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We humans have always been explorers. The great civilizations that have arisen across the world are owed to our restless ancestors. These days, there’s not much of Earth left to explore. But if we look up, there’s a whole universe out there waiting for us. Future generations may one day explore the cosmos and even settle entire other galaxies. But there is a hard limit to how much of the universe we can expand into. So, how big can humanity get?
Episodes Referenced:
How Much Of The Universe Can Humanity Ever See?: https://youtu.be/eVoh27gJgME
Is Interstellar Travel Possible?: https://youtu.be/wdP_UDSsuro
What If Humanity Is Among The First Spacefaring Civilizations?: https://youtu.be/uTrFAY3LUNw
The Edges of Our Universe by Toby Ord: https://arxiv.org/pdf/2104.01191.pdf
A causal limit to communication within an expanding cosmological civilization by S. Jay Olson: https://arxiv.org/pdf/2208.07871.pdf
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We humans have always been explorers. The
great civilizations that have arisen across the world are owed to our restless ancestors.
These days, there’s not much of Earth left to explore. But if we look up, there’s a whole
universe out there waiting for us. Future generations may one day explore the cosmos and
even settle entire other galaxies. But there is a hard limit to how much of the universe we
can expand into. So, how big can humanity get? Today we’re going to dream big and take a ver
y
long-term view of the future of human exploration. If we manage to survive the current
existential perils and master interstellar and even intergalactic travel, how far
could we go? How many planets could we walk on? How many human lives
could play out in the future? There are so many unpredictable factors
— sociological, technological, political, environmental. But the physics and
the cosmology? That we can compute. And these give a pretty clear limit
to how big our future could be. Th
is episode follows on from our previous one,
where we figured out how large our view of the universe would ultimately become. We’re going to
make heavy use of some of the tools we developed in that episode, so you might do well to
watch it first. If not, watch it after. In that episode we learned the maximum extent
of our potential view of the universe from the Milky Way—around 63 billion light years, only
about half again our current vista—the limit before our cosmological horizons collaps
e
in on us due to the work of dark energy. But there’s a way we can see
further, and that’s by leaving home. Let’s start by setting the conditions for
this thought experiment. The big one is that intergalactic travel at a reasonable
fraction of the speed of light is possible. We’re not going to argue this one in detail here.
We’ve talked about how interstellar travel is at least plausible, with various options for
extreme velocities and for shielding the ship from impacts and radiation. If
hopping between
stars is possible, then hopping between galaxies may also be possible—as long as there’s a
way to preserve your explorers for 100s of thousands of years per jump; cryonics,
generation ships, or just send the AIs. Exactly how we do it isn’t important for
today. We’re just assuming that it’ll one day be possible to hop between galaxies,
and in each new galaxy civilization will spread and launch new ships to
new galaxies in new directions. We’re also assuming that we don’t bu
mp into
other expanding civilizations along the way. Which we might, and we talked a bit about that in
our grabby aliens video. But today we’re trying to figure out the maximum extent for humanity,
so let’s imagine we’re alone in the universe. Given these assumptions, we have humanity—or
whatever succeeds us—occupying a growing bubble that gradually fills vast tracts
of space. But exactly how big can that bubble get? Even though the universe may last
forever, there is a fundamental limit t
o the possible future extent of our influence. As
we grasp for distant galaxies, they withdraw from us due to the accelerating expansion of the
universe. In the end we can only extend so far. For the first part of this analysis,
we’re going to draw on a paper by Toby Ord of the Future of Humanity Institute
at the University of Oxford. It’s linked in the description if you want to take a
look. We’re also going to make heavy use In the last episode we developed the idea of the
spacetime diag
ram in comoving coordinates. To summarize, if you shed 2 dimensions of space from
our 4-D spacetime, you are left with 1 spatial dimension which we put on the x-axis, and time
which becomes the y. Motion is a diagonal line, with the maximum speed being lightspeed at 45
degrees, and everything slower taking a steeper trajectory. In the previous episode we explored
the idea of the past lightcone—the region of past spacetime from which it's possible to receive
signals. But we also have a futur
e lightcone. The future lightcone defines all the spacetime
points a signal sent today could possibly reach, and it also represents all the
points we could ever visit if we launched our light-speed ships today.
