Paradoxes That Push the Limits of Reality

Why does reality have a speed limit? It is common knowledge that the speed of light is the fastest that anyone can go, but why does this cap on causality exist? And why is it exactly 299,792,458 meters per second? Why not more? Why not less? If you're like me, you've wondered about these strange properties of light, but recently, I think I might have found an answer, and it lies in hyperbolic geometry. And the more I've considered it, the more it's blown my mind. I'm Alex McColgan, and you're watching Astrum. Join with me today for the third part in our series on the unseen world, and bring together what we have learned so far to try to answer some of the biggest questions about why our universe is the way it is. Before we begin, I should mention that this is a continuation of a model that has been developed in collaboration between me and my brother, which we began in this video about 4D space, and continued exploring in this video about the shape of our universe. If you haven't watched those videos yet, I would highly recommend you check them out, as we will be blending both concepts together in this video. Check the links in the description or the top right if you need a refresher. Out of the way, let's talk a little bit about light. There is an interesting observation we can make about light. From an external perspective, it appears as if light is travelling at 299,792,458m per second. This is true no matter what perspective you look at it from, whether you are at standstill, whether you are moving towards it or away from it. It always looks as if it is travelling at this speed. However, there is a single interesting exception to this rule which had always puzzled me, the photons perspective. Einstein has proven that for an object travelling at light speed, time would slow down so much that it would be at zero. If you were to suddenly start travelling at the speed of light towards Jupiter, you would notice zero time passing, but would observe that you have travelled 679 million kilometres. And there would probably die of the lack of air, the punishing G forces and the friction burn along the way. But what happens if we try to calculate your speed using these figures? Well, speed is distance over time, so 679 million divided by zero equals… If you tried plugging this into your calculator, you would quickly run into an error here. Calculators do not like dividing by zero. This is because the smaller the denominator becomes on a fraction, the larger the total number becomes. If you reduce the value of the denominator all the way down to zero, the only way this can work is if your total answer becomes infinity. If you travel for zero time over any distance greater than zero, you have just travelled at infinite speed. So from light's perspective, it is travelling infinitely fast, not at 299,792,458 metres per second. Let's call that C from now on. So why is it that everyone else detects light travelling at sea, but light thinks it's going infinitely fast? What I'm about to share is one possible theory. It's going to involve a 4D hyperbolic space. That's quite a mouthful, so let's take our time exploring this space so we know what we're talking about. To quickly recap on the rules of a 4D space, let's imagine that all of 3D reality has been compressed into a single, flat line travelling horizontally across space. This leaves us free to make everything up or down in this space into the future or the past. To put it another way, the x-axis represents moving through space and the y-axis represents moving through time. This is how we can get the extra dimension, our fourth D. Here in 4D space, time is simply another direction we can go in. Hyperbolic might sound a little intimidating too, but simply put, all it means is that the lines diverge away from one another, always. This has the effect of warping space in a way our brains don't really process well, but essentially means there's more and more space the further out you go, but exponentially so. Other than that, travelling through this space obeys the same rules that travelling through 3D space uses in terms of the physics rules involved. Objects that start moving must be acted upon by another force or they will continue moving at the same rate. Objects at rest remain at rest, conservation of momentum is maintained. Now let's imagine for whatever reason there was some big expansion event in the past that centres all moving in the upwards direction. A big bang if you will. I wonder where one of those might have come from. But this expansion was not simply in space, but in time too. It's a 4D explosion. We are now in motion, moving solely up at the top of this expanding bubble. For now we are not moving anywhere in space, we are simply moving forwards in time. We travel consistently, and will continue to travel consistently until we are acted upon by another object or force. But as we are new and there is nothing but empty space above us, we are going to go up infinitely. There's nothing up there to bump into. Now let's imagine for a second that we decide we no longer want to go straight up. Let's try to change direction. In physics any change of direction is a form of acceleration. This may not make much sense intuitively, but it becomes easier to understand if we split our vector into two components, our velocity in the x direction and our velocity in the y direction. It then becomes easy to see that changing our direction comes about by decelerating with one of our values and accelerating with the other. We don't have to change both values though. Let's just give ourselves a little impetus in the x direction. Obviously, the more we are pushed, the faster we are going to travel, and the more our total vector begins to lean towards a perfect horizontal line. The size of our vector increases. However, let's say that we want to go faster. In fact, we want to go so fast that we are no longer travelling in the y direction and are only moving in the x direction or space. Is there any amount of push we can get in the x direction that will make it so that we are actually going completely horizontally? No. You can increase the distance in x by a larger and larger amount, but as long as y has some value you