It really seems like our universe could be part of a hypersphere, but... it's probably not

this video is sponsored by brilliant the cosmological principle this says that on a large scale the universe is homogeneous and isotropic homogeneous just means that if you take any large chunk of space it will look basically the same as another large chunk there is no special location in our universe isotropic means there's no special direction whichever way you look at the universe it will look mostly the same at least on a large scale literally the day I wrote this script an article was released that said research found the universe might not be isotropic as in the expansion rate varies in different places so take some of this with a grain of salt anyways when we look at images of the observable universe we can get a somewhat misleading picture that picture would be a sphere of galaxies which is expanding and then there's us in the middle but remember this is our observable universe if you move to a new location you'd have a new sphere of a new observable universe but it would still look basically the same as before due to the cosmological principle and with you in the middle you'd still find everything is expanding away from you so don't think of the universe as a 3d sphere of galaxies like this we're not at the center and neither is the Sun because actually there is no center to the universe people often think there's a center where the Big Bang happened and everything is moving away from that point but that's not what we observe all things moving away from a central location we instead observe the universe to be moving away from all locations anywhere you look from you'll find distant galaxies are moving away from you as if you're at the center and the further away they are the faster they're moving so it's kind of like the Big Bang happened everywhere at once so just don't think of the big bang as a traditional explosion I read in one source that the Big Bang wasn't actually an explosion of matter but was an explosion of space also on top of all of this we have not discovered any edge to our universe if we did the center could be the point equally far away from that edge boundary in all directions but that's just not the case at the moment so we say there is no center now I used to think that an expanding universe meant okay our universe is just all this stuff that's out there and the convex hole that encloses it essentially then that stuff is just moving away into an empty void thus the convex hull gets larger and the universe has expanded that is not correct in fact the stuff of our universe isn't moving through space at all it's moving with space if that sounds weird the famous comparison is with an expanding loaf of raisin bread the bread is our universe and the raisins are the stuff inside like galaxies as the loaf expands which corresponds to the universe expanding the raisins or galaxies are getting further away from one another no matter where you look from if you're here and measure the distance to all nearby galaxies you'd find those distances are all getting larger as if you're at the center but someone else living in this galaxy measuring all those distances would also notice them all getting larger it seemed like everything is expanding away from them as if they're at the center so everyone gets this impression even though there is no center in regards to the surface and notice that everything moved with the bread this would be a raisin moving through the bread but that isn't what happens with the expansion of this or our universe instead everything moves with that expansion locally gravity wins by the way so the raisins don't get ripped apart just like our atoms aren't separating or the earth isn't escaping the sun's pole but on a large scale distances are increasing okay last thing before we get to the hypersphere universe we need to understand the word flat according to experiments physicists believe the universe is mostly flat with a small margin of error yes there is local curvature since mass warps space-time from general relativity but on a large scale the universe seems to be flat that of course does not mean to D flat it's what I'll call 3d flat a piece of paper is 2d flat whereas the surface just the surface of a sphere is 2d but curved if you started walking parallel to your friend on the surface of a sphere like Earth assuming you walk perfectly straight which means along great circles of that sphere then you'd eventually meet it be strange but this is how parallel lines behave on positively curved surfaces whereas on a truly flat surface you'd never meet in both of these cases you're on a two dimensional manifold but being in that curved world changes what you'd experience so there are things you can do to determine what kind of surface you're on this analogy extends to our universe if you shine two beams of light parallel to one another so long as they aren't interrupted they'll run parallel to each other forever as far as we can tell because of that we say the universe is three dimensionally flat ok so far we've seen that it seems like our universe is flat looks about the same everywhere has no edge has no Center and is expanding regardless of where you look from so why have some people hypothesized that our universe could be part of a really big 4 dimensional hyper sphere because I mean our universe is 3-dimensional yes time is considered the fourth dimension but in this video anytime I say dimension I mean spatial dimension so our universe has three spatial dimensions but a hyper sphere has four seems like there's already some issue there however things work when we consider the surface of a hyper sphere see in the world of math the surface of a regular sphere is known as a two sphere whereas the entire object including the inside is called a three ball because it has three dimensions the surface just has two though it looks flat up close and a flat land creature living in that surface has two degrees of freedom like moving north or south and east and west or longitude and latitude but that's it there's no third degree or jumping-off / digging into the object this creatures entire universe could be this surface there'd be no inside or outside that com wouldn't even make sense to them and if the surface is really big they might never notice that it's actually curved so there'd be no complaints or limitations for these guys this would just be their 2d universe where they can move and play however they want okay now take this to the next level a hyper sphere or a four ball if we include the inside would have a 3d surface or shell we can't picture what that looks like but we can make the comparison just imagine this is a four dimensional hyper sphere and all the stuff you see here is just part of the surface not the inside that stuff could be our entire universe it's three dimensional so we'd be free to move however we want just on that 3d surface there'd be no limitations and we wouldn't ask about the inside because it wouldn't actually exist the entire universe is this surface and that's where this theory could be consistent when someone talks about our universe maybe being a hyper sphere they usually mean maybe on a global scale the 3d universe is just the 3d surface of a 4d hyper sphere and thus that would actually be curved it's very weird to think about everything in all directions being just the infinitely thin skin of a higher dimensional object but just take it down a dimension to get a bit of that intuition so on that note let's compare what would happen on a 3d sphere that we all know of and a 4d hyper sphere with a 3d universe on its surface now for the left object we know a flatland creature living in that surface would perceive it as two-dimensional E flat assuming they were relatively small in size