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The 2007 Microsoft Office Add-in: Microsoft Save as PDF or XPS add-in allows you. Search Information Technologies. Save Office files as a PDF without needing additional software or add-ins. Search Microsoft Search. 2007 Microsoft Office Add-in: Microsoft Save as PDF or XPS. Was this information. Amina Wadud - Wikipedia, the free encyclopedia. Amina Wadud. Born(1. September 2. 5, 1. Bethesda, Maryland. Alma mater. University of Pennsylvania, University of Michigan, American University in Cairo, Cairo University, Al- Azhar University. Religion. Liberal- Muslim. Era. 21st- century philosophy. Main interests. Islamic studies, Islamic feminism, theology, philosophy, interfaith dialogue. Notable ideas. Women as imams. Amina Wadud (born September 2. American scholar of Islamwith a progressive focus on Qur'anexegesis (interpretation of the holy text). Early life. Her father was a Methodist minister. She received her Bachelor of Science from the University of Pennsylvania, between 1. In 1. 97. 2 she pronounced the shahadah, that is, accepted Islam. By 1. 97. 4 she had changed her name officially to Amina Wadud, to reflect her chosen religion. The Women’s Islamic Initiative in. Amina Wadud is a visiting scholar at the Starr King School for the Ministry in California and a visiting. The basis of domestic violence in Islam and Muslim homes is found in. What do two Muslim women interpreters. Amina Wadud, Islamic. Amina Wadud and the Progressive Muslims. Amina Wadud Responds to Tarek Fatah. Quran And Women By Amina Wadud Pdf PrinterDuring graduate school, she studied in Egypt, including advanced Arabic at the American University in Cairo, Qur'anic studies and tafsir (exegesis or religious interpretation) at Cairo University, and philosophy at Al- Azhar University. Wadud's research specialities include gender and Qur'anic studies. From 1. 98. 9 to 1. Quranic Studies at the International Islamic University Malaysia. While there, she published her dissertation Qur'an and Woman: Rereading the Sacred Text from a Woman's Perspective and co- founded the non- governmental organization. Sisters in Islam. She retired in 2. Center for Religious and Cross Cultural Studies at Gadjah Mada University in Yogyakarta, Indonesia. Wadud has spoken at universities, grass roots level, government and non- government forums at various gatherings throughout the United States, the Middle East, Southeast Asia, Africa and Europe. Some of her speaking engagements have included the keynote address . As a result, there were attempts in Virginia by some Muslims to have her dismissed from her position at Virginia Commonwealth University. The call to prayer was given by another woman, Suheyla El- Attar. Amina wadud < > Most recent. Most popular Most recent. Hiding adult-oriented. Getting to Know Amina Wadud. Honoring the Work and Life of Amina Wadud (the link takes you to a full PDF of the. And as far as Amina Wadud is. Professor Wadud also stirred. Amina Wadud; Born September 25, 1952 (age 63) Bethesda, Maryland: Alma mater. Inside the gender Jihad: women's reform in Islam. It was sponsored by the Muslim Women's Freedom Tour, under the leadership of Asra Nomani, by the website . I want to encourage the hearts of Muslims, both in their public, private and ritual affairs, to believe they are one and equal. The scheduled lecture was cancelled because police cited possible law and order problems in view of opposition by Muslim