will never actually get that vector perfectly going across space. The only way you could get your vector in the time direction to slow down is if you pushed against something that's ahead of you, or pulled on something behind you. But if everything near you is in the same second you are in, there's nothing to push against. You can only push each other left or right. Nothing is ahead or behind. Interestingly, with only this available to you, your vector can trend closer and closer to flat, but it never actually reaches it. And increasing your speed produces diminishing returns on how much flatter you can get your vector. You have a limit. You would essentially need to go infinite speed to approximate a flat line, and to go infinite speed you would need infinite energy, difficult to get your hands on. Of course this is where the idea diverges from reality. There's nothing here so far that imposes a speed limit on our model. You should easily be able to go faster than the usual light speed limit. With infinite energy you could go 3 billion meters per second, or 3 trillion. But in the real universe we don't see that. Everything normally seems to be capped at sea. There is a similar trend where the more energy you put in, the less additional speed you get, but that occurs at close delight speed, not infinite speed. So our 4D model seems to have failed. But this is not regular 4D space. This is a hyperbolic 4D space. Let's observe what happens when you try to travel at near infinite speeds when the lines start to bend. Here you have zoomed along at a speed that's as fast as infinite as you can imagine. Speed is a tricky little concept here, but let's say that from your perspective you covered a distance of 400 million meters in a second. So faster than the speed of light. What happens? Well you hit this little curved line over here. Although it is bent to be almost a sea shape, if you follow the line down you will see that it is a timeline, not a space line. And because it is a hyperbolic space, there is more here than meets the eye. Let's jump over to that point and see where we ended up. Although in our movement vector, by our origin we only travelled one square high, by our end destination we have ended up at a point multiple squares high. By taking a journey sideways, and by only experiencing a second forward momentum through time ourselves, we have ended up many seconds into the future. We have taken a shortcut into the future. This is what we observe in the real world. Objects that move at great speeds seem to suddenly experience reduced time. They believe only a few seconds have passed, but far more time can occur to an external observer. And suddenly it really throws off our maths. Because how does an external observer record our speed? If we started at an origin point of zero, but ended at an origin point that's 10 seconds into the future, they have to say that we have travelled 400 million meters in 10 seconds per speed of 40 million meters per second. While below the speed of light, no matter what we thought we were doing. Which is kind of like what light seems to be experiencing. And the faster you push yourself in the x direction, the more you encounter the warping effects of hyperbolic geometry, and the more it keeps pulling you back towards the speed limit cap of the universe, it will never let you exceed it. This explains why there is a cap to the universe, not even light, which as far as it is concerned does travel infinitely quickly, would be able to overcome it. Provided the base we were resting on was ever so slightly curved. As soon as the photons slid onto the plane that was space, it would get swept up in the curvature of this hyperbolic 4D space. It would trace the limit of it true, but it would get caught in it. And then, from our perspective, it would start to look as if we were simply moving uniformly at a speed of C. We would see it leave, and then we would time how long it would take to arrive at its destination. It doesn't matter for us that it believed it had arrived there instantaneously by taking a shortcut through time, we would just record it as having arrived after some time had passed. So there you have it. Why is there a speed limit for our universe? Perhaps because space is curved, and our 4D space is hyperbolic. At least so claims this theory. It is, it must be stressed, just a theory. It's possible that smarter people than me in the comments will explain why this is wrong. However, it does neatly explain to me why time dilation happens, and why reality has a speed limit, which I find quite appealing. In fairness, perhaps the only way to test it would be to try to go faster than the speed of light, and we have never gotten close to that speed. The fastest a human has ever gone is 11,083 meters per second, when NASA astronauts returned in a spaceship from the moon. It would require incredible amounts of energy to travel sea from our perspective. If it is true though, it would provide firm evidence that our universe really was hyperbolic in nature, and sadly quash any hope of us travelling backwards in time at any point. So sorry time travel fans. But at least we can console ourselves that although we probably can't travel to the past, travelling through shortcuts to the future is definitely within the realms of possibility. What is time? In this channel we've talked a lot about time. As black holes warp space around them, we've learned that time slows down. We've discovered the time influencing effects of gravity, and even how the James Webb Telescope can peer through time to the distant past by taking advantage of the fixed speed of light. All this makes sense so far, but what actually is time? You can't taste it, touch it, or feel it, yet time has an unstoppable influence on us, and is pushing us forward whether we like it or not. Doesn't something that impacts everything we do deserve some additional understanding? I'm Alex McColgan and you're watching Astrum, and while this is an area that scientists have many theories about, I'd like to share with you today one model that might help you understand this mysterious concept that is ticking all around us. By the end of this video, we are going to have a possible explanation of why time slows down as velocity increases, and why shapes warp when undergoing velocities close to the speed of light. This video is a collaboration with my brother, based on Recognize Scientific Theory, where we have taken scientific concepts and combined them into something you may not have seen before. But before we get to that, we have to begin with one foundational idea. Time is actually another dimension. Now before you double check that you haven't logged into some sci-fi channel by mistake, let's discuss what I mean by dimensions. While in popular culture, different dimensions are often described as parallel worlds that are very similar to ours, yet subtly different. In this context, when we talk of different dimensions, we are referring to the dimensions of space, as in three-dimensional space, or 3D space, which may be far more familiar to you. This is by no means trivial though. 