Upcoming Event

Isotropy, principle of relativity and the possible structures for worldview transformations

Using a streamlined first-order logic axiom system centered around isotropy of space, we are going to present a characterization for all the sets of transformations that can be obtained as sets of world-view transformations corresponding to a fixed observer. We show that up to harmonizing units of measurements these sets are subsets of the Poincaré group or the Galilean group or the group of Euclidean isometries. We also show that these sets do not necessarily form groups under composition, but they can be obtained as unions of at most three cosets. If we assume the principle of relativity, then these sets form groups. Using this, we give a model for kinematics in which isotropy of space and homogeneity of space and time hold, but the principle of relativity fails.