quaternionia

Quaternionia is a hypothetical concept that explores the idea of a universe or dimension governed by quaternion algebra rather than the more familiar real or complex number systems. In such a reality, physical quantities and their interactions would be described using quaternions, which are four-dimensional number systems extending complex numbers. Unlike real numbers, which have one dimension, or complex numbers, which have two, quaternions introduce a fourth dimension with specific multiplication rules.

The fundamental properties of quaternion multiplication, particularly its non-commutative nature (the order of multiplication matters), would lead to fundamentally different physical laws. For instance, concepts like rotation in three-dimensional space are elegantly represented by quaternions, suggesting that if quaternionia were a physical reality, three-dimensional rotations might be the most natural geometric operation. The implications for physics could be profound, potentially altering our understanding of forces, energy, and spacetime itself.

While quaternionia remains purely speculative, it serves as a thought experiment in exploring the mathematical foundations of reality. Mathematicians and physicists sometimes use quaternion algebra in specific applications, such as in computer graphics and quantum mechanics, but the idea of a universe *entirely* based on quaternions is a theoretical construct. It highlights how different mathematical frameworks could, in principle, describe different kinds of universes with distinct physical characteristics. The concept encourages us to consider the possibility that the mathematical language we use to describe our universe might not be the only one capable of doing so.