groups. Syed Iqbal, state secretary of Indiya Towheed Jamad said that she comes with the backing of the US government and offers so- called progressive views that are against the basic tenets of Islam, and that his outfit would protest in front of the venues if she were allowed to talk. Egyptian academic Gamal al- Banna argued that her actions were supported by Islamic sources, and were, therefore, acceptable. Moosa, who called the prayer a . The women who are learned and frustrated that they cannot be the imam are going to see that someone got the guts to break ranks and do it. He responded that, while a woman could lead other women and even possibly her young children in salat, she could not lead a mixed group including non- mahram males: The currently extant juristic schools agree that it is not permissible for women to lead men in the obligatory Prayer, though some scholars voice the opinion that, under certain circumstances, a woman who is well- versed in the Qur'. Al- Qaradawi berated her actions on Al- Jazeera, calling it un- Islamic and heretical. Because Wadud said she had become the target of death threats, the police and her employer, fearing for her security and reacting to concerns from parents about their children's safety, asked her to conduct her classes from home through a video link. In spite of the criticism, Wadud has continued with her speaking engagements and to lead mixed- gender Friday prayer services. On October 2. 8, 2. International Congress on Islamic Feminism in Barcelona, Spain, she was invited to lead a congregation of about thirty people. She responded to questions and comments about other activities including women in gender- mixed Friday prayer service. New York: Oxford University Press. Inside the gender Jihad: women's reform in Islam. Alltel Wireless Cell Phone Service Provider. Alltel Wireless may not among the top names that pops to mind when discussing Lifeline program because the company offers Lifeline services only as a small part its diverse plans. However, the company has also created sizeable impact in the field and must not be entirely ignored. 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Starcraft + BroodWar + The Last Update Patch 1161 + CDKey RINGKASAN ULUMUL QUR'AN ~ Oz. Zz. 4y. A. PENGERTIAN ULUMUL QUR’ANUngkapan ulumul qur’an berasal dari bahasa arab yaitu dari kata ulum dan al- qur’an. Kata ulum jamak dari ilmu dan al- qur’an. Menurut Abu syahbah ulumul qur’an adalah sebuah ilmu yang memiliki banyak objek pembahasan yang berhubungan dengan al- qur’an,mulai dari proses penurunan, urutan penulisan,kodifikasi,cara pembaca,penafsiran,nasikh mansukh,muhkam mutashabih serta pembahasan lainnya. B. SEJARAH TURUNNYA ALQUR’AN DAN PENULISAN ALQUR’ANHikmah diwahyukan alqur’an secara berangsur- angsur adalah al- qur’an diturunkan dalam waktu 2. H. Proses turunnya ql- quran melalui 3 tahapan yaitu. Al- qur’an turun secara sekaligus dari Allah ke lauh mahfuzh yaitu tempat yang merupakan catatan tentang segala ketentuan dan kepastian Allah. Pokok-pokok materi dalam Buku Ulumul Quran ini: Pengantar Ulumul Quran. Buku Ulumul Quran downloads at Ebook-kings.com - Download free doc files,ebooks and documents - Modul Ulumul Quran Pesma Arroyan Surakarta(1). ULUMUL QUR’AN DAN PERKEMBANGANNYA I. PENGERTIAN ULUMUL QUR’AN Kata . Masalah ini terjadi pada zaman sahabat. Mereka membaca Quran yang di dalamnya terdapat kisah-kisah dan berita-berita. Ulumul Qur’an adalah sebuah metode yang lengkap dan menyeluruh