title: 16:9 aspect ratio

text: Once seen as exotic, since 2009, it has become the most common aspect ratio for televisions and computer monitors, and is also the international standard image format for UHD, HDTV, Full HD, and SD digital television. It has replaced the "fullscreen" 4:3 aspect ratio.


title: 16:9 aspect ratio

text: 16:9 (1.7:1) (spoken as "sixteen by nine" or "sixteen to nine") is the international standard format of Ultra HD, non-HD digital widescreen television and analog widescreen television systems PALplus and Wide-aspect Clear-vision. Japan's Hi-Vision originally started with a 5:3 (1.6:1) ratio but converted when the international standards group introduced a wider ratio of 16 to 9. Many digital video cameras have the capability to record in 16:9, and 16:9 is the only widescreen aspect ratio natively supported by the DVD standard. It is also the native aspect ratio of Blu-ray discs, but Blu-ray and DVD producers can also choose to show even wider ratios such as 1.85:1, 2.00:1, and 2.40:1 within the 16:9 DVD and Blu-ray frame by hard matting or adding black bars within the image itself.


title: 16:9 aspect ratio

text: Dr. Kerns H. Powers, a member of the SMPTE Working Group on High-Definition Electronic Production, first proposed the 16:9 (1.7:1) aspect ratio in 1984, when nobody was creating 16:9 videos. The popular choices in 1980 were 4:3 (based on TV standard's ratio at the time), 15:9 (the European "flat" 1.6:1 ratio), 1.85:1 (the American "flat" ratio) and 2.35:1 (the CinemaScope/Panavision) ratio for anamorphic widescreen.


title: 16:9 aspect ratio

text: Powers cut out rectangles with equal areas, shaped to match each of the popular aspect ratios. When overlapped with their center points aligned, he found that all of those aspect ratio rectangles fit within an outer rectangle with an aspect ratio of 1.7:1 and all of them also covered a smaller common inner rectangle with the same aspect ratio 1.77:1. The value found by Powers is exactly the geometric mean of the extreme aspect ratios, 4:3 and 2.35:1, formula_1≈1.77 which is coincidentally close to 16:9. Applying the same geometric mean technique to 16:9 and 4:3 yields an aspect ratio of around 1.5396:1, sometimes approximated as (1.5:1), which is likewise used as a compromise between these ratios.


title: 16:9 aspect ratio

text: While 16:9 (1.7:1) was initially selected as a compromise format, the subsequent popularity of HDTV broadcast has solidified 16:9 as perhaps the most common video aspect ratio in use. Most 4:3 (1.3:1) and 2.40:1 video is now recorded using a "shoot and protect" technique that keeps the main action within a 16:9 (1.7:1) inner rectangle to facilitate HD broadcast. Conversely it is quite common to use a technique known as center-cutting, to approach the challenge of presenting material shot (typically 16:9) to both an HD and legacy 4:3 audience simultaneously without having to compromise image size for either audience. Content creators frame critical content or graphics to fit within the 1.33:1 raster space. This has similarities to a filming technique called open matte.


title: 16:9 aspect ratio

text: In 1993, the European Union instituted the "16:9 Action Plan", to accelerate the development of the advanced television services in 16:9 aspect ratio, both in PALplus (compatible with regular PAL broadcasts) and also in HD-MAC (an early HD format). The Community fund for the "16:9 Action Plan" amounted to €228,000,000.


title: 16:9 aspect ratio

text: Over a long period in the late 2000s and early 2010s, the computer industry switched from 4:3 to 16:9 as the most common aspect ratio for monitors and laptops. A 2008 report by DisplaySearch cited a number of reasons for this shift, including the ability for PC and monitor manufacturers to expand their product ranges by offering products with wider screens and higher resolutions, helping consumers to more easily adopt such products and "stimulating the growth of the notebook PC and LCD monitor market". By using the same aspect ratio for both TVs and monitors, manufacturing can be streamlined and research costs reduced by not requiring two separate sets of equipment, and since a 16:9 is narrower than a 16:10 panel of the same length, more panels can be created per sheet of glass.


title: 16:9 aspect ratio

text: In 2011, Bennie Budler, product manager of IT products at Samsung South Africa, confirmed that monitors capable of resolutions are not being manufactured anymore. "It is all about reducing manufacturing costs. The new 16:9 aspect ratio panels are more cost-effective to manufacture locally than the previous 16:10 panels".


title: 16:9 aspect ratio

text: In March 2011, the 16:9 resolution became the most common used resolution among Steam's users. The previous most common resolution was (16:10). By July 2022, 16:9 resolution is preferred by 77% of users (1920x1080 with 67%; 2560 x 1440 with 10%).


title: 16:9 aspect ratio

text: 16:9 is the only widescreen aspect ratio natively supported by the DVD format. An anamorphic PAL region DVD video frame has a maximum resolution of , but a video player software will stretch this to .


title: 16:9 aspect ratio

text: Producers can also choose to show even wider ratios such as 1.85:1 and 2.4:1 within the 16:9 DVD frame by hard matting or adding black bars within the image itself. Some films which were made in a 1.85:1 aspect ratio, such as the U.S.-Italian co-production "Man of La Mancha" and Kenneth Branagh's "Much Ado About Nothing", fit quite comfortably onto a 1.7:1 HDTV screen and have been issued as an enhanced version on DVD without the black bars. Many digital video cameras have the capability to record in 16:9.


title: 16:9 aspect ratio

text: In Europe, 16:9 is the standard broadcast format for most digital SD TV channels and all HD broadcasts. Some countries adopted the format for analogue television, first by using the PALplus standard (now obsolete) and then by simply using WSS on normal PAL broadcasts.


title: Redox

text: Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a decrease in the oxidation state.


title: Redox

text: "Redox" is a combination of the words "reduction" and "oxidation". The term "redox" was first used in 1928. The processes of oxidation and reduction occur simultaneously and cannot occur independently. In redox processes, the reductant transfers electrons to the oxidant. Thus, in the reaction, the reductant or "reducing agent" loses electrons and is oxidized, and the oxidant or "oxidizing agent" gains electrons and is reduced. The pair of an oxidizing and reducing agent that is involved in a particular reaction is called a "redox pair". A "redox couple" is a reducing species and its corresponding oxidizing form, e.g., / .The oxidation alone and the reduction alone are each called a "half-reaction" because two half-reactions always occur together to form a whole reaction.


title: Redox

text: "Oxidation" originally implied a reaction with oxygen to form an oxide. Later, the term was expanded to encompass oxygen-like substances that accomplished parallel chemical reactions. Ultimately, the meaning was generalized to include all processes involving the loss of electrons. Substances that have the ability to "oxidize" other substances (cause them to lose electrons) are said to be "oxidative" or "oxidizing", and are known as oxidizing agents, oxidants, or oxidizers. The oxidant (oxidizing agent) removes electrons from another substance, and is thus itself reduced. And, because it "accepts" electrons, the oxidizing agent is also called an electron acceptor. Oxidants are usually chemical substances with elements in high oxidation states (e.g., , , , , ), or else highly electronegative elements (e.g. O, F, Cl, Br, I) that can gain extra electrons by oxidizing another substance.


title: Redox

text: Oxidizers are oxidants, but the term is mainly reserved for sources of oxygen, particularly in the context of explosions. Nitric acid is an oxidizer.


title: Redox

text: Substances that have the ability to "reduce" other substances (cause them to gain electrons) are said to be "reductive" or "reducing" and are known as reducing agents, reductants, or reducers. The reductant (reducing agent) transfers electrons to another substance and is thus itself oxidized. And, because it donates electrons, the reducing agent is also called an electron donor. Electron donors can also form charge transfer complexes with electron acceptors. The word "reduction" originally referred to the loss in weight upon heating a metallic ore such as a metal oxide to extract the metal. In other words, ore was "reduced" to metal. Antoine Lavoisier demonstrated that this loss of weight was due to the loss of oxygen as a gas. Later, scientists realized that the metal atom gains electrons in this process. The meaning of "reduction" then became generalized to include all processes involving a gain of electrons. Reducing equivalent refers to chemical species which transfer the equivalent of one electron in redox reactions. The term is common in biochemistry. A reducing equivalent can be an electron, a hydrogen atom, as a hydride ion.


title: Redox

text: Reductants in chemistry are very diverse. Electropositive elemental metals, such as lithium, sodium, magnesium, iron, zinc, and aluminium, are good reducing agents. These metals donate or "give away" electrons relatively readily. They transfer electrons.


title: Redox

text: "Hydride transfer reagents", such as NaBH and LiAlH, reduce by atom transfer: they transfer the equivalent of hydride or H. These reagents widely used in the reduction of carbonyl compounds to alcohols. A related method of reduction involves the use of hydrogen gas (H) as sources of H atoms.


title: Redox

text: The electrochemist John Bockris proposed the words "electronation" and "deelectronation" to describe reduction and oxidation processes, respectively, when they occur at electrodes. These words are analogous to protonation and deprotonation. They have not been widely adopted by chemists worldwide, although IUPAC has recognized the term electronation.


title: Redox

text: Redox reactions can occur slowly, as in the formation of rust, or rapidly, as in the case of burning fuel. Electron transfer reactions are generally fast, occurring within the time of mixing.


title: Redox

text: The mechanisms of atom-transfer reactions are highly variable because many kinds of atoms can be transferred. Such reactions can also be quite complex, i.e. involve many steps. The mechanisms of electron-transfer reactions occur by two distinct pathways, inner sphere electron transfer and outer sphere electron transfer.


title: Redox

text: Analysis of bond energies and ionization energies in water allow calculation of the thermodynamic aspects of redox reactions.


