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Chance the Rapper
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Chance the Rapper
Chance the Rapper in 2017
Background information
Birth name
Chancelor Johnathan Bennett
Also known as
Chano[1]
Born
(1993-04-16) April 16, 1993 (age 24)[2]
Chicago, Illinois, U.S.
Occupation(s)
Rapper
singer
songwriter
record producer
Instruments
Vocals
piano
sampler
Years active
2011–present
Associated acts
Jeremih
Lil B
Website
chanceraps.com
Chancelor Johnathan Bennett (born April 16, 1993), known professionally as Chance the Rapper, is an American rapper, singer, songwriter and record producer from the West Chatham neighborhood of Chicago, Illinois. In 2013, he began to gain recognition following the release of his second mixtape, Acid Rap. Apart from his solo career, he is a member of the Chicago collective Save Money (along with frequent collaborator Vic Mensa). He has worked as the lead vocalist for the band The Social Experiment; they released the album Surf in May 2015.
In May 2016, Bennett released his third mixtape Coloring Book to critical acclaim. It earned him three Grammy awards, including for Best Rap Album. Coloring Book became the first streaming-only album to receive a nomination for, and win, a Grammy. In July 2017, Bennett was nominated for an Emmy Award for his song "Last Christmas" that was performed on Saturday Night Live. He shares the nomination with Kenan Thompson, Eli Brueggemann, and Will Stephen in the category for Outstanding Original Music and Lyrics.
Contents
[hide]
1 Early life
2 Music career
2.1 2011–2012: Career beginnings and 10 Day
2.2 2012–2015: Acid Rap and The Social Experiment
2.3 2016–present: Coloring Book and debut album
3 Artistry
3.1 Musical style
3.2 Fashion
4 Personal life
4.1 Family
4.2 Beliefs
4.3 Activism and politics
5 Discography
6 Awards and nominations
7 Filmography
8 Concert tours
9 References
10 External links
Early life[edit]
Chancelor Johnathan Bennett was born in Chicago, Illinois to Ken Williams-Bennett, an aide to former Chicago mayor Harold Washington and then-Senator Barack Obama, and Lisa Bennett,[3] a secretary for the office of Illinois Attorney General. Bennett grew up in the middle-class neighborhood of West Chatham on Chicago's South Side.[4] When Bennett was thirteen, his father began to work for President Barack Obama during his first term in the Department of Labor.[5][6] Bennett personally met President Obama in his youth and discussed his aspirations to be a rapper, to which Obama responded with "word".[7] Bennett was originally going to move to Washington, D.C. following Obama's win in the 2008 presidential election though those plans eventually fell through.[8] Bennett attended Jones College Prep High School where he was a member of the Jewish Student Union.[9] During his time in high school, Bennett did not get good grades and was suspended often.[10]
Bennett's interest in music began with Michael Jackson, who he exclusively listened to on cassettes until the fifth grade.[11] Growing up, Bennett's parents music was constantly played, this included Billie Holiday and Sam Cooke and other artists in the jazz and gospel genres.[12] Bennett began listening to hip-hop after hearing "Through the Wire" by Kanye West on the radio whilst walking through Hyde Park, Chicago. After finding out the song was on West's debut album The College Dropout, Bennett purchased the album, making it the first hip-hop album that Bennett listened to.[13] Bennett considers West a huge influence on him and has said that he was inspired to begin rapping by West.[14][15][13] Bennett and West met each other in August 2014 at Bonaroo.[16]
Bennett began rapping in the sixth grade when his cousin let him start using his studio.[17] In his freshman year at Jones College Prep High School, Bennett formed the hip-hop duo Instrumentality alongside a friend.[18] Many of Chance's earliest performances took place at the YOUmedia Lyricist Loft at Harold Washington Library in Chicago.[19] After placing second in a local songwriting contest, Bennett met then-Chicago Mayor, Richard Daley who enjoyed his music.[8] Bennett spent most of his junior year and a small amount of his senior year writing a draft for his debut project, 10 Day,[10] which was later released after Bennett was suspended for ten days after being caught smoking cannabis.[20]
Music career[edit]
2011–2012: Career beginnings and 10 Day[edit]
At Jones College Prep High School, some of his teachers ridiculed his aspirations to become a musician.[21] Following a 10-day suspension in early 2011, during his senior year, for possessing marijuana on campus,[22] Bennett recorded his first full-length project, a mixtape titled 10 Day (also known as #10Day).[21][23][24] In December 2011, he released a song titled "Windows", and publicly announced his 10 Day project.[25] In February 2012, Bennett was highlighted as one of Complex magazine's "10 New Chicago Rappers to Watch Out For".[26] Bennett says he spent "about eight months recording, writing and making connections off of the hunger to put out something".[23] Bennett released the mixtape on April 3, 2012, and it has since been downloaded over 300,000 times via mixtape-sharing site DatPiff.[23][27] The mixtape was well received locally and helped Bennett make connections with producers such as Chuck Inglish, Kenny Jame$ and Blended Babies.[23] The mixtape also grabbed the attention of Forbes magazine, which featured it in the publication's Cheap Tunes column.[28]
2012–2015: Acid Rap and The Social Experiment[edit]
Main articles: Acid Rap and Surf (Donnie Trumpet & The Social Experiment album)
In July 2012, Bennett appeared on American rapper Childish Gambino's sixth mixtape, Royalty, on the track "They Don't Like Me". Gambino would go on to ask Bennett to join on his first concert tour of North America as his opening act.[23][29][30]
On April 30, 2013, Bennett released his second mixtape, Acid Rap,[31] on DatPiff. The record has been downloaded over 1.5 million times.[32] Bennett enlisted guest appearances from Twista, Vic Mensa, Saba, BJ the Chicago Kid, Action Bronson, Childish Gambino and Ab-Soul.[33] Acid Rap was well-received by critics.[34] At Metacritic, the mixtape received an average score of 86, based on 21 critics, which indicates "universal acclaim".[35] It was nominated for Best Mixtape at the 2013 BET Hip Hop Awards.[36] On May 6, 2013, the song "Paranoia" (produced by Nosaj Thing), after initially being featured as a hidden track on Acid Rap, was released as a contribution to Yours Truly and Adidas originals' "Songs from Scratch" series.[37]
In June 2013, Bennett was featured in a commercial for MySpace as part of their relaunch, alongside fellow American rappers Mac Miller, Pharrell Williams and Schoolboy Q, among others.[38] In July 2013, Acid Rap debuted at number 63 on the Billboard Top R&B/Hip-Hop Albums chart, due to downloads on iTunes and Amazon.[39] In August 2013, Bennett performed at the Chicago music festival Lollapalooza.[40] Acid Rap was listed on multiple 50 best albums of 2013 lists, including 26th for Rolling Stone,[41] 12th on Pitchfork's list,[42] and ranked 4th by Complex.[43] It was also listed as one of NPR Music's 50 Favorite Albums of 2013.[44] Bennett began his Social Experiment Tour in Champaign, Illinois on October 25, 2013, lasting until December 19, 2013.[45]
