There’s another option. Maybe faster than light travel is impossible so any travel to other star systems inherently means traveling at relativistic speeds. So you COULD get to other Star systems, but by the time you got there your planet would have gone through thousands of years and then you’d be on your own with no way back.
If that’s the case, the only reason it’d ever be worth it to go was as a last ditch effort to save the species.
The problem is that if we are in danger of extinction we'll no longer have the resources to send a handful of people to another star system. Only a prosperous people can spare the enormous amounts of energy and matter necessary for that, however, a prosperous people has no reason to do so. That's a sort of paradox.
If you spead out as soon as you can, you won't need a last dtich effort to save your species from some disaster, since your species will already be spread across many systems.
I used to get annoyed at old science fiction stories where an advanced citivilization lived on their planet countless thousands or millions of years and then discovered that their home planet was doomed and started a crash program to develop intersteallar travel to find and conquer a new planet to live on, which naturally was Earth.
It is perfectly possible to build artificial space habitats capable of supporting thosands of people, built out of materials from asteroids and comets. After centuries or millennia, there could be countless milllions of them in the solar system with a total population of trillions or quadrilllions.
If such a space habitat, or a fleet of them, is sent on a mission to a star 10 light years away at one percent of the speed of light, it will take it 1,000 years to arrive. If it takes the colonizers 1,000 years to build up their society enough to send out expediitons of their own, it will take about 2,000 years to expand a distance of of 10 light years, or about 200 years per light year.
So after about 16 million years the colonized area would expand to the far edge of the galactic disc about 80,000 light years from Earth.
Suppose that the habitats/ships travel at 10 percent of the speed of light, and a 10 lightyear voyage takes only 100 years,and it takes only 100 years at the new star to buld up the abillity to send out colonizing expeditions. In that case it will take 200 years to expand 10 ligh tyears, or a rate of 20 years per light year.. At that rate it will take only 1,600,000 years for the colonization process to reach the far edge of the galactic disc about 80,000 light years from Earth.
You mentioned travelling at relativistic speeds. At speeds fast enough for significent time dilation, a journey to a star only 10 light years from Earth would take only a little longer than 10 years, and will seem much shorter to those aboard. If they need help from their home star, a message back will take only 10 years, and help could arrive an another 11 or 12 years. And 21 or 22 years is a long.time to wait for a rescue mission, but it is a lot better than the thousands of years you claimed would have passed on the home planet.
Scientists now estimate that the vast majority of star systems have planets, and those with planets should have smaller bodies including asteroids and comets. So the vast majority of star systems should be suitable for colonization by such a space habitat civilization. And the nearest suitable star sytsem should usually be a lot closer than 10 light years from the home system.
So I think that waiting until a disaster threatens the survival of the species instead of colonizing otther sar systems as soon as possible is a silly course of action.
No, what you don't understand is that what I am saying is that if FTL is possible and if one space-faring civilization had begun only a million years ago, it would have already filled the universe. Just as one single virus can infect an entire population in no time. IOW, expansion is exponential. I don't believe it's that hard a concept to understand. And one million years at the scale of the universe is nothing.
You seem to have forgetting the various math problems in high school where you were given the speed and distance and had to claclulate the travel time, or given the travel time and the distance and had to calcuate the speed. (And a lot of space opera writers seem to have also forgotten those problems>)
Suppose that a space travelling civilization arose one million years ago with ships which could travel 1,000 the speed of light, and it arose on a planet one point one billion (or 1,100,000,000) light years from Earth. Even a ship which travelled at 1,000 times the speed of light for one million years could have travelled "only" one billion (1,000,000,000) light years in one millinyears, so that civilization's cimit of colonizatins would still be about one hudnrd million (100,000,000) light yers from Earth.
You can not claim that a faster than light civilization would have already colonized the entire universe unless you specifiy:
1) How large the universe is.
2) How fast their starships either accelerate or travel at a constant speed.
3) When the civilziation developed faster than light travel and began to colonize.
4) How long it takes the average colony to begin sending out colony expeditions of its own.
And of course you need to do the calculations to make certain that the civilization owuld have already filled the universe.by now.
If FTL were possible, that doesn’t mean it‘s safe and practical for living organic beings. Or they have any practical way to determine for sure that exoplanet they see in the distance supports their life. Or if it does they won’t immediately die from the microorganisms there. You have to solve radiation protection, you have to be able to navigate any asteroid dense regions, and you have to hope you don’t slam into a grain of dust at over a c.
If your ancestors have lived in space habitats for thousands of years, you probably won't be interested in colonizing any habitable plaents you may find, and will leave them alone.
If you have a faster than light spce drive, you can send faster than light space probes to check out a star system, or even send some kiind of manned starship to study the system, before deciding whether to colonize it.
Who worries about asteroid thickets in real life?
https://tvtropes.org/pmwiki/pmwiki.php/Main/AsteroidThicket
Running into a grain of sand at high slower than light speeds would be a disaster. But a faster than light drive would bypass most of the laws of motion and there would be no reason to assume that a ship on warp drive would suffer from hitting a grain of dust.
I think it's a matter of spreading logistics / infrastructure to support everything you need for new colonies.
Finding exact planets that are suitable for your species shouldn't be a simple thing, it takes time to make sure everything is compatible.
Let's look at the
Tholians, they have very specific Temperature requirements to exist naturally.
Tholian biology required high temperatures around 480 Kelvin (207 °C, 404 °F). They could tolerate lower temperatures for a brief period of time; if they were exposed to temperatures around 380 Kelvin or less, their carapace would fracture. This was painful or distressing; a Tholian subjected to such a temperature regime could be coerced to cooperate. In temperatures even lower, a Tholian would freeze solid and shatter.
There's got to be a small list of planets that are designed for the Tholians to exist naturally.
Same with the composition of the air needed for a species to breathe.
There's got to be only so many M-Class planets out there that are compatible with us standardized BiPaB's.
Do you known how many stars are in the Milky Way Galaxy?
As long ago as 1964, there was a book written about the probability of planets habitable for humans.
Habitable Planets for Man, Stephen H. Dole, 1964.
https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf
According to Dole's calculations and estimates, only a small minority of all stars would have a human habitable planet,and thus there would be only about six hundred million human habitable planets in our galaxy.
Modern estimates of the numbers of habitable worlds in the galaxy are for the number of worlds habitable for some types of liquid water using life in general, and not for planets habitable for humans in particular. Planets suited for the specific needs of humans will no doubt be a minoority of planets habitable for liquid water using lifeforms.
But since mosdern estimates of panets in our galaxy habitable for liquid water using life in general are billions of planets, human habitable planets should at least number in the millions.
And of course it is my suggestion above that almost every singe star system would be suitable for dwellers in artifical space habitats.