title: Redox

text: Each half-reaction has a "standard electrode potential" ("E"), which is equal to the potential difference or voltage at equilibrium under standard conditions of an electrochemical cell in which the cathode reaction is the half-reaction considered, and the anode is a standard hydrogen electrode where hydrogen is oxidized:


title: Redox

text: The electrode potential of each half-reaction is also known as its "reduction potential" "E", or potential when the half-reaction takes place at a cathode. The reduction potential is a measure of the tendency of the oxidizing agent to be reduced. Its value is zero for H + e →  H by definition, positive for oxidizing agents stronger than H (e.g., +2.866 V for F) and negative for oxidizing agents that are weaker than H (e.g., −0.763 V for Zn).


title: Redox

text: However, the potential of the reaction at the anode is sometimes expressed as an "oxidation potential":


title: Redox

text: The oxidation potential is a measure of the tendency of the reducing agent to be oxidized but does not represent the physical potential at an electrode. With this notation, the cell voltage equation is written with a plus sign


title: Redox

text: In the reaction between hydrogen and fluorine, hydrogen is being oxidized and fluorine is being reduced:


title: Redox

text: This reaction is spontaneous and releases 542 kJ per 2 g of hydrogen because the H-F bond is much stronger than the F-F bond. This reaction can be analyzed as two half-reactions. The oxidation reaction converts hydrogen to protons:


title: Redox

text: In this type of reaction, a metal atom in a compound (or in a solution) is replaced by an atom of another metal. For example, copper is deposited when zinc metal is placed in a copper(II) sulfate solution:


title: Redox

text: In the above reaction, zinc metal displaces the copper(II) ion from copper sulfate solution and thus liberates free copper metal. The reaction is spontaneous and releases 213 kJ per 65 g of zinc.


title: Redox

text: A disproportionation reaction is one in which a single substance is both oxidized and reduced. For example, thiosulfate ion with sulfur in oxidation state +2 can react in the presence of acid to form elemental sulfur (oxidation state 0) and sulfur dioxide (oxidation state +4).


title: Redox

text: Cathodic protection is a technique used to control the corrosion of a metal surface by making it the cathode of an electrochemical cell. A simple method of protection connects protected metal to a more easily corroded "sacrificial anode" to act as the anode. The sacrificial metal instead of the protected metal, then, corrodes. A common application of cathodic protection is in galvanized steel, in which a sacrificial coating of zinc on steel parts protects them from rust.


title: Redox

text: Oxidation is used in a wide variety of industries such as in the production of and oxidizing ammonia to produce nitric acid.


title: Redox

text: Redox reactions are the foundation of electrochemical cells, which can generate electrical energy or support electrosynthesis. Metal ores often contain metals in oxidized states such as oxides or sulfides, from which the pure metals are extracted by smelting at high temperature in the presence of a reducing agent. The process of electroplating uses redox reactions to coat objects with a thin layer of a material, as in chrome-plated automotive parts, silver plating cutlery, galvanization and gold-plated jewelry.


title: Redox

text: Many important biological processes involve redox reactions. Before some of these processes can begin iron must be assimilated from the environment.


title: Redox

text: Cellular respiration, for instance, is the oxidation of glucose (CHO) to CO and the reduction of oxygen to water. The summary equation for cell respiration is:


title: Redox

text: The process of cell respiration also depends heavily on the reduction of NAD to NADH and the reverse reaction (the oxidation of NADH to NAD). Photosynthesis and cellular respiration are complementary, but photosynthesis is not the reverse of the redox reaction in cell respiration:


title: Redox

text: Biological energy is frequently stored and released by means of redox reactions. Photosynthesis involves the reduction of carbon dioxide into sugars and the oxidation of water into molecular oxygen. The reverse reaction, respiration, oxidizes sugars to produce carbon dioxide and water. As intermediate steps, the reduced carbon compounds are used to reduce nicotinamide adenine dinucleotide (NAD) to NADH, which then contributes to the creation of a proton gradient, which drives the synthesis of adenosine triphosphate (ATP) and is maintained by the reduction of oxygen.


title: Redox

text: Free radical reactions are redox reactions that occur as a part of homeostasis and killing microorganisms, where an electron detaches from a molecule and then reattaches almost instantaneously. Free radicals are a part of redox molecules and can become harmful to the human body if they do not reattach to the redox molecule or an antioxidant. Unsatisfied free radicals can spur the mutation of cells they encounter and are, thus, causes of cancer.


title: Redox

text: The term "redox state" is often used to describe the balance of GSH/GSSG, NAD/NADH and NADP/NADPH in a biological system such as a cell or organ. The redox state is reflected in the balance of several sets of metabolites (e.g., lactate and pyruvate, beta-hydroxybutyrate, and acetoacetate), whose interconversion is dependent on these ratios. An abnormal redox state can develop in a variety of deleterious situations, such as hypoxia, shock, and sepsis. Redox mechanism also control some cellular processes. Redox proteins and their genes must be co-located for redox regulation according to the CoRR hypothesis for the function of DNA in mitochondria and chloroplasts.


title: Redox

text: Wide varieties of aromatic compounds are enzymatically reduced to form free radicals that contain one more electron than their parent compounds. In general, the electron donor is any of a wide variety of flavoenzymes and their coenzymes. Once formed, these anion free radicals reduce molecular oxygen to superoxide and regenerate the unchanged parent compound. The net reaction is the oxidation of the flavoenzyme's coenzymes and the reduction of molecular oxygen to form superoxide. This catalytic behavior has been described as a futile cycle or redox cycling.


title: Redox

text: Minerals are generally oxidized derivatives of metals. Iron is mined as its magnetite (FeO). Titanium is mined as its dioxide, usually in the form of rutile (TiO). To obtain the corresponding metals, these oxides must be reduced, which is often achieved by heating these oxides with carbon or carbon monoxide as reducing agents. Blast furnaces are the reactors where iron oxides and coke (a form of carbon) are combined to produce molten iron.The main chemical reaction producing the molten iron is:


title: Redox

text: Electron transfer reactions are central to myriad processes and properties in soils, and electron "activity", quantified as Eh (platinum electrode potential (voltage) relative to the standard hydrogen electrode) or pe (analogous to pH as -log electron activity), is a master variable, along with pH, that controls and is governed by chemical reactions and biological processes. Early theoretical research with applications to flooded soils and paddy rice production was seminal for subsequent work on thermodynamic aspects of redox and plant root growth in soils. Later work built on this foundation, and expanded it for understanding redox reactions related to heavy metal oxidation state changes, pedogenesis and morphology, organic compound degradation and formation, free radical chemistry, wetland delineation, soil remediation, and various methodological approaches for characterizing the redox status of soils.


title: Redox

text: The key terms involved in redox can be confusing. For example, a reagent that is oxidized loses electrons; however, that reagent is referred to as the reducing agent. Likewise, a reagent that is reduced gains electrons and is referred to as the oxidizing agent. These mnemonics are commonly used by students to help memorise the terminology:


title: Kevin Michael Richardson

text: Kevin Michael Richardson (born October 25, 1964) is an American actor. Known for his distinctively deep voice, he has mostly voiced villainous characters in animation and video games. In film, Richardson voiced Goro in "Mortal Kombat" (1995) and reprises in "" (2020), Captain Gantu in the "Lilo & Stitch" franchise, and Deus Ex Machina in "The Matrix Revolutions" (2003). He has also voiced characters on Seth MacFarlane's shows "Family Guy", "The Cleveland Show", and "American Dad!", as well as several characters on "The Simpsons".


title: Kevin Michael Richardson

text: Richardson is also known for his roles as Trigon, Mammoth & See-More in both "Teen Titans" and "Teen Titans Go!", Antauri in "Super Robot Monkey Team Hyperforce Go!," the Shredder in "Teenage Mutant Ninja Turtles" (2012), Stump Smash and Tree Rex in the "Skylanders" video game series, as the second voice of Dr. Hibbert and various others in "The Simpsons", Rosie in "F Is for Family", Barney Rubble in "", and the Mauler Twins and Monster Girl in "Invincible". He received two Daytime Emmy Award nominations for voicing the Joker in "The Batman" (2004–2008).


title: Kevin Michael Richardson

text: Richardson was born on October 25, 1964 in the Bronx borough of New York City. He earned a BFA in theater from Syracuse University in 1988.


title: Kevin Michael Richardson

text: Richardson began his live-action acting career in New York City, where he performed in commercials. His first professional acting job was in an AT&T commercial. He was frequently hired as a voice for television commercials. He later moved to Los Angeles. He has usually portrayed villainous characters due to his deep and powerful voice. In 1995, he obtained his first voice role as Mayor Tilton on the animated television version of "The Mask". Additionally, early in his career, he appeared in a PBS special directed by John Houseman.


title: Kevin Michael Richardson

text: Richardson's other credits include Captain Gantu in "Lilo & Stitch" and its franchise, Shnitzel in the "Chowder" pilot (and was later replaced by John DiMaggio), Goro in "Mortal Kombat", the second voice of Skulker on "Danny Phantom", Sarevok in the "Baldur's Gate" series, Jolee Bindo in "", Crunch Bandicoot in the "Crash Bandicoot" games, Sai Sahan in Elder Scrolls Online MMORPG series, Tartarus from "Halo 2", Chairman Drek in "Ratchet & Clank", Antauri in "Super Robot Monkey Team Hyperforce Go!", Openly Gator from "Queer Duck", Doctor Payne and others on "The Proud Family", Dark Laser on "The Fairly OddParents", Maurice from "The Penguins of Madagascar (replacing Cedric the Entertainer)", Slam Tasmanian and Tech E. Coyote on "Loonatics Unleashed" and the voice of Exile in the 1990s animated series "Road Rovers".


title: Kevin Michael Richardson

text: Richardson replaced Keith David as the voice of Tombstone on "The Spectacular Spider-Man". He provided a character voice set for "Icewind Dale": "" and "Icewind Dale II". He was the voice of Heihachi in the PlayStation 2 game "Soul Calibur II", though he is listed in the role as Victor Stone. He also voiced Stump Smash and Tree Rex in "", "" and "".


