How Big Is The Universe?

One of the first questions I remember asking, which is, what else is out there? And I would look out my childhood window at the little patch of the sky, and I just remember wondering what they were and what else was out there. And I remember having this feeling almost of restlessness. In 1823, German astronomer Heinrich Albers looked up at the night sky and saw darkness. He wondered, if the universe were infinite and eternally static, then surely shouldn't the night sky shine with the light of infinite stars, a dazzling, brilliant sky? Albers' paradox was so compelling that many considered it proof of a finite universe, a cosmos that at some point simply ends. It wasn't until a century later, when Edwin Hubble observationally established the reality of an expanding universe, that finally Albers' paradox was firmly solved. You see, Albers' second assumption was wrong. The universe is not static. But what does modern astronomy have to say about the size of the universe, though? Is it finite, and if so, does that mean there's an edge, a boundary? Or could it be infinite, an endless ocean of space with challenging philosophical consequences, if so? Join us today as we tackle this question, one of the grandest of scales. How big is the universe? It's the kind of question that a child might ask when they first encounter the concept of space, and yet it is one which continues to perplex and even haunt astronomers today. It's often said that astronomy is a humbling experience, for whilst early thinking considered the earth, the sun, the moon to be the de facto universe, our modern understanding establishes one which is unimaginably larger. At each stage in science's journey of revelation, humanity has had to swallow another pill of great demotion, being quietly ushered down to an ever lower seat in the great cosmic hierarchy. These demotions began in the 16th century when Copernicus, Kepler, and Galileo challenged the geocentric view of their time, revealing that the earth is just another planet. Next, in 1838, Friedrich Bessel pioneered the parallax method to measure the distance to the 61 Cygni, a staggering distance of more than 10 light years, or approximately 100 trillion kilometres. Skipping ahead to 1920, famed astronomers Harlow Shapley and Herbert Curtis debated at the Smithsonian Museum of Natural History as to whether distant nebulae were small clouds on the outset of our own galaxy, or entirely separate galaxies far further away. Soon after, Edwin Hubble established that it was Curtis who was right by proving that at a distance of 2.5 million light years. And today, equipped with our far superior telescopes, modern astronomy has pushed out our observations to distances undreamt of to even those pioneering astronomers. For example, look at this image. It is one of the most incredible photos ever taken. For you are looking at the most distant galaxy ever observed, GN-Z11. This galaxy is so far away that the light forming this image left it 13.4 billion years ago. A photographic time machine. The universe itself was just a few hundred million years old at this time, and so GN-Z11 is a glimpse at what the first galaxies to ever form must have looked like. If we could see GN-Z11 as it is now, it would probably be unrecognisable, and in fact likely have merged with other galaxies along the way. GN-Z11 is estimated to be 32 billion light years away. Now, at first that might seem impossible, because if the light left it 13.4 billion years ago, then surely it should be 13.4 billion light years away from us. The problem with that logic is that we have fallen once again into Olber's fallacy, because the universe is not static. In fact, GN-Z11 has been hurtling away from us ever since the light from this image departed. Or, more accurately, I should say that the space between us has been expanding ever since. And so a correct calculation of GN-Z11's current distance needs to account for this fact, and in doing so we find that it should be today far more distant. Objects like GN-Z11 can thus be thought of as establishing a minimum size to the universe. But remember it's 13.4 billion years old, and we know the universe is 13.8 billion years old, so surely it should be possible to image an object that's even older than GN-Z11, and thus even further away, and that in turn would extend the minimum size of the universe yet further. It's at this point that it's useful to distinguish between two distinct concepts. We have the observable universe and the visible universe. Now, neither of these really have anything to do with telescope capabilities, rather they are true limits dictated by spacetime itself. The observable universe encompasses a distance out to a hypothetical object that was present at the very dawn of the universe, the Big Bang, but whose light is only now just reaching us. Of course, the universe didn't have any galaxies or even stars at the beginning, so there are no objects to detect. Nevertheless, based on the expansion rate of the universe, measured using telescopes like ESA's Planck mission, we can estimate that this distance should be a staggering 45 billion light years away. Now, there may very well be something which lies beyond this hypothetical object, but it's so far away from us that the light from it has not had enough time yet to reach us given the age of the universe. We say that such objects lie beyond our horizon, much like how a ship beyond the ocean's horizon isn't visible to us. Now, it's worth highlighting here that the horizon of the observable universe has a special name, the particle horizon. Everything in the observable universe must lie within that boundary. Now, the visible universe is subtly different from this. In the first few hundred thousand years after the Big Bang, the universe was incredibly hot, so much so that it was filled with an ionised plasma which essentially acted like a thick fog. Light couldn't traverse the cosmos without interacting with this plasma, and so the bulk of the universe wasn't transparent, it was opaque. It was only when the universe cooled enough for atoms to form that the fog cleared away in an epoch known as recombination, finally