Here is the explanation and equations: http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.h...
2 * T(1250 lyr) = 2 * (c/a) arccosh (ad/c^2 + 1) = 2 * arccosh(1250 + 1) = 2 * 7.8 = 15.6 yr.
But a probe might be able to.
https://news.ycombinator.com/item?id=4534359
https://news.ycombinator.com/item?id=6238297
Although, I certainly wouldn't bet against it long term.
If you accept any ship could get there, you might as well consider that space travel isn't the only technology that will advance.
You are aware those don't actually exist?
People assume they will exist, but we have nothing to base that assumption on except "it would be cool".
???? Based on what exactly?
> But both a Mars trip and cryogenics seem pretty reasonable to me.
You think those are similar? We could do a Mars trip today with enough money. Every bit of money in the entire world would still not get you cryogenics - it requires a new idea that doesn't exist right now.