[api]

If we can get good enough at bioengineering, a 50,000 year flight to another star using conventional propulsion might not be such a big deal.

The seeming requirement of FTL to explore the universe is 100% a function of our short life span. If we can't make spacecraft go faster we have to make ourselves last longer.

[Beldin]

We'll also have to take food for the whole duration, or develop a taste for hydrogen atoms alongside a functioning Bussard ramjet.

Oh, the rocket equation really doesn't like option 1.

(Hypothesis: any process we can devise to turn hydrogen into sustenance will be orders of magnitude less efficient than using it as propellant.)

[api]

Food can be recycled pretty effectively, and if were that good at biotech I assume we could improve on the current state of the art.

They already recycle water very effectively on the ISS. It's the machine that "turns yesterday's coffee into today's coffee."

Of course if we were that good at biotech we could probably hibernate a good chunk of the flight time too. Might be necessary to wake up periodically to reset the body, but you could probably hibernate most of the duration. Maybe you'd do it with some kind of weird circadian cycle with extremely elongated sleep periods, sleeping like 10X-100X as long as you are awake. During each wake period you check to make sure everything is working properly.

You would not need a Bussard ramjet for the long duration flights I'm thinking of. A nuclear thermal rocket could get you a good deal past solar system escape velocity. Nuclear pulse propulsion could get you up to at least single digit percentages of the speed of light if you didn't mind a little boom-boom. Then you just cruse along on an interstellar transfer orbit until you do a retro-burn to enter the destination star system a few tens of thousands of years later. These are all technologies that are already feasible at least on paper. No new physics is needed.

[xyzzyz]

We would only small amounts of food, if we could efficiently recycle it. Right now, we use plants/animals and solar energy to upcycle our waste products into food. However, there are no physical reasons that we couldn’t use electricity and managed bioreactors to do that instead.