Chance the Rapper performing live in November 2013
In March 2014, Bennett appeared in a shoppable online video for Dockers, promoting the brand's spring line, in which Bennett talks his style, love for creating music, and how it feels to live in Los Angeles.[46][47][48] On May 5, 2014, XXL revealed Bennett was included in their annual freshman class, alongside fellow up-and-comers Isaiah Rashad, Ty Dolla $ign, Rich Homie Quan, Vic Mensa, August Alsina, Troy Ave, Kevin Gates, Lil Bibby, Jon Connor, Lil Durk and Jarren Benton.[49] During Fall 2014, Bennett and other artists participated in Verge Campus tour.[50] In November 2014, Bennett was presented Chicago's "Outstanding Youth of the Year Award" by Mayor Rahm Emanuel.[51]
In January 2015, Bennett was listed number 7 on the "Forbes 30 Under 30" 2015 music list.[52] In March 2015, Bennett released a short film called Mr. Happy, which was directed by Colin Tilley. Mr. Happy centers around the main character, named Victor, who is struggling from depression and was attempting to commit suicide. After many failed attempts to kill himself, he discovers Mr. Happy.[53][clarification needed] On April 30, 2015, Bennett gave a lecture at Harvard University's Hiphop Archive & Research Institute.[54]
Just before midnight on May 28, 2015, Surf was released for free on the American iTunes store as an iTunes Exclusive. The album received high acclaim from music critics, receiving an aggregate score of 86 on review site Metacritic, which indicates "universal acclaim", based on 17 reviews. In June 2015, Bennett performed at the Bonnaroo Music Festival in the superjam concert collection. He also made a guest performance with fellow rapper Kendrick Lamar, on stage with Earth, Wind & Fire. On July 19, 2015, Bennett and Lil B announced that they recorded a collaborative mixtape. The two rappers released it on August 5, titled Free (Based Freestyles Mixtape).[55]
On October 13, 2015, Bennett released a video for a new song, titled "Family Matters", on his website. The song, which shares the same name as his fall 2015 tour with D.R.A.M., Metro Boomin, Towkio (and Hiatus Kaiyote on select dates), is a rework of the Kanye West song "Family Business" from his 2004 album The College Dropout.[56][57][58] A few days before this, a video surfaced online of Bennett performing a new song live, ending the song by saying the words "third mixtape", leading many to believe the wait might be coming to a close for his next release.[59] On October 27, 2015, Bennett premiered a new song, titled "Angels" featuring Saba, on The Late Show with Stephen Colbert. On December 12, 2015, Bennett performed on Saturday Night Live, on a new song, titled "Somewhere in Paradise".[60]
2016–present: Coloring Book and debut album[edit]
Main article: Coloring Book (mixtape)
In 2016, Bennett was a prominent figure on Kanye West's album The Life of Pablo, co-writing and appearing on several tracks, namely "Ultralight Beam", "Father Stretch My Hands Pt. 1", "Famous", "Feedback", and "Waves". According to West, the album's release was delayed because Bennett wanted "Waves" to be on the album.[61][62] Bennett was also featured on a track titled "Need To Know" on Macklemore & Ryan Lewis's album This Unruly Mess I've Made. The following March, Bennett was featured on Skrillex's remix of Hundred Waters' "Show Me Love".[63] On April 16, 2016, Chance and other musicians, including Alicia Keys, Busta Rhymes, Janelle Monáe, and J. Cole, met with President Obama at the White House to discuss the My Brother's Keeper Challenge initiative.[64]
Chance the Rapper performing at a concert in May 2017.
On May 12, 2016, Chance's third mixtape, Coloring Book (promoted as Chance 3), was released, streaming exclusively on Apple Music.[65] In the first week, the mixtape was streamed over 57.3 million times, which was equivalent to 38,000 units sold, debuting at number eight on the US Billboard 200 chart. It became the first release to chart solely on streams.[66] The mixtape was met with widespread acclaim from music critics, and on review aggregator site Metacritic, received an average score of 90, based on 20 critics, which indicates "universal acclaim".
On July 13, at the 2016 ESPY Awards show, along with Kareem Abdul-Jabbar, he performed a tribute song titled "I Was A Rock" for the late Muhammad Ali.[67] On August 16, 2016, Chance wrote the single "We the People" paired in a Nike commercial titled "Unlimited Together", a film directed by Hiro Murai. A second commercial was released on October 4 by Nestlé to promote the Kit Kat bar, starring Chance in costume remixing their jingle. On September 15, 2016, Chance began his Magnificent Coloring World Tour in San Diego.
Bennett announced the Magnificent Coloring Tour with an event called Magnificent Coloring Day Festival at Chicago's U.S. Cellular Field, with a line up including Lil Wayne, Skrillex, and Lil Uzi Vert, taking place on September 24, 2016, being the first-ever music festival at U.S. Cellular Field.[68] Bennett launched a campaign in conjunction with rapperradio.com to get his music on the radio on August 17, 2016.[69]
In September 2016, H&M solicited Bennett to headline their new campaign.[70] In November 2016, he continued on the Magnificent Coloring World Tour, but canceled the rest of his shows on the European leg due to personal reasons.[71] In November 2016, Bennett announced during an interview with DJ Semtex that he was working on his debut album.[72] Bennett was offered a chance to sign with Kanye West's GOOD Music in December 2016, though he refused due to his popularity as an independent artist and the freedom of not being attached to a label.[73] In an August interview about his debut album, Bennett said he may sell the album, a departure from his previous projects' free distribution format.[74] After a report was leaked claiming that audio distribution platform SoundCloud was close to bankruptcy and had laid off most of its workers,[75] Bennett had a phone call with SoundCloud CEO Alex Ljung.[76] Following the phone call, Bennett went onto Twitter, posting that SoundCloud is "here to stay".[77] It was later reported that Bennett was just reflecting on what Ljung had previously published in a press release following the leak.[78]
Artistry[edit]
Musical style[edit]
Bennett has stated in interviews with XXL and Complex that Kanye West, James Brown, MC Hammer, Prince, Lupe Fiasco, Common, Lil Wayne, Esham, Eminem, Souls of Mischief and Freestyle Fellowship have influenced him.[79] When asked about the gospel influences in his music, he also has stated that Kirk Franklin is one of his favorite artists, and his favorite composer.[54]
Bennett's music has been described as versatile[80] and uplifting.[81] His music generally contains jazz-inspired melodies and gospel influences.[82] Bennett's lyrics usually have references to Christian theology,[83] his struggles with his faith[84] and his upbringing.[85] Chance incorporates choirs into his music to attempt to maximize the gospel undertones.[86] Sharde' Chapman at HuffPost has described Bennett's lyrics as "creative" and "colourful."[87]
