Thanks to Brilliant for sponsoring today’s video. 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 m/s? 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. Here are the links if you
need a refresher. With that out 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 m/s. 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 299,792,458 m/s. 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 0. If you were to suddenly start travelling at the
speed of light towards Jupiter, you would notice 0 time passing, but would observe that you have
travelled 679 million km. And then would promptly 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, S=D/T. So, 679million/0=… 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 0 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 m/s (let’s call it “c”). So why is it that everyone
else detects light travelling at “c”, but light thinks it is going infinitely fast? What I am
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 get the extra dimension, our 4th 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 all 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 that 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. 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, lets 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
could 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 hit 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, that is where this 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 299,792,458 m/s speed limit. With infinite energy,
you could go 3 billion m/s, or 3 trillion. But in the real universe, we don’t see that. Everything
normally seems to be capped at 299,792,458 m/s. There is a similar trend where the more energy
you put in, the less additional speed you get, but that occurs at close-to-light-speed, not infinite
speed. So, our 4D model seems to have failed. But this is not a 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 manage. “Speed” is a little tricky a concept here, but
let’s say that from your perspective, you covered a distance of 400,000,000m 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 “c” shape, if you follow the line down you will see that it
is a time line, not a space line. And because it is hyperbolic space, there is more here that 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
of 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 0, but ended at an origin point that’s seconds in
the future, they have to say that we travelled 400,000,000m in 10 seconds, for a speed of
40,000,000m/s. Far 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 speed 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 photon slid above 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 it were simply moving uniformly at a speed of c. 299,792,458 m/s. After all, 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 to me 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 even gotten close to this speed.
The fastest a human has ever gone is 11,083 m/s, when NASA astronauts returned in a spaceship
from the moon. It would require incredible amounts of energy to travel 299,792,458 m/s,
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 for 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. The universe around me has always fascinated me.
I love being able to learn new things about it, then share what I’ve discovered in videos
like this one. For this video in particular, I definitely had to do some learning, which is why
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– so hurry over there as fast as you can. Just don’t go faster than 299,792,458
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