## The Formulation and Interpretation of the Lorentz Transformation

**Authors:** Per Hokstad

Abstract. The Lorentz transformation of the special theory of relativity (STR) describes the time dilation between two reference frames moving relative to each other at a constant speed. The present work focuses on the fact that the time observed on the ‘other’ system depends on the location of the clocks used for time comparisons. First, the paper presents a unified framework for the various ‘observational principles’, i.e. the specification of which clocks to apply; throughout restricting to consider a single space coordinate. Next we suggest that the time can be defined by a two-dimensional variables, involving both ‘clock time’ and position. This two-dimensional (time, space)-vector intends to alleviate the inherent paradox of time dilation. One suggestion is to formulate this vector as a complex number. Here both the absolute value, as well as the real and imaginary part have simple interpretations. The real part is denoted ‘positional time’ and is actually invariant under the Lorentz transformation. The paper also includes a discussion of the travelling twin example.

**Comments:** 14 Pages.

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### Submission history

[v1] 2017-03-29 16:05:39

[v2] 2017-03-30 13:36:25

[v3] 2017-04-06 15:02:35

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