Fashion[edit]
While Bennett's fashion style is not a large part of his public image, he has taken interest in the industry. Bennett has designed hats for the Chicago White Sox.[88] The Hollywood Reporter has said that Bennett is "redefining fashion" with his style of generally wearing overalls and contesting traditional hip-hop fashion norms.[89] Bennett wore a suit that was meant to imitate Michael Jackson at the 2017 BET Awards.[90] Bennett was seen wearing Thom Browne clothing at the 2017 Grammys.[91]
Personal life[edit]
Bennett lives in his hometown, Chicago, Illinois. Bennett used to share a house in North Hollywood with James Blake before moving out at the six month mark.[92] Describing his time in North Hollywood, Bennett called it "ungodly".[93] After graduating high school, Bennett attended a community college for a week before dropping out.[94][7] Bennett has taken numerous recreational drugs during his lifetime, including LSD[95] and Xanax.[96]
Family[edit]
His younger brother, Taylor Bennett, is also a rapper.[97] Both Taylor and Chancelor began rapping at the same time and have a similar style.[98] Both the rappers also draw inspiration from Chicago native Kanye West.[99]
In July 2015, Bennett announced that he was expecting his first child with his girlfriend Kirsten Corley, whom he began to date in 2013.[100][101] In September 2015, Kirsten gave birth to their daughter, Kensli.[102][103] Kensli was kept out of social media until December 31, 2016, when Bennett posted a picture of her on Instagram.[104] In May 2016, after they had stopped living together, Kirsten wanted the courts to declare Bennett as the father of their daughter. He would have to pay child support.[105][106]
In February 2017, Bennett's child support case reopened in an attempt to work out child support terms and a parenting schedule as Bennett and his ex-girlfriend Kirsten moved to separate residences.[107] The Chicago Sun-Times published an article about a dispute between his ex-girlfriend Kirsten and Bennett in March 2017.[108] Bennett replied to the article saying "Y’all better do y’all jobs and stop worrying about how good my family is. Just a friendly reminder. Don’t let anybody get between you and your family."[109] On March 21, 2017, the dispute was settled in court.[110]
Bennett spends much of his freetime with his daughter, and takes her on activities with him. These have included a Chicago Bulls basketball game,[111] meeting the Obamas[112][113] and working out.[114][111]
Beliefs[edit]
Bennett is a Christian and refers to Jesus Christ in many of his songs.[115] Bennett was raised as a Christian by his grandmother but later fell out of the faith.[116] He rediscovered his faith when his daughter was born with atrial flutters.[117] Speaking about the situation, Bennett said "[I just] pray a whole lot, you know, and need a lot of angels and just see shit in a very, like, direct way. And…you know, God bless everything, it worked out well."[118] Bennett wrote on Twitter following the situation on January 31, 2016, "Today's the last day my old life, last day smoking cigs. Headed to church for help. All things are possible thru Christ who strengthens me."[119]
Bennett has labelled himself as a Christian rapper following the release of his mixtape Coloring Book.[120] Bennett believes that God is to thank for his "blessings" and his career being successful.[121]
Activism and politics[edit]
Bennett is an independent voter who leans left.[122] His father worked for Barack Obama as a presidential appointee[8] and as an aide.[4] His father also worked on the Barack Obama presidential campaign in 2008[8] and is an aide to Rahm Emanuel.[123] Despite his family's ties to the Democratic Party, Bennett is an independent voter though he has a history of supporting Democrats[124][125] volunteering with Barack Obama's reelection campaign by phonebanking in Hyde Park, Chicago.[122]
In November 2014, Bennett was named Chicago's Outstanding Youth of the Year by Chicago Mayor Rahm Emanuel.[126][127] Bennett has actively fought to combat gun violence in his hometown of Chicago and in 2014, along with his father, promoted the "#SaveChicago" campaign. The campaign sought to stop gun violence over Memorial Day Weekend, and saw Chicago go 42 straight hours without a shooting.[128] Bennett met with President Obama at the White House on April 16, 2016, to discuss My Brother's Keeper Challenge, an initiative of the United States Federal Government to promote intervention by civic leaders in the lives of young men of color to address their unique challenges and to promote racial justice, with other musicians, including Alicia Keys, Busta Rhymes, Janelle Monáe, J. Cole and others.[64] Bennet started a Twitter campaign for May 23, 2016 using #May23 to stop gun violence for 42 hours.[129]
On March 6, 2017, after a meeting with Governor Bruce Rauner that did not go well only days before,[130] Bennett announced his intention to donate $1,000,000 to Chicago Public Schools [131] in order to help offset the lack of government funding provided. Following this, a movement arose to try and inspire Bennett to run for mayor of Chicago.[132][133][18] This was backed by fellow media personalities including musician Drake.[134]
Bennett is an outspoken critic of President Donald Trump, having criticised him numerous times and drawn comparisons to former President Barack Obama.[135] During the 2016 Presidential election, Bennett said he was not scared of a Trump presidency.[136] When asked why by GQ, Bennett said "You gotta just understand, like, shit has been fucked-up, right? Like, "Make America Great Again", that's not a real thing because shit ain't really switched up for [white middle class]".[137] Bennett endorsed Democratic candidate Hillary Clinton on October 6, 2016, expressing concerns about the way she was treated in the media and also expressing that she could "fix Chicago"[138] though Bennett was not aware of any of Clinton's policies.[139] Following the victory of Donald Trump in the 2016 presidential election, Bennett said "Trump was going to win, anybody in the world who's surprised by the election of Donald Trump has been ignorant of racism, and the tides and patterns of American history and world history.”[140]
In February 2017, Bennett posted publicly on Twitter that he was worried President Trump was going to change constitutional term limits.[141]
Bennett has compared Trump's fascination with Chicago as "going to war".[142]
Bennett created controversy in August 2017 when he said that he had a "bigger voice than Donald Trump".[143] Though Bennett has been listed as one of the most influential social media personalities[143] Chicago Tribune has compared Trump and Bennett's social media followers to find that Trump had 30 million more.[144]
Discography[edit]
Main article: Chance the Rapper discography
Mixtapes
10 Day (2012)
Acid Rap (2013)
Coloring Book (2016)
Awards and nominations[edit]
BET Awards
Year
Recipient
Category
Result
Ref.
2017 Himself Best Male Hip-Hop Artist Nominated [145]
Best New Artist Won
Coloring Book Album of the Year Nominated
"No Problem" (with Lil Wayne and 2 Chainz) Best Collaboration Won
BET Hip Hop Awards
Year
Recipient
Category
Result
Ref.
