II. FIRST PRINCIPLES OF THE MECHANICAL THEORY OF THE UNIVERSE

1960 ◽  
pp. 58-61
Keyword(s):  
First Principles ◽  
Mechanical Theory ◽  
The Universe

Elements of ∞-Category Theory

2022 ◽  
Author(s):  
Emily Riehl ◽  
Dominic Verity
Keyword(s):  
First Principles ◽  
Category Theory ◽  
Higher Dimensional ◽  
Background Material ◽  
Model Independent ◽  
The Universe ◽  
Formal Category

The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.

scholarly journals Description of the Fission Process: Nuclear Models for Fission Dynamics

2020 ◽  
Vol 242 ◽  
pp. 03005
Author(s):  
M. Verriere ◽  
M.R. Mumpower ◽  
T. Kawano ◽  
N. Schunck
Keyword(s):  
National Security ◽  
Heavy Nucleus ◽  
First Principles ◽  
Energy Generation ◽  
Nuclear Fission ◽  
Theoretical Understanding ◽  
Fission Process ◽  
New Approaches ◽  
Nuclear Models ◽  
The Universe

Nuclear fission is the splitting of a heavy nucleus into two or more fragments, a process that releases a substantial amount of energy. It is ubiquitous in modern applications, critical for national security, energy generation and reactor safeguards. Fission also plays an important role in understanding the astrophysical formation of elements in the universe. Eighty years after the discovery of the fission process, its theoretical understanding from first principles remains a great challenge. In this paper, we present promising new approaches to make more accurate predictions of fission observables.

scholarly journals The Λ and the CDM as Integration Constants

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2076
Author(s):  
Priidik Gallagher ◽  
Tomi Koivisto
Keyword(s):  
Dark Matter ◽  
Gauge Theory ◽  
Symmetry Breaking ◽  
Cosmological Constant ◽  
Spontaneous Symmetry Breaking ◽  
First Principles ◽  
Cold Dark Matter ◽  
Dark Sector ◽  
Λcdm Model ◽  
The Universe

Notoriously, the two main problems of the standard ΛCDM model of cosmology are the cosmological constant Λ and the cold dark matter, CDM. This essay shows that both the Λ and the CDM arise as integration constants in a careful derivation of Einstein’s equations from first principles in a Lorentz gauge theory. The dark sector of the universe might only reflect the geometry of a spontaneous symmetry breaking that is necessary for the existence of spacetime and an observer therein.

Philolaus (c.470–380/9 BC)

2018 ◽  
Author(s):  
Hermann S. Schibli
Keyword(s):  
First Principles ◽  
Fifth Century ◽  
The Earth ◽  
Greek Philosopher ◽  
Noteworthy Feature ◽  
History Of ◽  
Psychological Functions ◽  
Explanatory Concept ◽  
The Universe

The Greek philosopher Philolaus of Croton, a contemporary of Democritus and Socrates, was a pre-eminent Pythagorean. His book counts as the first written treatise in the history of Pythagoreanism. Surviving in fragments, it constitutes an important source for our knowledge of fifth-century Pythagoreanism and supplements the picture given by Aristotle of Pythagorean doctrine. Like earlier Presocratics Philolaus sought to furnish a comprehensive cosmology. Arguing from logical propositions, he posited two pre-existing principles: ‘unlimited things’ and ‘limiting things’. United by harmony these two principles account for the formation of the cosmos and its phenomena. Since Philolaus also invokes number as an all-powerful explanatory concept, it is likely that he associated his first principles and the things originating from them with numbers. The emphasis on harmony and number accords with early Pythagoreanism. Philolaus also wrote on musical theory and astronomy. A noteworthy feature of his astronomy is the displacement of the earth from the centre of the cosmos by fire, pictured as the ‘hearth’ of the universe. The fragments further attest Philolaus’ interest in embryology, the causes of diseases, and physiology combined with psychological functions. It was not unusual for early Greek philosophers to treat such a wide variety of topics. The distinctive elements of the thought of Philolaus are the logical arguments evinced in the fragments and the epistemological role of number for understanding the structure of reality.

scholarly journals Coexistence of plastic and partially diffusive phases in a helium-methane compound

2020 ◽  
Vol 7 (10) ◽  
pp. 1540-1547
Author(s):  
Hao Gao ◽  
Cong Liu ◽  
Andreas Hermann ◽  
Richard J Needs ◽  
Chris J Pickard ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Phase Diagram ◽  
First Principles ◽  
Van Der Waals ◽  
Van Der Waals Interactions ◽  
First Principles Calculations ◽  
Helium Atoms ◽  
Wide Range ◽  
Pure Methane ◽  
The Universe