untuk membuka pintu awal dari kedalaman kandungan Al Quran. Karenanya, umat Islam secara umum, ataupun secara khusus bagi mahasiswa muslim yang merindukan. Dalam firmanya “ Bahkan yang didustakan mereka ialah Al- qur’an yang mulia yang tersimpan dalam lauh al- mahfuzh (Q. S AL- buruuj : 2. Al- qur’an diturunkan dari lauh al mahfuzh ke bait Al- Izzah ( tempat yang berada di langit dunia )3. Al- qur’an diturunkan dari bait al- Izzah ke dalam hati nabi melalui malaikat jibril dengan cara berangsur- angsur sesuai dengan kebutuhan. Memantapkan hati nabi. Menentang dan melemahkan para penentang Al- qur’an. Memudahkan untuk dihafal dan difahami. ASBAB AN- NUZULUngkapan asbab- nuzul merupakan bentuk idhofah dari asbab dan nuzul. Menurut Az- zargani Asbabuan- nuzul adalah sesuatu yang terjadi serta hubungan dengan turunya ayat Al- qur’an yang berfungsi sebagai penjelas hukum pada saat peristiwa itu terjadi. Menurut Az- zargani urgensi asbab an- nuzul dalam mmahami Al- qur’an adalah. Membantu dan memahami sekaligus mengatasi ketidak pastian dalam menangkap pesan ayat- ayat Al- qur’an. Mengatasi keraguan ayat yang diduga mengandung pengertian umum. Mengkhususkan hukum yang terkandung dalam ayat al- qur’an bagi ulama yang berpendapat bahwa yang menjadi pegangan adalah sebab yang bersifat kusus. Mengidentifikasi pelaku yang menyebabkan turunnya ayat al- qur’an. Memudahkan untuk menghapal dan memahami ayat serta untuk memantapkan wahyu ke dalam hati orang yang mendengarnya. D. MUNASABAH AL QUR’ANMenurut Manna Al- qathan munasabah adalah sisi keterikatan antara beberapa ungkapan di dalam satu ayat,atau antar ayat pada beberapa ayat atau antar surat dalam al- qur’an. As- Suyuti menjelaskan langkah- langkah yang diperhatikan dalam menemukan munasabah yaitu: a. Memperhatikan tujuan pembahasan suatu surat yang menjadi objek pencarianb. Memperhatikan uraian ayat- ayat yang sesuai dengan tujuan yang dibahas dalam suratc. Menentukan tingkatan uraian- uraian itu apakah ada hubungannya atau tidakd. Bandung, 2001 - Djalal, Prof. SEKOLAH TINGGI ILMU DAKWAH STIDA AL-MANAR TAHUN AKADEMIK 2009/2010 Mata Kuliah : Ulumul Qur`an Dosen : H.M. Semester : Dua (sore) Tema - Tema Materi dalam Kuliah Ulumul Qur`an : ILMU-ILMU AL-QUR’AN. Dalam mengambil keputusan,hendaknya memperhatikan ungkapan- ungkspan dengan benar dan tidak berlebihan. Macam- macam munasabah; 1. Munasabah antar surat dengan surat sebelumnya: berfungsi sebagai menyempurnakan surat sebelumnya. Munasabah antara nama surat dan tujuan turunya. Munasabah antar bagian suatu ayat. Munasabah antar ayat yang letaknya berdampingan. Munasabah antara suatu kelompok ayat dengan kelompok ayat disampingnya. Munasabah antara fashilah (pemisah)dan isi ayat. Munasabah antara awal surat dengan akhir surat yang sama. Munasabah antara penutup suatu surat dengan awal surat berikutnya. E. MAKIYAH DAN MADANIYAH“Makiyah ialah ayat – ayat yang diturunkan sebelum Rasulullah hijrah ke Madinah,kendatipun bukan turun di Mekkah . Madaniyah adalah ayat- ayat yang diturunkan sesudah Rasulullah hijrah ke Madinah,kendatipun bukan turun di madinah. Ayat- ayat yang turun setelah peristiwa hijrah di sebut Madaniyyah walaupun turun di Mekkah atau Arafah.”Ciri- ciri spesifik makiyah dan madaniyah. Di dalamnya terdapat sajadahb. Ayat- ayatnya dimulai dengan kallac. Dimulai dengan ya- ayuha an- nasd. Ayatnya mengandung tema kisah para nabi dan umat- umat terdahulue. Ayatnya berbicara tentang kisah nabi Adam dan Idris kecuali surat al- baqorohf. Ayatnya