The history and the meaning of Einstein’s Principle of Equivalence

We review from a historical and a didactic point of view the Equivalence Principle, which was considered by Einstein as the corner stone of his new theory of Gravitation: the General Relativity. Before and after the enormous success of his theory, this principle was the subject of studies and discussions. Still today, after more than one century, the debate about its interpretation, application and generalization is very fertile. Einstein soon understood the revolutionary significance of his idea and defined it as “the happiest thought of my life”

The M BH versus M G σ 2 Relation and the Accretion of Supermassive Black Holes

We propose a possible scenario that can explain the physical processes underlying the relation log10(M BH) = b + mlog10(M Gσ2/c 2) between the mass M BH of supermassive black holes, growing in the center of many galaxies, and the kinetic energy of the corresponding bulges (M G being the bulge mass and σ the velocity dispersion). In a series of papers, this scaling law proved to be very useful to describe the evolution of galaxies thanks to its close similarity to the Hertzsprung-Russell diagram. Studying the relation with different samples of galaxies, we have generally found a slope that can vary between two extremal theoretical possibilities, m = 3/4 and m = 1. We will try to describe a possible scenario compatible with the second one. Finally, we also examine a case of a relation that is linear, not in kinetic energy, but in momentum parameter

Spacetime contraction in the Einstein's elevator

Abstract The equivalence principle was explained by Einstein using the didactic "mental experiment" of a uniform gravitational field inside an elevator. The Earth gravitational field is not really uniform so the question about how to create a uniform gravitational field is legitimate. To this aim, instead of using metrics depending on spatial coordinates, we have studied a cosmological - like metric and we have found that, under suitable assumptions, it is possible to measure a uniformly accelerated motion for the test particles moving inside the elevator

Maximal acceleration or maximal accelerations?

We review the arguments supporting the existence of a maximal acceleration for a massive particle and show that different values of this upper limit can be predicted in different physical situations.Comment: 13 pages, Latex, to be published in Int. J. Mod. Phys.

Rotation induced in a coil moving in an electric field

The integral form of the fourth Maxwell's equation is often written in two different ways: in the first, the partial derivative of Electric field appears, while the second contains a time derivative of electric flux integral. It would be useful, from a didactic point of view, to discriminate between the two different interpretations. In this paper, starting from a previous work about Faraday's law, we analyze the derivative of the flux of the electric field and we shed light on the right way to write the Maxwell equations. We introduce a "magnetomotive force" and we find, from the corresponding generalization of the second Laplace's law, the effect of a rotation induced in a coil embedded in an electric field

Electromagnetic shape resonances of a dielectric sphere and radiation of portable telephones

The frequency band used by cellular telephones includes the eigenfrequencies of a dielectric sphere with physical characteristics close to those of a human head. Proceeding from the spatial features of the natural modes of such a sphere we propose an independent and clear evident accuracy test for the complicated numerical calculations which are conducted when estimating the potential hazard due to the use of cellular telephones, in particular, for the check of a proper handling of the electromagnetic shape resonances of a human head.Comment: 10 pages, 1 figure with 2 eps file

Mass dependent corrections of the orbital period of a planet

This paper has a didactic aim. Indeed, starting from the well-known principle of free fall discovered by Galileo Galilei, we want to make some reflections that we consider useful for secondary school students. Being the acceleration invariant with respect to Galilei's transformations, it is useful to underline that the free fall in a gravitational field is independent of the mass of the body that falls only if the attractive mass is an inertial frame. In general, the corrections to the motion of a test particle falling in a gravitational field due to its mass can be easily calculated avoiding misinterpretations of Galileo's principle. Moreover, it may be useful to observe that, in the case of periodic motions, these corrections increase with time and would lead, over the centuries, to not negligible effects

Unruh temperature with maximal acceleration

In this paper, we modify the geometry of Rindler space so as to include an upper limit on the acceleration. Caianiello and his collaborators, in a series of papers, have analyzed the corrections to the classical spacetime metrics due to the existence of a maximal acceleration. Our goal is to derive, in this context, in a very simple way, the so-called Unruh temperature