Related papers: Galileo's Discovery of Scaling Laws
Galileon gravity offers a robust gravitational theory for explaining cosmic acceleration, having a rich phenomenology of testable behaviors. We explore three classes of Galileon models -- standard uncoupled, and linearly or derivatively…
Four hundred years after its publication, Galileo's masterpiece Sidereus Nuncius is still a mine of useful information for historians of science and astronomy. In his short book Galileo reports a large amount of data that, despite its age,…
What can physics students learn about science from those scientists who got the answers wrong? Students encounter little science history, and what they have encountered typically portrays scientists as The People with the Right Answers. But…
Disclosure of scaling relationship between observable quantities gives direct information about dynamics of natural phenomenon. This is the main reason why scaling plays a key role in the methodology of natural sciences. In this talk, Part…
We present a way of teaching Einstein's special relativity. It starts with Galileo's relativity, the learners know from previous lectures. The lecture underlines that we can have three transformation equations for the space-time coordinates…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
The Galileon model is a modified gravity theory that may provide an explanation for the accelerated expansion of the Universe. This model does not suffer from instabilities or ghost problems (normally associated with higher-order derivative…
Unusual features of water waves that Galileo described in a letter to Cardinal Orsini in 1616 are revisited from the perspectives of singular optics and geometric analysis.
The trial and condemnation of Giordano Bruno was mainly based on arguments of philosophical and theological nature, and therefore different from Galilei's. Such elements contribute to unfairly devalue the scientific contribution of Bruno…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
Forest-fire waiting times, defined as the time between successive events above a certain size in a given region, are calculated for Italy. The probability densities of the waiting times are found to verify a scaling law, despite that fact…
We determine the Lorentz transformations and the kinematic content and dynamical framework of special relativity as purely an extension of Galileo's thoughts. No reference to light is ever required: The theories of relativity are logically…
A scalar-tensor theory of gravity can be made not only to account for the current cosmic acceleration, but also to satisfy solar-system and laboratory constraints, by introducing a non-linear derivative interaction for the scalar field.…
We study the cosmology of a galileon scalar-tensor theory, obtained by covariantizing the decoupling lagrangian of the Dvali-Gabadadze-Poratti (DGP) model. Despite being local in 3+1 dimensions, the resulting cosmological evolution is…
Murray Gell-Mann, after co-inventing QCD, recognized the interplay of the scale anomaly, the renormalization group, and the origin of the strong scale, Lambda_{QCD}. I tell a story, then elaborate this concept, and for the sake of…
There is a myth that Einstein's discovery of general relativity was due to his following beautiful mathematics to discover new insights about nature. I argue that this is an incorrect reading of the history and that what Einstein did was to…
Newton's deduction of the inverse square law from Kepler's ellipse and area laws together with his "superb theorem" on the gravitation attraction of spherically symmetric bodies, are the major steps leading to the discovery of the law of…
It is widely acknowledged that the Galilean Relativity Principle, according to which the laws of classical systems are the same in all inertial frames in relative motion, has played an important role in the development of modern physics. It…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which…