Additional notes

The Wikipedia page for Four velocity writes:

The norm or magnitude of the four-velocity is always exactly equal to the speed of light. Thus all objects can be thought of as moving through spacetime at the speed of light. This provides a way of understanding time-dilation: as an object like a rocket accelerates from our perspective, it moves faster through space, but slower through time in order to keep the four-velocity constant. Thus to an observer, a clock on the rocket moves slower, as do the clocks in any reference frame that is not comoving with them. Light itself provides a special case- all of its motion is through space, so it does not have any “left over” four-velocity to move through time. Therefore light, and anything else traveling at light speed, does not experience the “flow” of time.

The Reddit community has written a number of easy to understand illustrations of this phenomena. The first is from a thread called __Why does light travel?__:

Everything, by nature of simply existing, is “moving” at the speed of light (which really has nothing to do with light: more on that later). Yes, that does include you.
Our understanding of the universe is that the way that we perceive space and time as separate things is, to be frank, wrong. They aren’t separate: the universe is made of “spacetime,” all one word. A year and a lightyear describe different things in our day to day lives, but from a physicist’s point of view, they’re actually the exact same thing (depending on what kind of physics you’re doing).
In our day to day lives, we define motion as a distance traveled over some amount of time. However, if distances and intervals of time are the exact same thing, that suddenly becomes completely meaningless. “I traveled one foot for every foot that I traveled” is an absolutely absurd statement!
The way it works is that everything in the universe travels through spacetime at some speed which I’ll call “c” for the sake of brevity. Remember, motion in spacetime is meaningless, so it makes sense that nothing could be “faster” or “slower” through spacetime than anything else. Everybody and everything travels at one foot per foot, that’s just… how it works.
Obviously, though, things do seem to have different speeds. The reason that happens is that time and space are orthogonal, which is sort of a fancy term for “at right angles to each other.” North and east, for example, are orthogonal: you can travel as far as you want directly to the north, but it’s not going to affect where you are in terms of east/west at all.
Just like how you can travel north without traveling east, you can travel through time without it affecting where you are in space. Conversely, you can travel through space without it affecting where you are in time.
You’re (presumably) sitting in your chair right now, which means you’re not traveling through space at all. Since you have to travel through spacetime at c (speed of light), though, that means all of your motion is through time.
By the way, this is why time dilation happens: something that’s moving very fast relative to you is moving through space, but since they can only travel through spacetime at c, they have to be moving more slowly through time to compensate (from your point of view).
Light, on the other hand, doesn’t travel through time at all. The reason it doesn’t is somewhat complicated, but it has to do with the fact that it has no mass.
Something that isn’t moving that has mass can have energy: that’s what E = mc2 means. Light has no mass, but it does have energy. If we plug the mass of light into E=mc2, we get 0, which makes no sense because light has energy. Hence, light can never be stationary.
Not only that, but light can never be stationary from anybody’s perspective. Since, like everything else, it travels at c through spacetime, that means all of its “spacetime speed” must be through space, and none of it is through time.
So, light travels at c. Not at all by coincidence, you’ll often hear c referred to as the “speed of light in a vacuum.” Really, though, it’s the speed that everything travels at, and it happens to be the speed that light travels through space at because it has no mass.
edit: By the way, this also covers the common ELI5 question of why nothing can ever travel faster than light, and why things with mass cannot travel at the speed of light. Since everything moves through spacetime at c, nothing can ever exceed it (and no, traveling backwards in time would not fix that). Also, things with mass can always be “stationary” from someone’s perspective (like their own), so they always have to move through time at least a little bit, meaning they can never travel through space as fast as light does. They’d have to travel through spacetime faster than c to do that, which, again, is not possible.

