TITLE:
The Space Dilation: Analyzing Progressive Speed Reduction and Its Relativistic Parallels
AUTHORS:
Kreshnik Feka
KEYWORDS:
Asymptotic Limits, Special Relativity, Harmonic Series, Time Dilation, Diminishing Returns
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.8,
August
28,
2024
ABSTRACT: This paper presents a conceptual exploration that draws an intriguing parallelbetween a hypothetical travel scenario and the principles of special relativity. The scenario involves a traveler who reduces their speed by an amount proportional to the distance traveled. Despite initially traveling at a high speed towards a given destination, the continual reduction in speed results in an asymptotic approach to the goal, analogous to the unattainable speed of light in relativity. Mathematically, the scenario is expressed through the Harmonic Series, demonstrating that the total travel time increases without bound, making the destination theoretically unreachable within a finite timeframe. This exploration mirrors the relativistic velocity addition and time dilation effects, providing a compelling analogy for understanding asymptotic limits. By highlighting the profound implications of diminishing returns and unattainable goals, this paper aims to stimulate further discussion and exploration of these fascinating parallels.