Abstract
All the experiments supporting special relativity (SR) formulated with Einstein synchronization support as well SR with absolute synchronization, if the corresponding coordinate transformations foresee time dilation and length contraction. We first test absolute vs relative simultaneity with a non-relativistic model of the spin-orbit interaction by taking into account either the effect of the electron hidden momentum or the relativistic effect of the Thomas precession, based on
 non-conservation of simultaneity. As second test, we consider a thought experiment equivalent to the Sagnac effect, where a clock measures the time taken by a counter-propagating light signal to perform a round trip on a closed path. While these experiments are coherently described with absolute simultaneity, the result of our tests points out inconsistencies in the case of relative simultaneity, thus favoring the formulation of SR with absolute synchronization, while advocating that
 further research and tests on simultaneity are needed for the comprehension of relativistic theories.
Highlights
According to the conventionalist thesis, special relativity (SR) theory can be formulated with either Einstein or absolute clock synchronization (Mansouri & Sexl, 1977; de Abreu & Guerra, 2005; Bell, 1988; Anderson, Vetharaniam & Stedman, 1998)
In the non-relativistic approximation, the spin-orbit mechanism can be interpreted in the frame of the nucleus by taking into account either the hidden momentum of the orbiting electron or the precession of the electron spin derived by Thomas
If the existence of the hidden momentum is confirmed by observation, the interpretation of the spin-orbit mechanism in terms of absolute simultaneity is favored
Summary
According to the conventionalist thesis, special relativity (SR) theory can be formulated with either Einstein or absolute clock synchronization (Mansouri & Sexl, 1977; de Abreu & Guerra, 2005; Bell, 1988; Anderson, Vetharaniam & Stedman, 1998). At the moment, we are bound to restrict ourselves to re-examine the experiments supporting SR and select those suitable for discriminating absolute from relative simultaneity One of these experiments, referring to the measurement of the spin-orbit energy splitting in atoms, appears to be worth considering because it can be indirectly related either to the hidden momentum of the electron (Spavieri & Mansuripur, 2015), (Spavieri, 2016), or to the relativistic interpretation of the spin precession by Thomas (Thomas, 1926), based on non-conservation of simultaneity. In order to foresee the correct spin-orbit energy splitting, the non-relativistic equations of atomic physics, describing the electron orbiting the nucleus, have to introduce the Thomas precession, which is a relativistic effect due to nonconservation of simultaneity derived in the frame co-moving with the electron
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