Latticework

In the context of Spacetime Physics (Taylor and Wheeler), a latticework is equivalent to a "team of observers", and this construction represents a physical implementation of a coordinate system often used to interpret the mathematics of General Relativity (GR).

The Latticework as a "Team of Observers"

The book defines a latticework as a "work of the imagination" consisting of an assembly of clocks and meter sticks. In relativity, the term "observer" is specifically defined as a shorthand for the entire collection of recording clocks associated with one reference frame.

• Each clock in the lattice is viewed as a local witness that records events in its immediate vicinity.
• The set of these clocks forms a "team" or "congruence" where each individual clock follows a specific path (worldline) through spacetime.
• Holding the spatial coordinates $(x,y,z)$ constant in the lattice effectively defines the path of one hypothetical observer in that team.

A Particular Case of coordinate systems in GR

A coordinate system is mathematically just a set of arbitrary labels with no inherent physical meaning. However, the "team of observers" (the latticework) is a particular case where coordinates are adapted to a physical perspective:

• The time coordinate ($x^0$) represents the labels on the synchronized clocks in the team.
• The spatial coordinates ($x^1,x^2,x^3$) act as "comoving" labels that identify each specific observer within the team.
• While any set of numbers can be a coordinate system, the latticework represents a "regimented" way to map those numbers to physical measurements like proper time and distance.