Nothing can travel faster than light, so regions outside our future
lightcone are forever inaccessible. Our past and future lightcones change.
We move forward in time, and as we do, light from more distant regions has time to
reach us—our past lightcone expands. Also, more and more
of spacetime slips out of our
possible reach as our future lightcone moves up. The excluded region represents locations
in space, but also moments in time. Some distant spacetime points can’t be reached.
But from our spacetime diagram it looks like we should be able to eventually reach any
location in space, just at a later time. But as we saw last time, the expanding universe
limits how much of it we can either see or access. These lines represent the motion of points
fixed to the expansi
on of the universe. The galaxies move apart from each other following
these trajectories. At first, that expansion slows due to the mutual gravity of all matter, but then
it begins to speed up again due to dark energy. But let’s ignore both gravity and dark energy
for the moment and assume that every galaxy will always move at the same speed. Now
their trajectories are straight lines. More distant points in space are moving
away faster, and at a certain distance they’re retreating at the sp
eed of light. As
we saw last time, this is the Hubble horizon. We also saw that against intuition, light
can cross the Hubble horizon and reach us from the past. However, on the case of
a universe expanding at constant speed, we could never reach the Hubble horizon from
within because that horizon is expanding at lightspeed. However, in our universe the
Hubble horizon doesn’t keep moving away. Several billion years ago its motion
away from us started to slow down, and it’s now moving towar
ds us again. This
is due to dark energy. The expansion rate is accelerating, which means the boundary of
superluminal expansion—the Hubble horizon—is getting closer to us. Because of this, we
actually CAN cross our own Hubble horizon. 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 are comoving coordinates—they co-mo
ve
with the expansion of the universe. We can see this more easily if we rescale the
spacetime diagram’s y-axis so that light travels 45 degree angles, compressing time at the top
and expanding it at the bottom. The bottom of the plot is still the big bang, but the top is
the infinitely distant future. This is called a conformal transformation, by the way. So we now
have a conformal, comoving spacetime diagram, and despite how it sounds, it makes the life of the
cosmologist easier. For exa
mple, it’s now easy to see which light-speed signals can reach us at any
time, including infinitely far into the future. Only signals that merge with our collapsing
hubble horizon reach us, and that defines our ultimate view of the universe—our future
particle horizon. This boundary that I just drew is the cosmological event horizon,
and anything outside can never reach us. But just like a black hole’s event horizon,
the cosmological event horizon can be crossed in one direction but not the
other. In this
case it’s like a reverse black hole horizon, because you can escape it from the inside,
but never enter it from the outside. On the spacetime diagram, crossing this horizon at the
speed of light gets you out of our local bubble, and in principle you can travel for eternity,
covering infinite distance in the process. But beyond a certain point, you won’t actually
get anywhere interesting. Although you get further from the Milky Way, everything else is
racing away faster than
you can ever travel. If we leave home tomorrow on a lightspeed ship,
the furthest galaxies we’ll be able to reach are the ones on our current cosmological
event horizon. They’re currently 16 and a half billion light years away, although by the
time we reach them they’ll be much further. If we look at the spacetime diagram for
the perspective of our destination, we see that we can only reach destinations
if we are within their cosmological event horizon—which is 16 and a half billion
light
years in the modern universe. So that’s the theoretical upper limit on
the distance our civilization could spread. Toby Ord calls this the affectable universe,
It’s a sphere 16.5 billion light years in radius in comoving distance, but by the time
we reach it it’ll be much, much bigger. He estimates that the affectable universe
contains around 20 billion Galaxies and around a sextillion stars. If we assume that we occupy
every Earth-like planet around every Sun-like star in that region, the
n based on the Kepler
mission’s findings for the Milky Way, there should be of order 10^20 occupied planets and
perhaps 10^30 human descendants at any one time, if we’re any where close to
maximally prolific. Then integrate that over millions or perhaps trillions of
generations and, well, you get the idea. These numbers assume we leave basically
immediately and in all directions at the speed of light. I don’t think the starships are quite ready
yet, so how much universe do we lose by waiti
ng, or by traveling at a more reasonable speed? The
limit of our access is equal to the distance of the cosmological event horizon at the time we
leave, and that horizon is shrinking. Every year we procrastinate, an average of 3 galaxies
falls permanently out of our reach. If we wait long enough, the light cone will shrink so much
that only our local cluster of galaxies will be available to us, giving rise to what Toby Ord
calls the era of isolation. We have a bit of time to spare, however.
