Mass-Energy Relation

The τ-Mass-Energy Relation (IV.D23) is the categorical identity that locks the Mass Index (IV.D11) and the Energy Index (IV.D21) via the speed-of-light constant in relational units. In τ, E = Mc² is not a postulated equivalence but a derived equality between two Quantity-Template invariants.

Categorical invariant. MassEnergy(B) := (Energy Index of B) = c² · (Mass Index of B); the Quantity-Template identity that pairs E and M on every defect bundle.

Primary registry anchor: IV.D23

Supporting items: IV.D11, IV.D21, IV.D293

1. I.K0 — Universe Postulate establishes τ
2. IV.D11 — Physical Quantity Template — Mass Index on every Particle Kind
3. IV.D21 — Energy Index — the dual quantity-template invariant
4. IV.D293 — Speed of light in relational units fixes the τ-internal conversion factor c
5. IV.D23 — Mass-Energy Relation: the categorical identity E = Mc² between the two invariants

Lean modules referenced: TauLib.BookIV.Physics.MassEnergy

Numerical value: 8.987551787e16 ± 0 J/kg → m²/s² (dimensional consistency of c²)

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor)
2. c (speed-of-light constant, IV.D293)
3. c² conversion factor

Manuscript reference: manuscript-sources/book-04/part01-foundations/ch-mass-energy.tex

Status: Formalized

Module: TauLib.BookIV.Physics.MassEnergy

Lean kind: theorem

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-Q01-mass Mass
• PG-Q02-energy Energy