title: Louis van Gaal

text: Under Van Gaal, the Netherlands started their campaign to qualify for the 2002 World Cup poorly. Placed in Group 2, an injury-hit side could only manage to secure a late 2–2 draw at home to the Republic of Ireland, having been 2–0 down with 20 minutes to go. A 4–0 win over Cyprus was followed by a 2–0 defeat to Portugal.


title: Louis van Gaal

text: In 2001, the Netherlands beat Andorra, Cyprus and Estonia, but despite leading group leaders Portugal 2–0 with seven minutes left, drew 2–2 and fell three points behind second-place Republic of Ireland, who were unbeaten. When the sides met in Dublin, Van Gaal boasted before the match that his squad was so much more talented, even the Irish fans would want them to qualify. Ireland went down to ten men after 58 minutes but scored nine minutes later and won 1–0. The Netherlands fell seven points behind them with two games left to play, meaning that they failed to qualify for the World Cup for the first time since 1986. Van Gaal stepped down as manager on 31 January 2002 to be replaced by Dick Advocaat. After this, speculation began that Van Gaal would succeed Sir Alex Ferguson at Manchester United once Ferguson claimed he would retire that year. According to Van Gaal, Ferguson decided against retiring and the deal fell through.


title: Louis van Gaal

text: Van Gaal returned to Barcelona for the start of the 2002–03 season on a contract until June 2005, but results were inconsistent. The club won a record-equalling ten successive matches in the Champions League but struggled in La Liga. After four wins, four draws and three defeats from their opening 11 league matches, Barcelona lost three matches in a row, to Real Sociedad, relegation-threatened Rayo Vallecano and Sevilla. Two wins and a draw improved things but after successive defeats to Valencia and Celta de Vigo, he left by mutual consent on 28 January 2003 with the club in 12th place, just three points above the relegation zone and 20 points behind leaders Real Sociedad.


title: Louis van Gaal

text: His transfers, particularly the signings of goalkeeper Robert Enke, midfielder Gaizka Mendieta and playmaker Juan Román Riquelme, all disappointed. Riquelme had been bought to replace Rivaldo, whom Van Gaal had released on a free transfer despite having a year left on his contract. The two had fallen out during Van Gaal's previous tenure and after Van Gaal returned, Rivaldo said, "Van Gaal is the main cause of my departure. I don't like Van Gaal, and I am sure that he doesn't like me, either." Van Gaal replied that Rivaldo's lack of commitment was the reason he was released, saying that he "was only interested in making more money and playing less. He was chosen as the best player in 1999, but he has not handled himself well since then and has not behaved like a footballer should. He had illusions about Barca and was requesting to take holidays when important Champions League games were approaching. He then hides back home in Brazil. He plays for Brazil like we needed him to at Barcelona, and he has proved this in the World Cup finals, showing he reserved himself for Japan." Rivaldo joined A.C. Milan and won that season's Champions League.


title: Louis van Gaal

text: In 2004, Van Gaal returned to Ajax as a technical director, but resigned later that year due to an internal conflict with Ronald Koeman.


title: Louis van Gaal

text: In January 2005, it was announced that Van Gaal would replace Co Adriaanse as AZ manager on 1 July 2005. Under Van Gaal, AZ finished second in the Eredivisie in 2005–06 and third in 2006–07. Van Gaal also led AZ to a runners-up finish in the 2006–07 KNVB Cup and lost a 2007–08 Champions League qualification play-off to Ajax 4–2 on aggregate.


title: Louis van Gaal

text: Van Gaal initially announced he would leave AZ at the end of the 2007–08 season due to disappointing results, with the club finishing 11th in the Eredivisie. When several players of the AZ squad said that they would like him to stay with AZ, however, Van Gaal said he would give the players a chance to prove themselves.


title: Louis van Gaal

text: AZ started the 2008–09 season with two losses: 2–1 to NAC Breda and 0–3 to ADO Den Haag, but after that the Alkmaar-based club remained unbeaten until 18 April, topping the table ahead of Twente and Ajax for the entire season, despite being predicted to finish as low as 13th by pundits. AZ had the best defensive record in the Eredivisie and the second-best goalscoring record, behind Ajax, thanks to its offensive duo of league topscorer Mounir El Hamdaoui and Brazilian Ari. They were crowned league champions on 19 April, one day after AZ suffered an unexpected loss at home to Vitesse, which ended a string of 28 unbeaten games (surpassing the team's 1980–81 record of 25 unbeaten games). That same day Ajax, the only opponent still in theory able to surpass AZ, lost 6–2 to PSV.


title: Louis van Gaal

text: On 1 July 2009, Van Gaal took over as coach of Bayern Munich. He referred to his new employer as a "dream club". On 28 August 2009, he strengthened his team by signing compatriot Arjen Robben from Real Madrid; this reunited the two, with Van Gaal selecting Robben for his debut in the Netherlands U20 team.


title: Louis van Gaal

text: Van Gaal got off to a poor start as Bayern coach, winning only one of his first four matches in charge, and by November the club was on the brink of a Champions League group stage exit following two losses to Bordeaux. With Bayer Leverkusen at the top of the Bundesliga, speculation was rampant that he was on the brink of a departure from Bayern even earlier than his predecessor Jürgen Klinsmann. Van Gaal, however, kept insisting he is a ""prozesstrainer"", meaning that his team needs time to play the way he imagines.


title: Louis van Gaal

text: Van Gaal installed many youth players as fixtures in the starting 11, including Thomas Müller and Holger Badstuber, and also converted the winger Bastian Schweinsteiger into a defensive midfielder. A feud with Italian striker Luca Toni, who had played an important role in Bayern's 2007–08 league and cup double, led to Toni's move to Roma. Bayern Munich's form, however, improved with two Champions League victories including an impressive 4–1 victory over Juventus in Turin, which allowed them to progress from their group in second position behind Bordeaux. By March, Bayern had moved to the semi-finals of the DFB-Pokal and were top of the Bundesliga, ahead of Bayer Leverkusen.


title: Louis van Gaal

text: On 8 May 2010, Bayern were crowned Bundesliga champions following a 3–1 win at Hertha BSC, making Van Gaal the first ever Dutch coach to win the Bundesliga. On 15 May 2010, Bayern won the DFB-Pokal with a 4–0 victory over Werder Bremen, thus securing the domestic double.


title: Louis van Gaal

text: In the Champions League, Bayern won 4–4 on the away goals rule in the quarter-final against Manchester United and 4–0 on aggregate against Lyon in the semi-final, securing them a spot in the final, where Van Gaal was to meet his former pupil and assistant at Barcelona, Internazionale coach José Mourinho. Bayern, however, lost the final 2–0, handing Inter a first Italian treble and thus failing to secure the treble themselves. On 25 May 2010, Karl-Heinz Rummenigge expressed his desire to extend Van Gaal's contract as the club was very happy with his performance, despite Van Gaal still having one year of his contract to fulfil. At the end of the season, Van Gaal was voted Manager of the Year in the yearly poll organized by VDV (professional players' union in Germany) and German magazine "kicker".


title: Louis van Gaal

text: Van Gaal's Bayern started the 2010–11 season by winning the DFL-Supercup, which had been officially reinstated after a 14-year absence.


title: Louis van Gaal

text: On 7 March 2011, Bayern Munich declared that Van Gaal's contract was to be cancelled after the end of the 2010–11 season. However, he was instead sacked on 10 April 2011 after losing the third place in the Bundesliga.


title: Louis van Gaal

text: On 6 July 2012, Van Gaal was presented as the new Netherlands coach. "I am happy that the KNVB approached me", said Van Gaal, who was assisted by former Dutch internationals Danny Blind and Patrick Kluivert, both part of his successful Ajax squad from 1995. "This is the challenge which I have been waiting for."


title: Louis van Gaal

text: Van Gaal led the Netherlands through its 2014 World Cup qualification group as the team won nine and drew one of their ten matches with a goal difference of 34–5. Qualification was secured with two matches to spare, following a 2–0 away win against Andorra on 10 September 2013.


title: Louis van Gaal

text: Despite their successful qualifying campaign, expectations surrounding the Netherlands national team were comparatively low due to mixed pre-tournament friendly performances and the failure of the Dutch squad in Euro 2012, where they suffered three defeats out of three in the group stages in that tournament. In their first group game at the World Cup, at the Estádio Fonte Nova in Salvador, however, Van Gaal's Dutch team came from behind to defeat reigning champions Spain 5–1. The Dutch victory over Spain was attributed in part to Van Gaal's use of counter-attacking tactics which disrupted the "tiki-taka" possession-based football of the Spanish team. His use of a 3–5–2 formation was notable, as opposed to the typical Dutch 4–3–3 and this helped the Netherlands to tactically take advantage of Spain's weaknesses.


title: Louis van Gaal

text: In their next match, the Dutch were trailing 2–1 to Australia in the second half of their second group game, before winning 2–3 with the winning goal from young substitute Memphis Depay.


title: Louis van Gaal

text: Ahead of the last game in the group, Van Gaal accused FIFA of "playing tricks" in the scheduling of matches to advantage the home nation, as Brazil were to play their last group match four hours after the Dutch, who they could meet in the round of 16 depending on their result. Brazil manager Luiz Felipe Scolari reacted by saying, "It was FIFA who chose the kick-off time. Some people expressed a view that we were going to choose who we were going to play. Those sorts of comments are either stupid or ill-intentioned." Van Gaal also criticised the referees who had awarded penalties against the Dutch in both of their matches, calling the decisions "unjustified" and "incorrect".


title: Louis van Gaal

text: The Dutch won their last group match against Chile 2–0 to advance through as group winners. They then defeated Mexico 2–1 in the round of 16, coming behind from a Giovani dos Santos goal in the 45th minute, with Wesley Sneijder and Klaas-Jan Huntelaar scoring in the 89th and 90+2 minutes respectively.


