HIGHLIGHTS This paper is presenting an experiment based on Ehrenfest's paradox where an effect of special relativity was expected but not observed. The validity of special relativity in our macro world will be questioned and an alternative will be offered. Indeed, special relativity has been successful in describing the behaviour of particles (Rossi & Hall, 1941), but since particles obey quantum rules, there is no observation of special relativity in our everyday world. On the contrary, there are at least two paradoxes based on special relativity: the twin paradox (Langevin, 1911) and Ehrenfest's paradox (1909). ABSTRACT After presenting the history of special relativity, the non-simultaneity of special relativity is questioned in our macro world. In addition, some issues between light clocks and the application of Lorentz transformation are presented. All this indicates that special relativity appears to be correct only for particles and would be invalid in our macro world. A new hypothesis is presented based on an adaptation of special relativity; this new hypothesis solves the anomalies and could be a solution to the twin paradox. This new hypothesis has a prediction in disagreement with special relativity. To test that prediction, a new experiment has been carried out and the preliminary results support the new hypothesis. Previously, a lack of special relativistic effects has been observed in the universe (Davis et al., 2004); that second observation is also explained with the new hypothesis.

HIGHLIGHTS Mach's principle is linked with inertia and the mass around. Nowadays, physicists believe its effect is infinitesimal, so Mach's principle is simply ignored. This paper looks at the consequence of applying Mach's principle. It could replace dark matter. ABSTRACT After seeing the history of Mach's principle, we will work out a new model of galaxies inspired by Mach’s principle, which is more satisfactory than current dark matter models. This new model is just maths and needs an explanation. One possible explanation is obviously that Mach's principle is at work in a galaxy.