Underlying the study of physics is an implicit philosophical world view. In physics the accepted foundational basis for all understanding of the physical world is group theory. By casting the mathematical structure of group theory verbally via the use of a metaphor we unveil how the mathematics expresses that philosophical world view. In September of 1999 this paper was submitted to the British Journal for the Philosophy of Science and rejected. The revised version called "Is Symmetry Identity" was published in The concepts expressed in this exposition are explored visually as a drivable motion graphics tutorial at Physics As Symmetry |

MATHEMATICAL STRUCTURE OF IDENTITY

by Marvin Chester

email: chesterATphysicsDOTuclaDOTedu

ABSTRACT

The thesis: That the concept of *symmetry* and the concept of *identity * are operationally synonymous. The mathematical structure describing symmetry is group theory. Therefore this is
also the structure for identity.

The connection between symmetry and identity is uncovered via a metaphor which describes how group theory functions in its application to physical systems. The metaphor is *sameness under altered scrutiny*. We show that this phrase captures the underlying notion governing the mathematics. With it we build a verbal representation of how the theory functions in physics. In the process the connection between symmetry and identity emerges as do other aspects of the world view underlying physics.

1. The System and the Observer

3. The System Remains Inviolate

5. The Law of Intrinsic Sameness

6. Symmetry is apparent sameness under altered scrutiny

7. Identity resides in labels.

8. Measurables are observables

9. Altered scrutinies generate group representations

10. Irreducible representations yield identity labels.

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© m chester, August 1999, Occidental, CA