title: Louis van Gaal

text: During their quarter-final match against Costa Rica in the World Cup, Van Gaal made the decision to substitute first-choice goalkeeper Jasper Cillessen for Tim Krul in the final minute of extra time; as Krul had not played at all in the Netherlands' four prior matches at the tournament, Van Gaal saved one of his three allowed substitutions to bring Krul on. This decision paid off, as Krul saved two of the Costa Rican penalties to send the Netherlands through to the semi-finals to face Argentina. The Dutch team lost to Argentina in another penalty shootout. Van Gaal ended his tenure as Netherlands manager on 12 July 2014 when the Dutch beat the hosts Brazil 3–0 in the third/fourth place play-off match with goals from Robin van Persie, Daley Blind and Georginio Wijnaldum.


title: Louis van Gaal

text: Van Gaal was confirmed to replace David Moyes as the new manager for Manchester United on 19 May 2014, becoming the club's first manager from outside the British Isles. He signed a three-year contract coming into effect after the 2014 World Cup. He named Ryan Giggs as his assistant manager, Marcel Bout as assistant coach, specialising in oppositional scouting and Frans Hoek as goalkeeping coach. Albert Stuivenberg was appointed as assistant coach. Van Gaal said he had inherited a "broken" United squad, and that he would give youth a chance. Ed Woodward said Van Gaal had "impressed everyone around the club" and that there was "a real positive energy and buzz around the place".


title: Louis van Gaal

text: Van Gaal's first signings were midfielder Ander Herrera for £29 million, and defender Luke Shaw for £30 million. On 20 August, Argentine defender Marcos Rojo was bought for €20 million from Sporting CP and, on 26 August, United signed Argentine winger Ángel Di María from Real Madrid on a five-year contract. Di María's £59.7 million fee set a new record for a signing by an English club, and took the club's summer spending to a reported £130 million. On transfer deadline day, Van Gaal signed Daley Blind from Ajax for a fee of £14 million and was granted an extension to sign Radamel Falcao on loan from Monaco for a reported £6 million.


title: Louis van Gaal

text: On 24 July, Van Gaal managed United for the first time as they beat the LA Galaxy 7–0 in a pre-season friendly, using a 3–5–2 formation. Manchester United won the 2014 International Champions Cup under Van Gaal, winning the final 3–1 against rivals Liverpool on 4 August.


title: Louis van Gaal

text: Van Gaal lost his first official game in charge, a 2–1 home defeat to Swansea City in the opening match of the 2014–15 Premier League season. On 26 August, United lost 4–0 to League One side Milton Keynes Dons in the second round of the League Cup; it was United's earliest League Cup exit. He won his first competitive game in United's fourth match of the league season, a 4–0 home victory over Queens Park Rangers, with goals from Di María, Herrera, Wayne Rooney and Juan Mata.


title: Louis van Gaal

text: After 10 league matches, United were in ninth place with 13 points and three victories, their worst start to the season since 1986–87 under Ron Atkinson. Their poor run included a 5–3 defeat to newly promoted Leicester City. The squad was suffering from injuries, including to new signings Herrera, Rojo and Falcao. Van Gaal reacted to the poor form by saying that it would take three years to take his United team to their full potential.


title: Louis van Gaal

text: On 4 February 2015, Van Gaal was charged by The Football Association (FA) over comments he made about the referee Chris Foy, saying, "Every aspect of a match is against us – the pitch, the referee" during United's goalless draw in an FA Cup fourth-round match against Cambridge United. After a requested hearing with the FA, Van Gaal was cleared of his charges, but was warned of future conduct. On 8 February, Van Gaal was criticised by West Ham United manager Sam Allardyce for his long ball tactics after the Hammers conceded a late equaliser to United. Van Gaal responded to the criticism with statistics which seemed to show that West Ham played more long balls than his side. His tactics were defended by fellow managers Arsène Wenger and Garry Monk.


title: Louis van Gaal

text: United's form improved as the season progressed. A run of seven consecutive Premier League wins was part of a ten-match unbeaten run that started with a 1–0 home win over Crystal Palace on 8 November 2014 and was ended by Southampton, who won 1–0 at Old Trafford on 11 January 2015. United completed another sequence of seven league wins in a row between 28 February and 12 April, concluding with an impressive 4–2 defeat of champions and local rivals Manchester City. This was followed by three consecutive losses to Chelsea, Everton and West Bromwich Albion. United were also knocked out at the quarter-final stage of the 2014–15 FA Cup by holders and eventual winners Arsenal, who inflicted a 2–1 home defeat on Van Gaal's team on 9 March.


title: Louis van Gaal

text: In his first season, Van Gaal led Manchester United to a fourth-place finish, three places and six points higher than the previous season.


title: Louis van Gaal

text: During the summer transfer window, Van Gaal strengthened his squad by bringing in Memphis Depay from PSV, Matteo Darmian from Torino, Sergio Romero from Sampdoria, Morgan Schneiderlin from Southampton, Bastian Schweinsteiger from Bayern Munich and Anthony Martial from Monaco.


title: Louis van Gaal

text: United comfortably defeated Club Brugge in the qualifying round of the 2015–16 Champions League to earn a place in the group stage. Domestically, United were solid in defence and went top of the Premier League at the end of September; however, mixed results followed, leaving them in fourth position going into November. They were eliminated from the League Cup by Championship club Middlesbrough and were eliminated from the Champions League at the group stage on 8 December after a 3–2 loss away to VfL Wolfsburg. They finished third in their group and subsequently dropped down to the UEFA Europa League. Fifteen days later, Van Gaal walked out of a press conference after being questioned about his future, amid speculations of dismissal following a six-game run without a win. He concluded, "I wish you a merry Christmas and maybe also a happy new year when I see you."


title: Louis van Gaal

text: The new year began well for the Dutchman with wins against Swansea City, Sheffield United and Liverpool, and a draw against Newcastle United. Manchester United, however, lost to Southampton on 23 January, rekindling rumors about Van Gaal offering to resign, but having his resignation rejected by United executive Ed Woodward.


title: Louis van Gaal

text: After a 3–0 defeat away to Tottenham Hotspur on 10 April, several United players reportedly turned on Van Gaal in the dressing room, calling him "clueless" and questioning his tactics after he openly criticized young striker Marcus Rashford and several other players and made several questionable decisions during the match, a result which left United four points off fourth-placed Manchester City.


title: Louis van Gaal

text: On 21 May 2016, Van Gaal won his only trophy with Manchester United, the FA Cup, when his side defeated Crystal Palace 2–1 after extra time; Jesse Lingard's winning goal made United match Arsenal's then-record of 12 FA Cups. Two days later, Van Gaal and the Dutch members of his staff were sacked by the club.


title: Louis van Gaal

text: On 17 January 2017, it was announced that Van Gaal had retired "for family reasons". He later said that it was only a sabbatical. He announced his official retirement from football on 12 March 2019. Telstar announced that during the 2021–22 Eerste Divisie, van Gaal would be managing the Telstar squad for one single match as a charity event.


title: Louis van Gaal

text: On 4 August 2021, Van Gaal came out of retirement to take charge of the Netherlands national team for a third time. He replaced Frank de Boer, who left the position in June following the team's disappointing Euro 2020 campaign.


title: Louis van Gaal

text: Van Gaal's first match in his third stint at the Netherlands national team was a 1–1 draw against Norway on 1 September 2021.


title: Louis van Gaal

text: In the 2022 FIFA World Cup, the Netherlands finished top of their Group A, then they defeated the United States 3–1 in the round of 16. On 9 December, Van Gaal and his Netherlands side lost again to Argentina on penalties, this time in the quarter-finals. Following their exit from the World Cup, Van Gaal resigned as head coach of the Netherlands national team, after 20 matches without defeat in his third stint.


title: Louis van Gaal

text: The youngest of nine brothers and sisters, Van Gaal was brought up as a Catholic. His father, a salesman, died when Van Gaal was 11. At the age of 18, Van Gaal met Fernanda Obbes at a Catholic youth group. They married three years later, and had two daughters, Brenda and Renate. In 1994, Obbes died of liver and pancreatic cancer. Van Gaal was mocked by fans of Ajax's opponents for her illness. In 2008, Van Gaal married his current wife, Truus, with whom he shares a holiday home near Albufeira, Algarve, Portugal.


title: Louis van Gaal

text: According to "The Daily Telegraph", it emerged in 2009 that Van Gaal had lost millions of pounds investing in fraudster Bernie Madoff's Ponzi scheme.


title: Louis van Gaal

text: On 3 April 2022, Van Gaal said that he was receiving treatment for prostate cancer. On 12 April 2022, he said that his treatment was successful.


title: Louis van Gaal

text: In 2022, Geertjan Lassche made a two-hour documentary about Louis van Gaal, entitled "Louis", with the tagline "The man behind the legend". It premiered on 11 April in the Amsterdam Tuschinski Theatre. It was released on 14 April 2022.


title: Time dilation

text: In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them (special relativistic "kinetic" time dilation) or to a difference in gravitational potential between their locations (general relativistic gravitational time dilation). When unspecified, "time dilation" usually refers to the effect due to velocity.


title: Time dilation

text: After compensating for varying signal delays due to the changing distance between an observer and a moving clock (i.e. Doppler effect), the observer will measure the moving clock as ticking slower than a clock that is at rest in the observer's own reference frame. In addition, a clock that is close to a massive body (and which therefore is at lower gravitational potential) will record less elapsed time than a clock situated further from the said massive body (and which is at a higher gravitational potential).


title: Time dilation

text: These predictions of the theory of relativity have been repeatedly confirmed by experiment, and they are of practical concern, for instance in the operation of satellite navigation systems such as GPS and Galileo. Time dilation has also been the subject of science fiction works.


title: Time dilation

text: Time dilation by the Lorentz factor was predicted by several authors at the turn of the 20th century. Joseph Larmor (1897), at least for electrons orbiting a nucleus, wrote "... individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio: formula_1". Emil Cohn (1904) specifically related this formula to the rate of clocks. In the context of special relativity it was shown by Albert Einstein (1905) that this effect concerns the nature of time itself, and he was also the first to point out its reciprocity or symmetry. Subsequently, Hermann Minkowski (1907) introduced the concept of proper time which further clarified the meaning of time dilation.


