Polarized glasses solution

See the puzzle first

Polarized lenses can come in all directions, not just vertical and horizontal. For example, you can rotate a vertical filter 45 degrees, and get a diagonally polarized lens. For the 3D glasses to work, it is not necessary that the two lenses be horizontally and vertically polarized. They could also both be diagonally polarized. The difference between these two cases is best demonstrated with some illustrations.

Click to see picture

In this drawing, I represented the polarized lenses with lines indicating the orientation of the polarization. The left side represents the case in which the lenses are horizontally and vertically polarized. The right side represents the case in which the lenses are diagonally polarized. The glasses on the bottom are the ones you're wearing, and the ones on top are the ones your neighbor is wearing.

So let's say you close your right eye. In the case on the left, you can see your neighbor's left eye (which is on your right). In the case on the right, you can see your neighbor's right eye. Based on my description in my puzzle, you can conclude that the glasses are diagonally polarized, despite my suggestions otherwise.