title: Kevin Michael Richardson

text: In 2001, Richardson voiced Barney Rubble in the animated movie "". In 2004, he became the first Black actor to portray the Joker, voicing the character on the animated series "The Batman", a role for which he was twice nominated for the Daytime Emmy Award for Outstanding Performer in an Animated Program. In 2005, he voiced Trigon on the animated series "Teen Titans", taking over the role from Keith Szarabajka.


title: Kevin Michael Richardson

text: In 2006, he appeared in the comedy "Clerks II" in which he plays a cop who notices the words "Porch Monkey 4 Life" written on the back of Randal Graves' work jacket; he also voiced the elder dragon Terrador from "The Legend of Spyro" game series. In 2008, he performed the voice of Bishop for "Wolverine and the X-Men". Later, he did the voice of Nick Fury on "The Super Hero Squad Show". He also voiced Tyro in Nickelodeon's "" in 2004.


title: Kevin Michael Richardson

text: Richardson often plays characters based on comedian Bill Cosby, such as on "Family Guy" ("Brian Does Hollywood"), where Stewie is a contestant on the comedian's "Kids Say the Darndest Things"; as Cosby himself on "The Boondocks"; and Numbuh 5's father Mr. Lincoln, an homage to Cosby on "".


title: Kevin Michael Richardson

text: His most frequent role on "Family Guy" is Jerome, Lois's ex-boyfriend. He also is the voice of Cleveland Brown Jr. and voiced Lester Krinklesac and numerous others on "The Cleveland Show". He currently voices Principal Brian Lewis on "American Dad!" and is the current voice for Dr. Hibbert replacing Harry Shearer on "The Simpsons". His voice roles in 2011 included Panthro in the "Thundercats" series, Martian Manhunter on "Young Justice" and Bulkhead, one of the Autobots in "". He played Kilowog in "", the video game sequel to the live-action film "Green Lantern" and later reprised the role in "".


title: Kevin Michael Richardson

text: In September 2013, he provided the voice of Mr. Gus on the Cartoon Network show "Uncle Grandpa". In 2015, he did the voice of a Nigerian king on "The Simpsons" episode "The Princess Guide". Later, he provided the voice of Judge Michaels in Tyler Perry's first animated film, "Madea's Tough Love". In 2021, he provided the voice of Jimbo in "" (2018), the sequel to the 2017 film "The Boss Baby".


title: Kevin Michael Richardson

text: Richardson lives in Los Angeles with his wife, Monica, whom he married in 2006. He is the stepfather of her two sons from a previous marriage.


title: Special relativity

text: In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:


title: Special relativity

text: Special relativity was originally proposed by Albert Einstein in a paper published on 26 September 1905 titled "On the Electrodynamics of Moving Bodies". The incompatibility of Newtonian mechanics with Maxwell's equations of electromagnetism and, experimentally, the Michelson–Morley null result (and subsequent similar experiments) demonstrated that the historically hypothesized luminiferous aether did not exist. This led to Einstein's development of special relativity, which corrects mechanics to handle situations involving all motions and especially those at a speed close to that of light (known as ""). Today, special relativity is proven to be the most accurate model of motion at any speed when gravitational and quantum effects are negligible. Even so, the Newtonian model is still valid as a simple and accurate approximation at low velocities (relative to the speed of light), for example, everyday motions on Earth.


title: Special relativity

text: Special relativity has a wide range of consequences that have been experimentally verified. They include the relativity of simultaneity, length contraction, time dilation, the relativistic velocity addition formula, the relativistic Doppler effect, relativistic mass, a universal speed limit, mass–energy equivalence, the speed of causality and the Thomas precession. It has, for example, replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula formula_1, where formula_2 is the speed of light in a vacuum. It also explains how the phenomena of electricity and magnetism are related.


title: Special relativity

text: A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations. Time and space cannot be defined separately from each other (as was previously thought to be the case). Rather, space and time are interwoven into a single continuum known as "spacetime". Events that occur at the same time for one observer can occur at different times for another.


title: Special relativity

text: Until several years later when Einstein developed general relativity, which introduced a curved spacetime to incorporate gravity, the phrase "special relativity" was not used. A translation sometimes used is "restricted relativity"; "special" really means "special case". Some of the work of Albert Einstein in special relativity is built on the earlier work by Hendrik Lorentz and Henri Poincaré. The theory became essentially complete in 1907.


title: Special relativity

text: The theory is "special" in that it only applies in the special case where the spacetime is "flat", that is, where the curvature of spacetime (a consequence of the energy–momentum tensor and representing gravity) is negligible. In order to correctly accommodate gravity, Einstein formulated general relativity in 1915. Special relativity, contrary to some historical descriptions, does accommodate accelerations as well as accelerating frames of reference.


title: Special relativity

text: Just as Galilean relativity is now accepted to be an approximation of special relativity that is valid for low speeds, special relativity is considered an approximation of general relativity that is valid for weak gravitational fields, that is, at a sufficiently small scale (e.g., when tidal forces are negligible) and in conditions of free fall. General relativity, however, incorporates non-Euclidean geometry in order to represent gravitational effects as the geometric curvature of spacetime. Special relativity is restricted to the flat spacetime known as Minkowski space. As long as the universe can be modeled as a pseudo-Riemannian manifold, a Lorentz-invariant frame that abides by special relativity can be defined for a sufficiently small neighborhood of each point in this curved spacetime.


title: Special relativity

text: Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity. Einstein extended this principle so that it accounted for the constant speed of light, a phenomenon that had been observed in the Michelson–Morley experiment. He also postulated that it holds for all the laws of physics, including both the laws of mechanics and of electrodynamics.


title: Special relativity

text: Einstein discerned two fundamental propositions that seemed to be the most assured, regardless of the exact validity of the (then) known laws of either mechanics or electrodynamics. These propositions were the constancy of the speed of light in a vacuum and the independence of physical laws (especially the constancy of the speed of light) from the choice of inertial system. In his initial presentation of special relativity in 1905 he expressed these postulates as:


title: Special relativity

text: The constancy of the speed of light was motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous ether. There is conflicting evidence on the extent to which Einstein was influenced by the null result of the Michelson–Morley experiment. In any case, the null result of the Michelson–Morley experiment helped the notion of the constancy of the speed of light gain widespread and rapid acceptance.


title: Special relativity

text: The derivation of special relativity depends not only on these two explicit postulates, but also on several tacit assumptions (made in almost all theories of physics), including the isotropy and homogeneity of space and the independence of measuring rods and clocks from their past history.


title: Special relativity

text: Following Einstein's original presentation of special relativity in 1905, many different sets of postulates have been proposed in various alternative derivations. However, the most common set of postulates remains those employed by Einstein in his original paper. A more mathematical statement of the principle of relativity made later by Einstein, which introduces the concept of simplicity not mentioned above is:


title: Special relativity

text: Henri Poincaré provided the mathematical framework for relativity theory by proving that Lorentz transformations are a subset of his Poincaré group of symmetry transformations. Einstein later derived these transformations from his axioms.


title: Special relativity

text: Many of Einstein's papers present derivations of the Lorentz transformation based upon these two principles.


title: Special relativity

text: Reference frames play a crucial role in relativity theory. The term reference frame as used here is an observational perspective in space that is not undergoing any change in motion (acceleration), from which a position can be measured along 3 spatial axes (so, at rest or constant velocity). In addition, a reference frame has the ability to determine measurements of the time of events using a 'clock' (any reference device with uniform periodicity).


title: Special relativity

text: An event is an occurrence that can be assigned a single unique moment and location in space relative to a reference frame: it is a "point" in spacetime. Since the speed of light is constant in relativity irrespective of the reference frame, pulses of light can be used to unambiguously measure distances and refer back to the times that events occurred to the clock, even though light takes time to reach the clock after the event has transpired.


title: Special relativity

text: For example, the explosion of a firecracker may be considered to be an "event". We can completely specify an event by its four spacetime coordinates: The time of occurrence and its 3-dimensional spatial location define a reference point. Let's call this reference frame "S".


title: Special relativity

text: In relativity theory, we often want to calculate the coordinates of an event from differing reference frames. The equations that relate measurements made in different frames are called "transformation equations".


title: Special relativity

text: To gain insight into how the spacetime coordinates measured by observers in different reference frames compare with each other, it is useful to work with a simplified setup with frames in a "standard configuration." With care, this allows simplification of the math with no loss of generality in the conclusions that are reached. In Fig. 2-1, two Galilean reference frames (i.e., conventional 3-space frames) are displayed in relative motion. Frame S belongs to a first observer O, and frame S′ (pronounced "S prime" or "S dash") belongs to a second observer O′.


title: Special relativity

text: Since there is no absolute reference frame in relativity theory, a concept of 'moving' doesn't strictly exist, as everything may be moving with respect to some other reference frame. Instead, any two frames that move at the same speed in the same direction are said to be "comoving". Therefore, "S" and "S"′ are not "comoving".


title: Special relativity

text: The principle of relativity, which states that physical laws have the same form in each inertial reference frame, dates back to Galileo, and was incorporated into Newtonian physics. However, in the late 19th century, the existence of electromagnetic waves led some physicists to suggest that the universe was filled with a substance they called "aether", which, they postulated, would act as the medium through which these waves, or vibrations, propagated (in many respects similar to the way sound propagates through air). The aether was thought to be an absolute reference frame against which all speeds could be measured, and could be considered fixed and motionless relative to Earth or some other fixed reference point. The aether was supposed to be sufficiently elastic to support electromagnetic waves, while those waves could interact with matter, yet offering no resistance to bodies passing through it (its one property was that it allowed electromagnetic waves to propagate). The results of various experiments, including the Michelson–Morley experiment in 1887 (subsequently verified with more accurate and innovative experiments), led to the theory of special relativity, by showing that the aether did not exist. Einstein's solution was to discard the notion of an aether and the absolute state of rest. In relativity, any reference frame moving with uniform motion will observe the same laws of physics. In particular, the speed of light in vacuum is always measured to be "c", even when measured by multiple systems that are moving at different (but constant) velocities.


