Universal Journal of Physics and Application Vol. 16(2), pp. 11 - 24
DOI: 10.13189/ujpa.2022.160201
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Relativistic Polygonal and Circular Paths: Solution for the Twins' Paradox Reviewed and Extended

Luís Dias Ferreira ^*
Colégio Valsassina, Lisbon, Portugal

ABSTRACT

This article follows a previous one, which addressed the famous problem of Twins' Paradox: if one of two twins remains on Earth while the other gets on a rocket, travels at a speed close to the speed of light and returns, the traveler should find his brother older than himself. This is because, according to Special Relativity (SR), a moving clock runs slower than a 'stationary' one. The paradox lies in the fact that movement is relative, thus breaking the equivalence between frames of coordinates, a crucial principle at the heart of SR theory. The cited article highlighted the error in the premises that leads to the paradox, reanalyzing it and proving its non-existence either for a one-way or a round trip, despite the phenomenon of time dilation. An important extension of this conclusion is provided here. If one of the twins leaves the other, following a closed polygonal or circular path, in the end they find themselves at the same age. Thus, once again, the fundamental equivalency between frames of coordinates is fully respected. This – as before – is achieved by means of a new dilation factor, progressively "stronger" than Lorentz factor γ, but perfectly reflective. Issues concerning the geometry of space-time and apparently strange outcomes are also analyzed. In addition to strengthening theoretical consistency, restoring confidence in SR and allowing further developments, this study has possible experimental relevance in particle accelerators. Finally, one discovers the existence of a threshold speed for the shortest possible time to complete a closed path.

KEYWORDS
Special Relativity, Twin's Paradox, Time Dilation, Relativistic Asynchrony, Euclidean Geometry

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Luís Dias Ferreira , "Relativistic Polygonal and Circular Paths: Solution for the Twins' Paradox Reviewed and Extended," Universal Journal of Physics and Application, Vol. 16, No. 2, pp. 11 - 24, 2022. DOI: 10.13189/ujpa.2022.160201.

(b). APA Format:
Luís Dias Ferreira (2022). Relativistic Polygonal and Circular Paths: Solution for the Twins' Paradox Reviewed and Extended. Universal Journal of Physics and Application, 16(2), 11 - 24. DOI: 10.13189/ujpa.2022.160201.