Emergent Spacetime and Geometry from Order

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The fact that in physics concepts such as space, time, mass and energy are considered to be foundational has been conveniently serving a set of higher-level physical theories.

However, this keeps us from gaining a deeper understanding of such concepts which can in turn help us build a theory based on truly foundational concepts.

In this talk I introduce an alternate description of physical reality based on a simple foundational concept that there exist things that influence one another.

A network of objects that influence one another form a partially-ordered set (poset) that is called the influence network is considered. By consistently quantifying such a network with respect to a distinguished chain of events that is called an embedded observer, I demonstrate in relevant special cases that influence events can only be quantified by the familiar mathematics of space-time (Minkowski metric and Lorentz transformations), influence gives rise to basic concepts in Euclidean geometry such as direction, dimension and subspaces as well as the Pythagorean theorem, the dot product and geometrical figures. Thus a discrete version of some of the Euclidean geometry’s fundamental concepts is derived in this picture. Finally I talk about the concept of influence in quantum mechanics and how the case of a free particle is identical to the Feynman checkerboard problem for the electron which is known to give rise to the Dirac equation.