title: Time dilation

text: Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to them will be measured to tick slower than a clock that is at rest in their frame of reference. This case is sometimes called special relativistic time dilation. The faster the relative velocity, the greater the time dilation between one another, with time slowing to a stop as one approaches the speed of light (299,792,458 m/s).


title: Time dilation

text: Theoretically, time dilation would make it possible for passengers in a fast-moving vehicle to advance further into the future in a short period of their own time. For sufficiently high speeds, the effect is dramatic. For example, one year of travel might correspond to ten years on Earth. Indeed, a constant 1 g acceleration would permit humans to travel through the entire known Universe in one human lifetime.


title: Time dilation

text: With current technology severely limiting the velocity of space travel, however, the differences experienced in practice are minuscule: after 6 months on the International Space Station (ISS), orbiting Earth at a speed of about 7,700 m/s, an astronaut would have aged about 0.005 seconds less than those on Earth. The cosmonauts Sergei Krikalev and Sergei Avdeyev both experienced time dilation of about 20 milliseconds compared to time that passed on Earth.


title: Time dilation

text: Time dilation can be inferred from the observed constancy of the speed of light in all reference frames dictated by the second postulate of special relativity.


title: Time dilation

text: This constancy of the speed of light means that, counter to intuition, the speeds of material objects and light are not additive. It is not possible to make the speed of light appear greater by moving towards or away from the light source.


title: Time dilation

text: Consider then, a simple vertical clock consisting of two mirrors and , between which a light pulse is bouncing. The separation of the mirrors is and the clock ticks once each time the light pulse hits mirror .


title: Time dilation

text: In the frame in which the clock is at rest (see left part of the diagram), the light pulse traces out a path of length and the period of the clock is divided by the speed of light:


title: Time dilation

text: From the frame of reference of a moving observer traveling at the speed relative to the resting frame of the clock (right part of diagram), the light pulse is seen as tracing out a longer, angled path. Keeping the speed of light constant for all inertial observers requires a lengthening of the period of this clock from the moving observer's perspective. That is to say, as measured in a frame moving relative to the local clock, this clock will be running more slowly. Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity:


title: Time dilation

text: which expresses the fact that the moving observer's period of the clock formula_6 is longer than the period formula_7 in the frame of the clock itself.


title: Time dilation

text: Because all clocks that have a common period in the resting frame should have a common period when observed from the moving frame, all other clocksmechanical, electronic, optical (such as an identical horizontal version of the clock in the example)should exhibit the same velocity-dependent time dilation.


title: Time dilation

text: Given a certain frame of reference, and the "stationary" observer described earlier, if a second observer accompanied the "moving" clock, each of the observers would perceive the other's clock as ticking at a "slower" rate than their own local clock, due to them both perceiving the other to be the one that is in motion relative to their own stationary frame of reference.


title: Time dilation

text: Common sense would dictate that, if the passage of time has slowed for a moving object, said object would observe the external world's time to be correspondingly sped up. Counterintuitively, special relativity predicts the opposite. When two observers are in motion relative to each other, each will measure the other's clock slowing down, in concordance with them being in motion relative to the observer's frame of reference.


title: Time dilation

text: While this seems self-contradictory, a similar oddity occurs in everyday life. If two persons A and B observe each other from a distance, B will appear small to A, but at the same time, A will appear small to B. Being familiar with the effects of perspective, there is no contradiction or paradox in this situation.


title: Time dilation

text: The reciprocity of the phenomenon also leads to the so-called twin paradox where the aging of twins, one staying on Earth and the other embarking on space travel, is compared, and where the reciprocity suggests that both persons should have the same age when they reunite. On the contrary, at the end of the round-trip, the traveling twin will be younger than the sibling on Earth. The dilemma posed by the paradox, however, can be explained by the fact that the traveling twin must markedly accelerate in at least three phases of the trip (beginning, direction change, and end), while the other will only experience negligible acceleration, due to rotation and revolution of Earth. During the acceleration phases of space travel, time dilation is not symmetric.


title: Time dilation

text: In the Minkowski diagram from the first image on the right, clock C resting in inertial frame S′ meets clock A at "d" and clock B at "f" (both resting in S). All three clocks simultaneously start to tick in S. The worldline of A is the ct-axis, the worldline of B intersecting "f" is parallel to the ct-axis, and the worldline of C is the ct′-axis. All events simultaneous with "d" in S are on the x-axis, in S′ on the x′-axis.


title: Time dilation

text: The proper time between two events is indicated by a clock present at both events. It is invariant, i.e., in all inertial frames it is agreed that this time is indicated by that clock. Interval "df" is, therefore, the proper time of clock C, and is shorter with respect to the coordinate times "ef=dg" of clocks B and A in S. Conversely, also proper time "ef" of B is shorter with respect to time "if" in S′, because event "e" was measured in S′ already at time "i" due to relativity of simultaneity, long before C started to tick.


title: Time dilation

text: From that it can be seen, that the proper time between two events indicated by an unaccelerated clock present at both events, compared with the synchronized coordinate time measured in all other inertial frames, is always the "minimal" time interval between those events. However, the interval between two events can also correspond to the proper time of accelerated clocks present at both events. Under all possible proper times between two events, the proper time of the unaccelerated clock is "maximal", which is the solution to the twin paradox.


title: Time dilation

text: In addition to the light clock used above, the formula for time dilation can be more generally derived from the temporal part of the Lorentz transformation. Let there be two events at which the moving clock indicates formula_11 and formula_12, thus:


title: Time dilation

text: Since the clock remains at rest in its inertial frame, it follows formula_14, thus the interval formula_15 is given by:


title: Time dilation

text: where Δ"t" is the time interval between "two co-local events" (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on their clock), known as the "proper time", Δt′ is the time interval between those same events, as measured by another observer, inertially moving with velocity "v" with respect to the former observer, "v" is the relative velocity between the observer and the moving clock, "c" is the speed of light, and the Lorentz factor (conventionally denoted by the Greek letter gamma or γ) is:


title: Time dilation

text: Thus the duration of the clock cycle of a moving clock is found to be increased: it is measured to be "running slow". The range of such variances in ordinary life, where even considering space travel, are not great enough to produce easily detectable time dilation effects and such vanishingly small effects can be safely ignored for most purposes. It is only when an object approaches speeds on the order of 30,000 km/s (1/10 the speed of light) that time dilation becomes important.


title: Time dilation

text: In special relativity, time dilation is most simply described in circumstances where relative velocity is unchanging. Nevertheless, the Lorentz equations allow one to calculate proper time and movement in space for the simple case of a spaceship which is applied with a force per unit mass, relative to some reference object in uniform (i.e. constant velocity) motion, equal to "g" throughout the period of measurement.


title: Time dilation

text: Let "t" be the time in an inertial frame subsequently called the rest frame. Let "x" be a spatial coordinate, and let the direction of the constant acceleration as well as the spaceship's velocity (relative to the rest frame) be parallel to the "x"-axis. Assuming the spaceship's position at time being and the velocity being "v" and defining the following abbreviation:


title: Time dilation

text: In the case where "v"(0) = "v" = 0 and "τ"(0) = "τ" = 0 the integral can be expressed as a logarithmic function or, equivalently, as an inverse hyperbolic function:


title: Time dilation

text: The clock hypothesis is the assumption that the rate at which a clock is affected by time dilation does not depend on its acceleration but only on its instantaneous velocity. This is equivalent to stating that a clock moving along a path formula_27 measures the proper time, defined by:


title: Time dilation

text: The clock hypothesis was implicitly (but not explicitly) included in Einstein's original 1905 formulation of special relativity. Since then, it has become a standard assumption and is usually included in the axioms of special relativity, especially in the light of experimental verification up to very high accelerations in particle accelerators.


title: Time dilation

text: Gravitational time dilation is experienced by an observer that, at a certain altitude within a gravitational potential well, finds that their local clocks measure less elapsed time than identical clocks situated at higher altitude (and which are therefore at higher gravitational potential).


title: Time dilation

text: Gravitational time dilation is at play e.g. for ISS astronauts. While the astronauts' relative velocity slows down their time, the reduced gravitational influence at their location speeds it up, although to a lesser degree. Also, a climber's time is theoretically passing slightly faster at the top of a mountain compared to people at sea level. It has also been calculated that due to time dilation, the core of the Earth is 2.5 years younger than the crust. "A clock used to time a full rotation of the Earth will measure the day to be approximately an extra 10 ns/day longer for every km of altitude above the reference geoid." Travel to regions of space where extreme gravitational time dilation is taking place, such as near (but not beyond the event horizon of) a black hole, could yield time-shifting results analogous to those of near-lightspeed space travel.


title: Time dilation

text: Contrarily to velocity time dilation, in which both observers measure the other as aging slower (a reciprocal effect), gravitational time dilation is not reciprocal. This means that with gravitational time dilation both observers agree that the clock nearer the center of the gravitational field is slower in rate, and they agree on the ratio of the difference.


title: Time dilation

text: High-accuracy timekeeping, low-Earth-orbit satellite tracking, and pulsar timing are applications that require the consideration of the combined effects of mass and motion in producing time dilation. Practical examples include the International Atomic Time standard and its relationship with the Barycentric Coordinate Time standard used for interplanetary objects.


title: Time dilation

text: Relativistic time dilation effects for the solar system and the Earth can be modeled very precisely by the Schwarzschild solution to the Einstein field equations. In the Schwarzschild metric, the interval formula_29 is given by:


title: Time dilation

text: The coordinate time formula_40 is the time that would be read on a hypothetical "coordinate clock" situated infinitely far from all gravitational masses (formula_41), and stationary in the system of coordinates (). The exact relation between the rate of proper time and the rate of coordinate time for a clock with a radial component of velocity is:


title: Master of Science

text: A Master of Science (; abbreviated MS, M.S., MSc, M.Sc., SM, S.M., ScM or Sc.M.) is a master's degree in the field of science awarded by universities in many countries or a person holding such a degree. In contrast to the Master of Arts degree, the Master of Science degree is typically granted for studies in sciences, engineering and medicine and is usually for programs that are more focused on scientific and mathematical subjects; however, different universities have different conventions and may also offer the degree for fields typically considered within the humanities and social sciences. While it ultimately depends upon the specific program, earning a Master of Science degree typically includes writing a thesis.


