Newtonian free fall with an Einsteinian view

Free fall is revisited through the legendary Pisa tower experiment. We suppose the absence of air friction and neglect the Earth non-spherical shape, its inhomogeneities and rotation. Asking whether 1kg stone falls like one of 2kg, young pupils may reply negatively, possibly supposing a difference of a factor two. Instead, teachers may say "exactly yes". The right reply is multi-faceted. It is "exactly yes" only in the Earth fixed frame, that by construction is unaffected by any falling mass, whereas in all other frames the answer is "approximately yes". We start considering each mass being released separately and keep the Earth-stone initial distance as fixed throughout the work. If the observer is at a fixed distance from the Earth centre, e.g., on the Earth surface, he will measure the sum of the acceleration of the stone towards the Earth and of the Earth towards the stone: the larger the stone, the larger the sum perceived by the observer. If the observer is at a fixed distance from the system (Earth and stone) centre of mass (or else imagine that the stone is that heavy to shift the system centre of mass outside the Earth), he will observe the Earth and the stone falling toward him and reaching the system centre of mass at the same instant. Keeping the initial distance Earth-stone constant, by increasing the mass of the stone, the system centre of mass will shift towards the stone and this latter will undergo a smaller acceleration having to cover a smaller distance: the larger the stone, the smaller the acceleration.    In these two last frames, the difference in fall is minuscule, being of the order of the stone/Earth mass ratio, thus not yet measurable by state-of-the-art technology. For the Commander Scott of Apollo 15, the difference in fall between the plume and the hammer was in the order of 6x10-24 s. Nevertheless, this ratio may take large values and be of considerable impact in astronomy. But most stimulating, the heavier stone falls faster or slower than the lighter one depending on the observer. The physics dependency on the observer rises to feature of paramount significance in Einstein's general relativity and thus Newtonian radial fall may be used to introduce gauge dependence. Dealing with two masses released simultaneously, the answer to the three body-problem is numerical, knowing that the system centre of mass will not be equidistant to the two small, but different, masses. The preceding doesn’t violate in any manner the equivalence principle of inertial and gravitational mass. We briefly deal with radial fall in general relativity where the motion of the falling mass is influenced by the mass ratio as in Newtonian gravity but also by the radiation emitted. In the context of the Pisa tower, the energy-time Heisenberg indetermination impedes measuring the gravitational radiation. Instead, the capture of small black holes falling into supermassive ones is the source targeted by LISA to explore general relativity in the strong field. Finally, the analysis of falling observers in black holes during emission of Hawking radiation is of interest for combining quantum mechanics and general relativity. FURTHER READING Barausse E. et al. (2020). Prospects for fundamental physics with LISA. General Relativity and Gravitation, 52, 81. https://doi.org/10.1007/s10714-020-02691-1 Ritter P., Aoudia S., Spallicci A.D.A.M., Cordier S. (2016). Indirect (source-free) integration method. II. Self-force consistent radial fall, Int. J. Geom. Meth. Mod. Phys., 13, 1650019. https://doi.org/10.1142/S0219887816500195 Spallicci A., (2011). Self-force and free fall: an historical perspective, Springer Series on Fundamental Theory of Physics Vol. 162, L. Blanchet, A. Spallicci, B. Whiting, Eds., p. 561. https://link.springer.com/book/10.1007%2F978-90-481-3015-3 Spallicci A.D.A.M., van Putten M.H.P.M., (2016). Gauge dependence and self-force in Galilean and Einsteinian free falls, Pisa tower and evaporating black holes at general relativity centennial. International Journal of Geometric Methods in Modern Physics, 13(8), 1630014. https://doi.org/10.1142/S021988781630014

Testing the Ampère-Maxwell law on the photon mass and Lorentz-Poincaré symmetry violation with MMS multi-spacecraft data

International audienceThe photon is commonly believed being the only free massless particle. Deviations from the Ampère-Maxwell law, due to a photon mass, real for the de Broglie-Proca theory, or effective for the Lorentz-Poincaré Symmetry Violation (LSV) in the Standard-Model Extension (SME) were sought in six years of MMS satellite data. In a minority of cases, out of which $76\%$ in modulus and $65\%$ in Cartesian components for the highest time resolution burst data and best tetrahedron configurations in the solar wind and peripheries, deviations have been found. After currents error analysis, the minimal photon mass would be $1.74 \times 10^{-53}$ kg while the minimal LSV parameter $|\vec{k}^{\rm AF}|$ value would be $4.95 \times 10^{-11}$ m$^{-1}$. These values are compared with actual limits and discussed

FRB 121102 casts new light on the photon mass

The photon mass, mγ, can in principle be constrained using measurements of the dispersion measures (DMs) of fast radio bursts (FRBs), once the FRB redshifts are known. The DM of the repeating FRB 121102 is known to <1%, a host galaxy has now been identified with high confidence, and its redshift, z, has now been determined with high accuracy: z=0.19273(8). Taking into account the plasma contributions to the DM from the Intergalactic medium (IGM) and the Milky Way, we use the data on FRB 121102 to derive the constraint mγ≲2.2×10−14 eVc−2 (3.9×10−50 kg). Since the plasma and photon mass contributions to DMs have different redshift dependences, they could in principle be distinguished by measurements of more FRB redshifts, enabling the sensitivity to mγ to be improved

Virgo upgrade investigations

While the current interferometric gravitational wave detectors are approching their nominal sensitivity, the new generation of detectors is in an advanced design phase. The Virgo collaboration is defining now the path to arrive to a complete design of the advanced version of the detector within about two years. The upgrades needed to obtain a detector with improved sensitivity in a relatively short time are here discussed

Length Sensing and Control in the Virgo Gravitational Wave Interferometer

The gravitational wave detector Virgo is presently being commissioned. A significant part of the last three years was spent in setting up the cavity length control system. This paper was carried out with steps of increasing complexity: locking a simple Fabry-Perot cavity and then a Michelson interferometer (ITF) with Fabry-Perot cavities in both arms, and finally recycling the light beam into the ITF. The applied strategy and the main results obtained are described

Status of Virgo detector

Presented at the XI Gravitational Waves Data Analysis Workshop (GWDAW), Potsdam, Germany Dec 18th - 21st 200

Normal/independent noise in VIRGO data

International audienceThe analysis of data taken during the C7 VIRGO commissioning run showed strong deviations from Gaussian noise. In this work, we explore a family of distributions, derived from the hypothesis that heavy tails are an effect of a particular kind of nonstationarity, heterocedasticity (i.e. nonuniform variance), that appear to fit VIRGO noise better than a model based on the assumption of Gaussian noise. To estimate the parameters of the noise process (including the heterogeneous variance) we derived an expectation-maximization algorithm. We show the consequences of non-Gaussianity on the fitting of autoregressive filters and on the derivation of test statistics for matched filter operation. Finally, we apply the new noise model to the fitting of an autoregressive filter for whitening of data