According to general relativity theory (GRT), the clock at a position with lower geopotential ticks slower than an identical one at a position with higher geopotential. Here, we provide a geopotential comparison using a non-transportable hydrogen clock and a transportable hydrogen clock for altitude transmission based on the two-way satellite time and frequency transfer (TWSTFT) technique. First, we set one hydrogen clock on the fifth floor and another hydrogen clock on the ground floor, with their height difference of 22.8 m measured by tape, and compared the time difference between these two clocks by TWSTFT for 13 days. Then, we set both clocks on the ground floor and compared the time difference between the two clocks for seven days for zero-baseline calibration (synchronization). Based on the measured time difference between the two clocks at different floors, we obtained the height difference 28.0 $\pm$ 5.4 m, which coincides well with the tape-measured result. This experiment provides a method of height propagation using precise clocks based on the TWSTFT technique.

Applications of optical clocks in physical geodesy for determining geopotential are of increasing interest to scientists as the accuracy of optical clocks improves and the clock size becomes more and more compact. In this study, we propose a data processing method using the ensemble empirical mode decomposition technique to determine the geopotential difference between two sites in Wuhan based on the frequency comparison of two optical clocks. We use the frequency comparison record data of two Ca⁺ optical clocks based on the optical fiber frequency transfer method, provided by the Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences (Wuhan, China). By optical clock comparisons we obtained a geopotential difference of 42.50 ± 1.03 m²∙s⁻² (equivalent to height difference of 4.33 ± 0.11 m) between the two sites, which is excellent compared to the geopotential difference of 42.56 ± 0.29 m²∙s⁻² (equivalent to height difference of 4.34 ± 0.03 m) measured by a spirit leveling. The results show that the optical fiber frequency transfer method is promising in determining the geopotential and potential for unifying the world height system.

The Atomic Clock Ensemble in Space (ACES) mission, currently operating aboard the International Space Station (ISS), is designed to provide high-precision time and frequency measurements and to test fundamental aspects of relativistic physics. Gravitational redshift (GRS), a fundamental prediction of General Relativity (GR), implies that clocks positioned at different gravitational potentials experience relative time dilation. Previous GRS experiments have focused primarily on microwave technologies, with negligible experimental coverage in the optical domain, particularly for ground-to-space links. Motivated by the European Laser Timing (ELT) experiment and the high-precision laser-cooled cesium clock aboard ACES, we introduce and evaluate an optical time-transfer method designed to achieve high-accuracy measurements of GRS. In the absence of actual ELT/ACES optical data, a high-fidelity numerical simulation framework was developed to assess the performance of this method. The framework incorporates representative ELT/ACES mission parameters, including the space-based cesium clock and the H-MASER clock located at the reference ground station, both providing frequency stability at the level of ${10}^{-15}$ for 1000 s averaging time. Applying a $\pm 1\sigma$ filtering criterion, we obtain a simulated dataset comprising 33 ELT/ACES passes, representing a total observation time of 4.38 h over a single week. Analysis of this high-fidelity dataset reveals a GRS deviation from GR of $(-7.19\pm 0.63)\times {10}^{-5}$, achieving a 3.4 orders of magnitude improvement over the best previous laser-ranging experiment conducted at the University of Maryland (UMD), USA, 51 years ago. These simulation results demonstrate that the optical time-transfer link constitutes a powerful tool for testing fundamental physics and, when combined with next-generation optical atomic clocks, enables unprecedented capabilities in space-based timekeeping and geoscience applications.

Space-based atomic clocks provide unique conditions for testing General Relativity (GR) due to their stability in a low-disturbance environment and their exposure to significant variations in gravitational potential. Gravitational redshift (GRS), a direct consequence of the Einstein Equivalence Principle (EEP), causes clocks at different gravitational potentials to experience relative time dilation. Ground-to-space GRS experiments measure frequency shifts arising from differences in gravitational potential through signal exchange between ground and satellite clocks. While past experiments have relied on microwave links for time–frequency comparisons, optical time and frequency transfer has recently emerged as a promising alternative due to its immunity to ionospheric effects, reduced sensitivity to atmospheric delays, higher modulation bandwidth, and improved signal clarity. In this work, we investigate the GRS using ground-to-space observations from the Time Transfer by Laser Link (T2L2) experiment onboard the Jason-2 mission. Relative to the pioneering 1975 University of Maryland experiment, USA, the T2L2 mission achieves over an order-of-magnitude improvement in measurement precision, demonstrating the power of modern optical time transfer techniques. By comparing a ground-based hydrogen maser and a space-based ultra-stable quartz oscillator, with respective stabilities of $$10^{-15}$$ 10 - 15 and $$10^{-13}$$ 10 - 13 at 1000s, over 47 independent T2L2/Jason-2 passes (approximately 12 h total), we obtain a GRS deviation from GR of $$(-0.77 \pm 3.54) \times 10^{-3}$$ ( - 0.77 ± 3.54 ) × 10 - 3 . These results demonstrate that optical time-transfer links can achieve high-precision tests of GR, underscoring their potential for future space-based optical timing missions.

State-of-the-art atomic clocks, in combination with high-precision time-frequency transfer techniques, have established a novel relativistic geodetic approach for determining the Earth’s geopotential. By exploiting ultra-stable atomic clocks and GNSS Precise Point Positioning (PPP) time-frequency transfer, this study investigates the cross-sea Orthometric Height (OH) determination between two remote stations separated by over 8000 km, corresponding to an OH difference of approximately 2260 m. Simulation results indicate that, when employing clocks with a frequency stability of 1 × 10⁻¹⁸, the remote OH determination could achieve a limiting accuracy of approximately 20 cm. This limitation is primarily attributed to the finite precision of the PPP time-frequency transfer, which constrains the ultimate performance of the OH determination. Furthermore, aggregating multiple observation periods could further enhance the accuracy to approximately 6 cm. These findings demonstrate that the PPP time-frequency transfer facilitates high-precision OH determination over intercontinental distances and thereby provides a feasible pathway toward the realization of a centimeter-level International Height Reference System (IHRS).