Eppur si Espande

The rather wide-spread belief that cosmological expansion of a flat 3D-space (with spatial curvature k=0) cannot be observationally distinguished from a kinematics of galaxies moving in a flat and non-expanding space is erroneous. We suggest that the error may have its source in a non relativistic intuition that imagines the Universe not as a space-time but separates space from time and pictures the cosmological expansion as space evolving in time. The physical reality, however, is fundamentally different - the expanding Universe is necessarily a curved space-time. We show here that the fact that the space-time is curved implies that the interpretation of the observed cosmological redshift as being due to the expansion of the cosmological 3D-space is observationally verifiable. Thus it is impossible to mimic the true cosmological redshift by a Doppler effect caused by motion of galaxies in a non-expanding 3D-space, flat or curved. We summarize our points in simple space-time diagrams that illustrate a gedanken experiment distinguishing between expansion of space and pure kinematics. We also provide all relevant mathematics. None of the previously published discussions of the issue, including a recent popular Scientific American article by Lineveaver and Davis, offered a similarly clear way out of the confusion.