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 very  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.

This 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 collapse  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 bump 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 to 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 diagram 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 future 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 expansion 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 speed 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 towards 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-move  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 example, 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, then   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 waiting,   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.

Explorers 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 explorers.

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 the 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 messages 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 communications.

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 are 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 our 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!