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 Mccoan, and you're watching
Astramm. 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 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
traveling 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 traveling 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 traveling at light speed,
time would slow down so much that it
would be at zero. If you were to
suddenly start traveling at the speed of
light towards Jupiter, you would notice
zero time passing, but would observe
that you have traveled 679 million km
and then 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 /
0 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 traveled at infinite speed. So from
light's perspective, it is traveling
infinitely fast, not at 299,792,458
m/s.
Let's call that C from now on.
So why is it that everyone else detects
light traveling at C, 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 traveling 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 yaxis
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,
traveling through this space obeys the
same rules that traveling 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.
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 traveling 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 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 m/s or 3 trillion. But in
the real universe, we don't see that.
Everything normally seems to be capped
at C.
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 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 m 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 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 traveled 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 speed
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 traveled 400
million m in 10 seconds for a speed of
40 million m/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 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 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.
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
that 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
m/s. 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 traveling 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, traveling
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 Web 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 Mccoan and you're watching
Astramm. 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 recognized
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. 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° 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° 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. Their 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.
While 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 spaceime 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 zed 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 for 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 zed. 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 reorients 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 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 stickmen 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 traveled
at the speed of light did not advance so
quickly through time as the other who
remains 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 friends seems fairly normal.
However, as they start traveling 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 traveling 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 traveling 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
traveling'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 Astramm 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
mindbending 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 Mcolgan, and you're
watching Astramm. 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. It 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 Thorndikeke
experiment and experiments with muon
decay, where muon 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's 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 its 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 m pole
inside a 20 m 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 m.
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
nancond.
But what happens from the pole's
perspective?
Remember what I said earlier. Objects
traveling 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 m pole, never a 20 m one.
Even worse, now length contraction is
happening to the barn. So, the barn is
even less than its original 20 m length,
now just 10 m from the perspective of
the pole. So, how does a 40 m pole fit
inside a 10 m 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 superp position 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 color 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 colors
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 m. 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 back door 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 sensor
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
traveled 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 dordling
front with a further ahead back length
contraction? The only surprise is that
it seems that we can see this in
experiments in the Large Hydrron
Collider and other places. Somehow we
are seeing across 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? Could 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 mindbending
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
dayto-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 traveling 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, your 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 spled 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 four 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 Mccoan and you're watching
Astramm. 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 larger 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 pushed 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 forever 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? Actually, 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 will
quickly realize that your task is
impossible. All lines would converge
towards each other, intersecting at
least twice as they returned back to
where they started. What would a
universe that was based on these kind of
lines look like? Essentially, rather
than going in the straight line you
thought you were going in, you actually
would be traveling 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 visualize, 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 warp 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 five
squares all meeting up at a corner
instead of the usual three that is
possible in normal 2D space. All right,
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
traveling 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 recognize 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
center of mass as if it were being
forced down a narrow tube 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. H 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
lightyear you traveled out, you discover
another light years worth of space.
However, with hyperbolic space, you
discover more than another light years
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. Yet
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.
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