Abstract The theory termed ‘special relativity (SR) with a preferred frame’ incorporates the preferred frame into special relativity while retaining the fundamental space-time symmetry which, in the standard SR, manifests itself as Lorentz invariance. In this paper, the theory is extended to particle dynamics based on the concept of the ‘modified spacetime symmetry’ which allows to develop the theory along the lines of the standard relativity theory. The modified relativistic dynamics is applied to describing the interactions of the Ultra High Energy Cosmic Rays (UHECR) with universal diffuse background radiation and, in particular, to calculating the Greisen–Zatsepin–Kuzmin (GZK) threshold for the energy suppression due to pion photoproduction by UHECR protons. The result, that the GZK cutoff energy depends on the distance (cosmological redshift z) to the source of particles, may contribute to interpretation of the data on the mass composition of UHECR.

中文翻译：

---

相对论中的粒子动力学和 GZK 极限与首选框架

摘要 被称为“偏爱坐标系的狭义相对论（SR）”的理论将偏爱坐标系纳入狭义相对论，同时保留了在标准SR中表现为洛伦兹不变性的基本时空对称性。在本文中，该理论基于“修正时空对称性”的概念扩展到粒子动力学，这允许沿着标准相对论的路线发展该理论。修正的相对论动力学被应用于描述超高能宇宙射线 (UHECR) 与普遍漫射背景辐射的相互作用，特别是用于计算由 pion 光产生引起的能量抑制的 Greisen-Zatsepin-Kuzmin (GZK) 阈值由 UHECR 质子。结果，