Abstract Helium and methane are major components of giant icy planets and are abundant in the universe. However, helium is the most inert element in the periodic table and methane is one of the most hydrophobic molecules, thus whether they can react with each other is of fundamental importance. Here, our crystal structure searches and first-principles calculations predict that a He3CH4 compound is stable over a wide range of pressures from 55 to 155 GPa and a HeCH4 compound becomes stable around 105 GPa. As nice examples of pure van der Waals crystals, the insertion of helium atoms changes the original packing of pure methane molecules and also largely hinders the polymerization of methane at higher pressures. After analyzing the diffusive properties during the melting of He3CH4 at high pressure and high temperature, in addition to a plastic methane phase, we have discovered an unusual phase which exhibits coexistence of diffusive helium and plastic methane. In addition, the range of the diffusive behavior within the helium-methane phase diagram is found to be much narrower compared to that of previously predicted helium-water compounds. This may be due to the weaker van der Waals interactions between methane molecules compared to those in helium-water compounds, and that the helium-methane compound melts more easily.

Great Thinkers: (VIII) Spinoza

Philosophy ◽  
1936 ◽  
Vol 11 (43) ◽  
pp. 271-287
Author(s):  
W. G. de Burgh
Keyword(s):  
First Principles ◽  
Logical Necessity ◽  
Geometrical Form ◽  
Detailed Interpretation ◽  
Almost All ◽  
The Universe

The student of Spinoza is faced by a peculiar difficulty. On opening the Ethics—Spinoza's chief work, completed for publication shortly before his death in 1674—he finds a system of metaphysics set forth in geometrical form, starting from definitions, axioms, and postulates, and advancing synthetically from first principles to a detailed interpretation of the universe. The difficulty lies not in the language— Spinoza's Latin is easy to construe, and there are translations—nor in the lack of literary graces; his style indeed is singularly impressive in its austere dignity. It lies rather in this, that the method of exposition conveys a misleading suggestion of dogmatism and finality, and conceals almost all traces of the patient inquiries that issued in the finished structure. If once the principles of the system are admitted, the rest appears to follow by logical necessity. But by what processes of thought was Spinoza led to those principles? This is the problem that besets the reader: in order to understand the Ethics, he must penetrate behind the text of the propositions to their significance as answers to the questions that were stirring in Spinoza's mind.

scholarly journals Towards a More Well-Founded Cosmology

2017 ◽  
Author(s):  
Hartmut Traunmüller
Keyword(s):  
First Principles ◽  
Ad Hoc ◽  
Deep Understanding ◽  
Gravitational Effect ◽  
Big Bang ◽  
Inertial Forces ◽  
Cosmic Inflation ◽  
Cosmological Principle ◽  
The Universe ◽  
Galaxy Rotation Curves

First, this paper broaches the epistemological status of scientific tenets and approaches: phenomenological (descriptive only), well-founded (solid first principles, conducive to deep understanding), provisional (can be falsified if universal and verified if existential), and imaginary (fictitious entities or processes, conducive to empirically unsupported beliefs). The ΛCDM “concordance model” involves such beliefs: the emanation of the universe out of a non-physical stage, cosmic inflation (invented ad hoc), Λ (fictitious energy), and exotic dark matter. Big Bang cosmology further faces conceptual and pragmatic problems in delimiting what expands from what does not. The problems dissolve after untying inertia from space. The cosmology that emerges appears immediately compatible with the considered observations and the ‘perfect cosmological principle’. Waves and field perturbations that propagate at c expand exponentially with distance (a gravitational effect). The cosmic web of galaxies does not. Potential -Φ varies as H/(cz) instead of 1/r. Inertial forces arise from the gravitational action of the rest of the universe. Due to dilatation, they are reduced disproportionately at low accelerations. A cut-off value a0 = 0.168 cH is deduced. This explains the successful description of galaxy rotation curves by MoND. A fully elaborated physical theory is still pending. Wider implications are briefly discussed.

scholarly journals Perspective: Why Exercise Is Good and Its Lack Bad for Everything

2018 ◽  
Vol 13 (3) ◽  
pp. 269-274
Author(s):  
Walter M. Bortz
Keyword(s):  
First Principles ◽  
Energy Flow ◽  
Basic Mechanism ◽  
Big Bang ◽  
First Principle ◽  
Central Value ◽  
Laws Of Thermodynamics ◽  
Big Picture ◽  
The Big Bang ◽  
The Universe

Evidence of the central value of physical exercise in human health is rampant, yet the fundamental underlying explanation of this universal benefit evades comprehension. The first principles of this underlying effect are found within the laws of thermodynamics and are explicitly outlined within the metabolic field (Schrodinger) as presented herein. To understand the basic mechanism responsible for the universal positive benefits of exercise mandates that the first principle of energy flow be enunciated. “On the dry bones of atoms and the distribution of energy in the universe are assembled the flesh and blood of life” (Prigogine, 1984). The engine of metabolism requires the ready provision of the primal energy first evidenced at the Big Bang as described in The Big Picture.

Sign in / Sign up

Export Citation Format

Share Document