# Spacetime

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. Such slowing, called time dilation, is explained in special relativity theory. Spacetime in literature Mathematical concept is that

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Friedmann equations and pressure . The equations for negative spatial curvature were given by Friedmann in 1924.[2] Spacetime symmetries Spacetime symmetries are features of spacetime that can be described as exhibiting some form of symmetry. The role of symmetry in physics is important in simplifying solutions to many problems, spacetime symmetries finding ample application in the study of exact solutions of Einstein's field equations of general relativity. Physical motivation Physical problems are often investigated and solved by noticing features which have some form of symmetry.

Bezos-Backed 10,000 Year Clock Site Preparation and Fabrication Underway If you were worth a million dollars, you might buy a fine watch to measure time. Rolex, Breitling, Seiko, this watch could run a couple thousand dollars. If you’re Jeff Bezos, you spend \$42 million on a 200-foot clock inside a mountain, engineered to withstand Armageddon and tick 10,000 years. That sounds like a lot of money, but compared to Bezos’ \$25.2 billion, it’s akin to our millionaire buying a single Rolex. No big deal for Bezos. The last time we covered the 10,000 Year Clock project, Bezos was freshly aboard.

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. Four-dimensional space In modern physics, space and time are unified in a four-dimensional Minkowski continuum called spacetime, whose metric treats the time dimension differently from the three spatial dimensions (see below for the definition of the Minkowski metric/pairing). Spacetime is not a Euclidean space. History An arithmetic of four dimensions called quaternions was defined by William Rowan Hamilton in 1843. This associative algebra was the source of the science of vector analysis in three dimensions as recounted in A History of Vector Analysis. Soon after tessarines and coquaternions were introduced as other four-dimensional algebras over R.

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.

Time dilation Time dilation explains why two working clocks will report different times after different accelerations. For example, ISS astronauts return from missions having aged slightly less than they would have been if they had remained on Earth, and GPS satellites work because they adjust for similar bending of spacetime to coordinate with systems on Earth.[1] An accurate clock at rest with respect to one observer may be measured to tick at a different rate when compared to a second observer's own equally accurate clocks. This effect arises neither from technical aspects of the clocks nor from the fact that signals need time to propagate, but from the nature of spacetime itself.

Anthony Grafton Anthony Grafton, lecturing at the Gotha Research Center, 2010 Anthony Grafton (sometimes Anthony T. Grafton; born May 21, 1950) is one of the foremost historians of early modern Europe and the current Henry Putnam University Professor at Princeton University. He is also a corresponding fellow of the British Academy and a recipient of the Balzan Prize. From January 2011 to January 2012, he served as the President of the American Historical Association.[1] Early life and education

Wave–particle duality Origin of theory 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]

Convex regular polychoron The tesseract is one of 6 convex regular polychora In mathematics, a convex regular polychoron is a polychoron (4-polytope) that is both regular and convex. These are the four-dimensional analogs of the Platonic solids (in three dimensions) and the regular polygons (in two dimensions). These polychora were first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. Schläfli discovered that there are precisely six such figures. 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.

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