There’s a huge asterisk here.
IIRC, it is possible to get anywhere in the observable universe in one human lifetime assuming 1g of constant acceleration.
This does not permit you to slow down and halt at your target, which greatly increases travel times.
It is also effectively a one-way ticket for anything other than objects in our immediate stellar neighborhood. If you turned around and returned to Earth after getting to an object 1,000ly away—still well within our own arm of the galaxy—at least 2,000 years will have passed on Earth. It’s probable that no civilization you know of would still exist, nor would anyone be able to understand your language.
This isn’t even beginning to address the problem of running into stray atoms at 99.99…% of the speed of light. Or god forbid a handful of stray molecules. We also haven’t discussed the real elephant in the room which is the sheer amount of energy required to accelerate a human and human life support systems at 1g for several decades.
> nor would anyone be able to understand your language.
Huh? We already have machines that can understand any language from a sample.
Also, how much fuel do you need to bring along to accelerate a human and life support system and the whole craft including fuel, for a lifetime? Is it larger than a planet?
What to send is DNA along with some sort of robot that can grow it into a man upon arrival.
> IIRC, it is possible to get anywhere in the observable universe in one human lifetime assuming 1g of constant acceleration.
Huh? You can’t go faster than light speed, and the observable universe is way larger than ~100 light years.
> nor would anyone be able to understand your language.
Greek and Latin are still understood. I don't know if the Chinese spoken today resembles Chinese from 2000 years ago, but maybe some of the written language would be understandable. Both Hebrew and Tamil are comprehensible that far back, and farther. Arabic goes nearly that far back.
Of course, that's six languages out of... how many do we speak?
For the sake of pedantry, there are things in the observable universe which are increasing in distance from us by more than 1 light year per year. This means it's impossible to reach them unless the universe's rate of expansion changes. I think the Hubble volume is the region theoretically reachable; limiting acceleration to 1g would limit you to a slightly smaller region (only a tiny bit smaller, I think).
https://en.wikipedia.org/wiki/Hubble_volume