How Far Beyond Earth Could Humanity Spread? (Script) (Patreon)

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?

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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 our 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.

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 all 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. 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. In 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, 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 univers e, 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 descendents at any one time, if we’re close to maximally prolific. 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 travelling 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 lightcone will shrink so much that only our local cluster of galaxies will be available to us, giving rise to what Dr. 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 cosmological event horizon is around half the distance, so the sphere we ultimately can occupy is around an eighth the volume compared to light speed travel. 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 lightcone 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 bever 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 lightspeed 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 civilisation 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. If the average speed is closer to lightspeed, 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 realise 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’s a hell of a responsibility, if we do choose to send our descendents beyond the horizons of our local space time.