title: Special relativity

text: From the principle of relativity alone without assuming the constancy of the speed of light (i.e., using the isotropy of space and the symmetry implied by the principle of special relativity) it can be shown that the spacetime transformations between inertial frames are either Euclidean, Galilean, or Lorentzian. In the Lorentzian case, one can then obtain relativistic interval conservation and a certain finite limiting speed. Experiments suggest that this speed is the speed of light in vacuum.


title: Special relativity

text: Einstein consistently based the derivation of Lorentz invariance (the essential core of special relativity) on just the two basic principles of relativity and light-speed invariance. He wrote:


title: Special relativity

text: Thus many modern treatments of special relativity base it on the single postulate of universal Lorentz covariance, or, equivalently, on the single postulate of Minkowski spacetime.


title: Special relativity

text: Rather than considering universal Lorentz covariance to be a derived principle, this article considers it to be the fundamental postulate of special relativity. The traditional two-postulate approach to special relativity is presented in innumerable college textbooks and popular presentations. Textbooks starting with the single postulate of Minkowski spacetime include those by Taylor and Wheeler and by Callahan. This is also the approach followed by the Wikipedia articles Spacetime and Minkowski diagram.


title: Special relativity

text: Define an event to have spacetime coordinates in system "S" and in a reference frame moving at a velocity v with respect to that frame, "S"′. Then the Lorentz transformation specifies that these coordinates are related in the following way:


title: Special relativity

text: where formula_4 is the Lorentz factor and "c" is the speed of light in vacuum, and the velocity "v" of "S"′, relative to "S", is parallel to the "x"-axis. For simplicity, the "y" and "z" coordinates are unaffected; only the "x" and "t" coordinates are transformed. These Lorentz transformations form a one-parameter group of linear mappings, that parameter being called rapidity.


title: Special relativity

text: Solving the four transformation equations above for the unprimed coordinates yields the inverse Lorentz transformation:


title: Special relativity

text: Enforcing this "inverse" Lorentz transformation to coincide with the Lorentz transformation from the primed to the unprimed system, shows the unprimed frame as moving with the velocity , as measured in the primed frame.


title: Special relativity

text: There is nothing special about the "x"-axis. The transformation can apply to the "y"- or "z"-axis, or indeed in any direction parallel to the motion (which are warped by the "γ" factor) and perpendicular; see the article Lorentz transformation for details.


title: Special relativity

text: Writing the Lorentz transformation and its inverse in terms of coordinate differences, where one event has coordinates and , another event has coordinates and , and the differences are defined as


title: Special relativity

text: Spacetime diagrams (Minkowski diagrams) are an extremely useful aid to visualizing how coordinates transform between different reference frames. Although it is not as easy to perform exact computations using them as directly invoking the Lorentz transformations, their main power is their ability to provide an intuitive grasp of the results of a relativistic scenario.


title: Special relativity

text: To draw a spacetime diagram, begin by considering two Galilean reference frames, S and S', in standard configuration, as shown in Fig. 2-1.


title: Special relativity

text: Fig. 3-1a. Draw the formula_16 and formula_17 axes of frame S. The formula_16 axis is horizontal and the formula_17 (actually formula_20) axis is vertical, which is the opposite of the usual convention in kinematics. The formula_20 axis is scaled by a factor of formula_2 so that both axes have common units of length. In the diagram shown, the gridlines are spaced one unit distance apart. The 45° diagonal lines represent the "worldlines" of two photons passing through the origin at time formula_23 The slope of these worldlines is 1 because the photons advance one unit in space per unit of time. Two events, formula_24 and formula_25 have been plotted on this graph so that their coordinates may be compared in the S and S' frames.


title: Special relativity

text: Fig. 3-1b. Draw the formula_26 and formula_27 axes of frame S'. The formula_27 axis represents the worldline of the origin of the S' coordinate system as measured in frame S. In this figure, formula_29 Both the formula_27 and formula_26 axes are tilted from the unprimed axes by an angle formula_32 where formula_33 The primed and unprimed axes share a common origin because frames S and S' had been set up in standard configuration, so that formula_34 when formula_35


title: Special relativity

text: Fig. 3-1c. Units in the primed axes have a different scale from units in the unprimed axes. From the Lorentz transformations, we observe that formula_36 coordinates of formula_37 in the primed coordinate system transform to formula_38 in the unprimed coordinate system. Likewise, formula_36 coordinates of formula_40 in the primed coordinate system transform to formula_41 in the unprimed system. Draw gridlines parallel with the formula_27 axis through points formula_43 as measured in the unprimed frame, where formula_44 is an integer. Likewise, draw gridlines parallel with the formula_26 axis through formula_46 as measured in the unprimed frame. Using the Pythagorean theorem, we observe that the spacing between formula_27 units equals formula_48 times the spacing between formula_20 units, as measured in frame S. This ratio is always greater than 1, and ultimately it approaches infinity as formula_50


title: Special relativity

text: Fig. 3-1d. Since the speed of light is an invariant, the "worldlines" of two photons passing through the origin at time formula_51 still plot as 45° diagonal lines. The primed coordinates of formula_24 and formula_53 are related to the unprimed coordinates through the Lorentz transformations and "could" be approximately measured from the graph (assuming that it has been plotted accurately enough), but the real merit of a Minkowski diagram is its granting us a geometric view of the scenario. For example, in this figure, we observe that the two timelike-separated events that had different x-coordinates in the unprimed frame are now at the same position in space.


title: Special relativity

text: While the unprimed frame is drawn with space and time axes that meet at right angles, the primed frame is drawn with axes that meet at acute or obtuse angles. This asymmetry is due to unavoidable distortions in how spacetime coordinates map onto a Cartesian plane, but the frames are actually equivalent.


title: Special relativity

text: The consequences of special relativity can be derived from the Lorentz transformation equations. These transformations, and hence special relativity, lead to different physical predictions than those of Newtonian mechanics at all relative velocities, and most pronounced when relative velocities become comparable to the speed of light. The speed of light is so much larger than anything most humans encounter that some of the effects predicted by relativity are initially counterintuitive.


title: Special relativity

text: In Galilean relativity, length (formula_54) and temporal separation between two events (formula_55) are independent invariants, the values of which do not change when observed from different frames of reference.


title: Special relativity

text: In special relativity, however, the interweaving of spatial and temporal coordinates generates the concept of an invariant interval, denoted as


title: Special relativity

text: The interweaving of space and time revokes the implicitly assumed concepts of absolute simultaneity and synchronization across non-comoving frames.


title: Special relativity

text: The form of formula_57 being the "difference" of the squared time lapse and the squared spatial distance, demonstrates a fundamental discrepancy between Euclidean and spacetime distances. The invariance of this interval is a property of the "general" Lorentz transform (also called the Poincaré transformation), making it an isometry of spacetime. The general Lorentz transform extends the standard Lorentz transform (which deals with translations without rotation, that is, Lorentz boosts, in the x-direction) with all other translations, reflections, and rotations between any Cartesian inertial frame.


title: Special relativity

text: In the analysis of simplified scenarios, such as spacetime diagrams, a reduced-dimensionality form of the invariant interval is often employed:


title: Special relativity

text: Demonstrating that the interval is invariant is straightforward for the reduced-dimensionality case and with frames in standard configuration:


title: Special relativity

text: Consider two events happening in two different locations that occur simultaneously in the reference frame of one inertial observer. They may occur non-simultaneously in the reference frame of another inertial observer (lack of absolute simultaneity).


title: Special relativity

text: It is clear that the two events that are simultaneous in frame "S" (satisfying ), are not necessarily simultaneous in another inertial frame "S"′ (satisfying ). Only if these events are additionally co-local in frame "S" (satisfying ), will they be simultaneous in another frame "S"′.


title: Special relativity

text: The Sagnac effect can be considered a manifestation of the relativity of simultaneity. Since relativity of simultaneity is a first order effect in formula_64, instruments based on the Sagnac effect for their operation, such as ring laser gyroscopes and fiber optic gyroscopes, are capable of extreme levels of sensitivity.


title: Special relativity

text: The time lapse between two events is not invariant from one observer to another, but is dependent on the relative speeds of the observers' reference frames (e.g., the twin paradox which concerns a twin who flies off in a spaceship traveling near the speed of light and returns to discover that the non-traveling twin sibling has aged much more, the paradox being that at constant velocity we are unable to discern which twin is non-traveling and which twin travels).


title: Special relativity

text: Suppose a clock is at rest in the unprimed system "S". The location of the clock on two different ticks is then characterized by . To find the relation between the times between these ticks as measured in both systems, can be used to find:


title: Special relativity

text: This shows that the time (Δ"t"′) between the two ticks as seen in the frame in which the clock is moving ("S"′), is "longer" than the time (Δ"t") between these ticks as measured in the rest frame of the clock ("S"). Time dilation explains a number of physical phenomena; for example, the lifetime of high speed muons created by the collision of cosmic rays with particles in the Earth's outer atmosphere and moving towards the surface is greater than the lifetime of slowly moving muons, created and decaying in a laboratory.


title: Special relativity

text: The dimensions (e.g., length) of an object as measured by one observer may be smaller than the results of measurements of the same object made by another observer (e.g., the ladder paradox involves a long ladder traveling near the speed of light and being contained within a smaller garage).


title: Special relativity

text: Similarly, suppose a measuring rod is at rest and aligned along the "x"-axis in the unprimed system "S". In this system, the length of this rod is written as Δ"x". To measure the length of this rod in the system "S"′, in which the rod is moving, the distances "x"′ to the end points of the rod must be measured simultaneously in that system "S"′. In other words, the measurement is characterized by , which can be combined with to find the relation between the lengths Δ"x" and Δ"x"′:


title: Special relativity

text: This shows that the length (Δ"x"′) of the rod as measured in the frame in which it is moving ("S"′), is "shorter" than its length (Δ"x") in its own rest frame ("S").


