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ZENODO
Article . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Article . 2025
License: CC BY
Data sources: Datacite
ZENODO
Article . 2025
License: CC BY
Data sources: Datacite
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Achilles Paradox — A Formal Resolution within Return Theory (RT)

Authors: Hamed Hajizadeh;

Achilles Paradox — A Formal Resolution within Return Theory (RT)

Abstract

This note presents a formal and self-contained resolution of Zeno’s Achilles paradox within the framework of Return Theory (RT). The paradox is shown to arise purely from a nonlinear projection between shell-time and observer-time, rather than from any physical or logical inconsistency in motion or spacetime. Using the RT time-projection law, the note demonstrates that any Zeno-type infinite subdivision of motion in observer-time corresponds to a Riemann partition of a finite shell-time interval. The resulting infinite series of observer-time increments is proven to converge to a finite value, ensuring that Achilles reaches the target in finite observer-time and finite physical time. No modification of spacetime structure, continuity, or dynamical laws is required. The resolution is purely geometric and relies only on standard assumptions of smoothness and boundedness within the RT framework. This document is intended as a formal reference note within the RT Bookstore collection and complements the main Return Theory framework archived on Zenodo (DOI: 10.5281/zenodo.17857410).

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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