dimulai dengan huruf terpotong- potong seperti alif lam mim dan sebagainya. Mengandung ketentuan- ketentuan faroid dan haddb. Mengandung sindiran- sindiran terhadap kaum munafikkecuali surat al- ankabutc. Mengandung uraian tentang perdebatan dengan ahli kitab. F. MUHKAM DAN MUTASYABIHAyat- ayat muhkam adalah ayat yang maksudnya dapat diketahui dengan gamblang baik melalui ta’wil ataupun tidak. Ayat mutasyabih adalah ayat yang maksudnya dapat diketahui Allah seperti kedatangan kedatangan hari kiamat, kedatangan dajjal. Hikmah keberadaan ayat mutasabih dalam Al- qur’an adalah: 1. Memperlihatkan kelemahan akal manusia. Teguran bagi orang- orang yang mengotak atik ayat mutasabih. Memberikan pemahaman abstrak Illahi kepada manusia melalui pengalaman inderawi yang biasa disaksikannya. G. QIRO’AT AL- QUR’ANQiro’at adalah ilmu yng mempelajari cara- cara mengucapkan kata- kata al- qur’an dan perbedaan- perbedaannya dengan cara menisbatkan kepada penukilnya. Macam- macam qiro’at: 1. Qiro’at Sab’ah ( Qiro’at tujuh ) adalah imam- imam qiro’at ada tujuh orang, yaitu: a. Abu Amar (w. 1. 54 H ) dari Irake. Ya’kub (w. 2. 05 H ) dari Irakf. Qiro’ah Asyiroh adalah qiro’ah sab’ah ditambah dengan 3 imam yaitu: Abu Ja’far, Ya’kub bin Ishaq, kalaf bin hisyam. Qiro’ah Arba Asyiroh (qiro’ah empat belas) yaitu qiro’ah sepuluh ditambah dengan 4 imam yaitu Al- hasan al basri, muhammad bin abdul rohman,yahya bin mubarok,Abu fajr muhammad bin ahmad. Dari segi kualitas qiro’ah dapat dibagi menjadi. Qiro’ah Mutawwatir yaitu qiro’ah yang disampakan kelompok orang yang sanatnya tidak berbuat dusta. Qiro’ah Mashur yaitu qiro’ah yang memiliki sanad sahih dan mutawatir. Qiro’ah ahad yaitu memiliki sanad sahih tapi menyalahi tulisan mushaf usmani dan kaidah bahasa Arab. Qiro’ah Maudhu yaitu palsu. 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Recognizing that high-quality maternal and child health (MCH) services are vital to the health of the nation, NCEMCH was established in 1982 at Georgetown University as a national resource to the MCH community.
The most recent data on maternal health and mortality and newborn health and mortality are available on UNICEF’s data pages. UNICEF programming around maternal and newborn health seeks to reduce inequities of care. Association of Maternal and Child Health Programs (AMCHP) AMCHP provides leadership on issues affecting the health of women and children. Members include directors of maternal and child health programs. Wave Packet Quantum Mechanics Pdf BooksLecture 3: The Wave Function . And thisisagreatexampleofphysicalintuition,wildlydivorcedfromexperiment,pushingyouintherightdirection. I'mmakingitsoundalittlemoreshockingthan- -well,itwasshocking. In physics, a wave packet (or wave train) is a short 'burst' or 'envelope' of localized wave action that travels as a unit. A wave packet can be analyzed into, or can. The central mystery of quantum mechanics is that small chunks of matter sometimes seem to behave like particles, sometimes like waves. For most of the past century. Quantum mechanics is the science of the very small. Quantum mechanics explains the behaviour of matter and its interactions with energy on the scale of atoms and. Academia.edu is a platform for academics to share research papers. This note introduces Quantum Mechanics at an advanced level addressing students of Physics, Mathematics, Chemistry and Electrical Engineering. 4 5.4 Position Space and Momentum Space... 