title: Special relativity

text: Time dilation and length contraction are not merely appearances. Time dilation is explicitly related to our way of measuring "time intervals" between events that occur at the same place in a given coordinate system (called "co-local" events). These time intervals (which can be, and are, actually measured experimentally by relevant observers) are "different" in another coordinate system moving with respect to the first, unless the events, in addition to being co-local, are also simultaneous. Similarly, length contraction relates to our measured distances between separated but simultaneous events in a given coordinate system of choice. If these events are not co-local, but are separated by distance (space), they will "not" occur at the same "spatial distance" from each other when seen from another moving coordinate system.


title: Special relativity

text: Consider two frames "S" and "S′ " in standard configuration. A particle in "S" moves in the x direction with velocity vector formula_91 What is its velocity formula_92 in frame "S′ "?


title: Special relativity

text: Substituting expressions for formula_93 and formula_94 from into , followed by straightforward mathematical manipulations and back-substitution from yields the Lorentz transformation of the speed formula_95 to formula_96:


title: Special relativity

text: The inverse relation is obtained by interchanging the primed and unprimed symbols and replacing formula_97 with formula_98


title: Special relativity

text: There is nothing special about the "x" direction in the standard configuration. The above formalism applies to any direction; and three orthogonal directions allow dealing with all directions in space by decomposing the velocity vectors to their components in these directions. See Velocity-addition formula for details.


title: Special relativity

text: The composition of two non-collinear Lorentz boosts (i.e., two non-collinear Lorentz transformations, neither of which involve rotation) results in a Lorentz transformation that is not a pure boost but is the composition of a boost and a rotation.


title: Special relativity

text: Thomas rotation results from the relativity of simultaneity. In Fig. 4-2a, a rod of length formula_104 in its rest frame (i.e., having a proper length of formula_104) rises vertically along the y-axis in the ground frame.


title: Special relativity

text: In Fig. 4-2b, the same rod is observed from the frame of a rocket moving at speed formula_64 to the right. If we imagine two clocks situated at the left and right ends of the rod that are synchronized "in the frame of the rod," relativity of simultaneity causes the observer in the rocket frame to observe (not "see") the clock at the right end of the rod as being advanced in time by formula_107 and the rod is correspondingly observed as tilted.


title: Special relativity

text: Unlike second-order relativistic effects such as length contraction or time dilation, this effect becomes quite significant even at fairly low velocities. For example, this can be seen in the spin of moving particles, where Thomas precession is a relativistic correction that applies to the spin of an elementary particle or the rotation of a macroscopic gyroscope, relating the angular velocity of the spin of a particle following a curvilinear orbit to the angular velocity of the orbital motion.


title: Special relativity

text: In Fig. 4-3, the time interval between the events A (the "cause") and B (the "effect") is 'time-like'; that is, there is a frame of reference in which events A and B occur at the "same location in space", separated only by occurring at different times. If A precedes B in that frame, then A precedes B in all frames accessible by a Lorentz transformation. It is possible for matter (or information) to travel (below light speed) from the location of A, starting at the time of A, to the location of B, arriving at the time of B, so there can be a causal relationship (with A the cause and B the effect).


title: Special relativity

text: The interval AC in the diagram is 'space-like'; that is, there is a frame of reference in which events A and C occur simultaneously, separated only in space. There are also frames in which A precedes C (as shown) and frames in which C precedes A. However, there are no frames accessible by a Lorentz transformation, in which events A and C occur at the same location. If it were possible for a cause-and-effect relationship to exist between events A and C, then paradoxes of causality would result.


title: Special relativity

text: For example, if signals could be sent faster than light, then signals could be sent into the sender's past (observer B in the diagrams). A variety of causal paradoxes could then be constructed.


title: Special relativity

text: Consider the spacetime diagrams in Fig. 4-4. A and B stand alongside a railroad track, when a high-speed train passes by, with C riding in the last car of the train and D riding in the leading car. The world lines of A and B are vertical ("ct"), distinguishing the stationary position of these observers on the ground, while the world lines of C and D are tilted forwards ("ct′"), reflecting the rapid motion of the observers C and D stationary in their train, as observed from the ground.


title: Special relativity

text: It is not necessary for signals to be instantaneous to violate causality. Even if the signal from D to C were slightly shallower than the formula_26 axis (and the signal from A to B slightly steeper than the formula_16 axis), it would still be possible for B to receive his message before he had sent it. By increasing the speed of the train to near light speeds, the formula_27 and formula_26 axes can be squeezed very close to the dashed line representing the speed of light. With this modified setup, it can be demonstrated that even signals only "slightly" faster than the speed of light will result in causality violation.


title: Special relativity

text: Therefore, if causality is to be preserved, one of the consequences of special relativity is that no information signal or material object can travel faster than light in vacuum.


title: Special relativity

text: This is not to say that "all" faster than light speeds are impossible. Various trivial situations can be described where some "things" (not actual matter or energy) move faster than light. For example, the location where the beam of a search light hits the bottom of a cloud can move faster than light when the search light is turned rapidly (although this does not violate causality or any other relativistic phenomenon).


title: Special relativity

text: In 1850, Hippolyte Fizeau and Léon Foucault independently established that light travels more slowly in water than in air, thus validating a prediction of Fresnel's wave theory of light and invalidating the corresponding prediction of Newton's corpuscular theory. The speed of light was measured in still water. What would be the speed of light in flowing water?


title: Special relativity

text: In 1851, Fizeau conducted an experiment to answer this question, a simplified representation of which is illustrated in Fig. 5-1. A beam of light is divided by a beam splitter, and the split beams are passed in opposite directions through a tube of flowing water. They are recombined to form interference fringes, indicating a difference in optical path length, that an observer can view. The experiment demonstrated that dragging of the light by the flowing water caused a displacement of the fringes, showing that the motion of the water had affected the speed of the light.


title: Special relativity

text: According to the theories prevailing at the time, light traveling through a moving medium would be a simple sum of its speed "through" the medium plus the speed "of" the medium. Contrary to expectation, Fizeau found that although light appeared to be dragged by the water, the magnitude of the dragging was much lower than expected. If formula_114 is the speed of light in still water, and formula_64 is the speed of the water, and formula_116 is the water-bourne speed of light in the lab frame with the flow of water adding to or subtracting from the speed of light, then


title: Special relativity

text: Fizeau's results, although consistent with Fresnel's earlier hypothesis of partial aether dragging, were extremely disconcerting to physicists of the time. Among other things, the presence of an index of refraction term meant that, since formula_118 depends on wavelength, "the aether must be capable of sustaining different motions at the same time." A variety of theoretical explanations were proposed to explain Fresnel's dragging coefficient that were completely at odds with each other. Even before the Michelson–Morley experiment, Fizeau's experimental results were among a number of observations that created a critical situation in explaining the optics of moving bodies.


title: Special relativity

text: From the point of view of special relativity, Fizeau's result is nothing but an approximation to , the relativistic formula for composition of velocities.


title: Special relativity

text: Because of the finite speed of light, if the relative motions of a source and receiver include a transverse component, then the direction from which light arrives at the receiver will be displaced from the geometric position in space of the source relative to the receiver. The classical calculation of the displacement takes two forms and makes different predictions depending on whether the receiver, the source, or both are in motion with respect to the medium. (1) If the receiver is in motion, the displacement would be the consequence of the aberration of light. The incident angle of the beam relative to the receiver would be calculable from the vector sum of the receiver's motions and the velocity of the incident light. (2) If the source is in motion, the displacement would be the consequence of light-time correction. The displacement of the apparent position of the source from its geometric position would be the result of the source's motion during the time that its light takes to reach the receiver.


title: Special relativity

text: The classical explanation failed experimental test. Since the aberration angle depends on the relationship between the velocity of the receiver and the speed of the incident light, passage of the incident light through a refractive medium should change the aberration angle. In 1810, Arago used this expected phenomenon in a failed attempt to measure the speed of light, and in 1870, George Airy tested the hypothesis using a water-filled telescope, finding that, against expectation, the measured aberration was identical to the aberration measured with an air-filled telescope. A "cumbrous" attempt to explain these results used the hypothesis of partial aether-drag, but was incompatible with the results of the Michelson–Morley experiment, which apparently demanded "complete" aether-drag.


title: Special relativity

text: Assuming inertial frames, the relativistic expression for the aberration of light is applicable to both the receiver moving and source moving cases. A variety of trigonometrically equivalent formulas have been published. Expressed in terms of the variables in Fig. 5-2, these include


title: Special relativity

text: The classical Doppler effect depends on whether the source, receiver, or both are in motion with respect to the medium. The relativistic Doppler effect is independent of any medium. Nevertheless, relativistic Doppler shift for the longitudinal case, with source and receiver moving directly towards or away from each other, can be derived as if it were the classical phenomenon, but modified by the addition of a time dilation term, and that is the treatment described here.


title: Special relativity

text: Assume the receiver and the source are moving "away" from each other with a relative speed formula_126 as measured by an observer on the receiver or the source (The sign convention adopted here is that formula_64 is "negative" if the receiver and the source are moving "towards" each other). Assume that the source is stationary in the medium. Then


title: Special relativity

text: For light, and with the receiver moving at relativistic speeds, clocks on the receiver are time dilated relative to clocks at the source. The receiver will measure the received frequency to be


title: Special relativity

text: An identical expression for relativistic Doppler shift is obtained when performing the analysis in the reference frame of the "receiver" with a moving source.


title: Special relativity

text: The transverse Doppler effect is one of the main novel predictions of the special theory of relativity.


title: Special relativity

text: Classically, one might expect that if source and receiver are moving transversely with respect to each other with no longitudinal component to their relative motions, that there should be no Doppler shift in the light arriving at the receiver.


