On Spavieri's conundrum or the shadow of the twin paradox -- A submission to the One-Way Linear Effect (OWLE) Award

TL;DR

The paper examines a claimed inconsistency between the linear Sagnac effect (LSE) and special relativity (SR), linking the apparent 'time gap' to the twin paradox. It argues that the discrepancy arises from applying inconsistent frames and pasting together two distinct rest spaces, and then demonstrates a fully SR-consistent treatment using Lorentz transformations to frames comoving with the lower and upper fiber sections. By showing the photon traverses the entire fiber and that the total traversed length matches the appropriate SR length scale (2 ell0), the work confirms that SR does predict the LSE. The analysis highlights the subtle role of frame definitions and simultaneity in rolling or rotating systems and reinforces that no genuine SR inconsistency underpins the LSE, while connecting the issue to foundational twin-paradox reasoning.

Abstract

We deal with a problem concerning a supposed inconsistency in the special relativistic treatment of the so-called linear Sagnac effect. It is shown that, under modern clothes, the root of the difficulty perceived by some authors lies in their uneasiness with the standard solution of the twin paradox. In particular, since the linear Sagnac effect is an absolute effect, no tinkering with conventionality of simultaneity, so far as it preserves the physical content of special relativity, would get us out of the supposed trouble.

Figures (9)

• Figure 1: Linear Sagnac effect
• Figure 2: Return occurring in the lower section
• Figure 3: Return occurring in the upper section
• Figure 4: LSE with return in the lower section
• Figure 5: LSE with return in the upper section