103 5.5 Time Development of a Gaussian Wave Packet. Wave Packet Quantum Mechanics Pdf FreeIt wasjustshocking. OK,sowiththatsaid,letmeintroducethemovesforthenextfewlectures. Forthenextseverallectures,here's whatwe'regoingtodo. Iamnotgoingtogiveyouexperimentalmotivation. I'vegivenyouexperimentalmotivation. I'mgoingtogiveyouasetofrules,asetofpostulates. Thesearegoingtobetherulesofquantummechanics. Andwhatquantummechanicsisforusisasetofrulestoallowustomakepredictionsabouttheworld. Andtheseruleswillbeawesomeiftheirpredictionsaregood. Andiftheirpredictionsarebad,theseruleswillsuck. Wewillavoidbadrulesto thedegreepossible. I'm going togiveyouwhatwe'velearnedoverthepast. Thatisamazing. Wow. OK,yeah,overthepast. And. I'mgoingtogivethemto youasaseriesofpostulatesandthenwe're going toworkthroughtheconsequences,andthenwe'regoingtospendtherestofthesemesterstudyingexamplestodevelopanunderstandingforwhattherulesofquantummechanicsaregivingyou. Sowe'rejustgoingtoscrapclassicalmechanicsandstartoverfromscratch. Soletmedothat. Andtobegin,letmestartwiththedefinitionofasystem. Andtounderstandthatdefinition,Iwanttostartwithclassicalmechanicsasaguide. Soinclassicalmechanics- -let'sthinkabouttheeasiestclassicalsystemyoucan- -justasingleparticlesittingsomewhere. Inclassicalmechanicsofasingleparticle,howdoyouspecifytheconfiguration,orthestate- -justdifferentwords forthesamething- -howdoyouspecifytheconfigurationorstateofthesystem? AUDIENCE: Byposition andmomentum. PROFESSOR: Specify theposition andmomentum,exactly. Soinclassicalmechanics,ifyouwanttocompletelyspecifytheconfigurationof asystem,allyouhavetodoisgivemexandpformyparticle. Andifyoutellmethis,Iknoweverything. Ifyouknowthesenumbers,youknoweverything. Inparticular,what. Imeanbysayingyou know everythingisthat,ifthere'sanythingelseyouwanttomeasure- -theenergy,forexample. Theenergyisjustsomefunctionofthepositionandmomentum. Andif youknow theposition andmomentum,youcanunambiguouslycalculatetheenergy. Similarly,theangularmomentum,whichisavector,youcancalculateit ifyouknowx andp- -which isjustrcrossp. Sothisgivesyoucompleteknowledgeofthesystem. There'snothingmoretoknowifyouknowthatdata. Now,therearecertainlystillquestionsthat youcan'tanswergivenknowledgeofxandp. Forexample,arethere. I'mhere. I'mnotmoving. Arethere. 14invisiblemonkeysstandingbehind me? Youcan'tanswerthat. It'sastupidquestion,right? OK,letmegiveyouanotherexample. Theelectronisxandp,someposition. Isithappy? Right,sotherearestillquestionsyoucan'tanswer. Thepointis,completeknowledgeofthesystemtoansweranyphysicallyobservablequestion- -anyquestionthatcouldbemeaningfullyturnedintoanexperiment,theansweriscontainedinknowingthestateofthesystem. Butthiscan'tpossiblybetrueinquantummechanics,because,asyousaw intheproblem setandaswe'vediscussedpreviously,there's anuncertaintyrelationwhichsays thatyourknowledge- -oryouruncertainty,rather,inthepositionofaparticle,quantummechanically- -I'm notevengoing tosayquantummechanically. I'm just goingtosaytherealworld. Sointherealworld,ouruncertaintyinthepositionofourpoint- likeobjectandouruncertaintyinthemomentumisalwaysgreaterthanorroughlyequaltosomethingthat'sproportionalto. Planck'sconstant. Youcan'tbearbitrarilyconfidentofthepositionandof the momentumsimultaneously. Youworkedthroughagoodexampleofthisontheproblemset. Wesawthisinthetwo- slitexperimentandtheinterferenceofelectrons. Thisissomethingwe'regoingtohavetodeal with. Soasaconsequence,youcan'tpossiblyspecifythepositionandthemomentumwithconfidenceofasystem. Youcan'tdoit. Thiswasamyth. Itwasagoodapproximation- -turnedouttobefalse. Sothefirstthingweneedistospecifythestate,theconfigurationof