Over five years we have compared the hyperfine frequencies of 133 Cs and 87 Rb atoms in their electronic ground state using several laser cooled 133 Cs and 87 Rb atomic fountains with an accuracy of ∼ 10 −15 . These measurements set a stringent upper bound to a possible fractional time variation of the ratio between the two frequencies :d dt ln ν Rb ν Cs = (0.2 ± 7.0) × 10 −16 yr −1 (1σ uncertainty).The same limit applies to a possible variation of the quantity (µ Rb /µCs)α −0.44 , which involves the ratio of nuclear magnetic moments and the fine structure constant.PACS numbers: 06.30. Ft, 32.80.Pj, 06.20.Jr Since Dirac's 1937 formulation of his large number hypothesis aiming at tying together the fundamental constants of physics [1], large amount of work has been devoted to test if these constants were indeed constant over time [2,3].In General Relativity and in all metric theories of gravitation, variations with time and space of non gravitational fundamental constants such as the fine structure constant α = e 2 /4πǫ 0 c are forbidden. They would violate Einstein's Equivalence Principle (EEP). EEP imposes the Local Position Invariance stating that in a local freely falling reference frame, the result of any local non gravitational experiment is independent of where and when it is performed. On the other hand, almost all modern theories aiming at unifying gravitation with the three other fundamental interactions predict violation of EEP at levels which are within reach of near-future experiments [4,5]. As the internal energies of atoms or molecules depend on electromagnetic, as well as strong and weak interactions, comparing the frequency of electronic transitions, fine structure transitions and hyperfine transitions as a function of time or gravitational potential provides an interesting test of the validity of EEP.To date, very stringent tests exist on geological and cosmological timescales. The analysis of the Oklo nuclear reactor showed that, 2 × 10 9 years ago, α did not differ from the present value by more than 10 −7 of its value [6]. Light emitted by distant quasars has been used to perform absorption spectroscopy of interstellar clouds. For instance, measurements of the wavelengths of molecular hydrogen transitions test a possible variation of the electron to proton mass ratio m e /m p [7]. Comparisons between the gross structure and the fine structure of neutral atoms and ions would indicate that α for a redshift z ∼ 1.5 (∼ 10 Gyr) differed from the present value: ∆α/α = (−7.2 ± 1.8) × 10 −6 [8]. Today this is the only claim that fundamental constants might change.On much shorter timescales, several tests using frequency standards have been performed [9,10,11]. These laboratory tests have a very high sensitivity to changes in fundamental constants. They are repeatable, systematic errors can be tracked as experimental conditions can be changed.In this letter we present results that place a new stringent limit to the time variation of fundamental constants. By comparing the hyperfine energies of 13...

The interstellar medium (ISM) is a complex non-linear system governed by the interplay between gravity and magnetohydrodynamics, as well as radiative, thermodynamical, and chemical processes. Our understanding of it mostly progresses through observations and numerical simulations, and a quantitative comparison between these two approaches requires a generic and comprehensive statistical description of the emerging structures. The goal of this paper is to build such a description, with the purpose to permit an efficient comparison independent of any specific prior or model. We start from the Wavelet Scattering Transform (WST), a low-variance statistical description of non-Gaussian processes, developed in data science, that encodes long-range interactions through a hierarchical multiscale approach based on the Wavelet transform. We perform a reduction of the WST through a fit of its angular dependencies, allowing to gather most of the information it contains into a few components whose physical meanings are identified, and that describe, e.g., isotropic and anisotropic behaviours. The result of this paper is the Reduced Wavelet Scattering Transform (RWST), a statistical description with a small number of coefficients that characterizes complex structures arising from non-linear phenomena, in particular interstellar magnetohydrodynamical (MHD) turbulence, free from any specific prior. The RWST coefficients encode moments of order up to four, have reduced variances, and quantify the couplings between scales. To show the efficiency and generality of this description, we apply it successfully to three kinds of processes that are a priori very different: fractional Brownian motions, MHD simulations, and Herschel observations of the dust thermal continuum in a molecular cloud. With fewer than 100 coefficients when probing 6 scales and 8 angles on 256×256 maps, we were able with the RWST to perform quantitative comparisons, to infer relevant physical properties, and to produce realistic synthetic fields.