2013 Acid Rap Best Mixtape Nominated [36]
2016 Coloring Book Won [146]
Himself Best New Hip Hop Artist Won
Lyricist of the Year Nominated
2017 Nominated
Hot Ticket Performer Nominated
MVP of the Year Nominated
Hustler of the Year Nominated
"I'm the One" Sweet 16: Best Featured Verse Nominated
Emmy Awards
Year
Recipient
Category
Result
Ref
2017 "Last Christmas" — Saturday Night Live Outstanding Original Music and Lyrics Nominated [147]
Grammy Awards
Year
Recipient
Category
Result
Ref
2017 Himself Best New Artist Won [148]
"No Problem" (with Lil Wayne and 2 Chainz) Best Rap Performance Won
Best Rap Song Nominated
"Famous" (as songwriter) Nominated
"Ultralight Beam" (with Kanye West, Kirk Franklin, The-Dream and Kelly Price) Nominated
Best Rap/Sung Performance Nominated
Coloring Book Best Rap Album Won
iHeartRadio Music Awards
Year
Recipient
Category
Result
Ref
2017 Himself Best New Hip-Hop Artist Won [149]
Best New Artist Nominated
MOBO Awards
Year
Recipient
Category
Result
Ref.
2016 Himself Best International Act Nominated [150]
MTV Video Music Awards
Year
Recipient
Category
Result
Ref.
2016 "Angels" (with Saba) Best Hip-Hop Video Nominated [151]
2017 "Same Drugs" Nominated [152]
"I'm the One" (with DJ Khaled, Justin Bieber, Quavo and Lil Wayne) Nominated
MTV Video Music Awards Japan
Year
Recipient
Category
Result
Ref.
2016 "Angels" (with Saba) Best Hip Hop Video Nominated [153]
NAACP Image Awards
Year
Recipient
Category
Result
Ref.
2017 Himself Outstanding New Artist Won [154]
Outstanding Male Artist Nominated
Coloring Book Outstanding Album Nominated
Soul Train Music Awards
Year
Recipient
Category
Result
Ref.
2016 Himself Best New Artist Won [155]
"No Problem" (with Lil Wayne and 2 Chainz) Rhythm & Bars Award Nominated
Best Collaboration Nominated
Teen Choice Awards
Year
Recipient
Category
Result
Ref.
2017 Himself Choice R&B/Hip-Hop Artist Nominated [152]
Choice Breakout Artist Won
"I'm the One" (with DJ Khaled, Justin Bieber, Quavo and Lil Wayne) Choice R&B/Hip-Hop Song Won
Filmography[edit]
Television
Year
Show
Role
2013 The Eric Andre Show Himself
The Arsenio Hall Show
2014 Black Dynamite Bob Marley (voice)
2015 The Late Show with Stephen Colbert Himself
Saturday Night Live
2016 The Tonight Show Starring Jimmy Fallon
The Ellen DeGeneres Show
2017 Wild 'N Out Himself
Short films
Year
Film
Role
2015 Mr. Happy Victor
Concert tours[edit]
Magnificent Coloring World Tour (2016)
Be Encouraged Tour (2017)
References[edit]
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Jump up ^ Sia, Nicole (May 5, 2014). "XXL Freshmen 2014 Cover Revealed – XXL". XXLmag.com. Retrieved October 25, 2017.
Jump up ^ Frydenlund, Zach (September 2, 2014). "Chance The Rapper to Headline the 2014 Verge Campus Fall Tour". Complex. Retrieved October 25, 2017.
Jump up ^ Minsker, Evan (November 9, 2014). "Chance The Rapper Receives Chicago's Outstanding Youth of the Year Award From Mayor Rahm Emanuel". Pitchfork. Retrieved November 30, 2014.
Jump up ^ Zack O'Malley Greenburg; Natalie Robehmed (January 5, 2015). "Forbes' 30 Under 30 2015: Music". Forbes.com. Retrieved January 6, 2015.
Jump up ^ "Chance The Rapper Stars in "Mr. Happy"". TheBlenderWmuc.com. March 24, 2015. Retrieved October 25, 2017.
^ Jump up to: a b Leight, Elias (May 6, 2015). "All The Best Quotes From Chance The Rapper's Lecture At Harvard". The FADER. Retrieved October 25, 2017.
Jump up ^ Young, Alex (July 19, 2015). "Chance The Rapper and Lil B say they recorded an album together". Consequence of Sound. Retrieved July 27, 2015.
Jump up ^ "Chance The Rapper – "Family Matters"". YouTube. October 13, 2015. Retrieved October 22, 2015.
Jump up ^ Weatherby, Taylor (July 29, 2015). "Chance the Rapper Announces North American 'Family Matters' Tour". Billboard. Retrieved October 25, 2017.
Jump up ^ Minsker, Evan (October 13, 2015). "Chance The Rapper Covers Kanye West's "Family Business" in "Family Matters" Video". Pitchfork. Retrieved October 25, 2017.
Jump up ^ Schwartz, Danny (October 12, 2015). "Chance The Rapper Performs New Song, Mentions Third Mixtape". Hotnewhiphop.com. Retrieved October 25, 2017.
Jump up ^ Walker, Angus (December 13, 2015). "Chance The Rapper – Somewhere In Paradise Feat. Jeremih & R. Kelly | Stream [New Song]". Hotnewhiphop.com. Retrieved October 25, 2017.
Jump up ^ Dombal, Ryan (February 12, 2016). "Kanye West: "Ultralight Beam" [ft. Chance The Rapper, The-Dream, Kelly Price, and Kirk Franklin]". Pitchfork. Retrieved October 25, 2017.
Jump up ^ Kreps, Daniel (February 13, 2016). "'Blame Chance': Kanye West Explains 'Life of Pablo' Album Delay". Rolling Stone. Retrieved October 25, 2017.
Jump up ^ Brown, Harley (March 22, 2016). "Skrillex Recruits Chance the Rapper, Moses Sumney, Robin Hannibal for Hundred Waters' 'Show Me Love' Remix". Spin. Retrieved October 25, 2017.
^ Jump up to: a b Pearce, Sheldon (April 16, 2016). "President Obama Meets With Nicki Minaj, Chance The Rapper, J. Cole, More to Discuss "My Brother's Keeper" Initiative". Pitchfork. Retrieved October 25, 2017.
Jump up ^ Fitzgerald, Kiana (May 15, 2016). "Chance The Rapper's 'Coloring Book' Reveals Shades Of Gospel". KRCB. Retrieved October 25, 2017.
Jump up ^ Caulfield, Keith (May 22, 2016). "Chance the Rapper's 'Coloring Book' is First Streaming-Exclusive Album to Chart on Billboard 200". Billboard. Retrieved October 25, 2017.
Jump up ^ Rooney, Kyle (July 13, 2016). "Chance The Rapper To Honor Muhammad Ali At Tonight's ESPY Awards". HotNewHipHop. Retrieved July 15, 2016.
Jump up ^ Lobenfield, Claire (July 25, 2016). "Chance's Magnificent Coloring Tour". Factmag. Retrieved July 25, 2016.
Jump up ^ Low, Carver (August 17, 2016). "Chance the Rapper launches campaign to get music on the radio". HotNewHipHop. Retrieved October 25, 2017.
