Reading the Principia [1] it is easy to realize that Newton, without being aware of the fact, has corrected the law of the fall of bodies formulated by Galilei. In the present paper we examine the consequences of such a fact and show that they affect the entire Celestial Mechanics, being related to the very small 43” per century of the perihelion shift of Mercury as well as to the substantial 5...

This paper is dedicated to Prof. Alberto Galindo on occasion of his 70th birthday. We are delighted to write on Cosmology, which is one of his favourite subjects. He taught both of us at the Complutense University in Madrid, and we would like to thank him for his outstanding teaching. His insistence on logical reasoning, physical intuition and mathematical comprehension of natural laws followed...

The quantum mechanical model of electromagnetic waves is considered, in which the photon, as a particle, propagates with the speed of light, while the wave function of the photon spreads out with an infinite speed. The Lorentz transformation for the energy flux of electromagnetic wave is obtained while assuming the Galilei transformation for the space and time. The energy of the electromagnetic...

The " exotic " particle model with non-commuting position coordinates , associated with the two-parameter central extension of the planar Galilei group, can be used to derive the ground states of the Fractional Quantum Hall Effect. The relation to other NC models is discussed. Anomalous coupling is presented. Similar equations arise for a semiclassical Bloch electron, used to explain the anoma-...