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Cauchy Horizon
In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory of partial differential equations). One side of the horizon contains closed space-like geodesics and the other side contains closed time-like geodesics. The concept is named after Augustin-Louis Cauchy. Under the averaged weak energy condition (AWEC), Cauchy horizons are inherently unstable. However, cases of AWEC violation, such as the Casimir effect caused by periodic boundary conditions, do exist, and since the region of spacetime inside the Cauchy horizon has closed timelike curves it is subject to periodic boundary conditions. If the spacetime inside the Cauchy horizon violates AWEC, then the horizon becomes stable and frequency boosting effects would be canceled out by the tendency of the spacetime to act as a divergent lens. Were this conjecture to be shown empirically true, it would provide a counter-example to the strong ...
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Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ...
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Cosmic Censorship Hypothesis
The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of gravitational singularities arising in general relativity. Singularities that arise in the solutions of Einstein's equations are typically hidden within event horizons, and therefore cannot be observed from the rest of spacetime. Singularities that are not so hidden are called ''naked''. The weak cosmic censorship hypothesis was conceived by Roger Penrose in 1969 and posits that no naked singularities exist in the universe. Basics Since the physical behavior of singularities is unknown, if singularities can be observed from the rest of spacetime, causality may break down, and physics may lose its predictive power. The issue cannot be avoided, since according to the Penrose–Hawking singularity theorems, singularities are inevitable in physically reasonable situations. Still, in the absence of naked singularities, the universe, as described by the general theory of relativi ...
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Solos (TV Series)
''Solos'' is an American dramatic anthology streaming television miniseries created by David Weil and produced by Amazon Studios. It stars Morgan Freeman, Anne Hathaway, Helen Mirren, Uzo Aduba, Anthony Mackie, Constance Wu, Dan Stevens and Nicole Beharie. The seven-episode series premiered on May 21, 2021 on Amazon Prime Video in UK, United States, Australia, Canada, Ireland, India, New Zealand and later that year in additional territories. Premise The series ponders what it means to be human, arguing that we are connected to others through shared experiences, even in our most isolated moments. Cast * Morgan Freeman as Stuart, a patient in an Alzheimer's facility, later revealed to be a memory thief/junkie (by either hacking or by force). His confirmed thefts are Leah, Tom, Peg, Sasha, and Otto, whose memories he stole when Otto was a child, amongst hundreds of other victims. Freeman's character narrates the beginning of each episode and appears in his own. * Anne Hathaway as ...
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Amazon Prime
Amazon Prime is a paid subscription service from Amazon which is available in various countries and gives users access to additional services otherwise unavailable or available at a premium to other Amazon customers. Services include same, one- or two-day delivery of goods and streaming music, video, e-books, gaming and grocery shopping services. In April 2021, Amazon reported that Prime had more than 200 million subscribers worldwide. History Early history In 2005, Amazon announced Amazon Prime as a membership service offering free two-day shipping within the contiguous United States on all eligible purchases for an annual fee of $79 () and discounted one-day shipping rates. Amazon launched the program in Germany, Japan and the United Kingdom in 2007; in France (as "Amazon Premium") in 2008, in Italy in 2011, in Canada in 2013, in India in July 2016, in Mexico in March 2017, in Turkey in September 2020, in Sweden in September 2021, and in Poland in October 2021. Amazon Prime ...
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Time Loop
The time loop or temporal loop is a plot device in fiction whereby characters re-experience a span of time which is repeated, sometimes more than once, with some hope of breaking out of the cycle of repetition. The term "time loop" is sometimes used to refer to a causal loop; however, causal loops are unchanging and self-originating, whereas time loops are constantly resetting: when a certain condition is met, such as a death of a character or a clock reaching a certain time, the loop starts again, possibly with one or more characters retaining the memories from the previous loop. History An early example of a time loop is the 1915 Russian novel ''Strange Life of Ivan Osokin'', where the main character gets to live his life over again but struggles to change it the second time around. It was used in the short story "Doubled and Redoubled" by Malcolm Jameson that appeared in the February 1941 ''Unknown''; the story tells of a person accidentally cursed to repeat a "perfect" day, inc ...
