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Why Is Minkowski Spacetime Non-Euclidean?



J M. Cronkhite


The geometry of Minkowski spacetime is pseudo-Euclidean, thanks to the time component term being negative in the expression for the four dimensional interval. This fact renders spacetime geometry unintuitive and extremely difficult to visualize. I present here a truly Euclidean approach to spactetime that both allows the geometry to be visualized and makes many features of special relativity readily apparent. By recognizing that some aspects of spacetime are Euclidean, we can compare those that are with those that are not to illuminate how the peculiarities of time relative to the three spatial dimensions forces the time dimension into its pseudo-Euclidean position. This approach should be helpful to students struggling with relativity for the first time, and of interest to advanced students who take an interest in the fundamental structure of spacetime.
American Journal of Physics


Lorentz transformation, Minkowski, spacetime, special relativity, velocity transformation


Cronkhite, J. (2008), Why Is Minkowski Spacetime Non-Euclidean?, American Journal of Physics (Accessed April 15, 2024)
Created October 16, 2008