Events
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
...later...Minkowskian...Riemannian...
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
=> universe assumed infinite and
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 concept of absolute place no longer valid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
These two situations can't be different in a world without preferred places
- 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...
Principle of Galilean Relativity:
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
