Even if a galaxy is 10 million light-years away, you can get to it in 1 month of proper (spaceship) time, if you travel fast enough. This is time dilation due to special relativity.
By close to light speed I meant maybe 50%. You are right if you get much closer, but there are some huge problems you get too… like having the cosmic microwave background blue shifted into gamma rays or the fact that a dust particle will annihilate you.
I have wondered about the Alcubierre drive and similar concepts. Even if FTL is impossible due to causality protection principle issues, these may provide a theoretical way to travel at light speed (effectively) without the above issues. But we are talking very far future tech with outrageous energy requirements… if it is possible at all.
>like having the cosmic microwave background blue shifted into gamma rays
This is patently false.
It is indeed true that a relativistic spacecraft would see a highly anisotropic microwave background: a strong blueshift in the direction of travel, a strong redshift in the opposite direction.
But at 99.5% of the speed of light, the blueshift factor is only about 20. This would shift the 2.7 K microwave background to a temperature of about 54 K; that is still pretty darn cold.
But the example being replied to was going from 10 million years to 1 month, that’s γ = 1.2e8, so β ≈ 1 - (3.4e-17), so blueshift factor ≈ 2.4e8.
I think that means the wavelength goes from 2.7 K ≈ 1.07mm to 4.46pm. Is a blackbody spectrum still a blackbody under Lorentz transform? If so, 650 million K?
Kind of yes but also not really. The important thing is that the laws of physics are measured the same in all inertial reference frames. Consequently there is no non-contradictory sense in which an experiment could distinguish an absolute rest from other inertial motion. It's therefore not possible to talk about motion under constant velocity in an absolute sense, it must always be in relation to something else.
Any other body could have been chosen as a (relative) rest frame but the CMB is uniquely convenient to coordinate measurements with due to its age and the extent which it permeates the universe. Physics is still the same in that frame as any other inertial frame.
In the Earth time, the spaceship would take a bit longer than 10m years to reach it, however. Plus the energy required to reach such velocity would probably be more than mass of the Earth if we were to annihilate it.
Well, accelerating a 100 ton spaceship to 0.99c (assuming some sort of beamed propulsion) requires only 2000 Terawattyears [1].
Of course, to turn 1e6 years into 1 year relative time, one needs like 0.99999999c, one needs 2 million Terawatt years [2], which is a much bigger energy investment, but still not on the order of annihilating the planet.
Breaking is gonna be a bitch tho.
[1] 100000 kg * (0.99 * c)^2 / sqrt(1-.99^2) in Terawatt Years
[2] 100000 kg * ( 0.99999999 * c)^2 / sqrt(1-0.99999999^2) in Terawatt Years