I know this animation doesn't depict a flatlander but just pretend now going up a dimension this means a creature of like us living within the surface of a hypersphere would perceive it as three-dimensional E flat if that sphere were really big so this first observation wouldn't be too surprising even if on a global scale our universe was curved then if that 3d object had a bunch of flat 2d stars and galaxies spread out evenly among the surface that means a creature that surface would have a circular region as their observable universe this is what they could see and if they move to a new location they'd have a new observable universe that looks basically the same because of the even distribution of the 2d stars and galaxies take this up a dimension and that means on a hypersphere surface our observable universe would not be a circle but basically a sphere technically with some higher dimensional curvature but if the galaxies are evenly spread out on the hyper sphere then the observable universe would look mostly the same no matter where you are which is exactly what we observe so the second point also seems to be consistent with a hyper sphere achill universe then since we're talking about only the surfaces of these objects there would be no edge in either the 3-d or 4d case which is also consistent with what we observe and another property of these surfaces is that there is no sinner sure there is a center of a sphere when talking about the entire thing like a three or four ball but we're not these are the surfaces the two or three sphere that's all that exists and both of these have no center or edge and by the way on the hyper sphere we wouldn't perceived that curvature at all if you shined a beam of light or observed an object moving in deep space you'd think it's going straight but it really be curving in a higher dimension where it could eventually come back to where it started from and that would resolve the idea of an object just moving into the void of space forever then lastly let's say that hyper sphere is expanding that would mean all the stars and galaxies we observe would be getting further away from one another while simply moving with the universe not through it and no matter where you look from you'd find those distances are increasing as if you're at the center which matches exactly what we observe so boom QED the universe is on the surface of a hypersphere all right now in reality a lot of ideas and cosmology should always be preceded by the words we think that or we have evidence of because the thing is we often don't know for sure and there's the ban on whether we'll ever know the universe could be a hypersphere it could be flat it could be infinite or it could have an edge we don't know so let me carefully say we have reason to think our universe is not the surface of a hypersphere despite all these truth bombs I was totally dropping so why well first of all we have taken measurements of the curvature of the universe and we found it to be really flat see on a sphere it's possible to walk straight take two 90-degree turns and end up back where you started that is impossible on a flat surface so this is an experiment you could do to determine whether you're on a curved surface or not without ever leaving it but notice the triangle here because on a positively curved surface the angles add to more than 180 degrees always and that's the experiment researchers have done they've measured the angles of really big triangles in our universe using the Cosmic Microwave Background and found these angles to add up to just about 180 degrees indicating flatness if the universe were on a hypersphere then it'd be an extremely large hyper sphere where the observable universe would be a small speck on it so it's just more reasonable for us to say the universe is flat next up several analogies you see in cosmology get criticized because well they might be helpful in one aspect they can cause confusion elsewhere for example with the loaf of raisin bread it'd be fair to ask as the loaf or universe expands what's it expanding into if this loaf is the entire universe what's all this stuff out here before the universe even gets there this is tricky but the expansion is intrinsic it's the scale of space itself that changes and this does not expand into anything or require space to exist outside of it in a previous video I discussed the metric tensor which oversimplified helped us make corrections to the Thackeray and theorem on warp surfaces on a flat surface pythagoras and we can find the distance between two points no problem on warp surfaces we run into issues and that's where the metric tensor comes in so when we say the universe is expanding we really mean the metric tensor is changing so it's more like distances between points are increasing without space physically expanding into anything but loaf of raisin bread gave us a decent mental image but as with all these analogies it wasn't perfect then if the universe is flat and infinite which seems to be the most common belief it's reasonable to say the universe would look mostly the same no matter where we look assuming a fairly uniform distribution so this here doesn't necessarily point to any higher dimensional curvature plus a truly infinite universe would have no edge or center then instead of the loaf of race and bread example another one you might see is that of an infinite grid expanding where it's not expanding into anything since it's infinite but rather distances between points are increasing as in no matter where you look from the universe would be expanding if you use that as your go to analogy then that would resolve this last bullet point as this could also be true in a flat universe so although all of these seem to maybe work in a hyper spherical universe there's no reason to make any conclusions because these can all be true in a three-dimensional a flat universe I've even read some comments that say sometimes physicists don't really care about the extra dimensions if the physics works in three honestly I think most of this video was stuff we don't know with 100% certainty but realize these theories don't come out of nowhere there's evidence and their experiments that at least point towards one theory being more likely than another and if you want to look further into the current theories and mathematics that describe our universe you can do so over at brilliant the sponsor of this video two courses they have that directly relate to what we've seen here would be gravitational physics and astronomy in these you'll explore the shape of the universe what it would mean to have a flat versus open versus closed universe and even how this is all linked to the presence of dark matter they even cover some interesting future events and what the fate of our universe looks like which I also find really interesting in all courses come with intuitive visuals and animations which for me is one of the most important tools for gaining a true understanding of advanced math and physics concepts then on top of what you've seen you can dive into advanced differential equations the physics of waves and light group theory and plenty of other courses in math science and engineering plus the first 200 people to sign up using the link below or by going to brilliant orange slash takstar we'll get 20% off their annual premium subscription and with that I'm going to end that video there thanks as always my supporters on patreon social media links are down below and I'll see you guys in the next video

Channel: Zach Star

Views: 868,059

Keywords: hypersphere, hypersphere universe, universe, higher dimensions, universe as a hypersphere, hyper sphere, 4th dimensions, fourth dimension, big bang, cosmology, astrophysics

Id: e1dOnqCu9pQ

Length: 16min 23sec (983 seconds)

Published: Tue May 19 2020