Time and Space

Relating the standard deviation of time-error buildup, σ_t(T), at some time T after synchronization to a clock’s Allan deviation, σ_y(T), is problematic for several reasons. Notably, the stochastic integrals of various relevant noise types do not exist in closed form, and the standard deviation does not necessarily converge for the noise types of relevance for atomic clocks and crystal oscillators. Consequently, as an expedient, one often writes σ_t(T) = kσ_y(T)T, where k is a constant that depends on the noise type under consideration, as well as the statistical question of interest. Here, we consider the question of Clock Family Time-Error (CFTE) buildup and compute k for noise processes of relevance to atomic timekeeping in space. One of the interesting results of the present work is the k-value that we obtain for flicker frequency noise, which shows a dependence on the time after synchronization. Full article

The announcement of the KM3-230213A neutrino is generating a flood of astrophysics studies, mostly investigating its origin. We here focus on aspects of this observation that could be relevant for research programs on quantum gravity and spacetime quantization. It is at least amusing that KM3-230213A most likely traveled billions of light-years, but its rest-frame existence only lasted less than 0.1 seconds and ended with it being hit by a nucleon of Planckian energy. In addition, and perhaps more significantly, KM3-230213A is a remarkable probe of the types of microscopic structure of spacetime conjectured in some quantum-spacetime scenarios, and according to one of these scenarios, there is a candidate source: the gamma-ray burst GRB090401B observed 14 years earlier. Full article

As space systems evolve towards cis-lunar missions and beyond, the demand for precise yet low-size, -weight, and -power (SWaP) clocks and synchronization methods becomes increasingly critical. We introduce a novel clock synchronization approach based on the Kuramoto oscillator model that facilitates the creation of an ensemble timescale for satellite constellations. Unlike traditional ensembling algorithms, the proposed Kuramoto method leverages nearest-neighbor interactions to achieve collective synchronization. This method simplifies the communication architecture and data-sharing requirements, making it well suited for dynamically connected networks such as proliferated low Earth orbit (pLEO) and lunar or Martian constellations, where intersatellite links may frequently change. Through simulations incorporating realistic noise models for small-scale atomic clocks, we demonstrate that the Kuramoto ensemble can yield an improvement in stability on the order of 1/√N, while mitigating the impact of constellation fragmentation and defragmentation. The results indicate that the Kuramoto oscillator-based algorithm can potentially deliver performance comparable to established techniques like Equal Weights Frequency Averaging (EWFA), yet with enhanced scalability and resource efficiency critical for future spaceborne PNT and communication systems. Full article

This paper presents a theoretical framework modeling space-time as a quantized elastic medium. This elastic model is not intended to replace general relativity, but to offer a complementary mechanical interpretation in the approximation of the weak gravitational field. The goal is not to redefine gravity, but to explore whether this elastic formalism can simplify certain aspects of space-time dynamics, provide new insights, and generate falsifiable predictions—particularly in contexts where analytical solutions in general relativity are difficult to obtain. As originally envisaged by A. Sakharov, who associated general relativity with the concept of space-time behaving like an elastic medium, this paper introduces the notion of the “elasther” and reinterprets gravitational effects, time dilation, and phenomena commonly attributed to dark energy and dark matter through analogies with established mechanical principles such as Hooke’s law, thermal expansion, and creep. Full article

In vapor-cell atomic clocks, a buffer gas is employed to slow the collision rate of atoms with the vapor-cell’s walls, which dephases the atomic coherence and thereby contributes to the 0-0 hyperfine transition’s linewidth. However, the buffer gas also gives rise to a temperature-dependent pressure shift in the hyperfine transition, Δν_hfs. As a consequence, the clock’s frequency develops a temperature dependence, manifesting as a clock environmental sensitivity, which can degrade the clock’s long-term frequency stability. To mitigate this problem, it is routine to employ a buffer-gas mixture in a vapor cell. With an appropriate choice of buffer gases, d[Δν_hfs]/dT = 0 at a vapor temperature T_c, “zeroing out” the clock’s buffer-gas temperature sensitivity. Unfortunately, T_c depends on the exact mix of buffer-gas partial pressures, and if not properly achieved, T_c will be far from the vapor temperature that yields useful atomic clock signals, T_o. Therefore, understanding buffer-gas partial pressures in sealed vapor cells is crucial for optimizing a vapor cell clock’s performance, yet, to date, there have been no easy means for measuring buffer-gas partial pressures non-destructively in sealed glass vapor cells. Here, we demonstrate an optical technique that can accurately assess partial pressures in binary buffer-gas mixtures. Moreover, this technique is relatively simple and can be easily implemented. Full article

The instabilities in time and frequency transfer systems, a form of residual noise, can contribute significantly to the total uncertainty in time or frequency comparisons. Understanding the characteristics of transfer instabilities is increasingly important with the new high-stability optical frequency standards being developed. First-difference statistics such as the rms Time Interval Error (TIE_rms), the Frequency Transfer Uncertainty (FTU), and ADEVS (a novel use of the Allan deviation equation) provide a more direct and accurate measure of residual noise than second-difference statistics such as the Allan Deviation (ADEV), the Modified Allan Deviation (MDEV), and the Time Deviation (TDEV). A unifying discussion on the use of existing first-difference statistics with residual noise, introduced individually in two previous publications, is presented here. Simulated noise data is then analyzed to illustrate the differences in the various statistics. Their strengths and weaknesses are discussed. The impact of pre-averaging phase (time) data is also shown. Full article

In a purely Keplerian picture, the anomalistic, draconitic and sidereal orbital periods of a test particle orbiting a massive body coincide with each other. Such degeneracy is removed when post-Keplerian perturbing acceleration enters the equations of motion, yielding generally different corrections to the Keplerian period for the three aforementioned characteristic orbital timescales. They are analytically worked out in the case of the accelerations induced by the general relativistic post-Newtonian gravitoelectromagnetic fields and, to the Newtonian level, by the oblateness of the central body. The resulting expressions hold for completely general orbital configurations and spatial orientations of the spin axis of the primary. Astronomical systems characterized by extremely accurate measurements of orbital periods like transiting exoplanets and binary pulsars may offer potentially viable scenarios for measuring such post-Keplerian features of motion, at least in principle. As an example, the sidereal period of the brown dwarf WD1032 + 011 b is currently known with an uncertainty as small as ≃${10}^{-5}\mathrm{s}$, while its predicted post-Newtonian gravitoelectric correction amounts to $0.07\mathrm{s}$; however, the accuracy with which the Keplerian period can be calculated is just 572 s. For double pulsar PSR J0737–3039, the largest relativistic correction to the anomalistic period amounts to a few tenths of a second, given a measurement error of such a characteristic orbital timescale as small as $\simeq {10}^{-6}\mathrm{s}$. On the other hand, the Keplerian term can be currently calculated just to a $\simeq 9$ s accuracy. In principle, measuring at least two of the three characteristic orbital periods for the same system independently would cancel out their common Keplerian component, provided that their difference is taken into account. Full article