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We review the dynamics of a bouncing ball, both from the classical and the quantum points of view, studying the role of its inertial and gravitational masses. We analyze the behavior of quantum particles of different masses, embedded in a uniform gravitational field. We show that the bouncing ball is a useful didactic example to show that the coupling between rest mass and gravity cannot be avoided at the quantum level and that the equivalence principle must be reformulated in quantum mechanics. Galileo’s experiment of falling bodies can be still satisfied if one considers only the average quantum values of observables. [ABSTRACT FROM AUTHOR]

We want to shed light on some discussed aspects of the principle of equivalence. We consider two different phases in the evolution of the principle. We pay attention to the fact that some textbooks do not dwell on the mathematical meaning of ‘locally flat spacetime’, which can confuse students and, occasionally, can also lead to misinterpretations. For example, the non-eliminability of tidal forces, not even locally, may suggest that the equivalence principle is wrong. By contrast, we want to show that this is in perfect agreement with the Einstein geometrical interpretation of spacetime. Finally, in order to check the approximations used in the Gedankenexperiment of an elevator, we estimate explicitly the magnitude of the deflection of light and the effects of tidal forces in a ‘real lift’. [ABSTRACT FROM AUTHOR]

The aim of this paper is to make a determination of Hubble’s constant from the experimental data on the magnitude and redshift of supernovae. We proposed a very simple approach that could also be very useful from a didactic point of view. [ABSTRACT FROM AUTHOR]