So, what if it were possible to build a rocket which could accelerate constantly at 1g?
Doesn't sound like TOO big an ask.
How long would it take to get around?
Rocket years: 2.34 Earth Years: 5.127 --Proxima Cen (nearest star)
Rocket years: 10.9 Earth Years: 2.7x104 --Centre of Milky Way
Rocket years: 15.4 Earth Years: 2.4x106 --Andromeda (nearest galaxy)
Rocket years: 25.3 Earth Years: 5.0x1010 --Edge of Observable Universe
What a trip THAT would be! Here's the thing:
"Firstly, it would take a huge amount of energy to keep you accelerating at g. Secondly, by the time you got back, not only would all your friends and family be dead, but the Earth would probably be gone, swallowed by the Sun in its red giant phase, the Sun would have exhausted its fuel and shrivelled into a cold white dwarf star, and the Solar System, having orbited the Galaxy a thousand times, would be lost somewhere in its milky ways."
So the mileage is lousy and the return trip a real downer.
Would you go faster than light?
"No. From the point of view of a person at rest on Earth, you never go faster than the speed of light. From your own point of view, distances along your direction of motion are Lorentz-contracted, so distances that are vast from Earth's point of view appear much shorter to you. Fast as the Universe rushes by, it never goes faster than the speed of light."
Are we there yet?
"The Universe is expanding, so the distance to the edge of the currently observable Universe is increasing; it would actually take longer to reach the edge of the currently observable Universe. And if the Universe is accelerating, then you will never be able to reach the edge of the currently observable Universe, however fast you go."
http://casa.colorado.edu/~ajsh/sr/wheel.html