The scenario you're describing is a consequence of the theory of special relativity, specifically the relativity of simultaneity and time dilation effects. Let's break it down to understand how it can be physically possible.
According to the theory of special relativity, as an object approaches the speed of light, two important phenomena occur: time dilation and length contraction. Time dilation states that time appears to pass more slowly for a moving object relative to a stationary observer. Length contraction, on the other hand, suggests that objects in motion appear shorter in the direction of their motion.
In the case of a spaceship traveling at close to the speed of light, let's say it's moving at 0.99 times the speed of light. From the perspective of an observer on Earth, the spaceship's clocks will appear to run slower, and time will appear to pass more slowly on board the spaceship. This is time dilation.
Now, if the spaceship is located 1 light-year away from Earth when it starts its journey, the observer on Earth will see the light from the spaceship take 1 year to reach Earth. However, due to the effects of time dilation, the clocks on board the spaceship will appear to run slower relative to Earth. As a result, the spaceship will experience less elapsed time compared to the observer on Earth.
When the spaceship reaches its destination, let's say Proxima Centauri, according to the observer on Earth, it would have taken many years for the journey to be completed. However, from the perspective of the astronauts on board the spaceship, due to time dilation, they would have experienced a significantly shorter duration of time.
To address the apparent contradiction you mentioned, where the spaceship says we are 1 year in the future, it's essential to understand that simultaneity is relative. The concept of "now" is subjective and depends on the reference frame of the observer. The spaceship's frame of reference is different from that of the observer on Earth, so their perceptions of time and simultaneity differ.
In summary, the effects of time dilation and the relativity of simultaneity, as described by the theory of special relativity, lead to different perceptions of time and the ordering of events between observers in different reference frames. It is this relativistic nature of time and simultaneity that allows for such apparent paradoxes and differences in the perception of time between observers in relative motion.