Ask Lemmy

It's already possible in a "does it violate the laws of physics or not" sense, the real question is, will anyone that has the requisite resources to do it actually want to.

It would take such an incredibly long time (as in, millions of years or longer for the very closest galaxies) that anyone and any organization sending out such an expedition isn't going to get any meaningful return on their investment, so it would only bring a benefit to whoever was on the "ship" when it arrived. As such, to even have a motive for doing this, you either need a society that does things for the benefit of extremely distant descends, or which is extremely long lived and patient.

As to how you would actually do it, my guess (obviously though, the guess of someone from a society that lacks the technology to do a thing is likely to be wrong about how it later is done) would be that one would use a hypothetical type of structure called a stellar engine These are similar to the "dyson spheres" that science fiction sometimes likes to talk about (usually inaccurately to the actual concept but still), except that they would use the energy emitted by a star, or its mass, to do some particular task, like propel the star in a given direction.

Doing this, your "ship" is actually an entire solar system. Getting that up to speed could take millions of years even for the most efficient designs, and obviously requires an economy capable of building stuff at incredible scales, and having an entire star spare to use for the trip. However, you're going to be taking that kind of time anyway, and so you're probably going to need an entire self contained civilization to have a hope of keeping things running that long, and literal worlds worth of raw materials. There's not much else that even theoretically has enough fuel to move all that to notable fractions of lightspeed. Since there's little point to going to live in another galaxy if there are still unclaimed places to go within your own, a whole star system is probably a relatively small expense for the implied size of civilization that would even want to try to sebd such an expedition. Galaxies contain a huge number of them after all.

While this is all obviously far beyond us now, both in technology and sheer economic scale, there's nothing physically impossible about it, and at least some logical motive (the future resources of a galaxy for one's descendants, if alien life is rare enough for uninhabited galaxies to exist). Given that and just how huge the universe is, I'd actually be willing to bet that somewhere there is someone or something doing this, and that if humans last long enough and keep advancing our technology and infrastructure all the while, some descendant of our species might, though they'd probably seem pretty alien to us by the time it took to reach that point.