Derivation of the Lorentz Transformations for Three-Dimensional Relative Motion Between Inertial Frames of Reference

Chandra Bahadur Khadka

Advances in Mathematical Physics, 2025, vol. 2025, 1-25

Abstract: Lorentz transformations are central to relativistic mechanics, explaining phenomena such as the mass–energy relationship, spatial contraction, momentum transformation, velocity addition, and the geometric structure of Minkowski space-time. While traditionally derived for motion along a single spatial axis, these transformations can be generalized to three-dimensional space for greater applicability. In this article, we derive the Lorentz transformation equations for inertial frames in arbitrary three-dimensional relative motion. The resulting formalism provides a more symmetric and generalized framework, facilitating deeper insight into relativistic kinematics. Additionally, we introduce the concept of a position six-vector, comprising three spatial and three temporal components, which we employ to reformulate the Lorentz transformations, the d’Alembert operator, and the charge continuity equation within a six-dimensional space-time framework.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/amp/2025/5591426.pdf (application/pdf)
http://downloads.hindawi.com/journals/amp/2025/5591426.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:5591426

DOI: 10.1155/admp/5591426

Access Statistics for this article

More articles in Advances in Mathematical Physics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().