A billion years from now we’ll
only have lost 20% of the affectable universe, and the era of isolation won’t start
for another hundred billion years or so. The future size of humanity depends on when we
leave, but also on how fast we travel. The numbers I gave are for near light-speed travel. Because
the universe is expanding evenly everywhere, the size of the affectable universe is approximately
proportional to our speed. At half the speed of light, our affectable universe is around half
the radius, so the sphere we ultimately occupy is around an eighth the volume compared to light
speed travel. But that’s still a lot of galaxies. As long as we’re traveling at
least 20% light speed on average, we’ll have access to around
a billion galaxies or more. Now you have an idea of the potential size of
humanity’s future, let’s consider bigger numbers. In the last episode we figured out how much of the
universe we will eventually be able to see. We saw that in the far future—in the
era of isolation—our
past light cone will reach a limit in the amount of stuff it can encompass. Our observable universe
will be around 64 billion light years in radius, compared to the 46.5 billion light years of the
present. These are comoving units—so eventually we’ll be able to see light from objects that
are currently 64 billion light years away. But if we really are going to launch our
fleets and spread through the universe, future humans will have different past light
cones. Explore
rs and their descendents who leave soon and don’t stop, traveling at close
to light speed until the era of isolation, will see the Milky Way in the distances in one
direction, and their observable universe will be shifted 16.5 billion light years in the other
direction, encompassing billions of galaxies that Milky Way stay-at-homes will never see. We can
define a region of space that we can possibly one day observe as the combination of all past light
cones of all possible light speed explo
rers. Ord calls this the ultimately observable universe,
and it’s nearly 160 billion light years across. Although we may one day fill a vast region of
the cosmos and see even more of it, we won’t be able to tell each other what we found. Or even
really call ourselves a cosmic civilization. Our far future descendents will be scattered
across many millions of causally disconnected regions, beyond each other's event horizons.
No communication is possible between them, and so presumably over th
e billions of years these
outposts must diverge in culture and appearance. But that isolation begins much earlier. In a 2022
paper, S. Jay Olson studied the capacity for an expanding civilization to maintain contact across
its ever-increasing extent. He calculated the number of times an expanding civilization can have
two-way communication before the era of isolation. Let’s use our spacetime diagram again. A colony
ship travels outwards at, say, 20% light speed. They send intermittent messa
ges back home, which
travel at light speed—as does the reply message. If some of the explorers just keep
traveling then it takes a while for the reply to catch up to them. The total
number of back and forth messages depends on how far each colony group manages
to travel before the era of isolation. If our average speed is 20% light speed, then
a large fraction of our ultimate spread can have multiple communications with home, although
more than half of the volume will have had 2 or fewer c
ommunications. There’s an extensive
region at the rim that has been traveling too fast to ever get the return message from
any of its communications. But if the average speed is closer to light speed, then the
vast majority of expanding settlers never heard anything back from Earth in the billions
of years of their travel. And they never will. Humanity’s future may be very, very large. If
we want it to be. Maybe we’ll fill 20 billion galaxies with life and mind. Maybe we’ll realize
there a
re even better ways to spend eternity. But if we do decide to expand, then we should try
to maximize our chance of success. I would argue that flinging colony ships in all directions
as soon as possible is not necessarily the way to go. We have a billion years to fine tune our
intergalactic plans without missing too much of the universe. And, remember, Whoever we send will
have very limited contact with home base, and so the state of humanity at the moment of launch will
form the seed of ou
r cosmic legacy. “The sky calls to us. If we do not destroy ourselves, we will
one day venture to the stars” so said Carl Sagan. The cosmic extent of our species is potentially