3D space is all around you, it is the around you, and is very relevant to our topic. Let's begin by making sure we understand the 3Ds, and the relationships between them before we add the 4th D. Broadly speaking, 3D, or 3-dimensional space, simply refers to space that can be measured in three different perpendicular directions. The perpendicular nature of these dimensions is important, but we'll get to that later. Three-dimensional space is usually described as having height, width, and depth, and they all have 90 degree angles between them. Simply put, objects like us that exist in 3D space can move left and right, up and down, and forwards and backwards. We are comfortable with this kind of space. Using this as our basis, it becomes much easier to imagine what we mean by 2D space, and even 1D space. To move from one space to another, all we need to do is remove or add an extra dimension of measurement or movement that must be a 90 degree angle from all previously existing angles. So, 2D objects move in a plane that's bounded by the X and Y directions, or the X and Z directions, or the Y and Z directions, but not all three at once. 1D objects can only move either along X, or Y, or Z. Imagine a person who lived in such a 1D world. The whole existence would be found either moving one way or the other. All of reality would exist either to the left or to the right of them, and would appear as a singular dot. They could not move or see in any of the other directions, and probably could not even comprehend such directions as even existing. Photons whizzing by them would only be visible if they entered the singular line that was a 1D person's whole area of existence. Now, adding extra directions of movement is what's needed to move things up from 1D to 2D to 3D. So, in theory, we can predict what we need to do if we were to jump to 4D. However, here we hit a snag. Well it's easy to draw a line that's perfectly perpendicular to a single other line, or to draw another line on top of those lines that is perpendicular to the two previous lines. How would we draw a fourth line that's perpendicular to all three? Surely such a thing is impossible. Well, within 3D space, such a thing is impossible. The best we can do is draw approximations. For instance, it's possible to draw an approximation of a 3D shape on 2D paper by doing something like this. These lines are all two-dimensional, but we look at this and our brain recognizes that this is a picture of a 3D shape. So, in the same way, we could probably do something similar to what a 4D object might look like using just 3D lines. Mathematicians have attempted to do this, although their results tend to be a little confusing. Although this is mathematically sound as a basis for a 4D object, I personally don't find my understanding of 4D space deepened by looking at it, so I won't focus on it in this video. There is some evidence, however, that a fourth direction exists, and we are moving along it right now. That fourth direction, or dimension, is time. Einstein predicted this connection when he linked space and time into one unified space time in his theories of relativity. According to him, time and space are two parts of the same thing. To me, this connects with 4D space very nicely. Just as there is no real difference between the Z and the X or Y directions, so too would there not be any difference between time and space if time is just another direction, albeit one that we can't see. And time is important. Without time, our 3D space wouldn't move. It would perpetually be in one state, because it's time that allows us to move about in it. But why can't we see it? Why can't we look in the direction of time? To explain this, let's look at the difference between the different dimensional spaces. We best notice this when we consider what 2D objects might look like if they were to move around in 3D space. This is where we start to delve into the model. Let's begin by visualizing a standard 3D space. But because we want to eventually see all of space and time in one model, let's cheat a little. Let's compress all of 3D reality as we know it into a flat, two-dimensional place. In this plane, let's make that our XY plane, which we will label space, which frees up the Z dimension for time. In this model, all 3D people are now just 2D. A 2D person could exist and live their lives in the place marked space at the bottom of our chart. However, by moving them up on the chart at a constant rate, they are also moving through time. Let's put ease and convenience say that the top of our diagram is the future, while the bottom is the past. So the higher up our 2D person goes in this diagram, the older they get. As we don't seem to have a whole lot of control over our ability to travel through time, let's imagine for a second that our 2D person travels upwards at a constant rate, as if there is some consistent force or wind at play pushing them upwards towards the future. Sadly, we cannot slow down time for ourselves simply through willpower, no matter how much we might want to do so. However, it is misleading to say that we can't change it at all. The faster we travel in space, the slower we travel in time. This is one of the guiding principles of Einstein's relativity. This model can express this idea through the power of vectors. As our 2D person tries to move to their left or to their right, their vector