>According to some calculations, it should in principle be possible to colonize the entire observable universe in less than a hundred million years
...what? That doesn't seem right, just from a really quick gut check it looks like the observable universe has a radius of 45.7 billion light years [0]. Even if the universe wasn't expanding nobody could get to everything any faster than that number of years right? Maybe you saw something that was talking about the local (Virgo) supercluster, which I think has a radius of around 55 million light years, so that sounds more like something that could be done on that timescale "in theory". But there are millions and millions of superclusters in the observable universe overall.
Oops, yes, I don't know what I was thinking. A total brain fart. The paper I referred to is Sandberg and Armstrong's 2012 "Eternity in Six Hours", and of course they don't claim such a thing. Only that it's possible to start a colonization wave that has plenty of time to spread to everything visible now before they slip outside of our future light cone. The ~100M years refers to the colonization of the Milky Way. Sorry!
>> According to some calculations, it should in principle be possible to colonize the entire observable universe in less than a hundred million years
> ...what? That doesn't seem right, just from a really quick gut check it looks like the observable universe has a radius of 45.7 billion light years [0].
I guess it depends on whose hundred million years you're talking about: the colonists' or those who stay home's. I don't know how to do the calculations, but it seems plausible that you could traverse the entire observable universe at near light-speed in 100 million years ship time.
You need ridiculous speeds for time dilation to really kick in though. Mathematically, it starts as soon as an object moves. But if a spaceship travels at 90 % of light speed (0.9 c), their local time moves just approximately at half speed compared to local time on earth. A year for the astronauts is just over 2 years on earth.
At 0.995 c, the ship clock runs 10 x slower.
At 0.999 c, 22 x slower. Then if you push the turbo button to 0.9999 c, 71 x slower.
The fastest man-made object to date is the Parker Solar Probe, at 0.059 c.
...what? That doesn't seem right, just from a really quick gut check it looks like the observable universe has a radius of 45.7 billion light years [0]. Even if the universe wasn't expanding nobody could get to everything any faster than that number of years right? Maybe you saw something that was talking about the local (Virgo) supercluster, which I think has a radius of around 55 million light years, so that sounds more like something that could be done on that timescale "in theory". But there are millions and millions of superclusters in the observable universe overall.
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0: https://en.wikipedia.org/wiki/Observable_universe