About this guide: This step-by-step walkthrough explores experimental temporal metrology through energy flux effects on clock-rate drift, focusing on quantum predictions using atom interferometry and optical clocks.
Step 1: What This Paper Is
The paper rewrites GR in "lapse-first" variables and proposes two clock-native observables: flux → redshift-drift template and visibility kernel.
Step 2: Key Equations
Core formulas including the flux-drift relation, visibility kernel, and statistical estimators for experimental analysis.
Step 3: What Data Is Analyzed
Overview of the experimental platforms and data sources used for testing temporal geometry predictions.
Step 4: Flux-Clock Duality
The fundamental connection between energy flux and clock rate changes in temporal geometry.
Step 5: Classical Flux Template
Deriving the classical relationship between energy flux and redshift drift with 1/r scaling.
Step 6: Semiclassical Interferometer
How quantum interferometry probes temporal fluctuations through phase accumulation.
Step 7: Visibility Kernel
The quantum visibility function that bounds temporal fluctuations from interferometer data.
Step 8: Statistical Estimator
Maximum likelihood estimators and variance calculations for flux parameter extraction.
Step 9: Newtonian Noise
Understanding and mitigating gravitational noise from local mass density fluctuations.
Step 10: Lab Platforms
Overview of experimental setups including optical clocks and atom interferometers.
Step 11: Frequency Stability Data
Analysis of clock stability measurements and Allan deviation characterization.
Step 12: Stellar Systems
Application to astrophysical sources including pulsars and binary systems.
Step 13: Visibility Bounds
Deriving experimental limits on temporal fluctuations from visibility measurements.
Step 14: Upper Limits
Current experimental constraints and future sensitivity projections.
Step 15: Null Tests
Control experiments and systematic checks to validate temporal signatures.
Step 16: Conservative Reach
Realistic assessment of experimental capabilities and detection prospects.
Step 17: Extensions
Future directions including multi-clock networks and cosmological applications.
Step 18: Why Clocks Matter
The fundamental role of time measurement in probing gravitational physics.
Step 19: Conclusion
Summary of experimental predictions and the path forward for temporal metrology.