According to the theory of relativity, time dilation occurs when an object moves at relativistic speeds relative to another object. This means that observers in different frames of reference will measure different elapsed times. Let's analyze the scenario you presented:
From B's perspective (on Earth), A is traveling in a rocket at 86.6% of the speed of light. Due to time dilation, B observes that A's time slows down compared to B's own time. This means that when A returns to Earth after 10 seconds of their own experience, B will have experienced a longer time period.
From A's perspective (inside the rocket), A is at rest, and it is B who is moving away at 86.6% of the speed of light. Therefore, A perceives that B's time is dilated, meaning B's time is slowed down compared to A's own time.
The key here is that when A returns to Earth, there needs to be a comparison of the elapsed times between A and B. If A and B were to synchronize their clocks at the start and then compare their elapsed times at the end, they would find that A has experienced less time compared to B. This is known as the twin paradox, where one twin (A) experiences less time due to their motion at high speeds while the other twin (B) remains relatively stationary on Earth.
So, in summary, A can "travel into the future" relative to B because their different frames of reference and relative velocities cause time dilation, resulting in different elapsed times for A and B.