Purpose: Use as an organizing 'principle' to serve as a backdrop to express the historical evolution of various models of space and time

Components:

- Primitive elements called 'events' with no further substructure, organized
into a set E

- Relations among the elements imposed, representing fundamental structures
such as distance which provide key distinguishing features of given a spacetime
model
Spacetime Models to be Surveyed:

- Aristotelian Spacetime

- Galilean Spacetime

- Newtonian Spacetime

Aristotelian Spacetime

Assumptions:

- there is a privileged set of events associated with the center of the earth

- this set of privileged events is identified with the state of rest

- the events at the center of the earth possess a preferred sequencing identified
with a forward orientied temporal sequence

So, time is an absolute element in Aristotelian Spacetime:

Center earth identified with absolute rest

Center of earth 'possesses' a universal clock

Cosmos is finite in extent...no events are defined outside

Time slices give times of other events referenced to the central universal clock

Galilean Spacetime

- Consider a world without gravity, so there is no necessity for acceleration

- Remove the assumption that the cosmos is finite with the earth at the center

the same in all directions at each point

=> concept of absolute place no longer valid

...consider two inertial observers who observe the spatial interval between two points A and B:

- let A move relative to B with speed v

- let B move relative to A with speed v

- We elevate such classes of observers to a privileged position: they are the class
of observers which move respect to each other with constant relative velocities...

The laws of nature (i.e. certain organizations of the set of events E) do not depend on the velocity of a given observer relative to another inertial observer

Relation between velocities:

v3|1 = v3|2 + v2|1