New four coordinates are introduced which are related to the usual space-time coordinates. For these coordinates, the Euclidean four-dimensional length squared is equal to the interval squared of the Minkowski space. The Lorentz transformation, for the new coordinates, becomes an SO(4) rotation. New scalars (invariants) are derived. A second approach to the Lorentz transformation is presented. A mixed space is generated by interchanging the notion of time and proper time in inertial frames. Within this approach the Lorentz transformation is a 4-dimensional rotation in an Euclidean space, leading to new possibilities and applications.
CITATION STYLE
Gersten, A. (2003). Euclidean special relativity. In Foundations of Physics (Vol. 33, pp. 1237–1251). Springer Netherlands. https://doi.org/10.1023/A:1025631125442
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