Observerse

The observerse is the central mathematical object in the Theory of Geometric Unity. It is a mapping from a four-dimensional manifold [math]\displaystyle{ X^4 }[/math] to a manifold [math]\displaystyle{ Y }[/math], which replaces Einstein's spacetime. There are four different constructions of the observerse: exogenous, bundle-theoretic, endogenous, and tautological. Each generates a possible Geometric Unity theory.

ExogenousEdit

In the observerse's exogenous construction, the manifold [math]\displaystyle{ X^4 }[/math] includes into any manifold [math]\displaystyle{ Y }[/math] of four dimensions or higher which can admit it as an immersion.

[math]\displaystyle{ X^4 \hookrightarrow Y }[/math]

Bundle-TheoreticEdit

In the observerse's bundle-theoretic construction, the manifold [math]\displaystyle{ Y }[/math] sits over [math]\displaystyle{ X^4 }[/math] as a fiber bundle.

 

EndogenousEdit

In the observerse's endogenous construction, [math]\displaystyle{ Y }[/math] is the space of metrics on the manifold [math]\displaystyle{ X^4 }[/math].

 

TautologicalEdit

In the observerse's tautological construction, the manifold [math]\displaystyle{ X^4 }[/math] equals [math]\displaystyle{ Y }[/math].

[math]\displaystyle{ X^4 = Y }[/math]