of travel changes. While traveling at a fixed rate, like a sail on a ship catching a breeze, we can only go as fast as the wind takes us, so the vector coming out from their front must always remain the same. To travel the fastest through time, our 2D person must orient his vector completely in the future direction or upwards. However, if they are to travel any amount in either direction to their sides, they can only do so by pointing their vector away from their direction of travel. They have motion in the x direction now, but they have done so by reducing their motion in the z direction. They are moving through space, but at the cost of moving a little slower through time. Taking this to its furthest extreme, our individual has completely flipped on their side and now only has motion in the direction of x and none in the direction of z. They have velocity in space, but not time, so I suppose this implies our vector is the speed of causality or the speed of light. If this is the speed we're talking about, then moving at low speeds through space would not have any noticeable difference in our speed through time. We'd have to go really fast before we started to notice anything. The vector still mostly points upwards. An interesting result of this model is that, from the 2D man's perspective, nothing has really changed. He has his own view of what reality is. For him, the vector coming out of his chest is still time. The dimensions of the plane he's lying flat on is his space. To him, it's the rest of the universe that's gone a little weird, but he himself is perfectly normal. However, once he re-orient himself, it is clear that the rest of the universe has moved on without him. This is clearer if we add a second 2D person. Initially, both of our individuals do not move in space. All of their vector is pointing in the direction of time. Nothing that strange seems to happen so far. However, if our stick man on the right turns and vectors at near the speed of light for a bit, then re-orients himself, while the second 2D man on the left just stays where he is, it becomes clear that our 2D men have not moved at the same rate through time. Assuming that our two stick men can somehow still see each other, let's imagine that they somehow project an image of themselves onto the other person's space plane, they immediately notice that there is a difference in age. The one who travelled at the speed of light did not advance so quickly through time as the other, who remained stationary, and so is younger. But why do we find this model so compelling? Well, it is because of what those projections would look like during changes in direction. From the point of view of the first stick man, initially the projection of their friend seems fairly normal. However, as they start travelling very quickly in space and their vector oriented in a direction away from time, a 2D shape reveals its inherent flatness. And from a face arm perspective, it goes from this to this. The speedily travelling stick man appears to flatten, with an effect that's more pronounced the faster they go, and the flattening takes place in the direction of their travel. The stick man who remains stationary might wonder at the strange change that is occurring to their friend, never comprehending that it represents a re-orientation of a 2D figure in 3D space. Now what captures my imagination about this is that this same thing happens in real life. According to Einstein's theories of relativity, objects travelling at great speeds in 3D space would appear from an external observer to flatten in the direction of their travel. This squishing effect happens exactly in line with this model, and is to do with time dilation. However, from the person whose travelling's perspective, they do not flatten, but it is the rest of the universe that warps. I talk about this in greater depth in another video of mine, where we can see the effects of spatial warping in a computer model. From their perspective, everything would stretch at the edges of their vision, while their destination would seem further away, which is again what this model would predict. The only difference is that in this model we're just exploring a 2D object stretching. So the stretch is only in one direction, while in real life it's 3D, which means it stretches in two directions instead. But that is what you might expect, as you turn away from our conventional three dimensions and start orienting yourself away from time. But if this is correct, so what? Why does it matter? If time is truly a direction, then it deepens our understanding of the universe. It also raises more questions. What is the force that pushes us ever forward in time? Why does it seem that we can never move against it? Although in this model there is no reason why a vector could not point downwards, in real life that doesn't seem to ever happen. This model also answers the question of, if time is a direction, what is our shape in time? Does part of us protrude into the past, or into the future? According to this model, that does not happen. We are flat pancakes in the fourth dimension, pennies that look round when you look at us head on, but revealing our thinness when we turn away from you. That's a strange thought, but it may just be true. This might explain why we are unable to see through time. We just don't extend enough in that direction for it to be visible. Your form might be quite different than you first thought. Of course, this model is just a theory of ours. Although we have tried to base it on scientific observations and conventional theory, but what do you think? Does this model help you make sense of time as a fourth dimension? Please leave your ideas in the comments below on the nature of time, and what it might actually be instead. I hope to explore more strange concepts like this in a new series called The Unseen World, where I want to explore the shape of reality around us. While it's normally invisible to us, the shape and dimensions of the universe can explain why things are the way they are, and I'm excited to explore it with you if you are interested in it. Let me know. Have you ever wondered if it is possible to see the future? Humans throughout time have certainly hoped so. But for most of