Kinematic Spaces and De Vries Algebras: towards Possible Physical Meaning of De Vries Algebras

Traditionally, in physics, space-times are described by (pseudo-)Riemann spaces, i.e., by smooth manifolds with a tensor metric field. However, in several physically interesting situations smoothness is violated: near the Big Bang, at the black holes, and on the microlevel, when we take into account quantum effects. In all these situations, what remains is causality – an ordering relation. To describe such situations, in the 1960s, geometers H. Busemann and R. Pimenov and physicists E. Kronheimer and R. Penrose developed a theory of kinematic spaces. Originally, kinematic spaces were formulated as topological ordered spaces, but it turned out that kinematic spaces allow an equivalent purely algebraic description as sets with two related orders: causality and “kinematic" causality (possibility to influence by particles with non-zero mass, particles that travel with speed smaller than the speed of light). In this paper, we analyze the relation between kinematic spaces and de Vries algebras – another mathematical object with two similarly related orders.