enormous. It’ll be a hell of a responsibility, if we do choose to send our descendents
beyond the horizons of our local space time. Before we wrap up, we wanted to let you know
it’s Earth Month across PBS! As you can see, developing the science for light speed travel
and building spaceships capable of traveling into
the distant universe is going to be
quite difficult. So it's going to be a good idea that we take care of our home planet
until the time when we're ready for launch. And taking care of and appreciating our blue
marble is a big theme of Earth Month across PBS. One new series you might want to check
out is called Untold Earth on PBS Terra. A collaboration between Atlas Obscura and PBS
NATURE, Untold Earth explores the mysteries behind North America’s strangest and most unique
natural wonders
. We have a link below to the first episode on redwoods as well as link to the
complete (and growing) Earth Month playlist. And if you travel to other channels, please make sure
to tell them, politely, that Space Time sent you!
Comments
It's funny how you weren't planning on ever visiting that galaxy 100 billion light years away, but when science says you can't it's suddenly all you've ever wanted. So weird how these limits are still unfathomably huge, but still feel depressingly small when you realize they might be absolute limits of travel for the entirety of forever.
I love the thought experiment of the Slow Starship, that puts humans in stasis to travel to a distant star system only to awaken and find that future humans have already arrived by a faster starship and evolved both biologically and technologically!
I always thought of space and time being on such unfathomably massive time scales that we could never perceive a change without multigenerational record-keeping. Hearing that every year we lose 3 galaxies is so mindboggling.
hey matt, long time watcher and fan. The world is getting scarier as time marches on, but watching space time has consistently been there and given me something I can think about. Thank you for the work you and the rest of space time do. ❤
For some reason, the phrase “…humanity, or whatever succeeds us…” really caught my attention.
One of the biggest things I drew from this episode, that I've never really put much thought into, is that the speed in which we expand from Earth ultimately reduces the amount of communication we can have with it (same for any origin point).
That light cone and spacetime diagram animations was really neat and made the concept so much easier to follow.
These videos are something that keeps my mind going! Space Time is THE best channel on Youtube!
I feel like this channel is so good at slowly accumulating enough reference knowledge from past videos to bring up new and harder to explain topics. Very good programming.
A followup question I'd like to see explored: assuming we send Von Neumann probes in every direction as fast as possible and as soon as possible, programmed to retrofit every single star in the affectable universe with a stellar engine, and pilot them all toward each other at maximum speed, how much of the affectable universe could we bring together into a gravitationally bound cluster, so as not to be so isolated by the Era of Isolation?
I'm British and was at the Natural History Museum in NYC last month when I saw a very familiar, albeit beardless, Aussie physicist participating in one of the video exhibits in the space wing of the museum. Never knew you were quite so prolific, Matt!
Love this content. Please keep it coming, I share every time
PBS Space Time is the perfect combination of huge knowledge and flawless animations, both in an ideal setup to enjoy the content and also learn from it. I've been following it for years and I'm still impressed. I really hope there's content for more years to come, I can't imagine my Youtube feed without the joy of having a new video.
This is quickly becoming my favorite astronomy/physics channel on youtube.
Fantastic video, as always, Space Time team!
Instant subscription. I love this kind of stuff. Thank you.
Thank you for posting this video at the exact moment that I was available and able to watch it. These videos always make me so happy... even if they are existentially disturbing.
I wonder if the Great Attractor is an advanced civilization attempting to gravitationally bind a large chunk of the universe before the era of isolation.
Great job, man! As always! Great video
I love all of ypur videos and want to watch every single one, but man there's a lot :D keep them coming