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In non-relativistic classical mechanics, the use of Euclidean space instead of spacetime is appropriate, as time is treated as universal and constant, being independent of the state of motion of an observer.[disambiguation needed] In relativistic contexts, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer and also on the strength of gravitational fields, which can slow the passage of time for an object as seen by an observer outside the field. Until the beginning of the 20th century, time was believed to be independent of motion, progressing at a fixed rate in all reference frames; however, later experiments revealed that time slows at higher speeds of the reference frame relative to another reference frame. The term spacetime has taken on a generalized meaning beyond treating spacetime events with the normal 3+1 dimensions. Spacetime in literature[edit]

Light A triangular prism dispersing a beam of white light. The longer wavelengths (red) and the shorter wavelengths (blue) get separated Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, which is visible to the human eye and is responsible for the sense of sight.[1] Visible light is usually defined as having a wavelength in the range of 400 nanometres (nm), or 400×10−9 m, to 700 nanometres – between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths).[2][3] Often, infrared and ultraviolet are also called light. The main source of light on Earth is the Sun. In physics, the term light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not.[4][5] In this sense, gamma rays, X-rays, microwaves and radio waves are also light. Electromagnetic spectrum and visible light The behaviour of EMR depends on its wavelength. Speed of light Optics Refraction where

Libertarianism (metaphysics) The term "libertarianism" in a metaphysical or philosophical sense was first used by late Enlightenment free-thinkers to refer to those who believed in free will, as opposed to determinism.[9] The first recorded use was in 1789 by William Belsham in a discussion of free will and in opposition to "necessitarian" (or determinist) views.[10][11] Metaphysical and philosophical contrasts between philosophies of necessity and libertarianism continued in the early 19th century.[12] Explanations of libertarianism that do not involve dispensing with physicalism require physical indeterminism, such as probabilistic subatomic particle behavior – theory unknown to many of the early writers on free will. Physical determinism, under the assumption of physicalism, implies there is only one possible future and is therefore not compatible with libertarian free will. Nozick puts forward an indeterministic theory of free will in Philosophical Explanations.[6]

Mathematics of general relativity The mathematics of general relativity refers to various mathematical structures and techniques that are used in studying and formulating Albert Einstein's theory of general relativity. The main tools used in this geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime. This article is a general description of the mathematics of general relativity. Note: General relativity articles using tensors will use the abstract index notation. Why tensors? The principle of general covariance states that the laws of physics should take the same mathematical form in all reference frames and was one of the central principles in the development of general relativity. Spacetime as a manifold[edit] Most modern approaches to mathematical general relativity begin with the concept of a manifold. The rationale for choosing a manifold as the fundamental mathematical structure is to reflect desirable physical properties. Local versus global structure[edit] At at .

Wave–particle duality Origin of theory[edit] The idea of duality originated in a debate over the nature of light and matter that dates back to the 17th century, when Christiaan Huygens and Isaac Newton proposed competing theories of light: light was thought either to consist of waves (Huygens) or of particles (Newton). Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles also have a wave nature (and vice versa).[2] This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected.[3] Brief history of wave and particle viewpoints[edit] Thomas Young's sketch of two-slit diffraction of waves, 1803 Particle impacts make visible the interference pattern of waves. A quantum particle is represented by a wave packet.

Ultimate fate of the universe The ultimate fate of the universe is a topic in physical cosmology. Many possible fates are predicted by rival scientific theories, including futures of both finite and infinite duration. Once the notion that the universe started with a rapid inflation nicknamed the Big Bang became accepted by the majority of scientists,[1] the ultimate fate of the universe became a valid cosmological question, one depending upon the physical properties of the mass/energy in the universe, its average density, and the rate of expansion. There is a growing consensus among cosmologists that the universe is flat and will continue to expand forever.[2][3] The ultimate fate of the universe is dependent on the shape of the universe and what role dark energy will play as the universe ages. Emerging scientific basis[edit] Theory[edit] The theoretical scientific exploration of the ultimate fate of the universe became possible with Albert Einstein's 1916 theory of general relativity. Observation[edit] Big Rip[edit]

Einstein field equations The Einstein field equations (EFE) or Einstein - Hilbert equations are a set of 10 equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy.[1] First published by Einstein in 1915[2] as a tensor equation, the EFE equate local spacetime curvature (expressed by the Einstein tensor) with the local energy and momentum within that spacetime (expressed by the stress–energy tensor).[3] As well as obeying local energy-momentum conservation, the EFE reduce to Newton's law of gravitation where the gravitational field is weak and velocities are much less than the speed of light.[4] Exact solutions for the EFE can only be found under simplifying assumptions such as symmetry. Special classes of exact solutions are most often studied as they model many gravitational phenomena, such as rotating black holes and the expanding universe. Mathematical form[edit] where the scalar curvature,