title: Master of Science

text: The Master of Science degree was first introduced at the University of Michigan in 1858. One of the first recipients of the degree was De Volson Wood, who was conferred a Master of Science degree at the University of Michigan in 1859.


title: Master of Science

text: In Argentina, Brazil, Colombia, Ecuador, Mexico, Panama, Peru, Uruguay and Venezuela, the Master of Science or Magister is a postgraduate degree lasting two to four years. The admission to a Master's program (Spanish: "Licenciatura"; Portuguese: "Mestrado") requires the full completion of a four to five year long undergraduate degree, bachelor's degree, engineer's degree or a licentiate of the same length. Defense of a research thesis is required. All master's degrees qualify for a doctorate program. Depending on the country, one ECTS credit point can equal on average between 22 and 30 actual study hours. In most of these cases, the number of required attendance hours to the University classes will be at least half of that (one ECTS will mean around 11 to 15 mandatory hours of on-site classes).


title: Master of Science

text: Australian universities commonly have coursework or research-based Master of Science courses for graduate students. They typically run for 1–2 years full-time, with varying amounts of research involved.


title: Master of Science

text: All Bangladeshi private and public universities have Master of Science courses as postgraduate degree. These include most of the major state-owned colleges. A number of private colleges also do offer MS degrees. After passing Bachelor of Science, any student becomes eligible to study in this discipline.


title: Master of Science

text: Like all EU member states, Belgium follows the Bologna Process. In Belgium, the typical university track involved obtaining two degrees, being a two-year "Kandidaat" prerequisite track (replaced by "Bachelor") followed by a two- or three-year "Licentiaat" track. The latter was replaced by the Master of Science (M.Sc.) academic degree. This system was not exclusive to scientific degrees and was also used for other programs like law and literature.


title: Master of Science

text: In Canada, Master of Science (MSc) degrees may be entirely course-based, entirely research-based or (more typically) a mixture. Master's programs typically take one to three years to complete and the completion of a scientific thesis is often required. Admission to a master's program is contingent upon holding a four-year university bachelor's degree. Some universities require a master's degree in order to progress to a doctoral program (PhD).


title: Master of Science

text: In the province of Quebec, the Master of Science follows the same principles as in the rest of Canada. There is one exception, however, regarding admission to a master's program. Since Québécois students complete two to three years of college before entering university, they have the opportunity to complete a bachelor's degree in three years instead of four. Some undergraduate degrees such as the Bachelor of Education and the Bachelor of Engineering requires four years of study. Following the obtention of their bachelor's degree, students can be admitted into a graduate program to eventually obtain a master's degree.


title: Master of Science

text: While some students complete their master's program, others use it as a bridge to doctoral research programs. After one year of study and research in the master's program, many students become eligible to apply to a Doctor of Philosophy (Ph.D.) program directly, without obtaining the Master of Science degree in the first place.


title: Master of Science

text: Commonly the Chilean universities have used "Magíster" for a master degree, but other than that is similar to the rest of South America.


title: Master of Science

text: Like all EU member states, the Republic of Cyprus follow the Bologna Process. Universities in Cyprus have used either "Magíster Scientiae or Artium" or Master of Arts/Science for a master's degree with 90 to 120 ECTS and duration of studies between 1, 2 and 5 years.


title: Master of Science

text: Like all EU member states, Czech Republic and Slovakia follow the Bologna Process. Czech Republic and Slovakia both award two different types of Master's degrees; both award a title of "Mgr." or "Ing." to be used before the name.


title: Master of Science

text: Prior to reforms for compliance with the Bologna process, a Master's degree could only be obtained after 5 years of uninterrupted study. Under the new system, it takes only 2 years but requires a previously completed 3-year bachelor's program (a "Bc." title). Writing a thesis (in both master's and bachelor's programs) and passing final exams are necessary to obtain the degree. It is mostly the case that the final exams cover the main study areas of the whole study program, i.e. a student is required to prove their knowledge in the subjects they attended during the 2 resp. 3 years of their study. Exams also include the defence of a thesis before an academic board.


title: Master of Science

text: Ing. (Engineer) degrees are usually awarded for Master's degrees achieved in the Natural Sciences or Mathematics-heavy study programmes, whereas an Mgr. (Magister) is generally awarded for Master's studies in social sciences, humanities and the arts.


title: Master of Science

text: The Master of Science (M.Sc.) is an academic degree for post-graduate candidates or researchers, it usually takes from 4 to 7 years after passing the Bachelor of Science (B.Sc.) degree. Master programs are awarded in many sciences in the Egyptian Universities. A completion of the degree requires finishing a pre-master studies followed by a scientific thesis or research. All M.Sc. degree holders are allowable to take a step forward in the academic track to get the PhD degree.


title: Master of Science

text: Like all EU member states, Finland follows the Bologna Process. The Master of Science (M.Sc.) academic degree usually follows the Bachelor of Science (B.Sc.) studies which typically last five years. For the completion of both the bachelor and the master studies the student must accumulate a total of 300 ECTS credits, thus most Masters programs are two-year programs with 120 credits. The completion of a scientific thesis is required.


title: Master of Science

text: Like all EU member states, Germany follows the Bologna Process. The Master of Science (M.Sc.) academic degree replaces the once common "Diplom" or "Magister" programs that typically lasted four to five years. It is awarded in science-related studies with a high percentage of mathematics. For the completion the student must accumulate 300 ECTS Credits, thus most Masters programs are two-year programs with 120 credits. The completion of a scientific thesis is required.


title: Master of Science

text: In Slavic countries in European southeast (particularly former Yugoslavian republics), the education system was largely based on the German university system (largely due to the presence and influence of the Austria-Hungary Empire in the region). Prior to the implementation of the Bologna Process, academic university studies comprised a 4–5 year-long graduate "diplom" program, which could have been followed by a 2–4 year long "magistar" program and then later with 2–5 year long doctor of science program.


title: Master of Science

text: After the Bologna Process implementation, again based on the German implementation, "Diplom" titles and programs were replaced by entirely professional bachelor's and master's programs. The studies are structured such that a "master" program lasts long enough for the student to accumulate a total of 120 ECTS credits, so its duration would depend on a number of credits acquired during the bachelor studies. Pre-Bologna "magistar" programs were abandoned – after earning an M.Sc. degree and satisfying other academic requirements a student could proceed to earn a doctor of science degree directly, or skip M.Sc. if the "diplom" program lasted more than 3 years as it was possible to do so for some time.


title: Master of Science

text: In Guyana, all universities, including University of Guyana, Texila American University, American International School of Medicine have Master of Science courses as postgraduate degrees. Students who have completed undergraduate Bachelor of Science degree are eligible to study in this discipline.


title: Master of Science

text: In India, universities offer MS programs usually in sciences discipline. Generally, post-graduate scientific courses lead to MS degree while post-graduate engineering courses lead to ME or MTech degree. For example, a master's in automotive engineering would normally be an ME or MTech, while a master's in physics would be an MS. A few top universities also offer undergraduate programs leading to a master's degree which is known as integrated masters.


title: Master of Science

text: A Master of Science in Engineering (MS.Engg.) degree is also offered in India. It is usually structured as an engineering research degree, lesser than PhD and considered to be parallel to M.Phil. degree in humanities and science. Some institutes such as IITs offer an MS degree for postgraduate engineering courses. This degree is considered a research-oriented degree whereas MTech or ME degree is usually not a research degree in India. MS degree is also awarded by various IISERs which are one of the top institutes in India.


title: Master of Science

text: In Iran, similar to Canada, Master of Science (MSc) or in Iranian form "Karshenasi-arshad" degrees may be entirely course-based, entirely research-based or most commonly a mixture. Master's programs typically take two to three years to complete and the completion of a scientific thesis is often required.


title: Master of Science

text: Like all EU member states, Ireland follows the Bologna Process. In Ireland, Master of Science (MSc) may be course-based with a research component or entirely research based. The program is most commonly a one-year program and a thesis is required for both course-based and research based degrees.


title: Master of Science

text: In Israel, Master of Science (MSc) may be entirely course-based or include research. The program is most commonly a two-year program and a thesis is required only for research based degrees.


title: Master of Science

text: Like all EU member states, Italy follows the Bologna Process. The degree "Master of Science" is awarded in the Italian form, "Laurea Magistrale" (formerly "Laurea specialistica"; before the introduction of the "Laurea" the corresponding degree was "Laurea quinquennale" or "Vecchio Ordinamento").


title: Master of Science

text: In Nepal, universities offer the Master of Science degree usually in science and engineering areas. Tribhuvan University offers MSc degree for all the science and engineering courses. Pokhara University offers ME for engineering and MSc for science. Kathmandu University offers MS by Research and ME degrees for science and engineering.


title: Master of Science

text: Like all EU member states, the Netherlands follows the Bologna Process. In the past graduates of applied universities (HBO) were excluded from using titles such as MSc, as HBO institutions are formally not universities but polytechnic institutions of higher education. However, since 2014 academic titles are granted to any university graduate.


title: Master of Science

text: The bearers of these titles can use either the older title, of MSc, LL.M or MA but not both for the same field of study.


title: Master of Science

text: New Zealand universities commonly have coursework or research-based Master of Science courses for graduate students. They typically run for 2 years full-time, with varying amounts of research involved.


title: Master of Science

text: Norway follows the Bologna Process. For engineering, the Master of Science academic degree has been recently introduced and has replaced the previous award forms "Sivilingeniør" (engineer, a.k.a. engineering master) and "Hovedfag" (academic master). Both were awarded after 5 years of university-level studies and required the completion of a scientific thesis.


