Skip to content

The Relativistic Sagnac Effect: Two Derivations

  • Rizzi G
  • Ruggiero M
Citations of this article
Mendeley users who have this article in their library.
Get full text
This PDF is freely available from an open access repository. It may not have been peer-reviewed.


The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in this way the universality of the effect. Another derivation is based on a formal analogy with the phase shift induced by the magnetic potential for charged particles travelling in a region where a constant vector potential is present: this is the so called Aharonov-Bohm effect. Both derivations are carried out in a fully relativistic context, using a suitable 1+3 splitting that allows us to recognize and define the space where electromagnetic and matter waves propagate: this is an extended 3-space, which we call "relative space". It is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform': the geometry of this space turns out to be non Euclidean, according to Einstein's early intuition.




Rizzi, G., & Ruggiero, M. L. (2004). The Relativistic Sagnac Effect: Two Derivations. In Relativity in Rotating Frames (pp. 179–220). Springer Netherlands.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free