The first edition of *New Foundations for Classical Mechanics* (1986) by David Hestenes included “Foundations of Mechanics” as Chapter 9. This was removed for lack of space in the second edition, but is available online as a pdf *here*. This space-time foundation may serve as a guide for the foundation of mechanics for either space-time or time-space. To do so requires introducing abstract terminology, notably:

position space → position geometry; time → event order; particle → point body; instant → point event; clock → event order indicator; simultaneity → correspondence; reference frame → frame.

The application of this abstract theory is to interpret the 3D position geometry with event order as either 3D position space with temporal event order (space-time) or 3D position time with spatial event order (time-space). It could also be applied to derivatives or integrals of these, e.g., a velocity space.

Let’s focus on section 2 “The Zeroth Law of Physics” and start with the second paragraph on page 8, revising it for 3D space or 3D time:

To begin with, we recognize two kinds of bodies, *point bodies *and *bodies *which are composed of point bodies. Given a body *R *called a *frame*, each point body has a geometrical property called *its position with respect to **R*. We characterize this property indirectly by introducing the concept of *3D Position Geometry*, or *Relative Geometry*, if you prefer. **For each frame ***R*, **a position geometry ***P ***is defined by the following postulates:**

*P***is a 3-dimensional Euclidean geometry**.**The position (with respect to***R***) of any point body can be represented as a point in***P*.

The first postulate specifies the mathematical structure of a 3D position geometry while the second postulate supplies it with a physical interpretation. Thus, the postulates define a physical law, for the mathematical structure implies geometrical relations among the positions of distinct point bodies. Let us call it the **Law of Geometric Order**.