us, that's something in the realms of mystics and fortune tellers. The idea that there might be some way to actually glimpse it is usually considered the stuff of superstition. But that perspective might be wrong. What if you were already seeing parts of the future, just in fragments? What if time could be viewed with past, present and future at once? Before you worry, this is an astrum video. I originally intended this video to be the last one in my Unified Theory of Everything series, but as I was preparing the best way to demonstrate how strings could explain the principles of special relativity, I took another closer look, and I realized that there were some mind-bending implications of relativity that contradict our perception of what really exists in the now, which we had to tackle first. As it turns out, you might be seeing parts of the future already. And yes, it's time for me to explain with another diagram. I'm Alex McColgan and you're watching Astrum. And to understand everything, it's time to scrutinize time, space and relativity. We don't tend to think of relativity in the way I'm about to show you, but it's vital that we improve our intuitive understanding of this topic, or no attempt to explain why special relativity really happens will make sense. Besides, who doesn't like having their mind blown by cosmic weirdness from time to time? When it comes to special relativity, you might have felt like you understood the gist of it. When an object travels at high enough speeds, time slows down for it. At least it does from the perspective of an outside observer at rest. For the object itself, time seems to go the same speed, in a principle known as time dilation. And curiously, if you travel at light speed, from your perspective, you'd be ticking along as normal, but everything else would suddenly be slowing down, not you. Feels the universe shouldn't work this way, with both sides thinking the other is moving slower. But this does appear to be the fundamental rule of our universe. An object's rate of travel through time seems to be down to the relative position of your perspective. There is no true rate at which things travel through time. Weird already. But I wonder if you are aware of just how far this principle goes. The implications get pretty mind bending. Let's talk about a second element of special relativity, length contraction. This is a bit of a weird one. From the point of view of an outside observer at rest, if an object were to travel at a large enough percentage of the speed of light, the observer would start to see the object flatten. A ball would become a giant pancake. This flattening occurs in the direction of the object's travel, and it has been shown to occur both mathematically and experimentally. We fired protons in the Large Hadron Collider, and their collision patterns only make sense if this pancaking is occurring. It's very weird, but it does seem to be real. Multiple experiments seem to confirm length contraction, including the Kennedy-Thorn Dyke experiment and experiments with Mjoln decay, where Mjoln particles falling through our atmosphere don't decay as fast as they should thanks to this effect. It's worth noting, however, that just like with time dilation, length contraction is a matter of perspective. If you were the thing that had been accelerated to near the speed of light, you would not see yourself contract. Instead, just like with time, you would start to see everything else contract in the direction of your acceleration. There is some good maths that talks about why this is, but I won't get into that today, as it's the consequences of length contraction I want to talk about not so much as causes. After all, we want to get to the part where we start seeing the future. And for that, we are going to need a thought experiment. This thought experiment is known as the barn-pole paradox, and it goes like this. What happens if you try to fit a 40-meter pole inside a 20-meter barn? Let's imagine the barn has a door on each side, which you can slide the pole through. Now obviously, normally this task would be difficult to do without bending or breaking the pole. However, if we take advantage of special relativity, it is possible to do this. All you have to do is fire the pole into one open door of the barn at near light speed, let's pretend for a moment that you can do that, and hey presto! As long as it's going fast enough, length contraction would occur, causing the length of the pole to diminish to our necessary 20 meters. The pole would fit in the barn, for a tiny fraction of a second at least, before blasting out the other end. Mission success. It would even be possible, if you could do it fast enough, for you to close and then open both doors of the barn at once while the pole was still inside, proving once and for all that the pole was inside the barn completely for that nanosecond. But what happens from the pole's perspective? Remember what I said earlier. Objects travelling at speed do not see length contraction occurring to them, but rather everything else existing in the universe contracts in the direction of the object's travel. So, we hit a problem here. The pole would still see itself as a 40 meter pole, never a 20 meter one. Even worse, now length contraction is happening to the barn, so the barn is even less than its original 20 meter length, now just 10 meters from the perspective of the pole. So how does a 40 meter pole fit inside a 10 meter barn with both doors closed? It sounds impossible. Surely this would result in broken poles or barn doors. But this is not what the barn sees. So how can two different observers looking at the same event see two completely different things happen? Have we entered a state of quantum superposition where the pole is both in and not in the barn? Are we about to split apart the universe into differing multiverses? Or is special relativity wrong? No, our perception of reality is wrong. There is an answer to this, but you're not going to like it. Watch closely. According to relativity, this is what would happen from the pole's point of view. The pole enters the barn just like we would expect, and then there. Did you see it? Perhaps, but what did you just see? You just saw an example of the myth of