title: Special relativity

text: Special relativity predicts otherwise. Fig. 5-3 illustrates two common variants of this scenario. Both variants can be analyzed using simple time dilation arguments. In Fig. 5-3a, the receiver observes light from the source as being blueshifted by a factor of formula_133. In Fig. 5-3b, the light is redshifted by the same factor.


title: Special relativity

text: Time dilation and length contraction are not optical illusions, but genuine effects. Measurements of these effects are not an artifact of Doppler shift, nor are they the result of neglecting to take into account the time it takes light to travel from an event to an observer.


title: Special relativity

text: Scientists make a fundamental distinction between "measurement" or "observation" on the one hand, versus "visual appearance", or what one "sees". The measured shape of an object is a hypothetical snapshot of all of the object's points as they exist at a single moment in time. The visual appearance of an object, however, is affected by the varying lengths of time that light takes to travel from different points on the object to one's eye.


title: Special relativity

text: For many years, the distinction between the two had not been generally appreciated, and it had generally been thought that a length contracted object passing by an observer would in fact actually be "seen" as length contracted. In 1959, James Terrell and Roger Penrose independently pointed out that differential time lag effects in signals reaching the observer from the different parts of a moving object result in a fast moving object's visual appearance being quite different from its measured shape. For example, a receding object would "appear" contracted, an approaching object would "appear" elongated, and a passing object would have a skew appearance that has been likened to a rotation. A sphere in motion retains the circular outline for all speeds, for any distance, and for all view angles, although


title: Special relativity

text: Both Fig. 5-4 and Fig. 5-5 illustrate objects moving transversely to the line of sight. In Fig. 5-4, a cube is viewed from a distance of four times the length of its sides. At high speeds, the sides of the cube that are perpendicular to the direction of motion appear hyperbolic in shape. The cube is actually not rotated. Rather, light from the rear of the cube takes longer to reach one's eyes compared with light from the front, during which time the cube has moved to the right. At high speeds, the sphere in Fig. 5-5 takes on the appearance of a flattened disk tilted up to 45° from the line of sight. If the objects' motions are not strictly transverse but instead include a longitudinal component, exaggerated distortions in perspective may be seen. This illusion has come to be known as "Terrell rotation" or the "Terrell–Penrose effect".


title: Special relativity

text: Another example where visual appearance is at odds with measurement comes from the observation of apparent superluminal motion in various radio galaxies, BL Lac objects, quasars, and other astronomical objects that eject relativistic-speed jets of matter at narrow angles with respect to the viewer. An apparent optical illusion results giving the appearance of faster than light travel. In Fig. 5-6, galaxy M87 streams out a high-speed jet of subatomic particles almost directly towards us, but Penrose–Terrell rotation causes the jet to appear to be moving laterally in the same manner that the appearance of the cube in Fig. 5-4 has been stretched out.


title: Special relativity

text: Section "Consequences derived from the Lorentz transformation" dealt strictly with kinematics, the study of the motion of points, bodies, and systems of bodies without considering the forces that caused the motion. This section discusses masses, forces, energy and so forth, and as such requires consideration of physical effects beyond those encompassed by the Lorentz transformation itself.


title: Special relativity

text: As an object's speed approaches the speed of light from an observer's point of view, its relativistic mass increases thereby making it more and more difficult to accelerate it from within the observer's frame of reference.


title: Special relativity

text: The energy content of an object at rest with mass "m" equals "mc". Conservation of energy implies that, in any reaction, a decrease of the sum of the masses of particles must be accompanied by an increase in kinetic energies of the particles after the reaction. Similarly, the mass of an object can be increased by taking in kinetic energies.


title: Special relativity

text: In addition to the papers referenced above—which give derivations of the Lorentz transformation and describe the foundations of special relativity—Einstein also wrote at least four papers giving heuristic arguments for the equivalence (and transmutability) of mass and energy, for .


title: Special relativity

text: Mass–energy equivalence is a consequence of special relativity. The energy and momentum, which are separate in Newtonian mechanics, form a four-vector in relativity, and this relates the time component (the energy) to the space components (the momentum) in a non-trivial way. For an object at rest, the energy–momentum four-vector is : it has a time component which is the energy, and three space components which are zero. By changing frames with a Lorentz transformation in the x direction with a small value of the velocity v, the energy momentum four-vector becomes . The momentum is equal to the energy multiplied by the velocity divided by "c". As such, the Newtonian mass of an object, which is the ratio of the momentum to the velocity for slow velocities, is equal to "E"/"c".


title: Special relativity

text: The energy and momentum are properties of matter and radiation, and it is impossible to deduce that they form a four-vector just from the two basic postulates of special relativity by themselves, because these don't talk about matter or radiation, they only talk about space and time. The derivation therefore requires some additional physical reasoning. In his 1905 paper, Einstein used the additional principles that Newtonian mechanics should hold for slow velocities, so that there is one energy scalar and one three-vector momentum at slow velocities, and that the conservation law for energy and momentum is exactly true in relativity. Furthermore, he assumed that the energy of light is transformed by the same Doppler-shift factor as its frequency, which he had previously shown to be true based on Maxwell's equations. The first of Einstein's papers on this subject was "Does the Inertia of a Body Depend upon its Energy Content?" in 1905. Although Einstein's argument in this paper is nearly universally accepted by physicists as correct, even self-evident, many authors over the years have suggested that it is wrong. Other authors suggest that the argument was merely inconclusive because it relied on some implicit assumptions.


title: Special relativity

text: Einstein acknowledged the controversy over his derivation in his 1907 survey paper on special relativity. There he notes that it is problematic to rely on Maxwell's equations for the heuristic mass–energy argument. The argument in his 1905 paper can be carried out with the emission of any massless particles, but the Maxwell equations are implicitly used to make it obvious that the emission of light in particular can be achieved only by doing work. To emit electromagnetic waves, all you have to do is shake a charged particle, and this is clearly doing work, so that the emission is of energy.


title: Special relativity

text: Since nothing can travel faster than light, one might conclude that a human can never travel farther from Earth than ~100 light years. You would easily think that a traveler would never be able to reach more than the few solar systems which exist within the limit of 100 light years from Earth. However, because of time dilation, a hypothetical spaceship can travel thousands of light years during a passenger's lifetime. If a spaceship could be built that accelerates at a constant 1"g", it will, after one year, be travelling at almost the speed of light as seen from Earth. This is described by:


title: Special relativity

text: where "v"("t") is the velocity at a time "t", "a" is the acceleration of the spaceship and "t" is the coordinate time as measured by people on Earth. Therefore, after one year of accelerating at 9.81 m/s, the spaceship will be travelling at "v" = 0.712"c" and 0.946"c" after three years, relative to Earth. After three years of this acceleration, with the spaceship achieving a velocity of 94.6% of the speed of light relative to Earth, time dilation will result in each second experienced on the spaceship corresponding to 3.1 seconds back on Earth. During their journey, people on Earth will experience more time than they do - since their clocks (all physical phenomena) would really be ticking 3.1 times faster than those of the spaceship. A 5-year round trip for the traveller will take 6.5 Earth years and cover a distance of over 6 light-years. A 20-year round trip for them (5 years accelerating, 5 decelerating, twice each) will land them back on Earth having travelled for 335 Earth years and a distance of 331 light years. A full 40-year trip at 1"g" will appear on Earth to last 58,000 years and cover a distance of 55,000 light years. A 40-year trip at 1.1"g" will take 148,000 Earth years and cover about 140,000 light years. A one-way 28 year (14 years accelerating, 14 decelerating as measured with the astronaut's clock) trip at 1"g" acceleration could reach 2,000,000 light-years to the Andromeda Galaxy. This same time dilation is why a muon travelling close to "c" is observed to travel much farther than "c" times its half-life (when at rest).


title: Special relativity

text: Theoretical investigation in classical electromagnetism led to the discovery of wave propagation. Equations generalizing the electromagnetic effects found that finite propagation speed of the E and B fields required certain behaviors on charged particles. The general study of moving charges forms the Liénard–Wiechert potential, which is a step towards special relativity.


title: Special relativity

text: The Lorentz transformation of the electric field of a moving charge into a non-moving observer's reference frame results in the appearance of a mathematical term commonly called the magnetic field. Conversely, the "magnetic" field generated by a moving charge disappears and becomes a purely "electrostatic" field in a comoving frame of reference. Maxwell's equations are thus simply an empirical fit to special relativistic effects in a classical model of the Universe. As electric and magnetic fields are reference frame dependent and thus intertwined, one speaks of "electromagnetic" fields. Special relativity provides the transformation rules for how an electromagnetic field in one inertial frame appears in another inertial frame.


title: Special relativity

text: Maxwell's equations in the 3D form are already consistent with the physical content of special relativity, although they are easier to manipulate in a manifestly covariant form, that is, in the language of tensor calculus.


title: Special relativity

text: "Special" relativity can be combined with quantum mechanics to form relativistic quantum mechanics and quantum electrodynamics. How "general" relativity and quantum mechanics can be unified is one of the unsolved problems in physics; quantum gravity and a "theory of everything", which require a unification including general relativity too, are active and ongoing areas in theoretical research.


title: Special relativity

text: The early Bohr–Sommerfeld atomic model explained the fine structure of alkali metal atoms using both special relativity and the preliminary knowledge on quantum mechanics of the time.


title: Special relativity

text: In 1928, Paul Dirac constructed an influential relativistic wave equation, now known as the Dirac equation in his honour, that is fully compatible both with special relativity and with the final version of quantum theory existing after 1926. This equation not only described the intrinsic angular momentum of the electrons called "spin", it also led to the prediction of the antiparticle of the electron (the positron), and fine structure could only be fully explained with special relativity. It was the first foundation of "relativistic quantum mechanics".


title: Special relativity

text: On the other hand, the existence of antiparticles leads to the conclusion that relativistic quantum mechanics is not enough for a more accurate and complete theory of particle interactions. Instead, a theory of particles interpreted as quantized fields, called "quantum field theory", becomes necessary; in which particles can be created and destroyed throughout space and time.


