Related papers: A note on Gurzadyan theorem
Gyroscopic motion explanation in texts is relatively long and requires reasonable level of comfort with the mathematical tools used. On the other hand, popular explanation outside academic courses does not explain the phenomenon and only…
When a physicist says that a theory is fine-tuned, they mean that it must make a suspiciously precise assumption in order to explain a certain observation. This is evidence that the theory is deficient or incomplete. One particular case of…
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
Newtonian Cosmology is commonly used in astrophysical problems, because of its obvious simplicity when compared with general relativity. However it has inherent difficulties, the most obvious of which is the non-existence of a well-posed…
A comparison of the standard models in particle physics and in cosmology demonstrates that they are not compatible, though both are well established. Basics of modern cosmology are briefly reviewed. It is argued that the measurements of the…
The import of Bell's Theorem is elucidated. The theorem's proof is illustrated both heuristically and in mathematical detail in a pedagogical fashion. In the same fashion, it is shown that the proof is correct mathematically, but it doesn't…
We argue that, when a theory of gravity and matter is endowed with (classical) conformal symmetry, the fine tuning required to obtain the cosmological constant at its observed value can be significantly reduced. Once tuned, the cosmological…
The ongoing progress in quantum theory emphasizes the crucial role of the very basic principles of quantum theory. However, this is not properly followed in teaching quantum mechanics on the graduate and undergraduate levels of physics…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive…
The well-known fluid equation of cosmology is examined with a view to elucidating the precise conditions under which it is applicable.
The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor…
Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental…
The cosmological constant problem is usually considered an inevitable feature of any effective theory capturing well-tested gravitational and matter physics, without regard to the details of short-distance gravitational couplings. In this…
The purpose of this note is to give an (esentially optimal) effective version of Matsusaka's Big theorem for smooth projective surfaces.
We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions.
The previous version of this article was a first attempt to confront the Dark Gravity theory to cosmological data. However, more recent developments lead to the conclusion that the cosmological principle is probably not valid in Dark…
In gravitostatics, the minimally generalized Newtonian theory, the simplest cosmological model implies a cosmological redshift with acceleration parameter -1. If the gravitational potential satisfies a wave equation, the total mass density…
A theory of gravity with a generic action functional and minimally coupled to N matter fields has a nontrivial fixed point in the leading large N approximation. At this fixed point, the cosmological constant and Newton's constant are…
The present discussion contribution is some remarks concerning and review of the proposal by one of us (C. Balazs) to explain the cosmological constant by a/the principle of entropy. Used without further comment this principle of entropy…