simultaneity. And remember, this is really what happens according to special relativity. Events that are simultaneous from one point of view are not simultaneous from another. To be clear, this is not just a weird consequence of light taking its time to reach us. If we were just dealing with an optical illusion caused by light taking its time to move to our eyes, then we'd see the closer event happen first, and the more distant event happen second. But this is happening the opposite way around. In this case, and from the point of view of the pole, the more distant event spatially happens first, and the closer event happens second. In other words, this is not just a trick of the light, but the suggestion that something more fundamental is going on. And what is going on? When I first learned about this, it boggled my mind. It seemed wrong as a matter of principle, but the more I thought about it, the more it started to make sense based on my understanding of the universe, and the more startling implications started to arise. Don't worry, I've not forgotten about that seeing the future thing. I'll get to it. Let's take another look at what's happening here. But this time let's bring in a little colour coding, and our old friend, a 4D space-time diagram. Hopefully you are familiar with these already, as I've done a few videos that have included them. If not, here's a great video we did on the subject, which you should have a look at. To recap though, just imagine that all of space has been flattened down to the one line along the bottom of our graph, while an object's motion in time is tracked along the side of the graph. Here is the barn's timeline, according to its motion in space and time. From the point of view of the barn, it is not moving in space, so we draw the arrow directly up. It is only moving into the future. I've painted the shutting and opening of the two doors as two different colours here on the graph. Note that they are separated by space, but they occur at the same moment in time, at least from the barn's perspective. Now for our first complete perspective of this event, let's add the path of our pole. As our pole starts moving, length contraction occurs, and the pole drops down to 20 metres, eventually it arrives at the barn, and our two events occur. Both barn doors shut at the same time, and the pole is snugly inside. All good so far, from the barn's point of view. But what does the pole see? Let's make our pole the stationary object in this diagram. After all, this is relativity, and from the pole's perspective, it is the barn that is moving quickly towards it, not the other way round. This makes it easier to assign length contraction to the barn, which is what relativity says we should be getting. We cannot simply add the barn to this diagram as an object that's parallel in orientation to the pole. It just wouldn't work. The barn, now narrower, would intersect with the pole with both doors closing and opening at the same time, so the pole wouldn't fit. But what if we pivot our barn slightly, from this to this? Essentially, this isn't too unreasonable, as we've just turned the first diagram slightly on its side. Now, the sequence works. With this, the part of the barn furthest from the pole meets it first, and the pole sees the orange door shut and open. Then as time goes on, and the pole and the barn proceed further into the future, the pole's other end reaches the blue door, which also shuts, then opens. Thanks to this vector in time and space, it's possible for the barn to not hit either end of the pole with its shutting doors. The order of events is right, from the pole's point of view. The barn's further orange backdoor shuts and opens before the barn's blue front door does. This is what special relativity tells us should occur. But do you see why this configuration is so strange? It implies to me that the barn itself is not simultaneous while it is in motion. And here's where we're jumping from the paradox into my own thoughts about it. What do I mean by simultaneous? I mean that we expect the barn to exist as a discrete entity at a single point in time. It does exist, with every part of it happening at the same now, even if it's undergoing a little time dilation here and there. But the barn the pole sees is not happening in a single now. Part of it is ahead in time, and part of it is lagging behind. And you can see both parts at once. The barn is not simultaneous, because you can see it across a range of times. Its length might be contracting, but the dimensional space you see it occupy in time seems to you to be growing. We do not think like this, but the idea has a beautiful sensibility to it in the universe of 4D space. Like when a racing car swerving to the left causes its right wheel to protrude further forward, when you move to the left on our space time diagram, it causes the part of you furthest away from the direction of motion to protrude into the future more than the part that's closer. That's just geometry. For the record, this seems to happen as a gradient along the whole of the object in motion. This way of thinking also allows length contraction to conceptually make a lot more sense. After all, if our pole is in motion and the front of the pole is further in the past, and the back of the pole is further in the future, then it makes sense to consider where each part of the pole exists in space during those moments in time. The front of the pole that exists further back in time has not travelled as far as the rest of the pole, so the start of the pole is further back. Similarly, if the back of the pole which exists further forward in time has by then moved further through space compared to the rest of the pole, so the back of the pole is further forward. What happens when you combine a dawdling front with a further ahead back lengths contraction? The only surprise is that it seems that we can see this in experiments in the Large Hadron Collider and other places. Somehow we are seeing a cross-section of time. So it works. It just feels like it shouldn't. You might think this is a little out there, but consider, what would an object that didn't exist in all the same moment in time look like to you? Would you tell it apart from any other object? Well, it