title: Special relativity

text: Special relativity in its Minkowski spacetime is accurate only when the absolute value of the gravitational potential is much less than "c" in the region of interest. In a strong gravitational field, one must use general relativity. General relativity becomes special relativity at the limit of a weak field. At very small scales, such as at the Planck length and below, quantum effects must be taken into consideration resulting in quantum gravity. However, at macroscopic scales and in the absence of strong gravitational fields, special relativity is experimentally tested to extremely high degree of accuracy (10)


title: Special relativity

text: and thus accepted by the physics community. Experimental results which appear to contradict it are not reproducible and are thus widely believed to be due to experimental errors.


title: Special relativity

text: Special relativity is mathematically self-consistent, and it is an organic part of all modern physical theories, most notably quantum field theory, string theory, and general relativity (in the limiting case of negligible gravitational fields).


title: Special relativity

text: Newtonian mechanics mathematically follows from special relativity at small velocities (compared to the speed of light) – thus Newtonian mechanics can be considered as a special relativity of slow moving bodies. See classical mechanics for a more detailed discussion.


title: Special relativity

text: Several experiments predating Einstein's 1905 paper are now interpreted as evidence for relativity. Of these it is known Einstein was aware of the Fizeau experiment before 1905, and historians have concluded that Einstein was at least aware of the Michelson–Morley experiment as early as 1899 despite claims he made in his later years that it played no role in his development of the theory.


title: Special relativity

text: Particle accelerators routinely accelerate and measure the properties of particles moving at near the speed of light, where their behavior is completely consistent with relativity theory and inconsistent with the earlier Newtonian mechanics. These machines would simply not work if they were not engineered according to relativistic principles. In addition, a considerable number of modern experiments have been conducted to test special relativity. Some examples:


title: Special relativity

text: Special relativity uses a 'flat' 4-dimensional Minkowski space – an example of a spacetime. Minkowski spacetime appears to be very similar to the standard 3-dimensional Euclidean space, but there is a crucial difference with respect to time.


title: Special relativity

text: where are the differentials of the three spatial dimensions. In Minkowski geometry, there is an extra dimension with coordinate "X" derived from time, such that the distance differential fulfills


title: Special relativity

text: where are the differentials of the four spacetime dimensions. This suggests a deep theoretical insight: special relativity is simply a rotational symmetry of our spacetime, analogous to the rotational symmetry of Euclidean space (see Fig. 10-1). Just as Euclidean space uses a Euclidean metric, so spacetime uses a Minkowski metric. Basically, special relativity can be stated as the "invariance of any spacetime interval" (that is the 4D distance between any two events) when viewed from "any inertial reference frame". All equations and effects of special relativity can be derived from this rotational symmetry (the Poincaré group) of Minkowski spacetime.


title: Special relativity

text: To make the time coordinate look like the space coordinates, it can be treated as imaginary: (this is called a Wick rotation).


title: Special relativity

text: According to Misner, Thorne and Wheeler (1971, §2.3), ultimately the deeper understanding of both special and general relativity will come from the study of the Minkowski metric (described below) and to take , rather than a "disguised" Euclidean metric using "ict" as the time coordinate.


title: Special relativity

text: Some authors use , with factors of "c" elsewhere to compensate; for instance, spatial coordinates are divided by "c" or factors of "c" are included in the metric tensor.


title: Special relativity

text: These numerous conventions can be superseded by using natural units where . Then space and time have equivalent units, and no factors of "c" appear anywhere.


title: Special relativity

text: As illustrated in Fig. 10-3, the null geodesics can be visualized as a set of continuous concentric spheres with radii = "c dt".


title: Special relativity

text: This null dual-cone represents the "line of sight" of a point in space. That is, when we look at the stars and say "The light from that star which I am receiving is X years old", we are looking down this line of sight: a null geodesic. We are looking at an event a distance formula_142 away and a time "d/c" in the past. For this reason the null dual cone is also known as the 'light cone'. (The point in the lower left of the Fig. 10-2 represents the star, the origin represents the observer, and the line represents the null geodesic "line of sight".)


title: Special relativity

text: The cone in the −"t" region is the information that the point is 'receiving', while the cone in the +"t" section is the information that the point is 'sending'.


title: Special relativity

text: The geometry of Minkowski space can be depicted using Minkowski diagrams, which are useful also in understanding many of the thought experiments in special relativity.


title: Special relativity

text: Note that, in 4d spacetime, the concept of the center of mass becomes more complicated, see Center of mass (relativistic).


title: Special relativity

text: Above, the Lorentz transformation for the time coordinate and three space coordinates illustrates that they are intertwined. This is true more generally: certain pairs of "timelike" and "spacelike" quantities naturally combine on equal footing under the same Lorentz transformation.


title: Special relativity

text: The Lorentz transformation in standard configuration above, that is, for a boost in the "x"-direction, can be recast into matrix form as follows:


title: Special relativity

text: In Newtonian mechanics, quantities that have magnitude and direction are mathematically described as 3d vectors in Euclidean space, and in general they are parametrized by time. In special relativity, this notion is extended by adding the appropriate timelike quantity to a spacelike vector quantity, and we have 4d vectors, or "four vectors", in Minkowski spacetime. The components of vectors are written using tensor index notation, as this has numerous advantages. The notation makes it clear the equations are manifestly covariant under the Poincaré group, thus bypassing the tedious calculations to check this fact. In constructing such equations, we often find that equations previously thought to be unrelated are, in fact, closely connected being part of the same tensor equation. Recognizing other physical quantities as tensors simplifies their transformation laws. Throughout, upper indices (superscripts) are contravariant indices rather than exponents except when they indicate a square (this should be clear from the context), and lower indices (subscripts) are covariant indices. For simplicity and consistency with the earlier equations, Cartesian coordinates will be used.


title: Special relativity

text: The simplest example of a four-vector is the position of an event in spacetime, which constitutes a timelike component "ct" and spacelike component , in a contravariant position four vector with components:


title: Special relativity

text: where we define so that the time coordinate has the same dimension of distance as the other spatial dimensions; so that space and time are treated equally. Now the transformation of the contravariant components of the position 4-vector can be compactly written as:


title: Special relativity

text: More generally, all contravariant components of a four-vector formula_148 transform from one frame to another frame by a Lorentz transformation:


title: Special relativity

text: Examples of other 4-vectors include the four-velocity formula_150 defined as the derivative of the position 4-vector with respect to proper time:


title: Special relativity

text: The relativistic energy formula_153 and relativistic momentum formula_154 of an object are respectively the timelike and spacelike components of a contravariant four momentum vector:


title: Special relativity

text: The transformation rules for "three"-dimensional velocities and accelerations are very awkward; even above in standard configuration the velocity equations are quite complicated owing to their non-linearity. On the other hand, the transformation of "four"-velocity and "four"-acceleration are simpler by means of the Lorentz transformation matrix.


title: Special relativity

text: only in Cartesian coordinates. It's the covariant derivative which transforms in manifest covariance, in Cartesian coordinates this happens to reduce to the partial derivatives, but not in other coordinates.


title: Special relativity

text: More generally, the "co"variant components of a 4-vector transform according to the "inverse" Lorentz transformation:


title: Special relativity

text: The postulates of special relativity constrain the exact form the Lorentz transformation matrices take.


title: Special relativity

text: More generally, most physical quantities are best described as (components of) tensors. So to transform from one frame to another, we use the well-known tensor transformation law


title: Special relativity

text: An example of a four-dimensional second order antisymmetric tensor is the relativistic angular momentum, which has six components: three are the classical angular momentum, and the other three are related to the boost of the center of mass of the system. The derivative of the relativistic angular momentum with respect to proper time is the relativistic torque, also second order antisymmetric tensor.


title: Special relativity

text: The electromagnetic field tensor is another second order antisymmetric tensor field, with six components: three for the electric field and another three for the magnetic field. There is also the stress–energy tensor for the electromagnetic field, namely the electromagnetic stress–energy tensor.


title: Special relativity

text: The metric tensor allows one to define the inner product of two vectors, which in turn allows one to assign a magnitude to the vector. Given the four-dimensional nature of spacetime the Minkowski metric "η" has components (valid with suitably chosen coordinates) which can be arranged in a matrix:


title: Special relativity

text: which is equal to its reciprocal, formula_166, in those frames. Throughout we use the signs as above, different authors use different conventions – see Minkowski metric alternative signs.


title: Special relativity

text: The Poincaré group is the most general group of transformations which preserves the Minkowski metric:


title: Special relativity

text: The metric can be used for raising and lowering indices on vectors and tensors. Invariants can be constructed using the metric, the inner product of a 4-vector "T" with another 4-vector "S" is:


title: Special relativity

text: Invariant means that it takes the same value in all inertial frames, because it is a scalar (0 rank tensor), and so no appears in its trivial transformation. The magnitude of the 4-vector "T" is the positive square root of the inner product with itself:


title: Special relativity

text: One can extend this idea to tensors of higher order, for a second order tensor we can form the invariants:


title: Special relativity

text: similarly for higher order tensors. Invariant expressions, particularly inner products of 4-vectors with themselves, provide equations that are useful for calculations, because one doesn't need to perform Lorentz transformations to determine the invariants.


title: Special relativity

text: is an invariant. Notice that when the line element "dX is negative that is the differential of proper time, while when "dX is positive, is differential of the proper distance.


title: Special relativity

text: which means all velocity four-vectors have a magnitude of "c". This is an expression of the fact that there is no such thing as being at coordinate rest in relativity: at the least, you are always moving forward through time. Differentiating the above equation by "τ" produces:


title: Special relativity

text: We can work out what this invariant is by first arguing that, since it is a scalar, it doesn't matter in which reference frame we calculate it, and then by transforming to a frame where the total momentum is zero.


title: Special relativity

text: We see that the rest energy is an independent invariant. A rest energy can be calculated even for particles and systems in motion, by translating to a frame in which momentum is zero.