title: Master of Science

text: "Siv.ing", is a protected title exclusively awarded to engineering students who completed a five-year education at The Norwegian University of Science and Technology (, NTNU) or other universities. Historically there was no bachelor's degree involved and today's program is a five years master's degree education. The "Siv.ing" title is in the process of being phased out, replaced by (for now, complemented by) the "M.Sc." title. By and large, "Siv.ing" is a title tightly being held on to for the sake of tradition. In academia, the new program offers separate three-year bachelor and two-year master programs. It is awarded in the natural sciences, mathematics and computer science fields. The completion of a scientific thesis is required. All master's degrees are designed to certify a level of education and qualify for a doctorate program.


title: Master of Science

text: Master of Science in Business is the English title for those taking a higher business degree, "Siviløkonom" in Norwegian. In addition, there is, for example, the 'Master of Business Administration' (MBA), a practically oriented master's degree in business, but with less mathematics and econometrics, due to its less specific entry requirements and smaller focus on research.


title: Master of Science

text: Pakistan inherited its conventions pertaining to higher education from United Kingdom after independence in 1947. Master of Science degree is typically abbreviated as M.Sc. (as in the United Kingdom) and which is awarded after 16 years of education (equivalent with a bachelor's degree in the US and many other countries). Recently, in pursuance to some of the reforms by the Higher Education Commission of Pakistan (the regulatory body of higher education in Pakistan), the traditional 2-year Bachelor of Science (B.Sc.) degree has been replaced by the 4-year Bachelor of Science degree, which is abbreviated as B.S. to enable the Pakistani degrees with the rest of the world. Subsequently, students who pass a 4-year B.S. degree that is awarded after 16 years of education are then eligible to apply for M.S. degree, which is considered at par with Master of Philosophy (M.Phil.) degree.


title: Master of Science

text: Like all EU member states, Poland follows the Bologna Process. The Polish equivalent of Master of Science is "magister" (abbreviated "mgr", written pre-nominally much like "Dr"). Starting in 2001, the MSc programs typically lasting 5 years began to be replaced as below:


title: Master of Science

text: The degree is awarded predominantly in the natural sciences, mathematics, computer science, economics, as well as in the arts and other disciplines. Those who graduate from an engineering program prior to being awarded a master's degree are allowed to use the "mgr inż." pre-nominal ("master engineer"). This is most common in engineering and agricultural fields of study. Defense of a research thesis is required. All master's degrees in Poland qualify for a doctorate program.


title: Master of Science

text: The title of "master" was introduced by Alexander I at 24 January 1803. The Master had an intermediate position between the candidate and doctor according to the decree "About colleges structure". The master's degree was abolished from 1917 to 1934. Russia follows the Bologna Process for higher education in Europe since 2011.


title: Master of Science

text: Like all EU member states, Spain follows the Bologna Process. The Master of Science (MSc) degree is a program officially recognized by the Spanish Ministry of Education. It usually involves 1 or 2 years of full-time study. It is targeted at pre-experience candidates who have recently finished their undergraduate studies. An MSc degree can be awarded in every field of study. An MSc degree is required in order to progress to a PhD. MSci, MPhil and DEA are equivalent in Spain.


title: Master of Science

text: Like all EU member states, Sweden follows the Bologna Process. The Master of Science academic degree has, like in Germany, recently been introduced in Sweden. Students studying Master of Science in Engineering programs are rewarded both the English Master of Science Degree, but also the Swedish equivalent "Teknologisk masterexamen". Whilst "Civilingenjör" is an at least five year long education.


title: Master of Science

text: The Master of Science is a degree that can be studied only in public universities. The program is usually 2 years, but it can be extended to 3 or 4 years. The student is required to pass a specific bachelor's degree to attend a specific Master of Science degree program. The master of science is mostly a research degree, except for some types of programs held with cooperation of foreign universities. The student typically attends courses in the first year of the program and should then prepare a research thesis. Publishing two research papers is recommended and will increase the final evaluation grade.


title: Master of Science

text: The Master of Science (MSc) is typically a taught postgraduate degree, involving lectures, examinations and a project dissertation (normally taking up a third of the program). Master's programs usually involve a minimum of 1 year of full-time study (180 UK credits, of which 150 must be at master's level) and sometimes up to 2 years of full-time study (or the equivalent period part-time). Taught master's degrees are normally classified into Pass, Merit and Distinction (although some universities do not give Merit). Some universities also offer MSc by research programs, where a longer project or set of projects is undertaken full-time; master's degrees by research are normally pass/fail, although some universities may offer a distinction.


title: Master of Science

text: The more recent Master "in" Science (MSci or M.Sci.) degree (Master of Natural Sciences at the University of Cambridge), is an undergraduate (UG) level integrated master's degree offered by UK institutions since the 1990s. It is offered as a first degree with the first three (four in Scotland) years similar to a BSc course and a final year (120 UK credits) at master's level, including a dissertation. The final MSci qualification is thus at the same level as a traditional MSc.


title: Master of Science

text: The "Master of Science" ("Magister Scientiæ") degree is normally a full-time two-year degree often abbreviated "MS" or "M.S." It is the primary type in most subjects and may be entirely course-based, entirely research-based or (more typically) a combination of the two. The combination often involves writing and defending a thesis or completing a research project which represents the culmination of the material learned.


title: Master of Science

text: Admission to a master's program is normally contingent upon holding a bachelor's degree and progressing to a doctoral program may require a master's degree. In some fields or graduate programs, work on a doctorate can begin immediately after the bachelor's degree. Some programs provide for a joint bachelor's and master's degree after about five years. Some universities use the Latin degree names and due to the flexibility of word order in Latin, "Artium Magister" (A.M.) or "Scientiæ Magister" (S.M. or Sc.M.) may be used in some institutions.


title: Dhani Harrison

text: Dhani Harrison (; born 1 August 1978) is an English musician, composer and singer-songwriter. He is the only child of George and Olivia Harrison. Dhani debuted as a professional musician assisting in recording his father's final album, "Brainwashed", and completing it with the assistance of Jeff Lynne after his father's death in November 2001. Harrison formed his own band, thenewno2, in 2002 and has performed at festivals, including Coachella, where Spin magazine dubbed their performance as one of the "best debut performances of the festival." The band also played Lollapalooza three times, with Harrison joining the festival's founder Perry Farrell on a cover of The Velvet Underground's "Sweet Jane" at 2010's event. In 2017, Harrison released his debut solo album "IN///PARALLEL". The 2019 film "IN///PARALIVE", showcases the live version of his debut solo album and was recorded in the round at Henson Studios in Los Angeles. Harrison's latest single, "Motorways (Erase It)", was described by "Rolling Stone" as "a psychedelic track with a robust beat".


title: Dhani Harrison

text: In 2013, Harrison launched his career as a composer. Alongside his writing partner Paul Hicks, Harrison scored the Warner Bros. movie "Beautiful Creatures". Harrison has gone on to score the music for the TV show "Good Girls Revolt", AMC's "The Divide", "Seattle Road", "Learning to Drive", and for the Paul Giamatti–produced show "Outsiders". In 2018, Harrison and his writing partner Hicks received a nomination for 'Best Music Score' at the International Documentary Association Awards for their work on the Sundance Film Festival Award Winning documentary Matangi/Maya/M.I.A. Most recently, Harrison wrote and recorded the title song for the Netflix original series "Dogs" and, along with Paul Hicks, scored the four-part HBO documentary series "The Case Against Adnan Syed", the Bill Gates Netflix docuseries "", and the 2020 RZA movie "Cut Throat City".


title: Dhani Harrison

text: Harrison's music collaborations span a diverse range of genres that have seen him tour with Eric Clapton, appear on the Wu-Tang Clan track "The Heart Gently Weeps", and join Pearl Jam live on stage several times over the years. One of Harrison's notable collaborations was in 2004 at the Rock and Roll Hall of Fame, where he appeared alongside Tom Petty, Jeff Lynne, and Prince on "While My Guitar Gently Weeps", which was performed to mark the posthumous induction of his father. Harrison guests on the UNKLE album "The Road: Part II/Lost Highway", and also appears on Perry Farrell's solo album, "Kind Heaven". Harrison united with his long-time family friend Jeff Lynne when he opened for Jeff Lynne's ELO on the band's sold out 2019 North American summer tour.


title: Dhani Harrison

text: Harrison is named after the sixth and seventh notes of the Indian music scale, "dha" and "ni". "Dhani" is also a raga in North Indian classical music.


title: Dhani Harrison

text: Harrison was born on 1 August 1978 at HRH Princess Christian’s Hospital in Windsor, Berkshire. He grew up with his parents in Henley-on-Thames, in Friar Park, the estate on which his father had lived since 1970. His mother, Olivia Harrison, is an American of Mexican descent. One of Harrison's earliest memories, from the age of six, is receiving a drumming lesson from his father's friend and bandmate, "Uncle" Ringo Starr. He recalled that before the lesson, he had been an avid drummer. However, when Starr began to play, the loud noise frightened him so much that he ran out of the room screaming.


title: Dhani Harrison

text: Harrison attended Dolphin School near Twyford, a Montessori method school, followed by Badgemore Primary School, Henley-On-Thames. He later attended Shiplake College, also near Henley, where he enrolled in the Combined Cadet Force, and showed a keen interest in rowing which continued into his later years.


title: Dhani Harrison

text: Harrison is an alumnus of Brown University, where he studied industrial design and physics, earning a bachelor's degree. Harrison pursued a career as a car designer at McLaren Automotive before deciding to follow in his father's footsteps as a professional musician.


title: Dhani Harrison

text: Harrison assisted his father in home recording sessions which eventually became part of the "Brainwashed" album project. In this process he gained experience in performing and production techniques.


title: Dhani Harrison

text: After his father's death in 2001, Harrison, in collaboration with Jeff Lynne, completed his father's final album, "Brainwashed", which was released in 2002 and went on to win a Grammy for Best Pop Instrumental Performance, in "Marwa Blues", at the 46th Annual Grammy Awards in 2004. Harrison participated in the "Concert for George" on the first anniversary of his father's death. The concert was organized by Eric Clapton and featured some of his father's friends and collaborators, including former Beatles bandmates Paul McCartney and Ringo Starr as well as Clapton, Billy Preston, Ravi Shankar, Jeff Lynne, Tom Petty, Jim Keltner, and Joe Brown. Harrison played backup acoustic guitar for most of the concert. Before the finale, Paul McCartney relayed to the audience, "Olivia said that with Dhani up on stage, it looks like George stayed young and we all got old", referencing the physical similarities between father and son.


