Gravitational Redshift

Author: Tianjiang Says

Reference: Li Y et al. 2026 Chin. Phys. Lett. 43 031101

Website: https://cislunarspace.cn

Definition

Gravitational redshift is a fundamental prediction of general relativity describing how light wavelength shifts toward the red (longer wavelength) end of the spectrum when moving from a stronger to a weaker gravitational field. In a static gravitational field, clocks located at different gravitational potentials will tick at different rates—the deeper the gravitational potential, the slower time passes.

Physics

Within the framework of general relativity, the relative frequency shift between two clocks at different gravitational potentials is proportional to the gravitational potential difference:

Δff=(1+α)ΔUc2\frac{\Delta f}{f} = (1 + \alpha) \frac{\Delta U}{c^2}

Where:

  • Δf/f\Delta f/f is the relative frequency shift
  • ΔU\Delta U is the gravitational potential difference
  • cc is the speed of light in vacuum
  • α\alpha is the violation parameter (should be zero if Local Position Invariance holds)

Gravitational redshift experiments constrain α\alpha to test the Einstein Equivalence Principle.

Historical Verification Experiments

ExperimentYearPrecisionNotes
Pound-Rebka-Snider1960s~1%Harvard ground experiment
Tokyo Skytree20201.4×10−51.4 \times 10^{-5}Strontium optical lattice clock
Gravity Probe A19761.41×10−41.41 \times 10^{-4}Spaceborne maser clock
Galileo Satellites20180.19×10−50.19 \times 10^{-5}Elliptical orbit modulation
DRO-A Satellite20258.74×10−38.74 \times 10^{-3}First cislunar DRO measurement

Advantages in Cislunar Space

Gravitational redshift measurements conducted in Distant Retrograde Orbits (DRO) in cislunar space offer unique advantages:

  1. Large gravitational potential difference: DROs at ~300,000-450,000 km from Earth produce gravitational potential differences of ∼6.8×10−10\sim 6.8 \times 10^{-10}, orders of magnitude larger than ground experiments

  2. Long-term orbital stability: DROs at the gravitational saddle point between Earth and Moon provide natural long-term dynamic stability, reducing orbit maintenance interference

  3. Minimal environmental interference: Cislunar space avoids Earth's magnetic field and atmospheric interference, enabling long-term continuous precision measurements

Relation to DRO-A Experiment

In April 2025, China's DRO-A satellite conducted the world's first gravitational redshift measurement in a lunar DRO using an onboard Passive Hydrogen Maser (PHM). The experiment employed K-band Dual One-Way Ranging (DOWR), achieving a result of (8.74±4.17)×10−3(8.74 \pm 4.17) \times 10^{-3}. This validated the feasibility of gravitational redshift measurements in cislunar space and laid the foundation for higher-precision fundamental physics tests.

References

  • Li Y, Liu T et al. 2026 Chin. Phys. Lett. 43 031101
  • Will C M 2014 Living Rev. Relativ. 17 4
  • Delva P et al. 2018 Phys. Rev. Lett. 121 231101
  • Herrmann S et al. 2018 Phys. Rev. Lett. 121 231102