Time and Space

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.

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.

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.