A Note On Mass–Energy Equivalence as a Zero Set of Deviation

The relation E = mc² is often presented as if mass were an independent primitivequantity. In special relativity the primitive object is the four-momentum, the invariantmass is derived from it, and E = mc² is the special case of zero momentum. We recallthis structure and express the equivalence as the vanishing of a deviation parameter,in the notation of the Zulfia identity: ε = 0 if and only if the rest energy equals mc2.Three points describe the note:• Invariant mass is a function of the four-momentum, with E² = (pc)² + (mc²)²,and E = mc² holds exactly when p = 0;• The deviation ε = 1 − ∆m c²/E is a test parameter, with the sign of ε giving thedirection of any violation;• The most precise direct measurement, of Rainville et al. (2005), gives ε = (−1.4±4.4) × 10−7, consistent with zero.We expresses the equivalence as the vanishing of a deviation parameter ε, the notationof the Zulfia identity [4], in which an assumption is the zero set of a deviation mapwith a magnitude and a direction.