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Because travelling in space even if your spaceship travel at speed of light, it takes many years before we can reach the nearest star in our own galaxy

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It is true if time is measured in the reference frame of the earth.

It is false if your measure time with the own clock of the travelers, and this is the most important point.

For the travelers, time t'=t*(1-vÂ²/cÂ²)^1/2 where t is time measured on earth. It is a well known formula from special relativity.

Imagine you want to go on Alpha Orionis at v=0.9999*c.

For an observer on earth, the travel will need around 420 years which is the distance between earth and Alpha Orionis.

For the travelers, do the math: the travel is done in about 6 years in their own time.

Of course if they return on earth, they will find it 840 years older! So such travels have to be made without the idea of coming back to see again people that we left.

The conclusion is that there is no theoretical limit for visiting all the universe. It is a false idea to believe that a travel to a star at x light-years takes at least x light-year. It can be almost instantaneous for travelers, presuming they travel at near the speed of light (at the limit, the light speed, time doesn't elapse). Thanks to Einstein.