title: Special relativity

text: The mass of systems measured in their center of momentum frame (where total momentum is zero) is given by the total energy of the system in this frame. It may not be equal to the sum of individual system masses measured in other frames.


title: Special relativity

text: To use Newton's third law of motion, both forces must be defined as the rate of change of momentum with respect to the same time coordinate. That is, it requires the 3D force defined above. Unfortunately, there is no tensor in 4D which contains the components of the 3D force vector among its components.


title: Special relativity

text: If a particle is not traveling at "c", one can transform the 3D force from the particle's co-moving reference frame into the observer's reference frame. This yields a 4-vector called the four-force. It is the rate of change of the above energy momentum four-vector with respect to proper time. The covariant version of the four-force is:


title: Special relativity

text: In the rest frame of the object, the time component of the four force is zero unless the "invariant mass" of the object is changing (this requires a non-closed system in which energy/mass is being directly added or removed from the object) in which case it is the negative of that rate of change of mass, times "c". In general, though, the components of the four force are not equal to the components of the three-force, because the three force is defined by the rate of change of momentum with respect to coordinate time, that is, "dp"/"dt" while the four force is defined by the rate of change of momentum with respect to proper time, that is, "dp"/"dτ".


title: Special relativity

text: In a continuous medium, the 3D "density of force" combines with the "density of power" to form a covariant 4-vector. The spatial part is the result of dividing the force on a small cell (in 3-space) by the volume of that cell. The time component is −1/"c" times the power transferred to that cell divided by the volume of the cell. This will be used below in the section on electromagnetism.


title: Jack Huston

text: Jack Alexander Huston (born 7 December 1982) is a British actor. He appeared as Richard Harrow in the HBO television drama series "Boardwalk Empire". He also had a supporting role in the 2013 film "American Hustle", portrayed the eponymous "Ben-Hur" in the 2016 historical drama, and appeared as one of the main characters in the fourth season of the FX anthology series "Fargo" (2020).


title: Jack Huston

text: Huston was born on 7 December 1982 in King's Lynn, Norfolk, the son of Lady Margot Lavinia ("née" Cholmondeley) and actor, assistant director and writer Tony Huston. Huston decided to become an actor at the age of 6, after playing the title role in a school production of "Peter Pan". He later attended Hurtwood House, a drama institute.


title: Jack Huston

text: His mother is English and his father is American. His paternal aunt is actress Anjelica Huston, and his paternal half-uncle is actor Danny Huston. His paternal grandparents were American director John Huston (who became an Irish citizen) and model/dancer Enrica Soma, and his maternal grandparents were The 6th Marquess of Cholmondeley and Lavinia Margaret ("née" Leslie). Huston is the nephew of The 7th Marquess of Cholmondeley. On his father's side, he has Italian, Irish, Scottish, Scotch-Irish, Welsh, and English ancestry, and is a great-grandson of Canadian actor Walter Huston.


title: Jack Huston

text: Through his maternal grandfather's father, The 5th Marquess of Cholmondeley, Huston is descended from Sir Robert Walpole, the first Prime Minister of the Kingdom of Great Britain. Jack's maternal grandfather's mother, Sybil, Marchioness of Cholmondeley, was from a Jewish family (from Iraq, India, and Germany); through Sybil, Jack is descended from both David Sassoon, the Treasurer of Baghdad, and Mayer Amschel Rothschild, who founded the Rothschild family international banking dynasty.


title: Jack Huston

text: Huston started his film career with a small screen adaptation of "Spartacus", where he played Flavius. He then went on to having more prominent roles in such films as "Factory Girl", playing the American poet Gerard Malanga, the horror film "Shrooms", "Outlander" and "Shrink".


title: Jack Huston

text: In 2010, he played the minor role of Royce King in "". He appeared in HBO's "Boardwalk Empire" as Richard Harrow, a severely disfigured World War I marksman turned gangster. On 16 December 2010, it was announced Huston would be made a series regular after appearing in five episodes of the first season.


title: Jack Huston

text: After this he went on to be directed by Al Pacino in the 2011 film "Wilde Salome" and to having starring roles in "Not Fade Away", "Two Jacks" and "Night Train to Lisbon". In 2012, he played the part of narrator on avant-garde musician John Zorn's album A Vision in Blakelight, an homage to William Blake.


title: Jack Huston

text: In 2013, he appeared in David O. Russell's comedy-drama "American Hustle", as Pete Musane. Later that year, Huston played Charles Bruno in "Strangers on a Train" at London's Gielgud Theatre. In 2019 Huston played Bobby Kennedy in the Martin Scorsese film "The Irishman".


title: Jack Huston

text: In 2020, he had a supporting role in the fourth season of the FX black comedy crime drama "Fargo" as Odis Weff, a corrupt Kansas City police detective with severe OCD.


title: Jack Huston

text: Huston began dating American model Shannan Click in 2011. They have two children: a daughter (born 2013) and a son (born 2016).


title: Sheri Moon Zombie

text: Sheri Moon Zombie (born Sheri Lyn Skurkis; September 26, 1970) is an American actress, model, dancer and fashion designer.


title: Sheri Moon Zombie

text: Moon was born on September 26, 1970, in San Jose, California, the daughter of William "Bill" Skurkis (1947–2010) and Carol A. Skurkis, but was raised in Connecticut. She has a brother, Jeffrey. She graduated from Plainville High School in Plainville, Connecticut. After graduation, she moved to Los Angeles, California; however she soon found herself moving between homes in both states to attend school and seek work.


title: Sheri Moon Zombie

text: Moon had aspirations to do cartoon voice-overs and took classes. She briefly attended the Connecticut School of Broadcasting to become an MTV VJ, but Moon found herself preoccupied going on tour with Rob Zombie. When Rob Zombie's band White Zombie disbanded and he went solo, he took Moon on as a dancer where she also choreographed routines and created costumes for the tour.


title: Sheri Moon Zombie

text: Moon has appeared in eleven of Zombie's solo music videos and an additional four previous to that when he fronted White Zombie. She most famously starred in the "Cabinet of Dr. Caligari"-themed music video "Living Dead Girl". Moon appeared on the cover of the single for "Living Dead Girl" (1998), Zombie's remix album "American Made Music to Strip By" (1999), and the cover of the single for "Demon Speeding" (2002). Aside from Zombie's work, she also appeared in Black Label Society's video for "Stillborn" and Prong's video for "Rude Awakening". In 2003, Moon co-starred in her husband's first feature film, "House of 1000 Corpses", as Vera-Ellen "Baby" Firefly, but previous to that, she claims that she had never had aspirations of becoming an actress. As Moon explains her character in that film, "Baby is the angelic-looking bait to get the victims." Moon starred alongside genre actors Sid Haig, Bill Moseley and Karen Black. In 2004, she had a brief appearance in the Tobe Hooper film "Toolbox Murders" starring Angela Bettis, the only film she has been in not directed by Zombie.


title: Sheri Moon Zombie

text: Moon reprised her role as Baby Firefly in the 2005 sequel to "House of 1000 Corpses", titled "The Devil's Rejects". "The Devil's Rejects" was financially successful, recouping its roughly $7 million budget during its opening weekend, going on to earn over $16 million and better received by critics than its predecessor. Critic Roger Ebert gave the film three out of a possible four stars. Ebert wrote, "If you are a hardened horror-movie fan capable of appreciating skill and wit in the service of the deliberately disgusting, "The Devil's Rejects" may exercise a certain strange charm." Moon was awarded Spike TV's Scream Awards award for "Most Vile Villain" alongside co-stars Haig, Moseley and Leslie Easterbrook for their portrayal of the Firefly family. Following that, she was awarded a Fuse/Fangoria Chainsaw Award for best duo with her co-star Moseley.


title: Sheri Moon Zombie

text: Moon designed a clothing line, Total Skull, which debuted at the end of May 2006. She explains, "The phrase 'total skull' to me means awesome, rad, the best of the best."


title: Sheri Moon Zombie

text: In 2007, Moon starred as Eva Krupp in a short faux trailer segment for the film "Grindhouse", directed by Zombie and titled "Werewolf Women of the SS". She also appeared in her husband's remake of the 1978 horror classic "Halloween", portraying Deborah Myers, the mother of Michael Myers and Laurie Strode. At the time, it was the highest-grossing overall film in the "Halloween" franchise. Moon reprised her character in the sequel "Halloween II", which was released on August 28, 2009. Moon provides the voice for the character of Suzi-X in the animated film "The Haunted World of El Superbeasto", written and produced by her husband, Zombie. In 2010, she guest-starred on the series "" in the episode "L.A.", which was directed by her husband. She reprised the role of Baby Firefly in the sequel to "The Devil's Rejects", "3 from Hell", which was released in September 2019. Fathom events held a 3-day theatrical opening. It is set to appear one final time in theaters before being released on DVD and Blu-ray. Reviews for the film were mixed.


title: Sheri Moon Zombie

text: On October 31, 2002, she married heavy metal musician and film director Rob Zombie at the Graceland Wedding Chapel, after almost nine years of dating, and subsequently changed her name to Sheri Moon Zombie. As of 2019, she resided with Zombie between a home in Los Angeles and a farm in Connecticut. She is a vegan and animal rights supporter, and she houses rescued animals at her Connecticut farm.


title: Sexual attraction

text: Sexual attraction is attraction on the basis of sexual desire or the quality of arousing such interest. Sexual attractiveness or sex appeal is an individual's ability to attract other people sexually, and is a factor in sexual selection or mate choice. The attraction can be to the physical or other qualities or traits of a person, or to such qualities in the context where they appear. The attraction may be to a person's aesthetics or movements or to their voice or smell, among other things. The attraction may be enhanced by a person's adornments, clothing, perfume or style. It can be influenced by individual genetic, psychological, or cultural factors, or to other, more amorphous qualities. Sexual attraction is also a response to another person that depends on a combination of the person possessing the traits and on the criteria of the person who is attracted.