Jump up ^ Rooney, Kyle (September 22, 2016). "H&M chooses Chance the Rapper to headline campaign". HotNewHipHop. Retrieved October 25, 2017.
Jump up ^ Feig, Zakk (November 23, 2016). "Chance The Rapper Cancels Remaining Europe Concerts". HotNewHipHop. Retrieved October 25, 2017.
Jump up ^ Lozano, Kevin (November 23, 2016). "Chance the Rapper Is Working on His Debut Album". pitchfork.com. Retrieved October 25, 2017.
Jump up ^ Feig, Zakk (December 22, 2016). "Chance The Rapper Says It Wasn't Easy Turning Down Kanye West's Offer". HotNewHipHop. Retrieved October 25, 2017.
Jump up ^ "Chance the Rapper May Sell His Debut Albumwebsite=Rap-Up". March 13, 2017. Retrieved October 25, 2017.
Jump up ^ Wilson, Scott (July 13, 2017). "SoundCloud only has enough money to last 50 days, according to reports". FACT Magazine. Retrieved October 25, 2017.
Jump up ^ Lynch, John (July 14, 2017). "Chance the Rapper says SoundCloud is 'here to stay,' after a report says its cash will run out in 50 days". Business Insider. Retrieved October 25, 2017.
Jump up ^ Aswad, Jem (July 14, 2017). "Chance the Rapper Says 'SoundCloud Is Here to Stay' in Cryptic Tweet". Variety. Retrieved August 23, 2017.
Jump up ^ Sharples, Grant (July 14, 2017). "Updated: Chance the Rapper Just Saved SoundCloud". Paste Magazine. Retrieved October 25, 2017.
Jump up ^ "Chance The Rapper – XXL". XXLmag.com. May 9, 2014. Retrieved October 22, 2015.
Jump up ^ Miller, Matt (July 5, 2017). "This Proves Chance the Rapper Is the Most Versatile Artist in Hip-Hop". Esquire. Retrieved October 27, 2017.
Jump up ^ Kelly, Chris (October 7, 2016). "The pure and joyous uplift of Chance the Rapper". The Washington Post. ISSN 0190-8286. Retrieved August 23, 2017.
Jump up ^ Kelly, Robert (May 13, 2016). "How Chance the Rapper redefined the music business's boundaries". The Guardian. ISSN 0261-3077. Retrieved August 23, 2017.
Jump up ^ ex, kris (May 17, 2016). "Chance the Rapper: Coloring Book Album Review | Pitchfork". pitchfork.com. Retrieved October 27, 2017.
Jump up ^ Driscoll, Faf (June 3, 2016). "How Great Is His God?: A Review of Chance the Rapper's 'Coloring Book'". The Gospel Coalition Australia. Retrieved October 27, 2017.
Jump up ^ Swartz, Anna (May 13, 2016). "The Chance the Rapper 'Coloring Book' Lyrics That'll Awaken the '90s Kid in You". Mic. Retrieved October 27, 2017.
Jump up ^ Havens, Lyndsey (February 12, 2017). "Chance the Rapper Performs Gospel-Infused 'Coloring Book' Medley at Grammys". Billboard. Retrieved October 27, 2017.
Jump up ^ Chapman, Sharde' (October 12, 2016). "Kaleidoscope Of Meaning: Chance The Rapper's 'Coloring Book' And Making Religious Meaning In The Intersection". Huffington Post. Retrieved August 23, 2017.
Jump up ^ Cosman, Ben (April 7, 2016). "Check out the new White Sox hats designed by Chance the Rapper". Major League Baseball. Retrieved October 27, 2017.
Jump up ^ Reed, Sam (January 5, 2017). "How Chance the Rapper Is Redefining Hip-Hop Style, One Pair of Overalls at a Time". The Hollywood Reporter. Retrieved October 27, 2017.
Jump up ^ Gonzales, Erica (June 26, 2017). "Chance the Rapper Paid Tribute to Michael Jackson on His Death Anniversary". Harper's BAZAAR. Retrieved August 23, 2017.
Jump up ^ Carlos, Marjon (February 12, 2017). "Chance the Rapper Sweeps the Grammys in Thom Browne". Vogue. Retrieved October 2017, 2017. Check date values in: |access-date= (help)
Jump up ^ Baron, Zach (August 24, 2016). "How Chance the Rapper's Life Became Perfect". GQ. Retrieved August 23, 2017.
Jump up ^ "Why Chance The Rapper Returned to Chicago After "Ungodly" Experience in LA". DJBooth. Retrieved August 23, 2017.
Jump up ^ Power 106 Los Angeles (September 21, 2016), Chance The Rapper Talks Kanye Collab Project, The Beyonce VMA Moment, + Struggles To Success, retrieved August 23, 2017
Jump up ^ "Chance The Rapper Explains How Taking Acid Affected "Acid Rap"". HotNewHipHop. Retrieved August 23, 2017.
Jump up ^ "How Xanax Nearly Ruined Chance The Rapper’s Music Career". Genius. Retrieved August 23, 2017.
Jump up ^ Bleakmax "Hear Chance The Rapper Join Brother Taylor Bennett on 'Broad Shoulders". Rolling Stone. Rollingstone.com. Retrieved January 20, 2016.
Jump up ^ "Chance the Rapper's brother, Taylor Bennett, sounds an awful lot like him". The Michigan Daily. Retrieved August 23, 2017.
Jump up ^ "Taylor Bennett Is Headed For Big Things, Just As Soon As He Graduates High School". Chicagoist. Retrieved August 23, 2017.
Jump up ^ "Chance The Rapper Oyster Magazine Interview". Oyster Magazine. Brooklyn, New York: Genius Media Group. Retrieved October 22, 2015.
Jump up ^ Stutz, Colin (July 23, 2015). "Chance The Rapper Announces He's Expecting a Baby". Billboard.com. Prometheus Global Media. Retrieved October 27, 2015.
Jump up ^ "Chance The Rapper Welcomes His First Child, a Daughter". Fuse. Retrieved April 18, 2016.
Jump up ^ "Chance The Rapper Talks Fatherhood, Black Lives Matter & a Secret Project with Stephen Colbert". Youtube.
Jump up ^ Adams, Char (January 1, 2017). "'Say Cheese!' Chance the Rapper Posts Sweet Photo of Daughter Meeting the Obamas". People.
Jump up ^ Stephens, Brittney. "It's Complicated: Get the Details on Chance the Rapper's Relationship Status". POPSUGAR Celebrity.
Jump up ^ Walsh, S.M. (February 13, 2017). "Kristen Corley, Chance the Rapper’s Girlfriend: 5 Fast Facts You Need to Know". Heavy.com.
Jump up ^ "Chance the Rapper Child Support Dispute Back in Court | Pitchfork". pitchfork.com. Retrieved August 23, 2017.