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Palm Springs (2020 Film)
''Palm Springs'' is a 2020 American science fiction romantic comedy film directed by Max Barbakow (in his feature directorial debut), from a screenplay by Andy Siara. It stars Andy Samberg (who co-produced the film), Cristin Milioti, and J. K. Simmons, and follows two strangers who meet at a wedding in Palm Springs only to get stuck in a time loop. ''Palm Springs'' had its world premiere at the Sundance Film Festival on January 26, 2020, and was simultaneously released on Hulu and in select theaters by Neon on July 10, 2020. The film was praised for the cast's performances and its use of the concept. At the 78th Golden Globe Awards, it earned two nominations: Best Motion Picture – Musical or Comedy and Best Actor in a Motion Picture – Musical or Comedy for Samberg. Among other accolades, it won Best Comedy at the 26th Critics' Choice Awards. Plot On November 9, in Palm Springs, Nyles wakes up with his girlfriend Misty, who is cheating on him. That evening, Nyles and Sa ...
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Quanta Magazine
''Quanta Magazine'' is an editorially independent online publication of the Simons Foundation covering developments in physics, mathematics, biology and computer science. ''Undark Magazine'' described ''Quanta Magazine'' as "highly regarded for its masterful coverage of complex topics in science and math." The science news aggregator ''RealClearScience'' ranked ''Quanta Magazine'' first on its list of "The Top 10 Websites for Science in 2018." In 2020, the magazine received a National Magazine Award for General Excellence from the American Society of Magazine Editors for its "willingness to tackle some of the toughest and most difficult topics in science and math in a language that is accessible to the lay reader without condescension or oversimplification." The articles in the magazine are freely available to read online. ''Scientific American'', ''Wired'', ''The Atlantic'', and ''The Washington Post'', as well as international science publications like ''Spektrum der Wissensch ...
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Smooth Function
In mathematical analysis, the smoothness of a function (mathematics), function is a property measured by the number of Continuous function, continuous Derivative (mathematics), derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all Order of derivation, orders in its Domain of a function, domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or C^ function). Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an open set U on the real line and a function f defined on U with real values. Let ''k'' be a non-negative integer. The function f is said to be of ...
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Kerr–Newman Metric
The Kerr–Newman metric is the most general asymptotically flat, stationary solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding an electrically charged, rotating mass. It generalizes the Kerr metric by taking into account the field energy of an electromagnetic field, in addition to describing rotation. It is one of a large number of various different electrovacuum solutions, that is, of solutions to the Einstein–Maxwell equations which account for the field energy of an electromagnetic field. Such solutions do not include any electric charges other than that associated with the gravitational field, and are thus termed vacuum solutions. This solution has not been especially useful for describing astrophysical phenomena, because observed astronomical objects do not possess an appreciable net electric charge, and the magnetic fields of stars arise through other processes. As a model of realistic black ...
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Closed Timelike Curves
In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van Stockum in 1937 and later confirmed by Kurt Gödel in 1949,Stephen Hawking, '' My Brief History'', chapter 11 who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes. If CTCs exist, their existence would seem to imply at least the theoretical possibility of time travel backwards in time, raising the spectre of the grandfather paradox, although the Novikov self-consistency principle seems to show that such paradoxes could be avoided. Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of quantum gravity w ...
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Light-like
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. The physicist Albert Einstein helped develop the idea of spacetime as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain physical phenomena: Isaac Newton's laws of physics described the motion of massive objects, while James Clerk Maxwell's electromagnetic models explained the properties of light. However, in 1905, Einstein based a work on special relativity on two postulates: * The laws of physics are invariant ...
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