Energy as CR-Tension
Energy as CR-Tension (IV.D76) is the τ-categorical operational form of the Energy Index: the integrated holomorphic strain (Cauchy-Riemann tension) that a defect bundle exerts against its embedding in the T² fiber. It is the local form of energy density and the bridge from the abstract Quantity Template to manuscript-level Hamiltonian formulas.
τ-Definition
Energy as CR-Tension (IV.D76) is the τ-categorical operational form of the Energy Index: the integrated holomorphic strain (Cauchy-Riemann tension) that a defect bundle exerts against its embedding in the T² fiber. It is the local form of energy density and the bridge from the abstract Quantity Template to manuscript-level Hamiltonian formulas.
Categorical invariant. E_CR(B) := ∫ |∂̄ Φ_B|² dvol on T² = the holomorphic-strain functional of the bundle's defining section Φ_B; equals Energy Index up to dimensional normalization.
Primary registry anchor:
IV.D76
τ-Derivation Chain
-
I.K0— Universe Postulate establishes τ -
IV.D21— Energy Index is the abstract energy quantity -
IV.D76— Energy as CR-Tension supplies the operational integral form: ∫ |∂̄ Φ|² -
IV.D77— Graph Energy Density is the local form (energy per τ-volume) -
IV.D274— Defect functional realizes E_CR for many-body / macroscopic states
Lean modules referenced:
TauLib.BookIV.Physics.DefectFunctional,
TauLib.BookIV.QuantumMechanics.EnergyEntropy
SI Translation
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- c² via IV.D23 → energy scale
- E_CR translates to J via the dimensional cascade
Manuscript reference: manuscript-sources/book-04/part04-quantum-mechanics/ch-cr-tension.tex
Lean Coverage
See Also
Related glossary entries
Referenced by
Cross-domain bridges
This glossary term sits on the boundary between domains. The τ-framework's cross-domain pivots are the structural junctions where physics, life, and metaphysics readouts meet.