Why do the two waves add up? Because the electric field only has a single value at any point in space. The equations that describe this are linear (ignoring qu

Why do the two waves add up? Because the electric field only has a single value at any point in space. The equations that describe this are linear (ignoring quantum stuff irerelevant at these scales), so the waves combine by simple addition. Why can't they just coexist? In a way, they do continue to coexist (again due to the linearity): For example, if two waves pass each other by, you get back the original waves once you leave the region of interference. And if they do add up, doesn't that mean that the atoms are piggyback riding on the light wave and essentially slowing it down which shouldn't be possible? Rather, the electrons around the atoms start wiggling around, making new waves. I wonder if one could set up a mechanical analogue by putting some floating balls in a pool and attaching them to the bottom so that they breach the surface if a wave passes through, creating new waves...