The structure of spacetime: Simultaneity

A new UGA research study on structural aspects of relativistic spacetime reveals the basic structure of spacetime in rotating frames, which had not been previously settled. This work clarifies for the first time the actual fabric of spacetime in rotating frames – describing the exact combination of relativistic effects and simultaneity. The research team – Edward Kipreos, professor of cellular biology, and Riju S. Balachandran (Ph.D. '18) – used recent, high-resolution optical data to identify the transformation (i.e., set of equations) that describes rotating spacetime.  These are similar to special relativity though differing in how time and space interact.  "Understanding spacetime in rotating frames has wide applicability, as we live in the rotating frame of the Earth's surface, and most visible matter in the Universe is in rotational motion," Kipreos said.  

A transformation's combination of relativistic effects and simultaneity framework affects how light propagates. The four transformations have different predictions for the rotating-frame one-way speeds of light, two-way speed of light, and the Sagnac effect. This study derives the optical predictions for each transformation directly from their transformation equations, with several of the predictions not previously reported in the literature. The predictions are then compared to recent high-resolution optical experimental data. 

Optical resonator data on the two-way speed of light is among the highest resolution scientific measurements, with resolutions of 10-18. This high resolution is required to distinguish between the predictions of the transformations. The study reveals that ALT and the Franklin transformation prediction of the constant two-way speed of light, c, matches the optical resonator data, while the Langevin metric and Post transformation predictions are invalidated by the data. The failure of the Langevin metric and Post transformation to match optical resonator data is shown to be due to their exhibiting no (or no net) length contraction in the rotating frame. In contrast, the ALT and Franklin transformations exhibit length contraction, which allows their accurate predictions for the two-way speed of light.

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The paper Assessment of the relativistic rotational transformations can be found in the Modern Physics Letters A journal.

Image, via wikimedia commons. Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame.