International Journal on Science and Technology

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The Mathematics of Space-Time

Author(s) Mr. Abhishek Ramesh Chavan
Country India
Abstract Space and time are fundamental quantities used to describe events and physical processes in the universe. In classical mechanics, space and time are generally treated as independent quantities. The theory of special relativity, however, provides a mathematical framework in which space and time are combined into a four-dimensional structure known as space-time. The present study examines the mathematical foundations of space-time with particular emphasis on four-dimensional coordinates, the space-time interval, Minkowski space, the light cone, and Lorentz transformations. A numerical analysis of the Lorentz factor is carried out for different values of relative velocity. The study shows that the Lorentz factor remains close to unity at low velocities but increases rapidly as the velocity approaches the speed of light. The mathematical behaviour of time and spatial coordinates under Lorentz transformations is also examined, along with a brief discussion of real-world applications such as satellite-based navigation. The analysis demonstrates that the geometry of space-time provides a consistent mathematical description of relativistic motion and establishes the importance of invariants and coordinate transformations in modern mathematical physics. The study concludes that mathematics provides a powerful framework for understanding the structure of space-time and selected relativistic properties of the universe.
Keywords Space-time, Special Relativity, Minkowski Space, Light Cone, Lorentz Transformation, Lorentz Factor, Spacetime Interval, Mathematical Analysis, Universe.
Field Mathematics
Published In Volume 15, Issue 3, July-September 2024
Published On 2024-09-25
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Crossref DOI prefix of IJSAT is 10.71097/IJSAT

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