be curved by matter/energy), and one of time. Trying to then imagine the balloon analogy from a 2D surface, to a 3D volume is difficult, but not impossible.
The balloon analogy is not a scientific model. It’s just an attempt by someone to describe more complex stuff in normal language. You can’t then take the balloon and then extrapolate physics from it.
If the universe were closed on any of the plausible models we had for a closed universe prior to recent measurements that make it appear it’s probably flat, would it be closed in timelike dimensions, or only spacelike ones?
As mathematicians define it, a straight line is a geodesic.
You can always plot a geodesic. But they don’t always look “straight” if you apply them to a flat representation. A geodesic on a globe looks curved when transposed to a flat map.
Depends on the flat projection of the Earth. A polar projection will turn all great circles into straight lines. Or at least, all great circles that can be shown on the map at all: A polar projection of this sort can only cover less than a hemisphere.
This is not a property of all polar projections. For example the polar projection on the United Nations logo shows the equator as a circle. It is a feature of the gnomonic projection, whose point of projection is the center of the earth.
I was puzzling over this subject earlier. If the universe is expanding faster than the speed of light then doesn’t that violate the law that nothing can go faster than the speed of light?
I came across these links and apparently the answer is no:
The reason being that you can imagine the universe as a lump of dough with raisins in it. If you put the dough in the oven it will expand and the raisins will move farther apart relative to each other without actually moving themselves through the medium they are in.
So, if there were creatures that could move through dough, they would still be restricted by whatever factors restrict them but on a meta level they can be moved faster by the expansion of the dough
ie within the medium of the universe nothing can go faster than light but the universe itself is not restricted by that law. The universe itself is stretching which means that two things relative to each other can go faster than light. Everything is relative to everything else. Everything is moving away from everything else. The earth is moving away from distant galaxies at a faster than light speed but that doesn’t mean that things that are subject to the laws of the universe can go faster than light. The universe itself isn’t subject to the internal laws of the universe.
If there were two insects crawling on the surface of a balloon they may crawl away from each other at a certain rate but if you inflated the balloon while they were on it then they would move away from each other at a faster rate while still being restricted themselves by the speed they can walk. So in a way they are violating the law of how fast they can go but only because the surface they are walking on is also moving.
Which brings me to the points I still wondered:
A lump of dough still has an edge in the sense of anything external to the lump.
If you could get to that edge maybe you could break out
It would be hard to do because we are constrained by the medium in which we are working - the universe. Like wading through tar. But theoretically there could be something outside of this universe if we could think of a clever way to bypass the laws of the universe
Just because someone decided to use the analogy of a lump of dough to illustrate why the universe can expand faster than the speed of light doesn’t mean that the universe therefore follows every property of that fictional lump of dough. It’s just an analogy; the universe isn’t a lump of dough, and doesn’t have an edge just because the lump of dough in the analogy does. The universe also doesn’t rise into a nice tasty bready substance when heated.
The lump of dough only helps illustrate that one principle. It doesn’t illustrate the shape of the universe or anything.