allowing light to travel freely. So, because of this, the visible universe is a one incredibly large. The observable universe is mind-bogglingly big. No words or analogies can really do justice to just how preposterously, frankly unreasonably large it is. When trying to imagine the enormity of it, one has a sense that our awe only skirts the very fringes of its true wonder, and that if we ever did comprehend its volume, we might never come back, like falling from a great height. Yet, we are compelled to ask, could it be even bigger? Take the observable universe, corresponding to a distance 45 billion light years away. Now, usually at this point, videos like this take that number and double it, so 90 billion light years, and they would call that the diameter of the observable universe. We have to be a little bit careful about that though, because what if one day we discover another GNZ11 galaxy in the opposite direction to where we found the first? And I don't just mean a galaxy which is similar to GNZ11, I mean a galaxy which is identical. Well, that would imply that the universe somehow wraps around on itself, kind of like walking the surface of the spherical earth. And so the non-repeating plane of the universe, what we might call the fundamental plane, would have to be necessarily smaller than this 90 billion light year number. So do we actually see any evidence for this? Well, let's return to the moment of recombination in the early universe. This is the oldest, most ancient light that we can observe, and it comes from all directions. After all, the entire universe was filled with this ionised plasma. This light is known as the Cosmic Microwave Background, or CMB, and it encodes the temperature of the universe at this time. Any patch of the CMB more than two degrees away from another patch is simply too far away to have had time for light to have travelled between them, at least given the age of the universe at the time, just 380,000 years old. So if we see a particular pattern or ripple repeated in the CMB that is separated by more than two degrees, well, that implies that space somehow wraps around on itself, and that in turn means that the universe might be smaller than we initially thought. Detailed studies of the CMB reveal no such repeating structures though, and this lack of structure can actually be used to put lower limits on the size of the full, unobservable universe. But not surprisingly, these limits essentially correspond to the approximate size of the observable universe, 90 billion light years. Another way that we might try to determine the size of the universe is through a logical argument. Suppose that somebody lives in the distant galaxy GMZ11. They would be able to look towards us and see the faint, young milky way as it is in the process of forming, but they could also look the other direction. Would they see a boundary to the edge of the universe, a physical edge? Whilst we cannot truly know what they might see, a basic assumption in astronomy is the so-called cosmological principle, it's really an extension of the Copernican principle, which states that we do not live in a special part of the universe. So what we see around us in the local universe is typical, and thus by extension, what the inhabitants of GMZ11 see around them in their part of the universe is likely not that different from us, at least on the largest of scales. Now this cosmological principle doesn't rigorously prove anything about the size of the universe, it merely poses a logical premise. By the cosmological principle, inhabitants of the observable universe should themselves be able to see another entire observable universe around them, and naively we should be able to rinse, wash, repeat and just keep using this argument to fill out an infinite universe. But again, we have to be careful in this thinking because of the possibility that space might be curved. Consider in this direction, at the edge of our observable universe we have Alice. Alice looks out in that same direction and can see at the very edge of her observable universe someone else, let's call him Carlos. Okay, so now let's go back to the earth and look in the opposite direction. Over on the particle horizon we again have another person and we can tell that it isn't Alice, let's call him Bob. As before, Bob looks out in the same direction and he too can see someone else, just like Alice did. However, it turns out that Bob is in fact looking at Carlos again. To any individual observer there is no repetition, but Alice and Bob are in fact both able to see the same person, Carlos. And since Alice and Bob live far beyond each other's particle horizons, there's no way they can communicate this information to each other. And of course we can equally play this game in other directions too. In this scenario then, no one is able to actually tell that the universe repeats and thus therefore would be finite and compact in size. So really we can't use the cosmological principle to argue for a much larger size to the universe. All we can really say is that within the observable universe we don't see repeating patterns and thus as far as we can tell the universe appears to be 90 billion light years in extent as a minimum. Repeating patterns are not the only way to place limits on size though. Already I've mentioned the concept of curvature and so here perhaps we might finally have a clue as to its true size. Standing on the earth we can't directly see its curvature because the radius of curvature is just so vast that it's imperceptible. But the curvature of the earth can be detected with some geometry as was famously done so by Eratosthenes two millennia ago simply by comparing the lengths of shadows of sticks in the midday sun at two different locations. In an analogous way astronomers can use the CMB radiation and some geometry to measure the curvature of the universe itself. A simple way to think about this is that on a positively curved surface like say a sphere two initially parallel lines can eventually meet. For example if we both head straight north no matter where you live or I live we will eventually bump into each other at the north pole. In contrast on a flat