asystem. Sowhatspecifiestheconfigurationof asystem? Andsothisbringsustothefirstpostulate. Theconfiguration,orstate,ofasystem- -andhereagain,justforsimplicity,I'm goingtotalkaboutasingleobject- -ofaquantumobjectiscompletelyspecifiedbyasinglefunction,awavefunction,which. I willdenotegenerallypsiofx,whichisacomplexfunction. Thestateofthequantumobjectiscompletelyspecifiedonceyou knowthewavefunction of thesystem,whichisafunctionofposition. Let meemphasizethatthisisafirstpassatthepostulates. Whatwe'regoingtodoisgothroughthebasicpostulatesofquantummechanics,thenwe'llgothroughthemagainandgivethemalittlemoregenerality. Andthenwe'llgothroughthemagainandgivethemfullgenerality. Thatlastpassis. 8. Soletmegiveyousomeexamples. Letmejustdrawsomecharacteristicwavefunctions. Andthesearegoingtoturnouttobeusefulforus. Soforexample,considerthefollowingfunction. Sohereis. 0andwe'replottingasafunctionofx. Andthenplottingtherealpartofpsiofx. Sofirstconsider averynarrowlysupportedfunction. It'sbasically. 0everywhere,exceptithassomeparticularspotatwhat I'llcallx. Here'sanotherwavefunction- -0. It'sbasically. 0except forsomespecialspotatx. Andagain,I'mplottingtherealpartofpsi. And I'mplottingtherealpartofpsibecause. A,psiisacomplexfunction- -ateverypointitspecifiesacomplexnumber. And B,Ican'tdrawcomplexnumbers. Soto keepmyheadfromexploding,I'mjustplottingtherealpartofthewavefunction. Butyoushouldneverforgetthatthewavefunctioniscomplex. Soforthemoment,I'mgoingtoassumethattheimaginarypartis. I'mjustgoingtodrawtherealparts. Soletmedrawacouplemoreexamples. Whatelsecouldbeagoodwavefunction? Well,thosearefine. Whatabout- -again,wewantafunctionofx and. I'mgoingtodrawtherealpart. Andanotherone. Sothisisgoingtobeaperfectlygoodwavefunction. Andletmedrawtwomore. Sowhatelsecouldbeareasonablewavefunction? Well- -thisisharderthanyou'dthink. Oh,God. OK,sothatcouldbethewavefunction,Idon'tknow. Thatisactuallymysignature. Mywifecallsitalittle. It'sproportionaltothewavenumber. Anyenergyisproportionaltothefrequency. Now,lookatthosewavefunctions. Thosewavefunctionsgiveusnopositioninformationwhatsoever,buttheyhaveverydefinitewavelengths. Thoseareperiodicfunctionswithdefinitewavelengths. Inparticular,thisguyhasawavelengthoffromheretohere. Ithasawavenumberk. Sothattellsusthatifwemeasurethemomentumofthisparticle,wecanbeprettyconfident,becauseithasareasonablywell- definedwavelengthcorrespondingtosomewavenumberk- -2piupon thewavelength. It hassomemomentum,andifwemeasureit,weshouldbeprettyconfidentthat themomentumwillbeh- bark. Everybody agree withthat? Lookslikeasinewave. Andde Broglietellsusthatifyouhaveawave ofwavelengthlambda,thatcorrespondstoaparticlehavingmomentump. Now,howconfidentcanwebeinthatestimationofthemomentum? Well,if. Itellyouit'se to theik x,that'sexactlyaperiodicfunctionwithwavelengthlambda. Sohowconfidentarewe? Prettyconfident. Soour uncertaintyinthemomentumistiny. Everyoneagree? Similarly,forthiswave,againwehaveawavelength- -it's aperiodicfunction,butthewavelengthismuchshorter. Ifthewavelengthismuchshorter,thenkismuchlarger- -themomentumismuchlarger. Sothemomentumweexpecttomeasure,whichisroughlyh- bark. Whatabout ouruncertainty? Again,it'saperfectperiodicfunctionsoouruncertainty in themomentumissmall. Everyonecool withthat? Andthatcomes,again,fromthede Broglierelations. Soquestionsatthispoint? You guysarerealquiettoday. Questions? AUDIENCE: Sodelta. P is. 0,basically? PROFESSOR: It'sprettysmall. Now,again,Ihaven't drawn thisofftoinfinity,butifit'sexactlythei kx,then yeah,itturnsouttobe. Now, animportantthing,soletmerephraseyourquestionslightly. Sothequestionwas,isdelta. P0? Isitreally. 