Jump up ^ "Mitchell: Child-support spat could hurt Chance the Rapper's image". Chicago Sun-Times. Retrieved August 23, 2017.
Jump up ^ "Chance The Rapper responds to child support claims". NME. March 10, 2017. Retrieved August 23, 2017.
Jump up ^ "Chance the Rapper’s Child Support Case Has Been Resolved". Spin. March 21, 2017. Retrieved August 23, 2017.
^ Jump up to: a b "Chance the Rapper Takes Daughter Kensli to a Basketball Game — See the Cute Video!". PEOPLE.com. April 13, 2017. Retrieved August 23, 2017.
Jump up ^ "‘Say Cheese!’ Chance the Rapper Posts Sweet Photo of Daughter Meeting the Obamas". PEOPLE.com. January 1, 2017. Retrieved August 23, 2017.
Jump up ^ "Instagram post by Chance The Rapper • Jan 1, 2017 at 12:11am UTC". Instagram. Retrieved August 23, 2017.
Jump up ^ "Instagram post by Chance The Rapper • Apr 12, 2017 at 2:38pm UTC". Instagram. Retrieved August 23, 2017.
Jump up ^ Dark, David, "I Speak To God In Public: Chance The Rapper's Faith"za, MTV, May 18, 2016.
Jump up ^ "Chance The Rapper Says His Grandma's 'Turn to Dust' Prayer Helped Him Find His Way Back to God | Christian News on Christian Today". www.christiantoday.com. Retrieved August 23, 2017.
Jump up ^ "Chance the Rapper Says Daughter's Health Scare "Brought My Faith Back" – Music News". ABC News Radio. Retrieved August 23, 2017.
Jump up ^ "Chance the Rapper's grandmother helped him find his way back to God | God Reports". blog.godreports.com. Retrieved August 23, 2017.
Jump up ^ 79th, Lil Chano From (January 31, 2016). "Today's the last day my old life, last day smoking cigs. Headed to church for help. All things are possible thru Christ who strengthens me.". @chancetherapper. Retrieved August 23, 2017.
Jump up ^ "Chance the Rapper Says Working With Kanye West is 'Life-Affirming'". Billboard. Retrieved August 23, 2017.
Jump up ^ "Kendrick Lamar and Chance the Rapper are right about God". USA TODAY. Retrieved August 23, 2017.
^ Jump up to: a b Galil, Leor. "Chance the Rapper on Obama, LSD, and being pigeonholed as a high school MC". Chicago Reader. Retrieved August 23, 2017.
Jump up ^ "Ex-Obama Aide, Chance the Rapper's Dad Named Rahm's Neighborhood Liaison". DNAinfo Chicago. Retrieved August 23, 2017.
Jump up ^ 79th, Lil Chano From (June 2, 2016). "I'm voting for the democratic nominee.". @chancetherapper. Retrieved August 23, 2017.
Jump up ^ Chavez, Danette. "Chance The Rapper is modeling a "Thank You Obama" fashion line". News. Retrieved August 23, 2017.
Jump up ^ JON GRAEF, Chance The Rapper Receives 'Outstanding Youth Of The Year' Award From Mayor, November 9, 2014
Jump up ^ Chance the Rapper Wins Chicago's "Outstanding Youth of the Year Award" John Riti, November 10, 2014
Jump up ^ "Chance The Rapper Receives Chicago's Outstanding Youth of the Year Award From Mayor Rahm Emanuel". Pitchfork. Retrieved April 25, 2016.
Jump up ^ Chandler, D. L., "Chicago’s Chance The Rapper Helps Stop Gun Violence In City For 42 Hours", Newsone.
Jump up ^ http://www.chicagotribune.com/news/local/politics/ct-chance-the-rapper-bruce-rauner-met-0304-20170303-story.html
Jump up ^ http://www.chicagotribune.com/news/local/politics/ct-chance-the-rapper-chicago-schools-plan-met-20170306-story.html
Jump up ^ Vivanco, Leonor. "Chance the Rapper for mayor?". chicagotribune.com. Retrieved August 12, 2017.
Jump up ^ "Fans Urge Chance the Rapper to Run for Mayor of Chicago". Noisey. Retrieved August 12, 2017.
Jump up ^ "Drake backs Chance the Rapper to become Mayor of Chicago". NME. April 6, 2017. Retrieved August 12, 2017.
Jump up ^ Wilson, Samantha (August 4, 2017). "Chance The Rapper Slams Trump In Barack Obama Birthday Tribute". Hollywood Life. Retrieved August 12, 2017.
Jump up ^ "Chance The Rapper Covers 'GQ,' Talks Kanye West & Donald Trump Presidency". Billboard. Retrieved August 12, 2017.
Jump up ^ Davidson, Mark Anthony Green,Eric Ray (February 14, 2017). "The Gospel According to Chance the Rapper". GQ. Retrieved August 12, 2017.
Jump up ^ CNN, Deena Zaru. "Chance the Rapper backs Clinton". CNN. Retrieved August 12, 2017.
Jump up ^ "Chance the Rapper endorses Hillary Clinton". NY Daily News. Retrieved August 12, 2017.
Jump up ^ BBC Radio 1Xtra (November 23, 2016), Chance The Rapper – The DJ Semtex Interview, retrieved August 23, 2017
Jump up ^ http://hiphopdx.com, HipHopDX -. "Chance The Rapper Is Worried About Donald Trump". HipHopDX. Retrieved August 12, 2017.
Jump up ^ "Chance the Rapper: Trump Sounds Like He's 'Going to War With Chicago'". Rolling Stone. Retrieved August 12, 2017.
^ Jump up to: a b "Chance The Rapper: "I have a bigger voice than Donald Trump"". NME. August 10, 2017. Retrieved August 12, 2017.
Jump up ^ Janssen, Kim. "Chance the Rapper: 'I have a bigger voice than Donald Trump'". chicagotribune.com. Retrieved August 12, 2017.
Jump up ^ "Beyoncé and Bruno Mars lead 2017 BET Awards nominations". Channel. Retrieved May 15, 2017.
Jump up ^ Vulpo, Mike (October 5, 2016). "BET Hip Hop Awards 2016 Winners: The Complete List". E! Online News. Retrieved October 5, 2016.
Jump up ^ "Nominees/Winners". Television Academy. Retrieved October 23, 2017.
Jump up ^ "59th Annual GRAMMY Awards Winners & Nominees – GRAMMY.com". GRAMMY.com. The Recording Academy. Archived from the original on May 3, 2012. Retrieved December 6, 2016.
Jump up ^ "2017 iHeartRadio Music Awards: Complete List of Nominations". E! Online. January 3, 2017.
Jump up ^ "MOBO Awards 2016 nominations announced: Find out who made the shortlist". Glasgow Live. September 21, 2016. Retrieved October 24, 2016.
Jump up ^ "VMAs 2016: MTV Video Music Awards red carpet, winners, performances, more". Newsday. Retrieved August 30, 2016.
