A. Nontechnical Introduction. Plato’s cave and representation.

B. Technical Introduction and Summary.

Current quantum mechanics has a group representational form. This implies there is an underlying nonrepresentational form of the theory.

C. The Basics of Representation Theory.

1. The invariance group. Labeling solutions.

2. Representation theory in quantum mechanics.

D. General Form of the Underlying Theory.

1. An equation in currently unknown independent variables.

2. Space and Time.

3. The variational principle.

E. Example of an Underlying Theory.

1. The single particle partial differential equation in complex variables.

2. Symmetry operations.

3. Particlelike solutions.

4. An equation with interactions.

F. Spin ½ Particlelike Basis Vectors. A four-fermion SU(6) model.

1. Spin ½ basis functions.

2. An invariant molecular vacuum.

3. A broken SU(6) standard model-like vacuum.

4. Vector bosons.

5. Physical spin ½ states—quarks, electrons, neutrinos.

G. Gauge Theory.

1. Yang-Mills theory.

2. Speculation on gauge theory.

H. Details of an SU(6) Theory. (Under construction)

I. Highly Speculative Gravitational Conjecture. (Incomplete)

Concentrations of matter cause small changes in the structure of the vacuum.