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Under the International System of Units, the second is currently defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K.
You would in fact travel these vast distances in less time than it would take the light to get there.
Consider a space ship going from Earth to the nearest star system a distance d = 4.45 light years away, at speed v = 0.866c (i.e., 86.6% of the speed of light). The round trip will take t = 2d / v = 10.28 years in Earth time (i.e. everybody on earth will be 10.28 years older when the ship returns). Ignoring the effects of the earth's rotation on its axis and around the sun (at speeds negligible compared to the speed of light), those on Earth predict the aging of the travellers during their trip as reduced by the factor \epsilon = \sqrt[1 - v^2/c^2], the inverse of the Lorentz factor. In this case ε = 0.5 and they expect the travellers to be 0.5×10.28 = 5.14 years older when they return.
The ship's crew members calculate how long the trip will take them. They know that the distant star system and the earth are moving relative to the ship at speed v during the trip, and in their rest frame the distance between the earth and the star system is εd = 0.5d = 2.23 light years ("length contraction"), for both the outward and return journeys. Each half of the journey takes 2.23 / v = 2.57 years, and the round trip takes 2×2.57 = 5.14 years. The crew arrives home having aged 5.14 years, just as those on Earth expected.
If a pair of twins were born on the day the ship left, and one went on the journey while the other stayed on earth, the twins will meet again when the traveller is 5.14 years old and the stay-at-home twin is 10.28 years old. This outcome is predicted by Einstein's special theory of relativity. It is a consequence of the experimentally verified phenomenon of time dilation, in which a moving clock is found to experience a reduced amount of proper time as determined by clocks synchronized with a stationary clock. Examples of the experimental evidence can be found at Experimental Confirmation of Time dilation.