Can white people become black and vice versa?

This is NOT a racist question.
Please read and reply seriously.

We all know that black people are black because they come from a sunny place on earth, or that their parents (forefathers) did.
White people are white because… it’s too fucking cold.

Even though we’re not (excluding the color) identical, can we be?
Black people tend to have bigger and wider noses.
White people tend to be scared of almost everything.
Yellow people tend to blink in pink. (according to my research – watching some japanese tv programs)

Now think about this.

This is a highly theoretical hypothesis, but what if the earth suddenly became even, climate wise. So that wherever you go, it’s always the same temperature, same weather, etc.

If man were to live in that homogeneous world,
would we all look alike with, say 10 generations, of time ?

Which brings me to my ultimate questions;

Can a white “blood-line” become black without having sex with blacks?

And, you guessed it, can a black “blood-line” become white without having sex with whites?

Also, what happends with the physical aspects of man?