Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. M. C. Montanus, Phys. Essays 4, 350(1991); J. M. C. Montanus, Phys. Essays 6, 540 (1993); J. M. C. Montanus, Phys. Essays 10, 116, 666 (1997); J. M. C. Montanus, Phys. Essays 11, 280, 395 (1998); J. M. C. Montanus, Phys. Essays 12, 259 (1999).
J. M. C. Montanus, Hadr. J. 22, 625-673 (1999).
J. M. C. Montanus, Phys. Essays 10, 116-124 (1991).
S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper & Row, New York, 1964).
C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw–Hill, New York, 1985).
I. M. Gel'fand, R. A. Milnos, and Z. Ya. Shapiro, Representations of the Rotation and Lorentz Groups and their Applications (Pergamon, New York, 1963).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gersten, A. Euclidean Special Relativity. Foundations of Physics 33, 1237–1251 (2003). https://doi.org/10.1023/A:1025631125442
Issue Date:
DOI: https://doi.org/10.1023/A:1025631125442