Related papers: Galileo's Discovery of Scaling Laws
Scalar fields have had a long and controversial life in gravity theories, having progressed through many deaths and resurrections. The first scientific gravity theory, Newton's, was that of a scalar potential field, so it was natural for…
In this note, we illustrate how the two-dimensional theory of elasticity provides a physical example of field theory displaying scale but not conformal invariance.
We investigate the Universe at the late stage of its evolution and inside the cell of uniformity 150-370 Mpc. We consider the Universe to be filled at these scales with dust like matter, a minimally coupled Galileon field and radiation. We…
We consider the Gaussian free field $\varphi$ on $\mathbb{Z}^2$ at large spatial scales $N$ and give sharp bounds on the probability $\theta(a,N)$ that the radius of a finite cluster in the excursion set $\{\varphi \geq a\}$ on the…
In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…
Understanding how size influences the internal characteristics of a system is a crucial concern across various fields. Concepts like scale invariance, universalities, and fractals are fundamental to this inquiry and find application in…
We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This…
Observationally and experimentally, physical laws express how particles interact. Conversely, physical laws should be invariant under any re-arrangement of those particles, e.g., the laws of gravity do not change if one re-arranges the…
Hubble's name is associated closely with the idea of an expanding universe as he discovered the relation between the recession velocity and distances of galaxies. Hubble also did a lot of pioneering work on the distribution of galaxies in…
Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…
We show that every Galileon theory admits a dual formulation as a Galileon theory with new operator coefficients. In n dimensions a free scalar field in Minkowski spacetime is dual to a (n+1)-th order Galileon theory which exhibits the…
Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data…
At the end of the 19th century light was regarded as an electromagnetic wave propagating in a material medium called ether. The speed c appearing in Maxwell's wave equations was the speed of light with respect to the ether. Therefore,…
In a first historical part I shall give a detailed description of how Pauli discovered --before the advent of the new quantum mechanics -- his exclusion principle. The second part is devoted to the insight and results that have been…
We investigate a large class of infinitesimal, but fully nonlinear in the field, transformations of the Galileon and search for extended symmetries. The transformations involve powers of the coordinates $x$ and the field $\pi$ up to any…
Deterministic chaos, and even maximum computational complexity, have been discovered within Newtonian dynamics. Economists assume that prices and price changes can also obey abstract mathematical laws of motion. Sociologists and other…
Could a conformal Galileon be describing a gauge mode of a broader diffeomorphism invariant theory? We answer this question affirmatively in 3D by using a coset construction for a nonlinearly realized conformal symmetry. In particular, we…
We parameterize the evolutions of the slow expansion, which emerges from a static state in infinite past, into different classes. We show that the scale invariant adiabatical perturbation may be generated during these evolutions, and the…
Considering the conformal scaling gauge symmetry as a fundamental symmetry of nature in the presence of gravity, a scalar field is required and used to describe the scale behavior of universe. In order for the scalar field to be a physical…
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…