Einstein Equivalence Principle (EEP)

Author: Tianjiang Says

Reference: Li Y et al. 2026 Chin. Phys. Lett. 43 031101, Will C M 2014 Living Rev. Relativ. 17 4

Website: https://cislunarspace.cn

Definition

The Einstein Equivalence Principle (EEP) is the cornerstone of general relativity and the key framework for testing GR's validity. EEP states: within any freely-falling local reference frame in any gravitational field, the laws of non-gravitational physics have exactly the same form as in the absence of gravity.

EEP contains three sub-principles, each constraining the gravitational invariance of physical laws from different perspectives.

Three Sub-Principles

Weak Equivalence Principle (WEP)

The Weak Equivalence Principle is the most classical statement of equivalence, also known as "inertial mass equals gravitational mass":

All objects accelerate identically in a gravitational field, independent of their composition and structure.

Mathematically: mimg=1\frac{m_i}{m_g} = 1

WEP verification experiments include:

  • Free fall experiments since Newton's era
  • Eötvös torsion balance experiments
  • MICROSCOPE satellite (precision reaching 10−1510^{-15})

Local Lorentz Invariance (LLI)

Local Lorentz Invariance states:

In the local inertial frame at any spacetime point, the expressions of all non-gravitational physical laws are independent of the reference frame's velocity.

LLI verification typically involves comparing oscillator frequencies of atomic clocks with different spin orientations.

Local Position Invariance (LPI)

Local Position Invariance is the sub-principle most directly related to gravitational redshift:

In a freely-falling local reference frame, the results of any non-gravitational experiment are independent of when and where in spacetime the experiment is performed.

The core meaning of LPI is that fundamental physical constants (such as fine structure constant α\alpha, electron-proton mass ratio me/mpm_e/m_p, etc.) do not depend on gravitational potential. Gravitational redshift experiments test this assumption by constraining LPI.

Mathematical Formulation of LPI

The relationship between gravitational redshift and LPI is described by introducing a violation parameter α\alpha:

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 between two clocks
  • ΔU\Delta U is the gravitational potential difference
  • cc is the speed of light
  • α\alpha is the LPI violation parameter

If LPI holds, then α=0\alpha = 0; if LPI is violated, α\alpha deviates from zero.

Testing Status of Sub-Principles

Sub-PrincipleTesting PrecisionRepresentative Experiment
WEP10−1510^{-15}MICROSCOPE satellite
LLI10−2210^{-22}Atomic clock comparison
LPI10−510^{-5}Galileo satellite gravitational redshift

Currently, LPI is the least rigorously tested sub-principle of EEP, which is why gravitational redshift experiments continue to receive attention.

Relation to Gravitational Redshift Measurements

Gravitational redshift experiments are the primary means of testing LPI. By measuring the frequency difference between clocks at different gravitational potentials, one can constrain the LPI violation parameter α\alpha.

Historically significant gravitational redshift experiments:

  1. Pound-Rebka-Snider (1960s): Ground experiment, precision ~1%
  2. Gravity Probe A (1976): Space maser clock, precision 1.41×10−41.41 \times 10^{-4}
  3. Galileo Satellites (2018): Elliptical orbit modulation, precision 0.19×10−50.19 \times 10^{-5}
  4. DRO-A Satellite (2025): First cislunar DRO measurement, precision 8.74×10−38.74 \times 10^{-3}

Future Prospects for Cislunar Measurements

The unique environment of cislunar space provides new opportunities for LPI testing:

  1. Larger gravitational potential difference: DRO gravitational potential difference (∼6.8×10−10\sim 6.8 \times 10^{-10}) is orders of magnitude larger than ground experiments
  2. Longer observation time: DRO orbits are stable, enabling long-term continuous observation
  3. Higher precision atomic clocks: With clocks achieving 10−1610^{-16} accuracy, precision could reach 10−610^{-6}

References

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