surface the lines stay true and parallel forever and on a negatively curved surface like a saddle they actually diverge. So how curved is the universe? This curvature parameter known as omega k has been measured to ever greater precision thanks to an array of missions studying the CMB radiation from the primordial universe. The earliest scientific estimate done by the boomerang experiment in 2000 found that it was roughly flat with an error of six percent. Thirteen years later NASA's WMAP mission constrained it to be even flatter now with an error of just 0.4 percent. And most recently ESA's Planck mission published our most precise estimate to date which is again flat now within 0.19 percent. I think it's worth pausing here just to appreciate the amazing technical feat by legions of astronomers involved that we can measure the curvature of space itself to this level of precision. But what do these results really mean? Well consider that this curvature parameter is indeed exactly zero a perfectly flat universe. Now it's at this point that many would interpret that flatness to imply that the universe therefore must be infinite. If space-time really is perfectly flat then with the most simplistic application of Einstein's equations we get that the universe is infinite. Data from the WMAP as well as Planck's spacecraft however indicates that the universe is flat or nearly flat with an error of about 0.4 percent. A flat universe would be an infinite universe. Look it's perfectly reasonable to say that an infinite universe is a possible explanation to this zero curvature but it's not the only explanation. In fact it would be a non-sequitur to say that this flatness demands or requires an infinite universe. To cosmologists flatness doesn't really mean what we might naively think in a familiar day-to-day sense of the word. A flat universe doesn't have to be infinite. In fact we've already discussed an example of such a universe. Now let's go back to our friends Alice, Bob and Carlos and imagine that the universe really is a flat two-dimensional sheet as depicted here. Now if we had a warp drive ship and definitely not a USB charger we could leave from the earth head towards Alice and when we reach Carlos we would actually re-emerge on the other side and now be heading back home again. This is probably familiar to many computer gamers since games like Pac-Man and Snake often feature this very rule. So what this means is that the left side and the right side really represent the same boundary and the universe can be seen to wrap around itself at that point. Now if the up and down directions just go on forever then another way we can visualize this Pac-Man-esque rule is to fold this up and make a cylinder. In fact technically since I made this from a two-dimensional sheet this is really what we'd call a two-cylinder. Now this two-cylinder is really defined by this wraparound edge Pac-Man-esque rule that operates on the original 2D sheet what is known as the fundamental domain. It is that rule and really that rule alone that makes it a two-cylinder. Now when we roll this thing up what we're really doing is embedding this two-cylinder into three-dimensional space but really that's just us choosing to visualize it that way. Yes when it's embedded it has curvature but that's purely a product of the embedding. It's actually still a flat geometry in its fundamental domain. Now as intriguing as this topology is it doesn't really save us from an infinite universe because of course the top and the bottom extend out to infinity. So let's go back to the fundamental domain and look at these rules one more time. What if we add another rule that going past this lower edge takes you back up to the top? In fact we can represent that with these two blue lines and when we do that we now truly have full snake rules. Now a fundamental domain that is described by these two rules is no longer an but rather a finite two torus. Now we call it a torus because if I imagine re-embedding this domain in three dimensions I'd first connect the two red ends which would form a cylinder as before but now I have to connect the two blue ends together. In practice I can't really do that without distorting the plane but we can imagine that it should form something like a torus. Now at this point it's useful to discuss the work of the mathematician John Nash who you probably know from the biography and film A Beautiful Mind. The fact that you have to stretch and distort the fundamental plane in order to create this torus shape means that you failed to isometrically embed it and that isometric part is key because when we look around the universe we don't see distances distorted in this way. But John Nash proved that it was in fact possible to isometrically embed this two torus into three dimensions. How? Well by adding waves and waves of tiny corrugations during this embedding procedure. This was a beautiful proof but it didn't actually reveal what this two torus embedded into 3D would actually look like. In 2012 a French team used supercomputers to finally calculate what this shape would look like. This stunning morphology is in fact flat in the fundamental domain and it adheres to the two torus pacman style rules. It's a mind-bending topology riddled with infinite layers of ever smaller corrugations forming this baffling torus, one of strange beauty and fascination. And what's truly mind-blowing is that we may very well be looking at the topology of our universe, a finite flat cosmos embedded in some higher dimensional space. Of course remember that this is a two torus, it's made of a two-dimensional plane. Since our universe has three spatial dimensions then the universe would need to be a three torus, so a kind of hyperdimensional extension of this shape. Indeed the three torus was formally proposed as a possible shape of the universe by astrophysicists Starobinsky and Zeldovich back in 1984. The three torus is in fact just one of 10 possible manifolds which could represent a flat finite universe. Six of these are known as orientable and include the three torus but the other four are known as non-orientable manifolds and include this thing, the bizarre plein