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Anyone with a little ponder can find out the mankind cannot live on the earth forever.
There are a lot of threats for us on this planet: Global warming, probability of striking the space wandering masses to the earth, destruction of jungles, greenhouse gases, pollution of the environment, deathful illnesses, wars & WMDs, natural calamities & more cases. Therefore, the idea of leaving the earth to settle in some proper planets is reasonable, even necessary.
On the other hand, decreasing the population of the world via that way can solve many problems about scarcity of natural sources, fair distribution of the wealth, security & so on. So IMHO, colonizing other planets is a desired work to lessen the pressures on the earth. However, the question is: By which technology?
Now with an eye to cosmic distances measured by the speed of light in a year, it can be understood that every space travel in a plausible time should be comparable to the speed of light "c"; just think to the nearest star to us after sun, 4.28 light years away!
So more velocity in the space is needed, but stop! The final goal cannot be the final velocity!
The "c" is too tiny regarding the cosmic distances, the special relativity states more velocity causes inertia increasing / length decreasing effects.
Also, handling a spacecraft with high velocity amongst the interstellar dust, meteorites, wandering masses, asteroids & providing its propulsion fuel, is excessively difficult.
So absolute part of our attention has to be on the "distance reduction" instead; i.e., there is a locally simple displacement & the velocity of object is very less than c but the considered distance changes so that consequently would be less devoted time, finally in compared to a situation if a light pulse would be supposed to pass the same distance. In other words if we cannot change our velocity - never mind - but we change our course in which finally we arrive from the same origin to the same destination. There are several ideas on this scheme such as traversable wormholes (TWs) & warp drives (WDs); but there are problems in them, more than all the required energy to maintain them.
In the general relativity (GR), the distribution of matter-energy causes the configuration of spacetime & vice versa. It means the equations are nonlinear. Indeed, the TWs & WDs are particular configurations of spacetime one needs for transferring a spacecraft with a locally low velocity & velocity more than c effectively. Besides, the energy they need to be stable, has a negative sign, called the exotic matter, proposed to be generated in some ways, most famous of all by the Casimir effect ...
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