would probably look mostly the same, right up until some part of it changed what it was doing and you watched as the rest of it caught up. Which is what we see here. It's not so unreasonable to think of it this way, and it certainly helps our intuition. This is the state of affairs for objects that are moving. If we are moving, that's the way we see everything else, which has some pretty mind-bending implications about what we are seeing right now across the universe. Of course, this only applies when things are moving at a substantial portion of the speed of light, so in the day-to-day you probably wouldn't notice it. And because of the great speeds involved, it's difficult to imagine a scenario where you could take advantage of this principle, even if you could use the first barn door closing to predict the future of the second. There are limits on how fast information can travel after all, and this time stretching is only noticeable when objects are travelling near to that limit. And while I've talked about the future of the barn and the past of the barn, perhaps that's the wrong point of view. To you, these events are all in the now. You're now. It's just the barn that might see things differently, with its own now, where it's closing and opening its doors simultaneously, and you are the one who splayed out as a range across time. But it just causes me to think about the universe in a very different light. Space and time really are just a matter of perspective, because there is no one true now. There's just your own personal path, and the paths other objects take in 4D space. And just because I see time as being one thing in my reference frame, doesn't mean it works that way for you in yours. In yours, time might just be more space. So when I finally release part 4 of my unified theory of everything, that is the strange universe that I will be trying to explain. One where time and space really are relative points of view. Wish me luck. Is the universe inescapable? If we were to conquer the limitations of light speed, and were to travel to space's furthest edge, what might we find? Just more space? Infinite planets and planetary systems? Or would we somehow come back to where we started? Amazingly, according to scientists, all of these are possible, but which one is correct comes down to the nature of that unseen world all around us. I'm Alex McColgan, and you're watching Astrum. Join me today as we continue our series exploring the unseen world of 4D space, and discuss possible answers to the question, what is the shape of the universe itself? But first, let's begin by talking about infinity. You are likely already familiar with infinity. In maths, it is the concept of a number so large it cannot possibly be beaten. Of course, no such number exists. For any number you can name, I could come up with a number that is at least one large than it. But in a way, that's sort of the point. In infinity, there is always another number. And when it comes to our universe, we have so far discovered no edges. There may always be another star or planet. An infinite universe is a little mind-boggling for us. We live in a very finite world, with edges and endings, so the idea that there might be literally infinite more planets out there is a little bewildering. However, as we develop more and more powerful telescopes, and push back the darkness further and further at the edges of what we can observe in our universe, all we are finding is that even the darkest patches of the night sky are turning out to be brimming with stars. So increasingly, an infinite universe might be something we are forced to contemplate. But that is not to say that just because the universe is infinite, there are not a finite number of things in it. That may sound a little counterintuitive, but let me show you what I mean. Believe it or not, there are different kinds of infinity when it comes to our universe. Three possible scenarios could be true. A flat universe, a spherical one, or a hyperbolic universe. Allow me to explain. In a flat universe, if we were to form a grid to broadly represent reality, everything would seem fairly standard. All the lines would either be parallel to each other, or perpendicular. An infinite universe of this variety would simply extend outwards in all directions for ever and ever. This is a little boring, so I won't spend too much time on it. However, this is a lot like we perceive the universe to be. For the most part, all lines of direction appear straight to us. We can distinctly see the planets and stars around us, and we notice no real curving or warping. However, this is not the only way that the lines can be drawn. Consider for a moment a black hole. You may immediately notice the strange rings that appear to run around its equator, as well as across the top of it and along the bottom. This is something of an illusion. There are no rings across the top or bottom of this black hole. What you are seeing is the equatorial ring that's on the other side of the black hole. However, due to the powerful gravity of the black hole, the light that is hitting it is not bouncing off upwards or downwards into space. Instead, the rays are curving towards us as the black hole's gravity pulls them in. You are seeing the top and bottom of the ring at the same time. Light being bent by gravity, what do I mean by that? Clearly this is an excellent example of our second kind of universe. In a flat universe, all the lines that make up reality are fairly straight. But what if we were to come up with a rule? All the lines must instead curve towards each other. There is only one way such a universe could be drawn, and that is in a sphere. Consider trying to draw two parallel lines on a sphere. You might start off well, but we'll quickly realise that your task is impossible. All lines would converge towards each other, intersecting at least twice as they return back to where they started. What would a universe that was based on these kinds of lines look like? Essentially, rather than going in the straight line you thought you were going in, you actually would be travelling in a massive curve. It's a bit like those computer games where you travel off one end of the screen only to reappear from the other side. In a