bottle, a mind-bending shape of technically zero embedded volume. This orientability property is best understood by looking at a simpler manifold, the Mobius strip. Bizarrely if you travel along the Mobius after one circuit your left and your right have switched over you've become a mirror version of yourself. If our universe is truly one of these non-orientable manifolds it would have some bizarre consequences for a hypothetical warpship. Leave the earth and travel in one direction long enough and you would return home. Arriving back on the earth you would at first feel the familiarity and relief of being back on your home planet but you would quickly realize that something was off. Your family's faces would be strangely unfamiliar as mirror versions of their previous selves. Looking down at their wrists you might notice that their watches ticked anti-clockwise but from their perspective it would be you who was changed and taking you to the doctor for a medical examination they discovered that your heart was now on the right hand side. For all intents and purposes you would have become an alien. Remarkably all 10 of these manifolds are perfectly consistent and all 10 are finite so any of them could be true. But there is another possibility. The universe could be infinite. And that could mean either an infinite flat domain going out in all directions or perhaps even an infinite negatively curved saddle shaped universe. Either way we are forced to face an ontological crisis. What if the universe is infinite? Infinities are uncomfortable to physicists because they bring along some disturbing consequences. Given infinite possibilities everything that can happen must happen not just once but an infinite number of times. In seeking a way out of this one might consider that sure perhaps space is indeed infinite but at some point the nature of the universe itself radically changes and we could say that in effect there is an end to the universe. Indeed there is some theoretical work which at first seems to fit the bill here. In the so called eternal inflation model our local universe is really a bubble like region where the hyper expansion phase known as inflation simply subdued. But if you travelled far enough you would enter a region where the inflationary field has a different state expanding space so much that each bubble universe is separated by unimaginable distances. However since the entire landscape is still infinite there would be an infinite number of these bubble universes so in truth this doesn't really solve our dilemma. So let's just stop evading and finally face the possibility head on. An infinite cosmos. Infinities disrupt probability theory because all events will occur an infinite number of times like infinite number of monkeys typing on infinite typewriters. In some ways the idea challenges the cosmological principle because now we're surrounded by an infinite number of radically different cosmologies as well as an infinite number of identical ones. At a human level an infinite universe raises some unsettling consequences because it would mean that there is an infinite number of yous out there not just similar to yous but yous with the exact same arrangement of molecules and atoms right down to the quantum states of your subatomic particles. That immediately provides a kind of way out of the famous no cloning theorem that's a quantum theory proved by James Parr that states that it's impossible to ever create an independent and identical copy of an arbitrary quantum state. In other words it shouldn't be possible to produce an exact duplicate of you and that's philosophically convenient because if such a clone existed that shared every single quantum state to you then surely that is you but in the case of an infinite universe its very nature disrupts this ontological convenience. Going further some of these doppelgangers would sit inside an entire solar system, galaxy, even universe that was identical to that of our own right down to the last atom. Each one would be watching this video right now, their jaw dropping, their sense of self dissolving as they challenge the very meaning of who and what they are. Yet more in the past and in the future there are infinite doppelgangers of you slightly offset in time. A version of you one day behind or two weeks ahead or maybe even separated by eons. You are everywhere and you never end. As disconcerting and unsettling as this seems it perhaps provides some relief in other ways for it means that our close loved ones that we've lost continue to live somewhere both offset in space-time but also through different choices. It would mean there was an infinite number of loved doppelgangers who didn't get in the car that day, who decided not to take those terrible drugs or who got to the hospital in time. Still out there somewhere just unimaginably distant. At the same time an infinite universe can also paradoxically feel empty even nihilistic. For many we define our goals in life in terms of our impact on the world around us but that impact dissolves away in infinity. For example if your mission is to reduce suffering amongst humanity it is challenged by the fact that in an infinite universe there is infinite human suffering. Whatever you do, whatever you subtract from that infinity it's still infinite. In fact surely anything we do is futile when faced with the sheer cliff, the abyss of infinity. As we look further and further out let us finally turn back to inner space. We can't affect an infinite universe or realistically the infinitely smaller one that we see around us. Rather than trying to derive meaning from our impact on a cosmic scale, the ensemble of space, perhaps meaning lies closer to home. Because whilst there might be an infinite number of you's out there, only you can control your actions today. How you choose to live your life, how you treat others. And so even the smallest acts of kindness can carry infinite weight. So until the next video, stay thoughtful and stay curious. Your life is your life. Don't let it be clubbed into dank submission. Be on the watch. There are ways out. There is a light somewhere. It may not be much light but it beats the darkness.