^ Jump up to: a b "VMAs: Kendrick Lamar Tops Nominations as MTV Continues to Eliminate Gendered Categories". The Hollywood Reporter. July 25, 2017. Retrieved July 25, 2017.
Jump up ^ "Nominees Announced for the MTV Video Music Awards Japan 2016". ARAMA Japan. September 1, 2016. Retrieved October 24, 2016.
Jump up ^ Aiello, McKenna (February 12, 2017). "NAACP Image Awards 2017 Winners: The Complete List". E! News. Retrieved February 12, 2017.
Jump up ^ "Teen Choice Awards 2017 Winners: 'Wonder Woman', 'Beauty And The Beast', 'Riverdale' Among Honorees". Deadline. enske Business Media, LLC. August 13, 2017. Retrieved August 14, 2017.
External links[edit]
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2010
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2011
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2012
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2013
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2014
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Zac Brown Band (2010)
Esperanza Spalding (2011)
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Fun (2013)
Macklemore & Ryan Lewis (2014)
Sam Smith (2015)
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Chance the Rapper (2017)
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1 Postulates of special relativity
2 Alternative derivations of special relativity
3 Mathematical formulation of the postulates
4 Notes
Postulates of special relativity[edit]
1. First postulate (principle of relativity)
The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion. Or: the laws of physics are the same in all inertial frames of reference.
2. Second postulate (invariance of c)
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. Or: the speed of light in free space has the same value c in all inertial frames of reference.
The two-postulate basis for special relativity is the one historically used by Einstein, and it remains the starting point today. As Einstein himself later acknowledged, the derivation of the Lorentz transformation tacitly makes use of some additional assumptions, including spatial homogeneity, isotropy, and memorylessness.[1] Also Hermann Minkowski implicitly used both postulates when he introduced the Minkowski space formulation, even though he showed that c can be seen as a space-time constant, and the identification with the speed of light is derived from optics.[2]
Alternative derivations of special relativity[edit]
Historically, Hendrik Lorentz and Henri Poincaré (1892–1905) derived the Lorentz transformation from Maxwell's equations, which served to explain the negative result of all aether drift measurements. By that the luminiferous aether becomes undetectable in agreement with what Poincaré called the principle of relativity (see History of Lorentz transformations and Lorentz ether theory). A more modern example of deriving the Lorentz transformation from electrodynamics (without using the historical aether concept at all), was given by Richard Feynman.[3]
Following Einstein's original derivation and the group theoretical presentation by Minkowski, many alternative derivations have been proposed, based on various sets of assumptions. It has often been argued (such as by Vladimir Ignatowski in 1910,[4][5][6] or Philipp Frank and Hermann Rothe in 1911,[7][8] and many others in subsequent years[9]) that a formula equivalent to the Lorentz transformation, up to a nonnegative free parameter, follows from just the relativity postulate itself, without first postulating the universal light speed. (Also these formulations rely on the aforementioned various assumptions such as isotropy). The numerical value of the parameter in these transformations can then be determined by experiment, just as the numerical values of the parameter pair c and the Vacuum permittivity are left to be determined by experiment even when using Einstein's original postulates. Experiment rules out the validity of the Galilean transformations. When the numerical values in both Einstein's and other approaches have been found then these different approaches result in the same theory.[citation needed]
Mathematical formulation of the postulates[edit]
In the rigorous mathematical formulation of special relativity, we suppose that the universe exists on a four-dimensional spacetime M. Individual points in spacetime are known as events; physical objects in spacetime are described by worldlines (if the object is a point particle) or worldsheets (if the object is larger than a point). The worldline or worldsheet only describes the motion of the object; the object may also have several other physical characteristics such as energy-momentum, mass, charge, etc.
In addition to events and physical objects, there are a class of inertial frames of reference. Each inertial frame of reference provides a coordinate system ( x 1 , x 2 , x 3 , t ) {\displaystyle (x_{1},x_{2},x_{3},t)} for events in the spacetime M. Furthermore, this frame of reference also gives coordinates to all other physical characteristics of objects in the spacetime, for instance it will provide coordinates ( p 1 , p 2 , p 3 , E ) {\displaystyle (p_{1},p_{2},p_{3},E)} for the momentum and energy of an object, coordinates ( E 1 , E 2 , E 3 , B 1 , B 2 , B 3 ) {\displaystyle (E_{1},E_{2},E_{3},B_{1},B_{2},B_{3})} for an electromagnetic field, and so forth.
We assume that given any two inertial frames of reference, there exists a coordinate transformation that converts the coordinates from one frame of reference to the coordinates in another frame of reference. This transformation not only provides a conversion for spacetime coordinates ( x 1 , x 2 , x 3 , t ) {\displaystyle (x_{1},x_{2},x_{3},t)} , but will also provide a conversion for all other physical coordinates, such as a conversion law for momentum and energy ( p 1 , p 2 , p 3 , E ) {\displaystyle (p_{1},p_{2},p_{3},E)} , etc. (In practice, these conversion laws can be efficiently handled using the mathematics of tensors).
We also assume that the universe obeys a number of physical laws. Mathematically, each physical law can be expressed with respect to the coordinates given by an inertial frame of reference by a mathematical equation (for instance, a differential equation) which relates the various coordinates of the various objects in the spacetime. A typical example is Maxwell's equations. Another is Newton's first law.
1. First Postulate (Principle of relativity)
Under transitions between inertial reference frames, the equations of all fundamental laws of physics stay form-invariant, while all the numerical constants entering these equations preserve their values. Thus, if a fundamental physical law is expressed with a mathematical equation in one inertial frame, it must be expressed by an identical equation in any other inertial frame, provided both frames are parameterised with charts of the same type. (The caveat on charts is relaxed, if we employ connections to write the law in a covariant form.)
2. Second Postulate (Invariance of c)
There exists an absolute constant 0 < c < ∞ {\displaystyle 0<c<\infty } with the following property. If A, B are two events which have coordinates ( x 1 , x 2 , x 3 , t ) {\displaystyle (x_{1},x_{2},x_{3},t)} and ( y 1 , y 2 , y 3 , s ) {\displaystyle (y_{1},y_{2},y_{3},s)} in one inertial frame F {\displaystyle F} , and have coordinates ( x 1 ′ , x 2 ′ , x 3 ′ , t ′ ) {\displaystyle (x'_{1},x'_{2},x'_{3},t')} and ( y 1 ′ , y 2 ′ , y 3 ′ , s ′ ) {\displaystyle (y'_{1},y'_{2},y'_{3},s')} in another inertial frame F ′ {\displaystyle F'} , then
( x 1 − y 1 ) 2 + ( x 2 − y 2 ) 2 + ( x 3 − y 3 ) 2 = c ( s − t ) {\displaystyle {\sqrt {(x_{1}-y_{1})^{2}+(x_{2}-y_{2})^{2}+(x_{3}-y_{3})^{2}}}=c(s-t)\quad } if and only if ( x 1 ′ − y 1 ′ ) 2 + ( x 2 ′ − y 2 ′ ) 2 + ( x 3 ′ − y 3 ′ ) 2 = c ( s ′ − t ′ ) {\displaystyle \quad {\sqrt {(x'_{1}-y'_{1})^{2}+(x'_{2}-y'_{2})^{2}+(x'_{3}-y'_{3})^{2}}}=c(s'-t')} .
