we can all be a little self-absorbed at times acting like we're the center of the universe or something well let me first tell you where the center of the universe actually is before you decide that's where you are for most of history all of humanity has been pretty self-absorbed astronomically speaking we imagined the earth as the center of the cosmos until nicolas copernicus shoved us off our pedestal onto a random rocky planet orbiting an ordinary star in the outskirts of an unremarkable galaxy ever since then astronomers have embraced the copernican principle which states that we are not in a special place in the universe at least once you factor out the selection biases of needing to be somewhere moderately hospitable and the copernican principle inspired another important idea not only are we not the center of the universe but the universe doesn't have a center once you zoom out far enough the universe looks basically the same everywhere this is called the cosmological principle but neither the copernican principle nor the cosmological principle are actual laws of physics they are philosophical positions guiding principles that so far have not led us astray i think both must be right but i don't know for sure and it sure would be nice to feel special again today we're gonna ask a simple seeming question that will lead to some pretty wacky places the question is this if the universe has a center where is it you might imagine that the center of the universe is the place where the big bang happened the origin of the explosion that created everything well this would be wrong but it's easy to understand the misconception thanks to edwin hubble we know that distant galaxies are racing away from us and the further we look the faster they're moving it looks like the milky way is at the center of a colossal explosion or as calvin more poetically named it a horrendous space kublui but the big bang isn't an explosion emanating from one point in space the recession of the galaxies is just as well explained if all of space is expanding evenly everywhere galaxies appear to be receding due to the space between them stretching most importantly this looks the same no matter what galaxy you're in in this picture the big bang isn't something that happened at a single point in space instead it happened everywhere at the same time all space was created at that instant google where is the center of the universe or where did the big bang happen and you'll get this basic story for the first 50 pages and that's because the story is probably right but today i want to dig deeper and see what assumptions are behind this interpretation and also ask what it would mean if those assumptions are wrong but before we mess with the standard narrative let's make sure we understand what it is as with much it starts with einstein his general theory of relativity explains gravity as the warping of space and time due to the presence of mass and energy general relativity can be used to calculate the space-time curvature produced by the earth or the sun to determine their gravitational effects it can also give us the gravitational field of the entire universe which tells us the shape of all space-time it wasn't actually einstein who worked this out alexander friedman solved the einstein equations for the whole universe by doing the mathematical equivalent of grinding up everything in the universe into a fine paste and spreading it evenly through space that gave him equations of motion that described how the universe must evolve and a shape defined by something called the friedman lamatra robinson walker metric also named for those three others who came up with it at around the same time the simplification really paid off for one thing it predicted that the universe could not be static it had to be contracting or expanding and that was more than a decade before hubble discovered that it was the latter the flrw metric also predicts that there are only three possible global shapes to 4d space-time determined entirely by one number the curvature depending on whether the average curvature is positive negative or zero we get one of three shapes which we call closed open or flat the exact shape is determined by the relative amounts of matter and dark energy in the universe as well as its current expansion rate the presence of mata increases the curvature and the presence of dark energy decreases the curvature we can't visualize the center of a geometry if we can't fit it in our heads in order to do that we need to lose a dimension positively curved 3d space is the easiest first imagine the surface of a sphere that surface is two-dimensional but for a 2d being living on that surface those two dimensions are all that exists the surface is finite but there's no edge and there's no center at least no center that's part of that 2d universe a closed 3d universe is like the 3d surface of a 4-dimensional hypersphere and just like its 2d analog it's finite and centerless if i were to ask a 2-dimensional denizen of the surface of the sphere to point to the center of their universe they couldn't do it they can't point down to the center of the sphere because to them there is no down but from our perspective that direction exists so could it be that there's a higher dimensional space in which our 4d hypersphere lives could there be an equivalent of down in that space that we are just too dimensionally challenged to point to well not necessarily space can have curvature without there being anything for it to curve into and that's the most straightforward interpretation of the flrw metric for a closed universe those three spatial dimensions just loop back on themselves but actually we can sort of give a location to the center of the expanding hypersphere because at one point we were at that center so far we've ignored the dimension of time our universe is expanding in the case of the closed universe that means it started out as a very very tiny hypersphere surface and got bigger so very crudely we can think of the radial direction as the dimension of time it would be more accurate to say that the radial dimension of this expanding hypersphere is represented in the math by the scale factor and the scale factor increases as time increases but it's fun to think of the center of the expanding hyposphere as being a location in time because that means we really can point to the location