Photon Nomenclature[edit] In 1900, Max Planck was working on black-body radiation and suggested that the energy in electromagnetic waves could only be released in "packets" of energy. In his 1901 article [4] in Annalen der Physik he called these packets "energy elements". Physical properties[edit] The cone shows possible values of wave 4-vector of a photon. A photon is massless,[Note 2] has no electric charge,[13] and is stable. Photons are emitted in many natural processes. The energy and momentum of a photon depend only on its frequency (ν) or inversely, its wavelength (λ): where k is the wave vector (where the wave number k = |k| = 2π/λ), ω = 2πν is the angular frequency, and ħ = h/2π is the reduced Planck constant.[17] Since p points in the direction of the photon's propagation, the magnitude of the momentum is The classical formulae for the energy and momentum of electromagnetic radiation can be re-expressed in terms of photon events. Experimental checks on photon mass[edit]

Philosophy of physics Centuries ago, the study of causality, and of the fundamental nature of space, time, matter, and the universe were part of metaphysics. Today the philosophy of physics is essentially a part of the philosophy of science. Physicists utilize the scientific method to delineate the universals and constants governing physical phenomena, and the philosophy of physics reflects on the results of this empirical research. Purpose of physics[edit] According to Niels Bohr, the purpose of physics is:[1] not to disclose the real essence of phenomena but only to trackdown (...) relations between the manifold aspects of experience. Many, particularly realists, find this minimal formulation an inadequate formulation of the purpose of physics, which they view as providing, in addition, a deeper world picture. Philosophy of space and time[edit] Time[edit] Time, in many philosophies, is seen as change. Time travel[edit] A second, similar type of time travel is permitted by general relativity. Space[edit] Elsewhere:

Friedmann equations and pressure . The equations for negative spatial curvature were given by Friedmann in 1924.[2] Assumptions[edit] The Friedmann equations start with the simplifying assumption that the universe is spatially homogeneous and isotropic, i.e. the Cosmological Principle; empirically, this is justified on scales larger than ~100 Mpc. where is a three-dimensional metric that must be one of (a) flat space, (b) a sphere of constant positive curvature or (c) a hyperbolic space with constant negative curvature. Einstein's equations now relate the evolution of this scale factor to the pressure and energy of the matter in the universe. The equations[edit] There are two independent Friedmann equations for modeling a homogeneous, isotropic universe. which is derived from the 00 component of Einstein's field equations. is the spatial curvature in any time-slice of the universe; it is equal to one-sixth of the spatial Ricci curvature scalar R since in the Friedmann model. which eliminates to give: Here . . Set

Thermal radiation This diagram shows how the peak wavelength and total radiated amount vary with temperature according to Wien's displacement law. Although this plot shows relatively high temperatures, the same relationships hold true for any temperature down to absolute zero. Visible light is between 380 and 750 nm. Thermal radiation in visible light can be seen on this hot metalwork. Its emission in the infrared is invisible to the human eye and the camera the image was taken with, but an infrared camera could show it (See Thermography). Thermal radiation is electromagnetic radiation generated by the thermal motion of charged particles in matter. Examples of thermal radiation include the visible light and infrared light emitted by an incandescent light bulb, the infrared radiation emitted by animals and detectable with an infrared camera, and the cosmic microwave background radiation. Thermal radiation is one of the fundamental mechanisms of heat transfer. Overview[edit] Surface effects[edit] Here,

Determinism Determinism is the philosophical position that for every event, including human action, there exist conditions that could cause no other event. "There are many determinisms, depending upon what pre-conditions are considered to be determinative of an event."[1] Deterministic theories throughout the history of philosophy have sprung from diverse and sometimes overlapping motives and considerations. Other debates often concern the scope of determined systems, with some maintaining that the entire universe is a single determinate system and others identifying other more limited determinate systems (or multiverse). Varieties[edit] Below appear some of the more common viewpoints meant by, or confused with "determinism". Many philosophical theories of determinism frame themselves with the idea that reality follows a sort of predetermined path Philosophical connections[edit] With nature/nurture controversy[edit] Nature and nurture interact in humans. With particular factors[edit] With the soul[edit]