The Observer Lemma

The Observer Lemma

Lorentz structure forced by the mathematical restrictions of physical observation

Virgil Vail Waters II - VMS Institute - 2026

Abstract

Observation is performed using light or its physical equivalent. Light is also what is being

observed. Lorentz worked with fields, mathematically inheriting the limitations of field-based

assumptions; treating light as a physical object forces the same transformations from geometry

alone.

Light itself propagates as a finite physical boundary that defines the act of observation.

When inertial frames are related by linear reciprocal transformations, the requirement that this

boundary propagate consistently in all frames forces a single invariant speed and a specific

coupling between space and time.

From these constraints, the Lorentz transformation follows. A finite invariant boundary volume

then fixes how spatial dimensions scale under relative motion. No spacetime metric, invariant

interval, clock construction, nor postulated symmetry is assumed.

Lorentz transformations are not assumed but mathematically derived from these requirements.

Promoting it to theorem from a dangling assumption