A Causal Response Filter Presentation.pdf

A Causal Response Filter Presentation.pdf

• 1.
  Causal Response Filtering (CRF) AnIntegrated Framework for Vacuum Energy and Gravity
• 2.
  Motivation • QFT oncurved spacetime predicts enormous vacuum energy contributions. • Standard renormalization absorbs divergences into local counterterms. • Problem: Why do these local terms not gravitate dynamically? • CRF: Only causal, state-dependent parts of the effective action source geometry.
• 3.
  CTP Effective Actionand Filtering • CTP splits effective action into local and nonlocal parts. • Local terms → absorbed as constants (integration constants). • Nonlocal retarded kernels → dynamical backreaction. • Auxiliary constraint ensures only causal response enters Einstein equations.
• 4.
  Physical Justification • Equivalenceprinciple: constant energy is locally unobservable. • Thermodynamic analogy: only retarded response governs macroscopic dynamics. • Operator structure: commutators drive causal response.
• 5.
  Worked Examples • Minkowski:quartic divergences demoted; running couplings preserved. • FRW cosmology: removes threshold jumps; predicts global constant C. • Black holes: exterior GR intact; possible interior softening (no echoes).
• 6.
  Testable Predictions • Nothreshold kinks in H(z). • Small nonlocal corrections to growth and slip (≈ 10^-4 on horizon scales). • Casimir energy gravitates normally with E/ c^2. • No black-hole echoes; exterior Schwarzschild/Kerr unchanged.
• 7.
  Comparisons with OtherFrameworks • Unimodular gravity: cosmological constant as integration constant; CRF generalizes to all local terms. • Vacuum sequestering: global variables/4- forms; CRF embedded in CTP with causal selection. • Asymptotic safety / holography: complementary consistency principle at low energies.
• 8.
  Scope and OpenIssues • Rigorous in perturbative EFT; nonperturbative effects remain to be worked out. • Origin of the auxiliary constraint (e.g., 4- form/topological sector) needs clearer derivation. • Compute explicit retarded loop corrections for cosmology (μ(k,a), η(k,a), ISW).
• 9.
  Conclusion • CRF eliminatescatastrophic vacuum energy locally while preserving causal backreaction. • Framework is technically precise and falsifiable. • Clear observational targets: leakage bounds, scale-dependent growth/slip, Casimir gravitation, BH phenomenology.