spherical universe, you could travel infinitely, but ultimately you would only end up arriving back where you started. With a powerful enough telescope, and if light were to travel a whole lot faster all of a sudden, it would be possible to look at the back of your own head. This kind of universe contains a finite amount of things, but it appears infinite because you just keep bumping into the same things infinite times. Thanks to objects like black holes and powerful stars, we do indeed have evidence that our reality sometimes is a curved, spherical one. At least near large bodies of mass. The inside of a black hole's event horizon is this kind of infinite space. No matter what path you take, you can never get out of it. However, let's consider our last example, the hyperbolic universe. This one is the hardest to visualise, but the idea is simple. Instead of having all lines remain parallel or move towards each other, every line must move away from everything. Drawing this is inherently tricky because everything keeps getting wider exponentially. The only way you can do that is to either buckle your nice flat disc until it becomes something like this, or walk what you are seeing like this. All of the objects in this image are squares. However, they are squares that are obeying our rule that all their lines must be diverging away from each other. This leads to the very strange situation where you can have 5 squares all meeting up at a corner instead of the usual 3 that is possible in normal 2D space. Alright, this seems a little confusing. What does it mean if space is hyperbolic? Well, let's consider what it is we are curving around. You might have noticed when we talked about our spherical shape that there must be something we are curving around. That direction of curvature is in regards to time. Imagine if you will a series of timelines. We go a little more in depth with the interplay between space and time in my last video which I would really recommend you check out. But for now, just remember for this model that objects in time move forward along their timelines in the direction of up or the future. If they move left or right, they are moving through space, getting closer to each other. If we introduce a large mass into this model, it warps the timelines. Now if you were a small object travelling along one of those arrows that got too close to the mass, suddenly your path of travel no longer goes directly up towards the future. It pulls you left or right towards the mass. There are several reasons for this, but the essential thing to recognise here is that now your straight path towards the future pulls you in towards the planet. So you'll have to accelerate away from it just to stay on a straight path. In a nutshell, you are experiencing gravitational pull. Even the planet is affected by this. The atoms on either side of it are squeezed towards the centre of mass, as if it were being forced down and narrowed true by giant invisible hands. Let's get back to hyperbolic space. In this model, the opposite thing is happening. All lines are moving away from each other. We could represent this by curving space and letting our timelines be straight, which is nice because it captures the idea that from your perspective, your time is always ticking forward normally. But let's warp this slightly so that space is flat. It's all a matter of perspective after all. Here parallel lines are also impossible, but this time, rather than converging, all parallel lines diverge more and more. Everything moves further and further apart. Hmm, why does that sound familiar? It is because that is what the universe is doing. This is not noticeable within a galaxy, where there is enough mass and gravity to keep everything together. However, from what we can see of the universe as a whole, every galaxy is moving away from every other galaxy. Scientists try to explain that with dark energy, but maybe all that is happening is that the universe is just naturally hyperbolic in its shape. So what would that mean if the universe really was hyperbolic? It would mean that the universe was really infinite. The flat space we looked at was infinite. For each light year you travelled out, you discover another light year's worth of space. However, with hyperbolic space, you discover more than another light year's worth of space. It's like opening infinite doors, except inside each door are two new ones. The possibilities would be far more endless, far more infinite than in just regular flat space models. But also, it means that given enough time, the rest of the universe would drift away from us until our galaxy was all that was left. Scientists have looked across the universe, however have not noticed this hyperbolic space in action. In fact, things all look pretty flat. So perhaps flat space is the correct answer. But this still leaves room to me for hyperbolic space to be the default. After all, if matter is curving space towards it, and the universe appears flat, it would make sense that the universe was curved in the inverse, at least to some degree. Perhaps all three models are true. Perhaps the universe is by default hyperbolic, but mass brings it together in such a way that it perfectly offsets the inverse curves of the universe to the point where everything appears flat. There certainly seems to be some evidence that this is the case, but it's very difficult to know for sure. Which model do you think is correct? Or maybe you feel that we do not live in an infinite universe at all? Please leave a comment down below to tell me what you think. But for now, just remember, the unseen world might be a lot more influential on our universe than we are currently aware of. You may have noticed this video didn't have any sponsors, and that's because it was brought to you by our astronauts on Patreon. Consider joining our Patreon to keep these videos thriving even when they're sponsor-free. It's the reason we can research deep into the topics we love, without cutting corners or chasing clicks. Every new Astrum note allows us to explore bigger ideas, and make every upload even better than the last. So if you've ever thought about being a bigger part of this channel, join the crew to power Astrum and keep space, curiosity, alive.