Chapter 1: Why does reality have a speed limit?
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 metres 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. With that 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 299,792,458 metres 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 photon's 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 then would probably die of the lack of air, the punishing g-forces and the friction burnt 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 0 equals… If you tried plugging this into your calculator, you would quickly run into an error here.
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Chapter 2: How does hyperbolic geometry explain the speed of light?
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 sent us 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.
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Chapter 3: What is the significance of a photon's perspective on time?
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 for 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 recognised 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 fourth D. Broadly speaking, 3D, or three-dimensional space, simply refers to space that can be measured in three different perpendicular directions.
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Chapter 4: How does 4D space relate to our understanding of time?
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 reorients 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. 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 stickman, 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-on perspective, it goes from this to this. The speedily travelling stickman 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 stickman who remains stationary might wonder at the strange change that is occurring to their friend, never comprehending that it represents a reorientation 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 who's 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?
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Chapter 5: What happens when objects move at high speeds through space?
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 20m.
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 40m pole, never a 20m one.
Even worse, now length contraction is happening to the barn, so the barn is even less than its original 20m length, now just 10m 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.
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