A second explanation came from a thread called __Why exactly can nothing go faster than the speed of light?__:

First, let’s talk about directions, just to get ourselves oriented. “Downward” is a direction. It’s defined as the direction in which things fall when you drop them. “Upward” is also a direction; it’s the opposite of downward. If you have a compass handy, we can define additional directions: northward, southward, eastward and westward. These directions are all defined in terms of something — something that we in the business would call an “orthonormal basis” — but let’s forget that right now. Let’s pretend these six directions are absolute, because for what we’re about to do, they might as well be.
I’m going to ask you now to imagine two more directions: futureward and pastward. You can’t point in those directions, obviously, but it shouldn’t be too hard for you to understand them intuitively. Futureward is the direction in which tomorrow lies; pastward is the direction in which yesterday lies.
These eight directions together — upward, downward, northward, southward, eastward, westward, pastward, futureward — describe the fundamental geometry of the universe. Each pair of directions we can call a “dimension,” so the universe we live in is four-dimensional. Another term for this four-dimensional way of thinking about the universe is “spacetime.” I’ll try to avoid using that word whenever necessary, but if I slip up, just remember that in this context “spacetime” basically means “the universe.”
So that’s the stage. Now let’s consider the players.
You, sitting there right now, are in motion. It doesn’t feel like you’re moving. It feels like you’re at rest. But that’s only because everything around you is also in motion. No, I’m not talking about the fact that the Earth is spinning or that our sun is moving through the galaxy and dragging us along with it. Those things are true, but we’re ignoring that kind of stuff right now. The motion I’m referring to is motion in the futureward direction.
Imagine you’re in a train car, and the shades are pulled over the windows. You can’t see outside, and let’s further imagine (just for sake of argument) that the rails are so flawless and the wheels so perfect that you can’t feel it at all when the train is in motion. So just sitting there, you can’t tell whether you’re moving or not. If you looked out the window you could tell — you’d either see the landscape sitting still, or rolling past you. But with the shades drawn over the windows, that’s not an option, so you really just can’t tell whether or not you’re in motion.
But there is one way to know, conclusively, whether you’re moving. That’s just to sit there patiently and wait. If the train’s sitting at the station, nothing will happen. But if it’s moving, then sooner or later you’re going to arrive at the next station.
In this metaphor, the train car is everything that you can see around you in the universe — your house, your pet hedgehog Jeremy, the most distant stars in the sky, all of it. And the “next station” is tomorrow.
Just sitting there, it doesn’t feel like you’re moving. It feels like you’re sitting still. But if you sit there and do nothing, you will inevitably arrive at tomorrow. That’s what it means to be in motion in the futureward direction. You, and everything around you, is currently moving in the futureward direction, toward tomorrow. You can’t feel it, but if you just sit and wait for a bit, you’ll know that it’s true.
So far, I think this has all been pretty easy to visualize. A little challenging maybe; it might not be intuitive to think of time as a direction and yourself as moving through it. But I don’t think any of this has been too difficult so far. Well, that’s about to change. Because I’m going to have to ask you to exercise your imagination a bit from this point on.
Imagine you’re driving in your car when something terrible happens: the brakes fail. By a bizarre coincidence, at the exact same moment your throttle and gearshift lever both get stuck. You can neither speed up nor slow down. The only thing that works is the steering wheel. You can turn, changing your direction, but you can’t change your speed at all.
Of course, the first thing you do is turn toward the softest thing you can see in an effort to stop the car. But let’s ignore that right now. Let’s just focus on the peculiar characteristics of your malfunctioning car. You can change your direction, but you cannot change your speed.
That’s how it is to move through our universe. You’ve got a steering wheel, but no throttle. When you sit there at apparent rest, you’re really careening toward the future at top speed. But when you get up to put the kettle on, you change your direction of motion through spacetime, but not your speed of motion through spacetime. So as you move through space a bit more quickly, you find yourself moving through time a bit more slowly.
You can visualize this by imagining a pair of axes drawn on a sheet of paper. The axis that runs up and down is the time axis, and the upward direction points toward the future. The horizontal axis represents space. We’re only considering one dimension of space, because a piece of paper only has two dimensions total and we’re all out, but just bear in mind that the basic idea applies to all three dimensions of space.
Draw an arrow starting at the origin, where the axes cross, pointing upward along the vertical axis. It doesn’t matter how long the arrow is; just know that it can be only one length. This arrow, which right now points toward the future, represents a quantity physicists call four-velocity. It’s your velocity through spacetime. Right now, it shows you not moving in space at all, so it’s pointing straight in the futureward direction.
If you want to move through space — say, to the right along the horizontal axis — you need to change your four-velocity to include some horizontal component. That is, you need to rotate the arrow. But as you do, notice that the arrow now points less in the futureward direction — upward along the vertical axis — than it did before. You’re now moving through space, as evidenced by the fact that your four-velocity now has a space component, but you have to give up some of your motion toward the future, since the four-velocity arrow can only rotate and never stretch or shrink.
This is the origin of the famous “time dilation” effect everybody talks about when they discuss special relativity. If you’re moving through space, then you’re not moving through time as fast as you would be if you were sitting still. Your clock will tick slower than the clock of a person who isn’t moving.
This also explains why the phrase “faster than light” has no meaning in our universe. See, what happens if you want to move through space as fast as possible? Well, obviously you rotate the arrow — your four-velocity — until it points straight along the horizontal axis. But wait. The arrow cannot stretch, remember. It can only rotate. So you’ve increased your velocity through space as far as it can go. There’s no way to go faster through space. There’s no rotation you can apply to that arrow to make it point more in the horizontal direction. It’s pointing as horizontally as it can. It isn’t even really meaningful to think about something as being “more horizontal than horizontal.” Viewed in this light, the whole idea seems rather silly. Either the arrow points straight to the right or it doesn’t, and once it does, it can’t be made to point any straighter. It’s as straight as it can ever be.
That’s why nothing in our universe can go faster than light. Because the phrase “faster than light,” in our universe, is exactly equivalent to the phrase “straighter than straight,” or “more horizontal than horizontal.” It doesn’t mean anything.
Now, there are some mysteries here. Why can four-velocity vectors only rotate, and never stretch or shrink? There is an answer to that question, and it has to do with the invariance of the speed of light. But I’ve rambled on quite enough here, and so I think we’ll save that for another time. For right now, if you just believe that four-velocities can never stretch or shrink because that’s just the way it is, then you’ll only be slightly less informed on the subject than the most brilliant physicists who’ve ever lived.

