Energy

Energy is the τ-categorical Energy Index (IV.D21): a dimensional invariant assigned to every τ-state that measures the integrated CR-tension carried by its defect configuration. It is the dual partner of mass under the τ-mass-energy relation and the natural pairing of the dimensional-load functional with τ-time.

Categorical invariant. Energy(B) := Energy Index of the defect-bundle B; an E1 invariant on every Particle Kind / τ-state, equal to ⟨dimensional-load, τ-time⟩.

Primary registry anchor: IV.D21

Supporting items: IV.D11, IV.D23, IV.D76, IV.D274

1. I.K0 — Universe Postulate establishes τ
2. IV.D11 — Physical Quantity Template assigns dimensional invariants to τ-states
3. IV.D21 — Energy Index — the energy-axis quantity in the Quantity Template
4. IV.D76 — Energy as CR-Tension identifies the operational form: integrated holomorphic strain of the defect configuration
5. IV.D23 — Mass-Energy Relation locks Energy to Mass via the τ-categorical equation E = M c²

Lean modules referenced: TauLib.BookIV.Physics.MassEnergy, TauLib.BookIV.QuantumMechanics.EnergyEntropy

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor)
2. c (speed-of-light constant in relational units, IV.D293)
3. E = m c² via IV.D23

Manuscript reference: manuscript-sources/book-04/part04-quantum-mechanics/ch-energy-entropy.tex

Status: Formalized

Module: TauLib.BookIV.Physics.MassEnergy

Lean kind: def

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-Q01-mass Mass

Referenced by

• PG-Q03-mass-energy-relation Mass-Energy Relation
• PG-Q04-entropy Entropy
• PG-Q05-enthalpy Enthalpy
• PG-Q06-temperature Temperature
• PG-Q09-frequency Frequency
• PG-Q13-energy-cr-tension Energy as CR-Tension
• PG-Q14-graph-energy-density Graph Energy Density
• PG-Q17-force-as-boundary-mode Force as Boundary Mode
• PG-Q19-action-space Action (Crossing-Point Action Space)
• PG-Q22-vacuum-energy Vacuum Energy