of the big bang by pointing to the past and conveniently you can point to the past by pointing in any direction whatsoever i'm serious hear me out you can point at say the moon by ensuring that a line drawn from your outstretched finger intersects the moon of course you wouldn't be pointing at the moon of the present it would be the moon of the past because you're aligning your finger with light that has only now reached you from the moon and that light started travelling one second ago now imagine that 2d dweller points at a random direction draw a line in that direction and at the same time reverse the flow of time to see what it intersects the line loops around the closed universe as the sphere shrinks until eventually all points in the universe including the line that we're tracing coincide with the center it's the same with our universe pointing any direction and you're pointing at the big bang and if the universe really is closed you're also pointing at the point where all space occupied the geometric center of the hypersphere a lot of this stuff is also true for a flat or open universe the 2d analog of the flat universe is an infinite flat plane while the open universe corresponds to a sort of saddle shape what we call a hyperbolic plane which also stretches on forever in both of these cases there's no geometric center even in a fictional higher dimension however you can still point at the big bang by pointing in a random direction because the line traced from your finger also ends up at the beginning of time these lines we've traced have a name they're called null geodesics they're the grid that define the fabric of space-time in general relativity and correspond to paths followed by light no matter the geometry of our flrw universe all geodesics converge to a single point in the past and end there in the language of gr we call this ending of space-time paths geodesic incompleteness geodesic incompleteness is just a fancy way to say singularity there is literally no direction that you could point that would not intersect the big bang if traced backwards and that's true anywhere in the universe we say that the big bang is a past space-like singularity which means it occupies all of space at t equals zero and is in the past of all paths through space-time okay so maybe the location of the big bang isn't at one point in this universe but can we still say that the big bang happened at one point i mean if all points converged onto the same point at the beginning if all geodesics emerged from that point does that mean the universe started out point-like in the case of the closed universe that's easier to imagine rewind the growing sphere and it approaches a single point at t equals zero but what about an infinite universe the math of the flrw metric and the friedman equations tell us that as time approaches zero the distance between any two points approaches zero but at the same time there are infinite points so did the universe start out point like at t equals zero and then suddenly become infinite in size well the size of the universe at t equals zero is zero times infinity which is neither zero nor infinity it's the point where the math breaks and that's the nature of singularities they are discontinuities in the math we use to describe the universe they probably also represent places where our understanding of physics breaks apart standby for our theory of quantum gravity to resolve that one by the way there are close parallels with the singularity of the black hole we might ask whether the big bang is a reverse black hole also called a white hole we might but we won't that's a topic worth its own video although as a spoiler the answer isn't as obviously in the negative as you might think okay so we have the state of the current wisdom on the shape of the universe and the non-existence of its center but i promise to tell you how this might not be true remember that alexander friedman came up with his solution for the shape of the universe by assuming that matter and energy are evenly spread out everywhere he assumed a homogeneous universe and assumed the cosmological principle but what if he was wrong it turns out there are ways to make sense of hubble's observation of the receding galaxies that don't require an infinite universe nor a hypospherically looping universe and you can do it without breaking einstein's general relativity one of the alternative solutions was discovered by george le matra who was the l in the flrw metric lemetra asked what the universe might look like if it was not homogeneous he sought solutions to the einstein equations for a universe that is lumpy on the larger scales in one of his solutions mata was distributed with constant density across a spherically symmetric cloud but beyond that cloud the density could change or space could be empty he found that an observer in a sufficiently large cloud that was expanding or contracting would observe an expanding or contracting universe that looked exactly like an flrw universe at around the same time richard tallman made the same discovery and so we call this solution the lematra tolman metric such a universe would have a center the center of the cloud assuming that the cloud is finite i should point out that this doesn't necessarily break the cosmological principle because it could still be that our bubble is small on the most ridiculously gigantic scales and that if you zoom out to many many many times larger than the observable universe everything evens out smoothly so you can find a le metra tolman universe inside a greater flrw universe and there's even a scenario where this might be the case that's eternal inflation which proposes that our universe is just one bubble of relatively slowly expanding space embedded within an unthinkably colossal region of exponentially accelerating space check out our episode on that for this insane seeming proposition long story short the universe probably doesn't have a center and if it does we may never know the evidence of there being a boundary to our bubble is very likely far beyond our cosmic horizon in that case as far as we know there could be a center and we could be at it so go right ahead and get back on that pedestal we know it's almost certainly not true but no one is ever going to prove that the earth humanity even you personally are not at the very centre of a very non-copernican space-time you