I probably have a fundamental misunderstanding, so correct me if I'm wrong.
When travelling close to the speed of light, movers experience time dilation, which is what results in the phenomenon of slower ageing in various thought experiments. If someone travels close to the speed of light, they will age slower than others, and will physically manifest itself in differing appearances. (Is this correct?)
This is down to relativistic effects, where everything boils down to frames of reference. So I'm confused as to why these ageing effects are observed:
Consider two people, $A$ and $B$. Person $A$ actually travels close to the speed of light, whilst person $B$ remains stationary. However, from person $A$'s reference frame, they are stationary whilst person $B$ travels at the speed of light, and vice versa. So why do they not both observe the other person ageing slowly, and thus observe no difference in experiencing time?
Please could you explain where I am misunderstanding?
