Does the Universe Have A Center? (Script) (Patreon)

We can all be a little self-absorbed sometimes, acting like we’re the center of the universe or something. Well first let me tell you where the center of the universe is before you decide that’s where you are.

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For most of history all of humanity has been pretty self-absorbed, astronomically speaking. We imagined the earth the center of the cosmos until Nicolaus Copernicus shoved us from 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’re 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 going to ask a simple-seeming question that will lead to so 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  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 an colossal explosion, or as Calvin more poetically named it - a horrendous space kablooie. 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 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 this 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.  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 spacetime 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 of spacetime.

It wasn’t actually Einstein who worked this out. The first to solve this was Alexander Friedman - he ignored all those little gravitational bumps - doing the mathematical equivalent of grinding up everything into 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-Lemaitre-Robertson-Walker metric, also named for those three other guys who came up with it right after Friedman. This simplification really paid off. For one thing it predicted that the universe could not be static - it had to be expanding or contracting, and that as more than a decade before Hubble discovered it was the latter. The FLRW metric also predicts that there are only three possible global shapes to 4D spacetime, 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’, and flat.’ The exact shape is determined by the relative amounts of matter and dark energy in the universe. The presence of matter 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 2-dimensional. But for a 2-D 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 - or at least, no center that’s part of the 2-D universe. A closed 3-D universe is like the 3-D surface of a 4-dimensional hypersphere. And just like it’s 2-D analog, it’s finite and center-less.

If I were to ask a denizen of the surface of the sphere to point to the center of the 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 4-D hypersphere lives? Could there be an equivalent of “down” in that space that we are just too dimensionally-challenged to point to? 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 - a closed universe loops whose three spatial dimensions loop back on themselves.

But actually, we can sort of define a center of this sphere - because at one point we were AT the center of that sphere. 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 sphere 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 sphere 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 hypersphere as being a location in time. 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 would intersect the moon. Of course your 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 the light that only now reached you from the moon, and that light has been traveling for one second.

Now imagine that 2-D dweller points in 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 pointed line, coincide with the center.

It’s the same with our universe - point in 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 geometrical center of this hypersphere.

A lot of this stuff is also true for the flat or open universe. The 2-D 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 is no geometrical 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 you finger also ends up at the beginning of time.

These lines we’ve been tracing have a name - they’re called null geodesics. They’re the grid that defines the fabric of space time in general relativity, and correspond to the 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 spacetime 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 space at t=0 and is in the past of all paths through spacetime.

OK, 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=0. But what about an infinite universe? The math of the FLWR 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 pointlike at t=0 and then suddenly become infinite in size? Well the size of the universe at t=0 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. Stand by 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 it’s own video - although as a spoiler, the answer isn’t as obviously in the negative as you might think.

OK, so we have the state of the current wisdom on the shape of the universe, and the non-existence of its center. But I promised 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 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 doesn’t require an infinite universe, nor a hyperspherically looping universe. And you can do it without breaking Einstein’s general relativity.

One of the alternative solutions to FLRW was discovered by Georges Lemaitre, the L in the FLRW metric.  Lemaitre asked what the universe might look like if it was NOT homogeneous. He sought solutions to the Einstein equation for a universe that is lumpy on the largest scales. In one of his solutions, dust 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 looks exactly like a FLRW universe.  At around the same time, Richard Tolman made the same discovery, and so we have the Lemaitre-Tolman metric,

Such a universe WOULD have a center - the center of the cloud, assuming 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 Lemaître-Tolman universe inside a greater Friedman 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 that 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 then as far as we know there could be a center and we could be at it. So go ahead and get right back on that pedestal - we know it’s almost certainly not tru, but no one is ever going to prove that the earth, humanity, even you personally, are not at the very center of a very non-Copernican spacetime.