Lunar and Terrestrial Time Transformation Based on the Principle of General Relativity

TL;DR

This paper derives a new, relativity-consistent transformation formula between lunar and terrestrial time, proposing a universal lunar time standard and analyzing its long-term variations based on Einstein's principles.

Contribution

It introduces a simplified, physically grounded formula for LTC to TT conversion using the Earth-Moon system, adhering to general relativity principles.

Findings

Derived a coordinate time transformation formula consistent with relativity.

Proposed a universal lunar time standard independent of Earth-based systems.

Identified long-term secular variation in the time transformation coefficient.

Abstract

Lunar time metrology necessitates a unified temporal framework beyond Earth, requiring an independent lunar system for timekeeping, dissemination, and calendrics. Recent American publications define Lunar Coordinate Time (LTC) within relativity and propose a Terrestrial Time (TT) to LTC conversion formula. However, this formula's derivation and assumptions are contested. The complex dynamics within the solar system can be simplified by decomposing relationships into hierarchical wide-area (external problem) and local-area (internal problem) levels. Grounded in the symmetry and conservation laws of physics, Einstein's general relativity emphasizes two key principles: (i) Equal weighting: Relationships among multi-level coordinate systems are independent and self-similar (analogous to fractals). (ii) *Locality*: The laws of physics retain invariant forms only in local coordinate systems. Specifically, a non-rotating system corresponds to the Frenet frame along a particle's geodesic. Preserving physical law invariance requires restricting rotating references strictly to the local domain; defining the orientation of an Earth-centered system using distant celestial bodies violates general relativity's locality principle. This work derives the relationship between coordinate time and proper time. Using the Earth-Moon system as an intermediary, it obtains a simplified transformation formula between LTC and TT. An independent and universal lunar standard time framework is proposed. Crucially, the derived coordinate time transformation coefficient exhibits long-term secular variation. This variation can be measured and predicted through precise Earth-Moon time comparisons.