Related papers: Galileo's Discovery of Scaling Laws

I argue that in the Lagrangian formulation of standard, Galilei-invariant Newtonian mechanics there are subtle but concrete signs of {\em Lorentz} invariance. In fact, in a specific sense made explicit in the paper, Newtonian mechanics is…

An important scientific debate took place regarding falling bodies hundreds of years ago, and it still warrants introspection. Galileo argued that in a vacuum all bodies fall at the same rate relative to the earth, independent of their…

Astronomy is a precise and relatively simple science because objects accelerate in a gravitational field at the same rate, irrespective of their composition. Galileo knew this, and Einstein took it as the basis for general relativity.…

An alternative for the construction of fundamental theories is the introduction of Galileons. These are fields whose action leads to non higher than second-order equations of motion. As this is a necessary but not sufficient condition to…

Work published in Sky and Telescope in 2004 discusses Galileo's observations of the star Mizar. These observations raise questions regarding Galileo's assumptions about the universe and the conclusions he drew from his observations. Galileo…

We review the different frameworks in which Galileon scalar fields have been seen to emerge such an in DGP, New Massive Gravity and Ghost-free massive Gravity and emphasize their relation with the Lovelock invariant in braneworld models.…

It is difficult for the common sense to admit that an object dropped from the top of the mast of a ship moving at a constant velocity falls down at the bottom of the mast because it keeps inside the horizontal movement of the ship. This…

In 1640's, Blaise Pascal discovered a remarkable property of a hexagon inscribed in a conic - Pascal Theorem, which gave birth of the projective geometry. In this paper, a new geometric invariant of algebraic curves is discovered by a…

In a previous article we gave the general foundations of the theory of movement considered from a philosophical and mathematical point of view. Philosophical it meant to understand the opposition of the one and the multiple, mathematically…

We show a model of the slow expansion, in which the scale invariant spectrum of curvature perturbation is adiabatically induced by its increasing mode, by applying a generalized Galileon field. In this model, initially \epsilon << -1, which…

In the middle of the seventeenth century, Andr\'e Tacquet, S.J. briefly discussed a scientific argument regarding the structure of a Copernican universe, and commented on Galileo Galilei's discussion of that same argument -- Galileo's…

This paper presents two interesting scaling laws, which relate some critical exponents in the critical behavior of spherically symmetric gravitational collapses. These scaling laws are independent of the details of gravity theory under…

Scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action and do not lead to conservation laws. Nevertheless, by an extension of Noether's theorem, scaling symmetries lead to useful {\em…

Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…

Galileon inflation is a radiatively stable higher derivative model of inflation. The model is determined by a finite number of relevant operators which are protected by a covariant generalization of the Galileon shift symmetry. We show that…

An intriguing reference to the existence of a self-portrait by Galileo Galilei is contained in the biography of the scientist by Thomas Salusbury dated ca. 1665, of which only one incomplete and inaccessible copy exists. Galileo grew up in…

Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a nonuniform field of force by small steps. It is generally not known that…

It is shown that the characteristic observed radius, velocity, and temperature of a typical galaxy can be inferred from Planck action constant through a phenomenological scaling law on all cosmological scales.

Since Galileo and (more recently) D'Arcy Thompson, it has been understood that physical processes and constraints influence biological structures and their resulting functions. However these cross-discpline connections -- and their…

The Galileon model is a modified gravity model that can explain the late-time accelerated expansion of the Universe. In a previous work, we derived experimental constraints on the Galileon model with no explicit coupling to matter and…