title: Dhani Harrison

text: In 2004 Harrison appeared onstage with Tom Petty, Steve Winwood, Jeff Lynne, Prince and others for a performance of "While My Guitar Gently Weeps" during his father's induction into the Rock and Roll Hall of Fame.


title: Dhani Harrison

text: In March 2006, Harrison made a guest appearance on Liam Lynch's Podcast Video Variety Show, "Lynchland". They performed a duet that will appear on a Lynch album. He collaborated with Jakob Dylan on the John Lennon song "Gimme Some Truth" for the Lennon tribute album "", which was released on 12 June 2007.In April 2006, it was announced that Harrison's band, thenewno2, had begun recording. The band released a music video, "Choose What You're Watching", on its website. thenewno2 features Harrison on lead guitar, synthesiser and vocals and Oli Hecks on drums and synths. He was involved in a re-working of the Beatles' "While My Guitar Gently Weeps" entitled "The Heart Gently Weeps", which was the first single on the Wu-Tang Clan's album "8 Diagrams", released in December 2007.


title: Dhani Harrison

text: Thenewno2's debut album, "You Are Here", was released online on 11 August 2008 and in stores on 31 March 2009. The song "Yomp" was featured as a downloadable song for the "Rock Band" series, and "Crazy Tuesday" was featured as one of the 20 free songs that were downloadable with the purchase of "Rock Band 2".


title: Dhani Harrison

text: Harrison's dedication to his father's musical legacy resulted in a week long run of shows on "Conan" in September 2014, dedicated to George Harrison, which culminated in a sold out George Fest event at The Fonda Theatre in Los Angeles, which was later released as an album and documentary. He participated in "" the same year.


title: Dhani Harrison

text: Harrison produced "George Fest", a live album and concert DVD package documenting The George Fest tribute concert in honor of his father. The tribute was held at the Fonda Theatre in Los Angeles on 28 September 2014. The album and documentary were released on 26 February 2016.


title: Dhani Harrison

text: In 2017 Harrison played his first-ever solo show at the Panorama Festival in New York City. Harrison released his first solo album, "In Parallel", in October 2017.


title: Dhani Harrison

text: In 2019, he toured as the opening act for Jeff Lynne's ELO, and typically performed with the group singing the vocals for the Traveling Wilburys song "Handle with Care."


title: Dhani Harrison

text: In between working on albums, Harrison, along with Paul Hicks, began their film composing partnership scoring the 2013 film "Beautiful Creatures". In 2014, they scored the film "Learning to Drive" and the television series "The Divide". In 2016, they composed music for the Amazon Video television series "Good Girls Revolt" and continue scoring the WGN TV series "Outsiders".


title: Dhani Harrison

text: More recently, Harrison wrote and recorded the title song for the Netflix original series "Dogs" and, along with Paul Hicks, scored the four-part HBO documentary series "The Case Against Adnan Syed" and the 2020 RZA movie "Cut Throat City".


title: Dhani Harrison

text: Harrison married Sólveig "Sóla" Káradóttir in 2012. They announced their separation in 2016. The couple had no children.


title: Dhani Harrison

text: Harrison collaborated in the development of "", a music video game released on 9 September 2009 on the Xbox 360, PlayStation 3 and Wii gaming platforms. He was instrumental in the creation of the game and urged McCartney and Starr to participate. When asked about the game production Dhani stated, "I took the project to Apple and sort of convinced everybody to have a presentation. My job description is... being enthusiastic. We've been working on it for the past two years. This is the first one that is going to be totally, historically accurate. It's been a real headache, but it's been the most enjoyable work I've done in my life."


title: Dhani Harrison

text: To promote the game's release, he appeared on "The Tonight Show with Conan O'Brien" on 8 September 2009 and at the end of the show they played "Birthday" with Dhani on drums, Conan O'Brien on bass, and Aaron Bleyaert and Mark Pender on guitar.


title: Dhani Harrison

text: Harrison told the "Chicago Tribune" in an interview that he is "working on "Rock Band 3" and making the controllers more real so people can actually learn how to play music while playing the game".


title: Alternating current

text: Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans and electric lamps into a wall socket. A common source of DC power is a battery cell in a flashlight. The abbreviations "AC" and "DC" are often used to mean simply "alternating" and "direct", as when they modify "current" or "voltage".


title: Alternating current

text: The usual waveform of alternating current in most electric power circuits is a sine wave, whose positive half-period corresponds with positive direction of the current and vice versa. In certain applications, like guitar amplifiers, different waveforms are used, such as triangular waves or square waves. Audio and radio signals carried on electrical wires are also examples of alternating current. These types of alternating current carry information such as sound (audio) or images (video) sometimes carried by modulation of an AC carrier signal. These currents typically alternate at higher frequencies than those used in power transmission.


title: Alternating current

text: Electrical energy is distributed as alternating current because AC voltage may be increased or decreased with a transformer. This allows the power to be transmitted through power lines efficiently at high voltage, which reduces the energy lost as heat due to resistance of the wire, and transformed to a lower, safer, voltage for use. Use of a higher voltage leads to significantly more efficient transmission of power. The power losses (formula_1) in the wire are a product of the square of the current ( I ) and the resistance (R) of the wire, described by the formula:


title: Alternating current

text: This means that when transmitting a fixed power on a given wire, if the current is halved (i.e. the voltage is doubled), the power loss due to the wire's resistance will be reduced to one quarter.


title: Alternating current

text: The power transmitted is equal to the product of the current and the voltage (assuming no phase difference); that is,


title: Alternating current

text: Consequently, power transmitted at a higher voltage requires less loss-producing current than for the same power at a lower voltage. Power is often transmitted at hundreds of kilovolts on pylons, and transformed down to tens of kilovolts to be transmitted on lower level lines, and finally transformed down to 100 V – 240 V for domestic use.


title: Alternating current

text: High voltages have disadvantages, such as the increased insulation required, and generally increased difficulty in their safe handling. In a power plant, energy is generated at a convenient voltage for the design of a generator, and then stepped up to a high voltage for transmission. Near the loads, the transmission voltage is stepped down to the voltages used by equipment. Consumer voltages vary somewhat depending on the country and size of load, but generally motors and lighting are built to use up to a few hundred volts between phases. The voltage delivered to equipment such as lighting and motor loads is standardized, with an allowable range of voltage over which equipment is expected to operate. Standard power utilization voltages and percentage tolerance vary in the different mains power systems found in the world. High-voltage direct-current (HVDC) electric power transmission systems have become more viable as technology has provided efficient means of changing the voltage of DC power. Transmission with high voltage direct current was not feasible in the early days of electric power transmission, as there was then no economically viable way to step down the voltage of DC for end user applications such as lighting incandescent bulbs.


title: Alternating current

text: Three-phase electrical generation is very common. The simplest way is to use three separate coils in the generator stator, physically offset by an angle of 120° (one-third of a complete 360° phase) to each other. Three current waveforms are produced that are equal in magnitude and 120° out of phase to each other. If coils are added opposite to these (60° spacing), they generate the same phases with reverse polarity and so can be simply wired together. In practice, higher "pole orders" are commonly used. For example, a 12-pole machine would have 36 coils (10° spacing). The advantage is that lower rotational speeds can be used to generate the same frequency. For example, a 2-pole machine running at 3600 rpm and a 12-pole machine running at 600 rpm produce the same frequency; the lower speed is preferable for larger machines. If the load on a three-phase system is balanced equally among the phases, no current flows through the neutral point. Even in the worst-case unbalanced (linear) load, the neutral current will not exceed the highest of the phase currents. Non-linear loads (e.g. the switch-mode power supplies widely used) may require an oversized neutral bus and neutral conductor in the upstream distribution panel to handle harmonics. Harmonics can cause neutral conductor current levels to exceed that of one or all phase conductors.


title: Alternating current

text: For three-phase at utilization voltages a four-wire system is often used. When stepping down three-phase, a transformer with a Delta (3-wire) primary and a Star (4-wire, center-earthed) secondary is often used so there is no need for a neutral on the supply side. For smaller customers (just how small varies by country and age of the installation) only a single phase and neutral, or two phases and neutral, are taken to the property. For larger installations all three phases and neutral are taken to the main distribution panel. From the three-phase main panel, both single and three-phase circuits may lead off. Three-wire single-phase systems, with a single center-tapped transformer giving two live conductors, is a common distribution scheme for residential and small commercial buildings in North America. This arrangement is sometimes incorrectly referred to as "two phase". A similar method is used for a different reason on construction sites in the UK. Small power tools and lighting are supposed to be supplied by a local center-tapped transformer with a voltage of 55 V between each power conductor and earth. This significantly reduces the risk of electric shock in the event that one of the live conductors becomes exposed through an equipment fault whilst still allowing a reasonable voltage of 110 V between the two conductors for running the tools.


title: Alternating current

text: A third wire, called the bond (or earth) wire, is often connected between non-current-carrying metal enclosures and earth ground. This conductor provides protection from electric shock due to accidental contact of circuit conductors with the metal chassis of portable appliances and tools. Bonding all non-current-carrying metal parts into one complete system ensures there is always a low electrical impedance path to ground sufficient to carry any fault current for as long as it takes for the system to clear the fault. This low impedance path allows the maximum amount of fault current, causing the overcurrent protection device (breakers, fuses) to trip or burn out as quickly as possible, bringing the electrical system to a safe state. All bond wires are bonded to ground at the main service panel, as is the neutral/identified conductor if present.