Informally, the Second Postulate asserts that objects travelling at speed c in one reference frame will necessarily travel at speed c in all reference frames. This postulate is a subset of the postulates that underlie Maxwell's equations in the interpretation given to them in the context of special relativity. However, Maxwell's equations rely on several other postulates, some of which are now known to be false (e.g., Maxwell's equations cannot account for the quantum attributes of electromagnetic radiation).
The second postulate can be used to imply a stronger version of itself, namely that the spacetime interval is invariant under changes of inertial reference frame. In the above notation, this means that
c 2 ( s − t ) 2 − ( x 1 − y 1 ) 2 − ( x 2 − y 2 ) 2 − ( x 3 − y 3 ) 2 {\displaystyle c^{2}(s-t)^{2}-(x_{1}-y_{1})^{2}-(x_{2}-y_{2})^{2}-(x_{3}-y_{3})^{2}}
= c 2 ( s ′ − t ′ ) 2 − ( x 1 ′ − y 1 ′ ) 2 − ( x 2 ′ − y 2 ′ ) 2 − ( x 3 ′ − y 3 ′ ) 2 {\displaystyle =c^{2}(s'-t')^{2}-(x'_{1}-y'_{1})^{2}-(x'_{2}-y'_{2})^{2}-(x'_{3}-y'_{3})^{2}}
for any two events A, B. This can in turn be used to deduce the transformation laws between reference frames; see Lorentz transformation.
The postulates of special relativity can be expressed very succinctly using the mathematical language of pseudo-Riemannian manifolds. The second postulate is then an assertion that the four-dimensional spacetime M is a pseudo-Riemannian manifold equipped with a metric g of signature (1,3), which is given by the Minkowski metric when measured in each inertial reference frame. This metric is viewed as one of the physical quantities of the theory, thus it transforms in a certain manner when the frame of reference is changed, and it can be legitimately used in describing the laws of physics. The first postulate is an assertion that the laws of physics are invariant when represented in any frame of reference for which g is given by the Minkowski metric. One advantage of this formulation is that it is now easy to compare special relativity with general relativity, in which the same two postulates hold but the assumption that the metric is required to be Minkowski is dropped.
The theory of Galilean relativity is the limiting case of special relativity in the limit c → ∞ {\displaystyle c\to \infty } (which is sometimes referred to as the non-relativistic limit). In this theory, the first postulate remains unchanged, but the second postulate is modified to:
If A, B are two events which have coordinates ( x 1 , x 2 , x 3 , t ) {\displaystyle (x_{1},x_{2},x_{3},t)} and ( y 1 , y 2 , y 3 , s ) {\displaystyle (y_{1},y_{2},y_{3},s)} in one inertial frame F {\displaystyle F} , and have coordinates ( x 1 ′ , x 2 ′ , x 3 ′ , t ′ ) {\displaystyle (x'_{1},x'_{2},x'_{3},t')} and ( y 1 ′ , y 2 ′ , y 3 ′ , s ′ ) {\displaystyle (y'_{1},y'_{2},y'_{3},s')} in another inertial frame F ′ {\displaystyle F'} , then s − t = s ′ − t ′ {\displaystyle s-t=s'-t'} . Furthermore, if s − t = s ′ − t ′ = 0 {\displaystyle s-t=s'-t'=0} , then
( x 1 − y 1 ) 2 + ( x 2 − y 2 ) 2 + ( x 3 − y 3 ) 2 {\displaystyle \quad {\sqrt {(x_{1}-y_{1})^{2}+(x_{2}-y_{2})^{2}+(x_{3}-y_{3})^{2}}}}
= ( x 1 ′ − y 1 ′ ) 2 + ( x 2 ′ − y 2 ′ ) 2 + ( x 3 ′ − y 3 ′ ) 2 {\displaystyle ={\sqrt {(x'_{1}-y'_{1})^{2}+(x'_{2}-y'_{2})^{2}+(x'_{3}-y'_{3})^{2}}}} .
The physical theory given by classical mechanics, and Newtonian gravity is consistent with Galilean relativity, but not special relativity. Conversely, Maxwell's equations are not consistent with Galilean relativity unless one postulates the existence of a physical aether. In a surprising number of cases, the laws of physics in special relativity (such as the famous equation E = m c 2 {\displaystyle E=mc^{2}} ) can be deduced by combining the postulates of special relativity with the hypothesis that the laws of special relativity approach the laws of classical mechanics in the non-relativistic limit.
Notes[edit]
Jump up ^ Albert Einstein, Morgan document, 1921
Jump up ^ Minkowski, Hermann (1909), "Raum und Zeit", Physikalische Zeitschrift, 10: 75–88
Various English translations on Wikisource: Space and Time.
Jump up ^ Feynman, R.P. (1970), "21–6. The potentials for a charge moving with constant velocity; the Lorentz formula", The Feynman Lectures on Physics, 2, Reading: Addison Wesley Longman, ISBN 0-201-02115-3
Jump up ^ Ignatowsky, W. v. (1910). "Einige allgemeine Bemerkungen über das Relativitätsprinzip". Physikalische Zeitschrift. 11: 972–976.
English Wikisource translation: Some General Remarks on the Relativity Principle
Jump up ^ Ignatowsky, W. v. (1911). "Das Relativitätsprinzip". Archiv der Mathematik und Physik. 18: 17–40.
Jump up ^ Ignatowsky, W. v. (1911). "Eine Bemerkung zu meiner Arbeit: "Einige allgemeine Bemerkungen zum Relativitätsprinzip"". Physikalische Zeitschrift. 12: 779.
Jump up ^ Frank, Philipp & Rothe, Hermann (1910), "Über die Transformation der Raum-Zeitkoordinaten von ruhenden auf bewegte Systeme", Annalen der Physik, 339 (5): 825–855, Bibcode:1911AnP...339..825F, doi:10.1002/andp.19113390502
English translation: On the Transformation of Space-Time Coordinates from Stationary to Moving Systems
Jump up ^ Frank, Philipp & Rothe, Hermann (1912). "Zur Herleitung der Lorentztransformation". Physikalische Zeitschrift. 13: 750–753.
Jump up ^ Baccetti, Valentina; Tate, Kyle; Visser, Matt (2012), "Inertial frames without the relativity principle", Journal of High Energy Physics: 119, arXiv:1112.1466  , Bibcode:2012JHEP...05..119B, doi:10.1007/JHEP05(2012)119 ; See references 5–25 therein.
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