Reality error and relative velocity

Suppose a person is walking in rain carrying an umbrella. He is tilting his umbrella at some angle with the vertical so as to protect himself from the rain. But a neutral observer who is standing still will find it really absurd because he will find the rain falling vertically downward, how come there are two realities for the same event?

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Natural next question: physics.stackexchange.com/q/19499/2451 – Qmechanic Feb 28 '13 at 16:17

From his point of view, the man walking in the rain sees raindrops falling along a line that makes an angle $\theta$ such that $\tan \theta = v_M/v_r$, with $v_M=$speed of the man, $v_r=$(constant) speed of raindrops. That's why he tilts the umbrella at the same angle. On the other hand, from the neutral observer point of view, it's true that the raindrops fall vertically, but is also true the man is moving horizontally: he is escaping from raindrops falling directly from a point above him. I think you can have a good intuition of this by thinking of two points moving in perpendicular directions, the second towards the first at $t=0$: it's clear that it won't hit the first point.