title: Alternating current

text: The frequency of the electrical system varies by country and sometimes within a country; most electric power is generated at either 50 or 60 Hertz. Some countries have a mixture of 50 Hz and 60 Hz supplies, notably electricity power transmission in Japan. A low frequency eases the design of electric motors, particularly for hoisting, crushing and rolling applications, and commutator-type traction motors for applications such as railways. However, low frequency also causes noticeable flicker in arc lamps and incandescent light bulbs. The use of lower frequencies also provided the advantage of lower transmission losses, which are proportional to frequency. The original Niagara Falls generators were built to produce 25 Hz power, as a compromise between low frequency for traction and heavy induction motors, while still allowing incandescent lighting to operate (although with noticeable flicker). Most of the 25 Hz residential and commercial customers for Niagara Falls power were converted to 60 Hz by the late 1950s, although some 25 Hz industrial customers still existed as of the start of the 21st century. 16.7 Hz power (formerly 16 2/3 Hz) is still used in some European rail systems, such as in Austria, Germany, Norway, Sweden and Switzerland. Off-shore, military, textile industry, marine, aircraft, and spacecraft applications sometimes use 400 Hz, for benefits of reduced weight of apparatus or higher motor speeds. Computer mainframe systems were often powered by 400 Hz or 415 Hz for benefits of ripple reduction while using smaller internal AC to DC conversion units.


title: Alternating current

text: A direct current flows uniformly throughout the cross-section of a homogeneous electrically conducting wire. An alternating current of any frequency is forced away from the wire's center, toward its outer surface. This is because an alternating current (which is the result of the acceleration of electric charge) creates electromagnetic waves (a phenomenon known as electromagnetic radiation). Electric conductors are not conducive to electromagnetic waves (a perfect electric conductor prohibits all electromagnetic waves within its boundary), so a wire that is made of a non-perfect conductor (a conductor with finite, rather than infinite, electrical conductivity) pushes the alternating current, along with their associated electromagnetic fields, away from the wire's center. The phenomenon of alternating current being pushed away from the center of the conductor is called skin effect, and a direct current does not exhibit this effect, since a direct current does not create electromagnetic waves.


title: Alternating current

text: At very high frequencies, the current no longer flows "in" the wire, but effectively flows "on" the surface of the wire, within a thickness of a few skin depths. The skin depth is the thickness at which the current density is reduced by 63% (a reduction of one neper). Even at relatively low frequencies used for power transmission (50 Hz – 60 Hz), non-uniform distribution of current still occurs in sufficiently thick conductors. For example, the skin depth of a copper conductor is approximately 8.57 mm at 60 Hz, so high current conductors are usually hollow to reduce their mass and cost. Since the current tends to flow in the periphery of conductors, the effective cross-section of the conductor is reduced. This increases the effective AC resistance of the conductor, since resistance is inversely proportional to the cross-sectional area. The AC resistance is often many times higher than the DC resistance, causing a much higher energy loss due to ohmic heating (also called IR loss).


title: Alternating current

text: For low to medium frequencies, conductors can be divided into stranded wires, each insulated from the others, with the relative positions of individual strands specially arranged within the conductor bundle. Wire constructed using this technique is called Litz wire. This measure helps to partially mitigate skin effect by forcing more equal current throughout the total cross section of the stranded conductors. Litz wire is used for making high-Q inductors, reducing losses in flexible conductors carrying very high currents at lower frequencies, and in the windings of devices carrying higher radio frequency current (up to hundreds of kilohertz), such as switch-mode power supplies and radio frequency transformers.


title: Alternating current

text: As written above, an alternating current is made of electric charge under periodic acceleration, which causes radiation of electromagnetic waves. Energy that is radiated is lost. Depending on the frequency, different techniques are used to minimize the loss due to radiation.


title: Alternating current

text: At frequencies up to about 1 GHz, pairs of wires are twisted together in a cable, forming a twisted pair. This reduces losses from electromagnetic radiation and inductive coupling. A twisted pair must be used with a balanced signalling system, so that the two wires carry equal but opposite currents. Each wire in a twisted pair radiates a signal, but it is effectively cancelled by radiation from the other wire, resulting in almost no radiation loss.


title: Alternating current

text: Coaxial cables are commonly used at audio frequencies and above for convenience. A coaxial cable has a conductive wire inside a conductive tube, separated by a dielectric layer. The current flowing on the surface of the inner conductor is equal and opposite to the current flowing on the inner surface of the outer tube. The electromagnetic field is thus completely contained within the tube, and (ideally) no energy is lost to radiation or coupling outside the tube. Coaxial cables have acceptably small losses for frequencies up to about 5 GHz. For microwave frequencies greater than 5 GHz, the losses (due mainly to the dielectric separating the inner and outer tubes being a non-ideal insulator) become too large, making waveguides a more efficient medium for transmitting energy. Coaxial cables often use a perforated dielectric layer to separate the inner and outer conductors in order to minimize the power dissipated by the dielectric.


title: Alternating current

text: Waveguides are similar to coaxial cables, as both consist of tubes, with the biggest difference being that waveguides have no inner conductor. Waveguides can have any arbitrary cross section, but rectangular cross sections are the most common. Because waveguides do not have an inner conductor to carry a return current, waveguides cannot deliver energy by means of an electric current, but rather by means of a "guided" electromagnetic field. Although surface currents do flow on the inner walls of the waveguides, those surface currents do not carry power. Power is carried by the guided electromagnetic fields. The surface currents are set up by the guided electromagnetic fields and have the effect of keeping the fields inside the waveguide and preventing leakage of the fields to the space outside the waveguide. Waveguides have dimensions comparable to the wavelength of the alternating current to be transmitted, so they are feasible only at microwave frequencies. In addition to this mechanical feasibility, electrical resistance of the non-ideal metals forming the walls of the waveguide causes dissipation of power (surface currents flowing on lossy conductors dissipate power). At higher frequencies, the power lost to this dissipation becomes unacceptably large.


title: Alternating current

text: At frequencies greater than 200 GHz, waveguide dimensions become impractically small, and the ohmic losses in the waveguide walls become large. Instead, fiber optics, which are a form of dielectric waveguides, can be used. For such frequencies, the concepts of voltages and currents are no longer used.


title: Alternating current

text: Alternating currents are accompanied (or caused) by alternating voltages. An AC voltage "v" can be described mathematically as a function of time by the following equation:


title: Alternating current

text: The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak. Since the maximum value of formula_10 is +1 and the minimum value is −1, an AC voltage swings between formula_11 and formula_12. The peak-to-peak voltage, usually written as formula_13 or formula_14, is therefore formula_15.


title: Alternating current

text: Rather than using instantaneous power, formula_18, it is more practical to use a time averaged power (where the averaging is performed over any integer number of cycles). Therefore, AC voltage is often expressed as a root mean square (RMS) value, written as formula_19, because


title: Alternating current

text: The RMS voltage is the square root of the mean over one cycle of the square of the instantaneous voltage.


title: Alternating current

text: where the trigonometric identity formula_23 has been used and the factor formula_24 is called the crest factor, which varies for different waveforms.


title: Alternating current

text: To illustrate these concepts, consider a 230 V AC mains supply used in many countries around the world. It is so called because its root mean square value is 230 V. This means that the time-averaged power delivered is equivalent to the power delivered by a DC voltage of 230 V. To determine the peak voltage (amplitude), we can rearrange the above equation to:


title: Alternating current

text: For 230 V AC, the peak voltage formula_5 is therefore formula_29, which is about 325 V. During the course of one cycle the voltage rises from zero to 325 V, falls through zero to −325 V, and returns to zero.


title: Alternating current

text: Alternating current is used to transmit information, as in the cases of telephone and cable television. Information signals are carried over a wide range of AC frequencies. POTS telephone signals have a frequency of about 3 kHz, close to the baseband audio frequency. Cable television and other cable-transmitted information currents may alternate at frequencies of tens to thousands of megahertz. These frequencies are similar to the electromagnetic wave frequencies often used to transmit the same types of information over the air.


title: Alternating current

text: The first alternator to produce alternating current was a dynamo electric generator based on Michael Faraday's principles constructed by the French instrument maker Hippolyte Pixii in 1832. Pixii later added a commutator to his device to produce the (then) more commonly used direct current. The earliest recorded practical application of alternating current is by Guillaume Duchenne, inventor and developer of electrotherapy. In 1855, he announced that AC was superior to direct current for electrotherapeutic triggering of muscle contractions. Alternating current technology was developed further by the Hungarian Ganz Works company (1870s), and in the 1880s: Sebastian Ziani de Ferranti, Lucien Gaulard, and Galileo Ferraris.


title: Alternating current

text: In 1876, Russian engineer Pavel Yablochkov invented a lighting system where sets of induction coils were installed along a high voltage AC line. Instead of changing voltage, the primary windings transferred power to the secondary windings which were connected to one or several 'electric candles' (arc lamps) of his own design, used to keep the failure of one lamp from disabling the entire circuit. In 1878, the Ganz factory, Budapest, Hungary, began manufacturing equipment for electric lighting and, by 1883, had installed over fifty systems in Austria-Hungary. Their AC systems used arc and incandescent lamps, generators, and other equipment.


title: Alternating current

text: Alternating current systems can use transformers to change voltage from low to high level and back, allowing generation and consumption at low voltages but transmission, possibly over great distances, at high voltage, with savings in the cost of conductors and energy losses. A bipolar open-core power transformer developed by Lucien Gaulard and John Dixon Gibbs was demonstrated in London in 1881, and attracted the interest of Westinghouse. They also exhibited the invention in Turin in 1884. However these early induction coils with open magnetic circuits are inefficient at transferring power to loads. Until about 1880, the paradigm for AC power transmission from a high voltage supply to a low voltage load was a series circuit. Open-core transformers with a ratio near 1:1 were connected with their primaries in series to allow use of a high voltage for transmission while presenting a low voltage to the lamps. The inherent flaw in this method was that turning off a single lamp (or other electric device) affected the voltage supplied to all others on the same circuit. Many adjustable transformer designs were introduced to compensate for this problematic characteristic of the series circuit, including those employing methods of adjusting the core or bypassing the magnetic flux around part of a coil. The direct current systems did not have these drawbacks, giving it significant advantages over early AC systems.


