ABSTRACT
In quantum theory, a particle is allowed to be in a state of coherent superposition among a set of orthogonal states. A vivid picture of this concept is the “Schrödinger cat”: a cat is alive and dead simultaneously. This would be no surprise if one means a large number of an ensemble of cats with 50% alive and 50% dead. But, “Schrödinger cat” is a cat. People are talking about a cat being alive and dead simultaneously. In mathematics, the best word to characterize the relationship between states “alive” and “dead” is perhaps “orthogonal”. In quantum mechanics, the superposition of orthogonal states is used to describe the state of a quantum object, or a particle. The superposition principle is indeed a mystery compared to our everyday classical life experience. Beyond the superposition of orthogonal single-particle states, the superposition of orthogonal multi-particle states represents an even more troubling concept in classical theory.