0? Sohere'saproblemfor us rightnow. Wedon'thaveadefinition fordelta. P. Sowhatisthedefinitionofdelta. P? I haven'tgivenyouone. Sohere,when. Isaiddelta. Pissmall,what. I meanis,intuitively,just byeyeball,ourconfidenceinthatmomentumisprettygood,usingthede Broglierelations. I havenotgivenyouadefinition,andthatwillbepartofmyjoboverthenextcoupleoflectures. Verygoodquestion. Yeah. AUDIENCE: How doyoucodenoise inthatfunction? PROFESSOR: Awesome. AUDIENCE: Do youjust havedifferentwavelengths. PROFESSOR: Yeah. AUDIENCE: As yougo along? PROFESSOR: Awesome. Soforexample,this- -doesithave adefinitewavelength? Notsomuch. Soholdthatquestionandwaituntil youseethenextexamplesthat. Iputonthisboard,andifthatdoesn'tansweryourquestion,askitagain, becayseit'saveryimportantquestion. OK. AUDIENCE: When you talkabout aphoton,youalwayssayaphotonhasacertainfrequency. Doesn'tthatmeanthatitmustbea wavebecauseyouhavetofixthewavenumber k? PROFESSOR: Awesomequestion. Doeseverywavepacketoflightthathitsyour eye,doesitalwayshaveasingle,uniquefrequency? No,youcantakemultiplefrequencysourcesandsuperposethem. Aninterestingchoiceofwords. I usedthere. All right,sothequestionis,sincelighthassomewavelength,doeseverychunkoflighthaveadefinite- -thisisthequestion,roughly. Yeah,soand theanswer is,lightdoesn'talwayshaveasingle- -You canhavelightcomingatyouthathasmanydifferentwavelengthsandput itinaprismandbreakitupintoitsvariouscomponents. Soyoucanhaveasuperpositionofdifferentfrequenciesoflight. We'llseethesameeffecthappeningforus. OK,soagain,de. Brogliemadethisconjecturethat. E ish- baromegaand. Pish- bark. Thiswasverifiedinthe. Davisson- Germerexperimentthatweran. Buthere,one ofthethingsthat'ssortoflatentinthisis,whathemeansis,look,associatedtoeveryparticlewithenergy. N andmomentum. Pisaplanewaveoftheforme to theikxminusomegat. Andthis,properly,inthreedimensionsshouldbekdot x. Butatthispoint,thisisanimportantsimplification. Fortherestof. 8. 0. So. I'mgoingtoremovearrowmarksand dotproducts. There'sgoingtobeonespatialdimensionandonetimedimension. We'realwaysgoingtohavejustonetime dimension,butsometimeswe'llhavemorespatialdimensions. Butit'sgoingtobeawhileuntilwegetthere. Sofornow,we'rejustgoingtohavekx. Sothisisageneralplanewave. Andwhatde. Brogliereallywassayingisthat,somehow,associatedtotheparticle withenergy. Eandmomentum. Pshouldbesomewave,aplanewave,withwavenumberkandfrequencyomega. Andthat'sthewavefunctionassociatedtoit. Thethingis,noteverywavefunctionisaplanewave. Somewavefunctionsarewelllocalized. Someofthemarejustcomplicatedmorasses. Someofthemarejustamess. Sonowisthemostimportantpostulateinquantummechanics. Iremembervividly,vividly,when. Itooktheanalogofthisclass. It wascalled. Physics. Aat. Harvard. Andtheprofessoratthispointsaid- -Iknow himwell now,he'safriend- -he said,thisiswhatquantummechanicsisallabout. Fluid mechanics suggests alternative to quantum orthodoxy. Close- ups of an experiment conducted by John Bush and his student Daniel Harris, in which a bouncing droplet of fluid was propelled across a fluid bath by waves it generated. Credit: Dan Harris. The central mystery of quantum mechanics is that small chunks of matter sometimes seem to behave like particles, sometimes like waves. For most of the past century, the prevailing explanation of this