Random Topics
Get flash to fully experience Pearltrees
Phase space - Wikipedia, the free encyclopedia
Phase space of a dynamical system with focal stability. In mathematics and physics , a phase space , introduced by Willard Gibbs in 1901, [ 1 ] is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space. For mechanical systems , the phase space usually consists of all possible values of position and momentum variables i.e. the cotangent space of configuration space .A phase diagram in physical chemistry , engineering , mineralogy , and materials science is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium .
Phase diagram - Wikipedia, the free encyclopedia
Chaos theory is a field of study in mathematics , with applications in several disciplines including physics , engineering , economics , biology , and philosophy . Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the butterfly effect . Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general. [ 1 ] This happens even though these systems are deterministic , meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. [ 2 ] In other words, the deterministic nature of these systems does not make them predictable. [ 3 ] [ 4 ] This behavior is known as deterministic chaos, or simply chaos .
Chaos theory - Wikipedia, the free encyclopedia
The Structure of Scientific Revolutions by Thomas Kuhn , is an analysis of the history of science , published in 1962 . Its publication was a landmark event in the history , philosophy , and sociology of scientific knowledge and it triggered an ongoing worldwide assessment and reaction in — and beyond — those scholarly communities.
The Structure of Scientific Revolutions - Wikipedia, the free encyclopedia
Wave function - Wikipedia, the free encyclopedia
A wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of space and time. The laws of quantum mechanics (the Schrödinger equation ) describe how the wave function evolves over time.
Wave function collapse - Wikipedia, the free encyclopedia
In quantum mechanics , wave function collapse (also called collapse of the state vector or reduction of the wave packet ) is the phenomenon in which a wave function —initially in a superposition of several different possible eigenstates —appears to reduce to a single one of those states after interaction with an observer . In simplified terms, it is the reduction of the physical possibilities into a single possibility as seen by an observer. It is one of two processes by which quantum systems evolve in time, according to the laws of quantum mechanics as presented by John von Neumann . [ 1 ] The reality of wave function collapse has always been debatable, i.e., whether it is a fundamental physical phenomenon in its own right or just an epiphenomenon of another process, such as quantum decoherence . [ 2 ] In recent decades the quantum decoherence view has gained popularity and is commonly taught at the graduate level (e.g. Cohen-Tannoudji 's standard textbook [ 3 ] ).
Quantum state - Wikipedia, the free encyclopedia
defines the state of an electron within a hydrogen atom and are known as the electron's quantum numbers . Other examples could be some "given direction and energy, or some other given condition" [ 1 ] , when we are talking about scattering. More generally, the state of the system is represented by a single vector known as a ket . Typically, one postulates some experimental apparatus and procedure which "prepares" this quantum state; the mathematical object reflects the operations performed by this apparatus.
Artist's representation of a black hole The black hole information paradox results from the combination of quantum mechanics and general relativity . It suggests that physical information could permanently disappear in a black hole , allowing many physical states to evolve into the same state.
Black hole information paradox - Wikipedia, the free encyclopedia
Causal dynamical triangulation (abbreviated as CDT ) invented by Renate Loll , Jan Ambjørn and Jerzy Jurkiewicz , and popularized by Fotini Markopoulou and Lee Smolin , is an approach to quantum gravity that like loop quantum gravity is background independent .
Causal dynamical triangulation - Wikipedia, the free encyclopedia
Black hole complementarity is a conjectured solution to the black hole information paradox , proposed by Leonard Susskind [ 1 ] and Gerard 't Hooft . [ 2 ] Ever since Stephen Hawking suggested information is lost in evaporating black hole once it passes through the event horizon and is inevitably destroyed at the singularity and that this can turn pure quantum states into mixed states , some physicists have wondered if a complete theory of quantum gravity might be able to conserve information with a unitary time evolution . But how can this be possible if information can't escape the event horizon without traveling faster than light?
Black hole complementarity - Wikipedia, the free encyclopedia
Quantum gravity (QG) is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics (describing three of the four known fundamental interactions ) with general relativity (describing the fourth, gravity ). It is hoped that development of such a theory would unify into a single mathematical framework all fundamental interactions and to describe all known observable interactions in the universe, at both subatomic and cosmological scales.
Quantum gravity - Wikipedia, the free encyclopedia
Induced gravity (or emergent gravity ) is an idea in quantum gravity that space-time background emerges as a mean field approximation of underlying microscopic degrees of freedom, similar to the fluid mechanics approximation of Bose–Einstein condensates . The concept was originally proposed by Andrei Sakharov in 1967. Sakharov observed that many condensed matter systems give rise to emergent phenomena which are identical to general relativity . For example, crystal defects can look like curvature and torsion in an Einstein-Cartan spacetime .
Induced gravity - Wikipedia, the free encyclopedia
Localized time-varying charge and current densities can act as sources of electromagnetic waves in a vacuum.