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If galaxies are moving apart from each other faster than the speed of light, does that mean that it's impossible to travel to another galaxy, regardless of what technology get discovered? Because you can't exceed the speed of light?

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Not every galaxy is moving away from us at faster-than-light speeds. That's typically only the case for very distant galaxies (the further away two points are in space, the faster they're moving away from each other, according to Hubble's law).

Indeed, some galaxies are actually travelling towards the Milky Way, a case in point being the Andromeda galaxy.

In addition, wormholes might allow matter to quickly travel between very distant points in the Universe without violating the speed of light limit, but that's a more speculative topic.

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