Not sure the source on this one

The reason why the speed of light is a hard limit on the universe is that everything is travelling within this four-dimensional thing called spacetime, with the same amount of speed.
When a photon (a particle of light) travels through spacetime at the speed of light,
That’s how it is to move through our universe. You can steer, but you can't accelerate. When you sit at apparent rest, you’re really careening toward the future at top speed. But when you get up to go to the fridge, you change your direction of motion through spacetime, but not your speed of motion through spacetime. So as you move through space a bit more quickly, you find yourself moving through time a bit more slowly.
To reiterate that last point, as it is important: The faster you travel through space, the more you have to give up your movement through time. At the speeds that we're used to on Earth, the effect is negligible. To give you some idea of how fast we need to be talking before time dialation starts to happen, lets look at GPS satellites. A GPS satellite orbits the Earth at 14,000 km/h (8,700 mph). Once every sixty years their clocks will be ahead by one second due to the effects of time dialation.
The fastest object every built by human beings thus far is the Voyager 1 Spacecraft, having flown past Saturn and is now travelling through interstellar space. It is travelling at speeds of about 62,140 km/h (38,610 mph), or 17 kilometres (10.5 miles) per second. That is so fast that it could:
At these speeds, Voyager 1 experiences one second of time dialation every 13.7 years.
Voyager 1's speed is just 0.00006% of the speed of light. Once you reach the speed of light, that time dialation becomes total. You stop experiencing time.

From a Reddit thread called Why does light travel?
Time and space are orthogonal, which is sort of a fancy term for “at right angles to each other.” North and east, for example, are orthogonal: you can travel as far as you want directly to the north, but it’s not going to affect where you are in terms of east/west at all. Just like how you can travel north without traveling east, you can travel through time without it affecting where you are in space. Conversely, you can travel through space without it affecting where you are in time.
You’re (presumably) sitting in your chair right now, which means you’re not traveling through space at all. Since you have to travel through spacetime at c (speed of light), though, that means all of your motion is through time.
Particles with mass (everything made out of atoms) and particles without mass (like light and other electromagnetic radiation) travel through the dimensions of spacetime in different allocations. For particles with mass, it can vary. Particles that do not have mass have maxed out their speed in the direction of space, and don't travel through time at all.
All matter is travelling same speed through the totality of all dimensions, but each dimension in a different allocation.
Human beings are made up of particles, atoms, that have mass and therefore we, nor anything else made of atoms, will be able to travel at the speed of light.
//As human beings have mass, we will never be able to approach the speed of light.
//To go faster than the speed of light, you'd need to go backwards in time. This seems impossible. - Can't be right.