title: Alternating current

text: In the autumn of 1884, Károly Zipernowsky, Ottó Bláthy and Miksa Déri (ZBD), three engineers associated with the Ganz Works of Budapest, determined that open-core devices were impractical, as they were incapable of reliably regulating voltage. In their joint 1885 patent applications for novel transformers (later called ZBD transformers), they described two designs with closed magnetic circuits where copper windings were either wound around a ring core of iron wires or else surrounded by a core of iron wires. In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air (see toroidal cores). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs. The Ganz factory in 1884 shipped the world's first five high-efficiency AC transformers. This first unit had been manufactured to the following specifications: 1,400 W, 40 Hz, 120:72 V, 11.6:19.4 A, ratio 1.67:1, one-phase, shell form.


title: Alternating current

text: The ZBD patents included two other major interrelated innovations: one concerning the use of parallel connected, instead of series connected, utilization loads, the other concerning the ability to have high turns ratio transformers such that the supply network voltage could be much higher (initially 1400 V to 2000 V) than the voltage of utilization loads (100 V initially preferred). When employed in parallel connected electric distribution systems, closed-core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces. Bláthy had suggested the use of closed cores, Zipernowsky had suggested the use of parallel shunt connections, and Déri had performed the experiments;


title: Alternating current

text: The other essential milestone was the introduction of 'voltage source, voltage intensive' (VSVI) systems' by the invention of constant voltage generators in 1885. In early 1885, the three engineers also eliminated the problem of eddy current losses with the invention of the lamination of electromagnetic cores. Ottó Bláthy also invented the first AC electricity meter.


title: Alternating current

text: The AC power system was developed and adopted rapidly after 1886 due to its ability to distribute electricity efficiently over long distances, overcoming the limitations of the direct current system. In 1886, the ZBD engineers designed the world's first power station that used AC generators to power a parallel-connected common electrical network, the steam-powered Rome-Cerchi power plant. The reliability of the AC technology received impetus after the Ganz Works electrified a large European metropolis: Rome in 1886.


title: Alternating current

text: In the UK, Sebastian de Ferranti, who had been developing AC generators and transformers in London since 1882, redesigned the AC system at the Grosvenor Gallery power station in 1886 for the London Electric Supply Corporation (LESCo) including alternators of his own design and transformer designs similar to Gaulard and Gibbs. In 1890, he designed their power station at Deptford and converted the Grosvenor Gallery station across the Thames into an electrical substation, showing the way to integrate older plants into a universal AC supply system.


title: Alternating current

text: In the U.S., William Stanley, Jr. designed one of the first practical devices to transfer AC power efficiently between isolated circuits. Using pairs of coils wound on a common iron core, his design, called an induction coil, was an early transformer. Stanley also worked on engineering and adapting European designs such as the Gaulard and Gibbs transformer for US entrepreneur George Westinghouse who started building AC systems in 1886. The spread of Westinghouse and other AC systems triggered a push back in late 1887 by Thomas Edison (a proponent of direct current) who attempted to discredit alternating current as too dangerous in a public campaign called the "war of the currents". In 1888, alternating current systems gained further viability with introduction of a functional AC motor, something these systems had lacked up till then. The design, an induction motor, was independently invented by Galileo Ferraris and Nikola Tesla (with Tesla's design being licensed by Westinghouse in the US). This design was further developed into the modern practical three-phase form by Mikhail Dolivo-Dobrovolsky, Charles Eugene Lancelot Brown, and Jonas Wenström.


title: Alternating current

text: The Ames Hydroelectric Generating Plant and the original Niagara Falls Adams Power Plant were among the first hydroelectric alternating current power plants. The first long distance transmission of single-phase electricity was from a hydroelectric generating plant in Oregon at Willamette Falls which in 1890 sent power fourteen miles downriver to downtown Portland for street lighting. In 1891, a second transmission system was installed in Telluride Colorado. The San Antonio Canyon Generator was the third commercial single-phase hydroelectric AC power plant in the United States to provide long-distance electricity. It was completed on December 31, 1892, by Almarian William Decker to provide power to the city of Pomona, California, which was 14 miles away. In 1893, he designed the first commercial three-phase power plant in the United States using alternating current—the hydroelectric Mill Creek No. 1 Hydroelectric Plant near Redlands, California. Decker's design incorporated 10 kV three-phase transmission and established the standards for the complete system of generation, transmission and motors used today. The Jaruga Hydroelectric Power Plant in Croatia was set in operation on 28 August 1895. The two generators (42 Hz, 550 kW each) and the transformers were produced and installed by the Hungarian company Ganz. The transmission line from the power plant to the City of Šibenik was long on wooden towers, and the municipal distribution grid 3000 V/110 V included six transforming stations. Alternating current circuit theory developed rapidly in the latter part of the 19th and early 20th century. Notable contributors to the theoretical basis of alternating current calculations include Charles Steinmetz, Oliver Heaviside, and many others. Calculations in unbalanced three-phase systems were simplified by the symmetrical components methods discussed by Charles LeGeyt Fortescue in 1918.


title: Cock ring

text: A cock ring or cockring (also called a C ring, erection ring, penis ring, shaft ring, tension ring, or Arab strap) is a ring worn around the penis, usually at the base. The primary purpose of wearing a cock ring is to restrict the flow of blood from the erect penis to produce a stronger erection or to maintain an erection for a longer period of time. Genital adornment is another purpose, as is repositioning the genitals to provide an enhanced appearance.


title: Cock ring

text: Cock rings are also called C rings, penis rings or shaft rings. When used in cases of erectile dysfunction (ED), they are known by various other names, such as erection rings and tension rings.


title: Cock ring

text: Cock rings worn just behind the corona of the glans of the penis are known as glans rings, head rings or cock crowns. A ring that is worn around the penis and scrotum is also usually called a cock ring, but is sometimes referred to as a cock and ball ring. Rings that are worn just around the scrotum, in order to hold the testicles, are usually called testicle cuffs or ball stretchers.


title: Cock ring

text: An erection ring may be worn to treat erectile dysfunction (ED). When used for ED, a purpose-designed vacuum pump is used to produce an erection by simple mechanical and hydrodynamical action in spite of vascular or nerve damage, and the ring is slid off the pump's cylinder onto the base of the penis to maintain the erection before it is lost. The testicles are not ringed in this case.


title: Cock ring

text: A cock ring may be used during sex or masturbation to prolong or enhance erections, delay orgasm, or for the sensation of tightness and engorgement that wearing one produces; vibrating models apply vibration to the base of the user's penis and to their partner. They can be worn as sex toys or for aesthetic reasons.


title: Cock ring

text: The purpose of a cock ring is to trap blood inside the penis in order to maintain an erection, or encourage a stronger erection. In order to do this, it must be placed at the base of the penis.


title: Cock ring

text: A ring made of stretchy material is simply stretched over the penis (and optionally also the scrotum, except when used with a pump for impotence) and situated against the body. Rigid rings are used differently: first each testicle is fed through the ring and the entire scrotum is pulled through, then the flaccid penis is pushed through the ring and the ring is situated against the body.


title: Cock ring

text: When used with a pump, a lubricating gel is always used to help the pump maintain a vacuum, in the same way vacuum grease is used with a vacuum pump in scientific applications. The gel also makes it easier for the ring to slide off the pump, and later, to remove it from the penis.


title: Cock ring

text: Some models include a protruding clitoral stimulator, designed to tickle the clitoris, vulva, or anus during sex (and during masturbation while the ring is used on a dildo). Others, such as the vibrating ring, vibrate, either vibrating the ring itself, or using two removable bullet vibrators to provide stimulation to the testicles and clitoris. Some cock rings have vibrators attached that can be worn to stimulate the scrotum or perineum of a partner during sexual intercourse. Many women find that rings with vibrator attachments provide clitoral stimulation that is needed for achieving orgasm.


title: Cock ring

text: A triple cock ring or triple crown is a cock ring that has additional rings for restraining the testicles. In orgasm, the testicles usually retract towards the body before ejaculation. A triple crown changes and intensifies the sensation of orgasm by forcing the testicles to stay away from the body.


title: Cock ring

text: Vendors of cock rings and medical sources indicate that cock rings are not to be worn for more than about 30 minutes. Falling asleep or using illicit drugs at the same time is very dangerous. The first sign of pending problems is when the penis starts to become numb, painful, or cold. As soon as this happens, the cock ring must be removed.


title: Cock ring

text: Cock rings that are too tight, or worn for too long can be dangerous: this may cause priapism, a medical emergency that, if not treated promptly, can result in severe and permanent damage, including penile gangrene that can result in the destruction and possible amputation of the penis. Rings for erectile dysfunction are invariably supplied with the instruction that they should not be left on for more than thirty minutes. Falling asleep with a ring on is a particular danger. This may lead to temporary or permanent nerve damage. Numbness in the glans penis, penis becoming cold or penis becoming white may be signs that a cock ring has been worn for too long and medical advice should be sought.


title: Cock ring

text: Cock rings must not be used without medical advice by those who have cardiovascular problems or who take blood-thinning medication.


title: Cock ring

text: Commercially available cock rings are made from many different materials, including: leather, rubber, silicone, neoprene, nylon, metals (including: aluminium, steel, titanium, silver, gold and platinum), wood, plastic, bone, horn, ceramic, glass, and semi precious stone. They also come in a wide variety of sizes, with an inner diameter ranging from .


title: Cock ring

text: Designs range from the simple to the complex. Simple rings may lie flat on a surface, while others are ergonomically curved to fit more comfortably on the wearer. Some designs are horseshoe shaped with a closure. In cross section, the rings may vary from round to flattened oval, the latter offering more friction on the penis and are therefore less likely to slip. Many of the newer rings also have different accessories and projections.


title: Cock ring

text: Today, cock rings can be bought with accessories that stimulate the clitoris or anal area during intercourse. Other cock rings go around the scrotum and can significantly enhance erection and intensity of orgasms.


title: Cock ring

text: However, there is one disadvantage: the more accessories that are added on, the greater the chance of developing discomfort or cold sensations from the device.