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Space is big. Really big. You just won't believe how vastly hugely mind-bogglingly
big it is. In fact, the near 100 billion light year wide observable universe is
only a tiny fraction of the greater bigness of space beyond. And for a little while,
we will see more and more of that universe beyond until the cosmological horizons collapse on us
and cut off our view forever. So how long do we have, and what will we see before that happens?
There is an absolute limit to our access to the universe beyond our own galaxy.
There’s a limit to what we can ever hope to explore or send signals to,
and a very different limit to what we can ever hope to witness.
Today we’re going to explore the latter. We’re going to figure out the absolute limit of our
future view of the universe, and of the universe’s ability to influence us. Next time we’ll turn it
around and ask: how much of the external universe can we potentially influence, and even explore?
But let’s start by thinking about the light that we can see from the distant universe.
We know that light doesn’t travel instantaneously. That means when we look into the distance,
we’re seeing objects as they were in the past. We see the moon as it was 1.3 seconds
ago, the Sun as it was 8 minutes ago, and Milky Way stars as they were 100s to many 1000s of
years ago. With our greatest telescopes like the James Webb we’ve seen galaxies whose light
has been travelling to us for many billions of years. This is old light from a younger universe.
Although the night sky looks like a sphere surrounding the Earth,
you can imagine it as a set of shells, which each shell representing light that has come to
us from a particular distance.The most distant light we can see is from the cosmic microwave
background radiation - the CMB - which has been travelling to us for almost the entire
age of the universe—13.7 billion years more or less. This is the light emitted by the hot
hydrogen plasma around 300,000 years after the big bang when the universe became cool
enough to form the first atoms, and at the same time first became transparent.
Surely this is the limit of our vision, so how far away is the CMB?
Well, this is where things get confusing. When the CMB light started its journey towards us,
the universe was 1100 times smaller than it is today. A photon of CMB light observed today was
emitted from particles of primordial plasma that were around 40 million light years away from the
region that would one day become the Milky Way. That’s right next door on cosmological
scales. But that light was running the wrong way against the cosmic travelator. The expanding
universe forced it to travel 13.7 billion light years in order to reach us just now.
Meanwhile, the galaxies that those CMB blobs would eventually form into have now been shoved
in the opposite direction to a distance of 46.5 billion light years by that expansion.
We often say that the observable universe is 46.5 billion light years in radius because if you froze
the expansion now, that would be the current distance of the furthest objects we can see.
The CMB is the practical limit of our view because at earlier times and greater distances
the universe was opaque. But it’s possible that one day we’ll get signals from those times. For example,
neutrinos can pass through the dense primordial plasma and could take us closer to the big bang.
And there are events in the first fraction of a second that may
have created gravitational waves whose influence might one day be detectable.
The earliest time we can ever in principle observe is the instant of the big bang itself.
The big bang happened everywhere, but if we could observe the big bang, we would be observing it
as it happened on a spherical shell just beyond the cosmic microwave background.
We call that shell the particle horizon. It’s the absolute limit of the observable universe.
At least for now. If we wait, signals from more distant parts will have had time to reach us.
The particle horizon expands, and the shell from which we observe the CMB also expands,
changing over time. But there’s a limit to the amount of universe we’ll be able to see,
even if we wait infinite time. To figure out that limit we’re going to need a spacetime diagram.
Long-time watchers have seen these before, but today we’re going to do
things with the spacetime diagram may not have seen—at least not from me.
Consider the spherical shells representing light coming to us from earlier epochs. Now get rid of 2
of our 3 dimensions of space so we just see a pair of points on each sphere in opposite directions,
with arrows for the light travelling to us. Now sort vertically according to when that light was
emitted. This is a spacetime diagram—one dimension of space plotted against time. Light is travelling
through space and time towards us, forming a light cone—in particular, our past light cone.
The boundaries of the cone are at 45 degrees. This is the angle light makes
on our spacetime diagram. Slower speeds have steeper angles, and that means only
things inside or on this cone can potentially send a signal to or travel to our location in
spacetime. Events outside the past lightcone can’t get signals to us here in our present.
Our particle horizon is at the bottom of the light cone, and the CMB is just above it. But there’s a
problem here. Remember we constructed this light cone by layering a series of shells that represent
the current size of those regions. But the universe has been expanding, so at earlier times
those regions were smaller. These lines represent the past and future expansion of the universe.
The big bang singularity has all space compacted into a point, after which it
expands. That expansion at first slows due to the gravitational pull of all matter in the universe,
but after a while dark energy takes over and the
expansion begins to accelerate. And that started just a few billion years ago.
While the lightcone encompasses more and more stuff into the past, at some point it starts
to encompass less and less physical space. It comes to a point at the particle horizon. Even
at the big bang, the particle horizon doesn’t encompass nothing, nor does it encompass
everything. It represents a finite portion of the compacted everything at the beginning of time.
It’s easier to see that if we make a modification to our diagram.
Imagine we redefine the tick marks on the x-axis so that instead of representing absolute distance,
they represent points fixed to the expanding space. These could be galaxies for example.
Currently those reference galaxies follow these lines. But we can stretch the graph differently
at each layer to straighten the lines, so that now each tick represents more and more space going up.
We’ll label that axis with the distances those galaxies will be from us at the present moment.
But at the bottom of the diagram, each tick really represents a tiny physical distance.
That distance approaches zero towards the very bottom of the plot, but at any non-zero time after the
big bang, we can see that our particle horizon encompasses a finite amount of the universe.