conundrum has been what's called the . That's because Yves Couder, Emmanuel Fort, and colleagues at the University of Paris Diderot have recently discovered a macroscopic pilot- wave system whose statistical behavior, in certain circumstances, recalls that of quantum systems. Couder and Fort's system consists of a bath of fluid vibrating at a rate just below the threshold at which waves would start to form on its surface. A droplet of the same fluid is released above the bath; where it strikes the surface, it causes waves to radiate outward. The droplet then begins moving across the bath, propelled by the very waves it creates. But are they philosophically distinct? Credit: Dan Harris. Bush believes that the Copenhagen interpretation sidesteps the technical challenge of calculating particles' trajectories by denying that they exist. First, in the fluidic system, both the bouncing droplet and its guiding wave are plainly visible. If the droplet passes through a slit in a barrier—as it does in the re- creation of a canonical quantum experiment—the researchers can accurately determine its location. The only way to perform a measurement on an atomic- scale particle is to strike it with another particle, which changes its velocity. The second advantage is the relatively recent development of chaos theory. Pioneered by MIT's Edward Lorenz in the 1. A weather- system model, for instance, might yield entirely different results if the wind speed at a particular location at a particular time is 1. The fluidic pilot- wave system is also chaotic. It's impossible to measure a bouncing droplet's position accurately enough to predict its trajectory very far into the future. But in a recent series of papers, Bush, MIT professor of applied mathematics Ruben Rosales, and graduate students Anand Oza and Dan Harris applied their pilot- wave theory to show how chaotic pilot- wave dynamics leads to the quantumlike statistics observed in their experiments. Credit: Dan Harris. What's real? In a review article appearing in the Annual Review of Fluid Mechanics, Bush explores the connection between Couder's fluidic system and the quantum pilot- wave theories proposed by de Broglie and others. The Copenhagen interpretation is essentially the assertion that in the quantum realm, there is no description deeper than the statistical one. When a measurement is made on a quantum particle, and the wave form collapses, the determinate state that the particle assumes is totally random. According to the Copenhagen interpretation, the statistics don't just describe the reality; they are the reality. But despite the ascendancy of the Copenhagen interpretation, the intuition that physical objects, no matter how small, can be in only one location at a time has been difficult for physicists to shake. Albert Einstein, who famously doubted that God plays dice with the universe, worked for a time on what he called a . In his 1. 97. 6 Nobel Prize lecture, Murray Gell- Mann declared that Niels Bohr, the chief exponent of the Copenhagen interpretation, . Credit: Dan Harris. Then there's David Griffiths, a physicist whose . In that book's afterword, Griffiths says that the Copenhagen interpretation . Annual Review of Fluid Mechanics, Vol. Volume publication date December 2. Code=fluid. Provided by: Massachusetts Institute of Technology. This story is republished courtesy of MIT News (web. MIT research, innovation and teaching. |
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