Teori String Sebuah Pengantar
الَّذِينَ
يَذْكُرُونَ اللَّهَ قِيَامًا وَقُعُودًا وَعَلَىٰ جُنُوبِهِمْ وَيَتَفَكَّرُونَ
فِي خَلْقِ السَّمَاوَاتِ وَالْأَرْضِ رَبَّنَا مَا خَلَقْتَ هَٰذَا بَاطِلًا
سُبْحَانَكَ فَقِنَا عَذَابَ النَّارِ
Artinya: “(yaitu) orang-orang yang
mengingat Allah sambil berdiri atau duduk atau dalam keadan berbaring dan
mereka memikirkan tentang penciptaan langit dan bumi (seraya berkata): "Ya
Tuhan kami, tiadalah Engkau menciptakan ini dengan sia-sia, Maha Suci Engkau,
maka peliharalah kami dari siksa neraka.” (Ali Imran 191)
Dalam rangka tafakkur lebih lanjut terhadap kebesaran Allah SWT di alam semesta, bahwa betapa alam semesta ini begitu mengagumkan nalar dan penuh "sidik" karya dan "tanda-tanda" Maha hebat, Maha berilmu dan Maha bijaksana dari sang Maha pencipta, maka dalam tulisan kali ini akan ditampilkan sebuah teori sains fisika kontemporer yang digadang-gadangkan merupakan puncak dari intelek manusia saat ini dalam usaha mengurai teka-teki alam ciptaan.
Dari sisi religius Teori ini dapat dipandang sebagai Buah dari "penjelajahan" yang sangat mendebarkan sekaligus sangat menakjubkan dari perjalanan akal budi manusia memahami beberapa aspek dari Nama-Nama Allah SWT di alam terindra. Teori tersebut dikenal sebagai teori String.
Harap diingat sebelum lebih jauh melangkah, bahwa semangat "ilmiah" yang dipaparkan dalam Blog ini diupayakan sedaya upaya berasal dari nilai-nilai "jati Islam", di mana wawasan-wawasan sains didudukkan dalam kerangka adab ilmu Islami yang tepat. Dalam arti, ketika kita berbicara Sains kontemporer dalam konteks tafakkur, maka pembicaraan kita bukan sebuah wawasan "hipokrit" campur aduk berbagai wawasan sekular yang digabungkan begitu saja dengan wawasan Islam yang sering ditampilkan oleh banyak sistem pendidikan modern di dunia muslim dewasa ini. Seyogyanya ketika kita berbicara alam dalam konteks sains modern, kita tidak boleh tiba-tiba telah berubah "world view" dan "manhaj" bahkan "akidah" bahwa seolah-olah pandangan metafisis sains modern tentang alam yang sangat materialistik dan sekular telah dengan "tiba-tiba kita anut pula" untuk tiba-tiba dalam suatu loncatan konseptual yang tidak alami kita kembali kepada pandangan Islam. Di artikel lain di Blog ini penulis menunjukkan bahwa hal yang bersifat implisit ini benar-benar menjadi biang keladi kekacauan umat Islam dalam mendefinisikan apa yang disebut modernisme dan tajdid.
Jadi sebelum kita mulai perjalanan tafakkur ini, terlebih dahulu kita tekankan perbedaan antara manhaj kita dengan manhaj dunia sekular dalam memandang alam semesta. Menurut Islam, terdapat banyak alam selain alam fenomenal terindra ini. Terdapat juga alam Entitas-Entitas Tetap, alam ruh, selain alam fenomenal yang terindra. Manusia modern sekarang lebih terfokus pada alam terakhir dan telah mengerahkan pikiran terbaik dan dana habis-habisan dalam menguak rahasia jagad raya fenomenal, mulai dari skala Kosmos maha besar hingga skala ukuran sangat kecil dunia subatomik. Namun demikian, Allah SWT telah meninggalkan "sidik karyaNya" di manapun akal pikiran dan hati memandang, di manapun lapisan alam ini kita "jelajahi" kita akan selalu melihat "stempel" demi stempel berupa "kuantum demi kuantum" Asma'ul Husna yang memberitakan keesaan dari empuNya segala alam.
Allah Subhanahu wa Ta’ala berfirman :
وَلِلَّهِ الْمَشْرِقُ وَالْمَغْرِبُ فَأَيْنَمَا تُوَلُّوا فَثَمَّ وَجْهُ اللَّهِ إِنَّ اللَّهَ وَاسِعُ عَلِيمُُ{115}
Artinya :”Dan kepunyaan Allahlah timur dan
barat, maka kemanapun kamu menghadap maka disitulah wajah Allah.
