Okay, first a little science. According to the Standard Model, there are only two types of elementary particles: fermions and bosons. Fermions are matter particles. They are the physical stuff of the universe. Bosons are force particles, and they’re responsible for phenomena such as light, gravity and magnetism. I’m aware this is a dramatic oversimplification, but the distinction between fermions and bosons is essentially the distinction between the material and the ethereal.
This is where the poetry comes in. Supersymmetry is a theoretical extension of the Standard Model that predicts a corresponding boson for every fermion and vice-versa. In other words, every matter particle has a corresponding force partner, and every force particle has a corresponding matter partner. Supersymmetry links them. It is an elegant scientific principle that poetically bridges the divide between the material and the ethereal.
The idea of supersymmetry is repeatedly invoked as a conceptual metaphor for what it’s like to still feel linked to someone who no longer exists ( i mean, in this dimension, of course). With one simple word, it encapsulates existential grief, one of the most powerful emotions in the human condition.
Simply put, it’s a reference to the concept of “soulmates”. This is the case in Spike Jonze’s „HER”. In the context of the film, Supersymmetry is a lament – a simple expression of the pain one feels after the loss of a loved one.