We just created a new coordinate system. These are comoving coordinates—they co-move with the
expansion of the universe. Our past lightcone in this system is curved—light travels many ticks
per unit time at the bottom but fewer going up. Let’s make one more change—we’re going to adjust
the time axis so that each tick represents less and less time as we get closer to the big bang,
to the same degree that space is compressed. Do this right and our lightcone and all light
speed paths make straight 45 degree lines like they’re supposed to.
With our new tool in hand, we can really see how our particle horizon really changes over time.
As we move forward in time our past lightcone follows us.
In the regular coordinate system, it still converges to a point, but in comoving coordinates
we see that it encompasses more and more of the universe. Naively, it might seem that there’s no
limit—if we want to see any distant point we just have to wait long enough. And that would
be the case if it weren’t for dark energy. The fact that the expansion of our universe is
accelerating means there’s an absolute upper limit on how much of the universe we can ultimately see.
But to understand the future limits of that view, we need to understand some
new horizons—horizons that aren’t getting bigger. In fact they’re racing towards us.
In an expanding universe like ours, more distant points seem to be moving away
from us more quickly. A point that’s far enough away will be moving away from us at
the speed of light. While objects can’t move through space faster than light,
space itself can move at any speed relative to other space, and it can carries objects with it.
So, there’s a sphere that surrounds us where the recession velocity equals the speed of light. It’s
called the Hubble horizon, after Edwin Hubble, the guy who discovered the expansion of the universe.
The hubble horizon is currently 14 and a half billion light years away.
Now you might think it would be impossible to see things further than this. After all, light
emitted by galaxies in that distant space will be pulled away from us like fish swimming against a current.
But we can see the cosmic microwave background, and that’s 46.5 billion light years. So what gives?
In fact we routinely observe galaxies that were moving away from us faster than light at the time
they emitted the light that we see. To understand how this can work, imagine you’re a photon.
You’re spat out by a bright star in a galaxy millions of light years from of the Milky
Way. Initially you find yourself in a region space that’s moving away from the Milky Way at
3c — three times your own speed of light. You’re dragged with that space and so the
Milky Way seems to be racing away from you. But because you’re moving towards the Milky Way,
you escape that patch of space that’s traveling at 3c. That patch moves in the opposite direction
to you. Now you find yourself in a region of space that’s traveling a little less
quickly away from your destination. You’re still dragged away from the Milky Way, but not as fast.
After billions of years of losing ground, you eventually find yourself at the Milky Way’s
Hubble horizon where space is receding at exactly 1c - your own speed. The Milky Way finally stops
moving away from you, and as you struggle across that horizon and can finally make progress.
You have to retrace a lot of ground—billions of light years in fact—but eventually you reach the
Milky Way, then the Earth, then fall into a telescope where you reveal secrets about your
ancient origin to a group of bipedal apes that evolved long, long after you started your journey.
The reason that light from beyond the Hubble horizon can reach us is that for the first several
billion years after the big bang, the Hubble horizon was expanding. Galaxies were moving away
at a more or less constant speed, in fact actually slowing down a bit. That means the point where
the recession speed equaled the speed of light was getting further away from us. This enabled
light from more distant objects to creep inside the Hubble horizon and make their way to us.
By the way this is great news by the way—otherwise we would never have seen the CMB and probably couldn’t have
proved that the Big Bang happened. But this won’t always be the case. Like I said, the expansion
of the universe is accelerating. At some point the Hubble horizon will stop moving away and
actually collapse back on us. The boundary of light-speed expansion will eventually surround
the local group of galaxies and stop there, walling us off from the rest of the universe.
Only the light that can cross the Hubble horizon before it collapses can ever reach us.
So now we introduce our final horizon—the horizon that’s going to determine our ultimate view of
the universe. This is the cosmological event horizon. It's the boundary beyond which no signal can ever be
received, no matter how long we wait. Light coming from beyond the cosmological event horizon won’t
make it across the Hubble horizon before it collapses. The event horizon started out much,
much larger than the Hubble horizon—63 billion light years in comoving distance,
but it shrinks over time, because light released at later times has less time to get to us.
It’s now around 16 billion light years in radius. At some point—in 10 billion years
give or take—the cosmological event horizon will merge with the collapsing Hubble horizon.
At that point we’ll never be able to see new events from beyond this horizon.
But that doesn’t mean the universe will suddenly go dark. This is also when we get our broadest
view of the universe. Light from the most distant points that we will ever see will
then cross the shrinking Hubble horizon just in the nick of time. Those photons will struggle against space
that’s moving just less than light speed, and will eventually make their way into our local
bubble of non-expanding space. They’ll carry with them light from the cosmological event
horizon as it was in the beginning of time, when it was 63 billion light years in radius.
And that will become the final size of our particle horizon.
We’ll be able to see things that are currently 63 billion light years away. That’s about half again
the size of our current view. But we won’t have that view forever. While the photons
continue to trickle in from the collapsed horizon for eternity, they will be increasingly
redshifted—sapped of energy—from their long fight against the outward flow of space.
When we first get close to our our full panorama of the universe in about 10 billion years,
the galaxies will shine mostly in infrared light. After a few hundred billion years,
even the most energetic photons will be stretched to the point that we’d need a radio antenna
larger than our contracted Hubble horizon to see them. The sky would finally be dark.
So that is the extent of humanity’s potential to see the universe.
There is one way we can see further—and that’s by traveling as fast as possible to escape
our collapsing Hubble horizon. We’ll then be in a different Hubble horizon with different view.
But we’ll save that for next episode, when we explore the limits of our ability to influence
and explore the universe. How far can humanity eventually expand and when
we need to leave to avoid getting trapped forever in our local bubble of space time.
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