Sesungguhnya Allah Mahaluas (rahmatNya) lagi Mahamengetahui”. (QS.al-Baqarah: 115)
Oleh karena itu ketika kita berbicara "alam" dalam konteks sains modern, kita hanya berbicara sebuah subhimpunan dari "Alam" yang lebih luas dan misterius sebagaimana di afirmasi dalam sistem "world view" kita sebagai muslim beriman yang jauh lebih universal dibanding cara pandang dunia sekuler yang "sumpek" dan "picik".
Dalam konteks lain, dalam dikotomi "timur" dan "barat", sains modern seolah merupakan sebuah representasi dari dua cara pandang dunia seorang manusia. Dunia barat adalah sebuah representasi dari pengaktifan akal rasional dan eksperimental yang buahnya kita kenal sebagai "metode ilmiah". Dunia barat menghasilkan capaian-capaian material badaniyyah yang profan, berupa sains dan teknologi. Dunia barat juga diberkahi dengan semangat rasional, matematis cermat dan presisi. Sedangkan khazanah timur menggali lebih dalam lewat lorong lain kemanusiaan karena kayanya mereka dengan warisan sains suci kewahyuan dengan diberkahi oleh banyak nabi, waliyullah dan orang-orang tercerahkan secara ruhani. Timur merpresentasikan sebuah dunia imaginal yang mistis yang menyimpan keindahannya dalam representasi "qalbu" melalui kontemplasi dan "pentahkikan maqamat spiritual". Timur akrab dengan puisi, serta cinta yang holistik di mana fragmen-fragmen pengalaman disatupadukan dalam sebuah celupan dan leburan penghambaan terhadap Wujud Absolut .
Barat sebaliknya cenderung analitik dan mereduksi pengalaman dan pengetahuan menjadi fragmen-fragmen saling asing yang untuk kemudian saling dikontraskan dalam faset kesadaran. Barat oleh karena sifat reduksionisnya telah merinci pengalaman manusia menjadi kuantitas ketimbang kualitas dan akrab dengan dunia material. Sehingga gagal melihat hikmah tertinggi segala sesuatu walaupun telah tenggelam dalam abstraksi dan rincian yang memukau. Dua wajah dari potensialitas kemanusiaan ini, yaitu timur dan barat tidak lagi menjadi dikotomi karena masing-masing harus di ingat, "kemanapun kamu menghadap maka disitulah wajah Allah". Timur dan barat dengan tatanan wawasan seimbang akan menghantarkan kita kepada jalan yang benar kepada kebahagiaan dunia dan akhirat. Lebih-lebih di era globalisasi di mana segala capaian peradaban akan berbaur dalam satu wadah yang semakin padu dan kecil. Namun harap diingat, kita tidak akan sekali-kali silau dengan capaian peradaban barat ini, karena dalam sudut pandang kita, capaian sains teknologi Barat tidak akan pernah mencapai status "kemitraan" namun selamanya diposisikan sebagai "hamba abdi" dalam setting universal pandangan dunia kita selaku muslim. Lain artikel penulis Blog mencoba berdialog dengan sejumlah tulisan pemikir Islam soal pandangan universal islam dan kontrasnya dengan program sekularisme barat.
Walaupun "hanya", kita akan segera paparkan, alam syahadah ini saja tak habis-habisnya rahasia dan misterinya terurai dan "ujungnya pun" dari untaian tasbih semesta raya ini tak diketahui di mana.
Allâh Subhanahu wa Ta’ala berfirman :
قُلْ لَوْ كَانَ الْبَحْرُ مِدَادًا لِكَلِمَاتِ رَبِّي لَنَفِدَ الْبَحْرُ قَبْلَ أَنْ تَنْفَدَ كَلِمَاتُ رَبِّي وَلَوْ جِئْنَا بِمِثْلِهِ مَدَدًا
Katakanlah (wahai Muhammad), “Sekiranya lautan menjadi tinta untuk (menulis) kalimat-kalimat Rabbku, sungguh habislah lautan itu sebelum kalimat-kalimat Rabbku habis (ditulis), meskipun Kami datangkan tambahan sebanyak itu (pula). [al-Kahfi/18:109].
Untuk jiwa-jiwa yang paling kering sekalipun, seperti ditampilkan oleh sejumlah Ilmuwan sekuler, tidak berdaya untuk menyembunyikan rasa sahdu dan agung yang mereka rasakan ketika menghayati keluasan dan kedahsyatan alam semesta ini yang menyergap ruhani mereka
| "Skala dahsyat dari alam semesta tiba-tiba menyingkapkan padaku suatu jenis perasaan religius, ada keagungan dan kedahsyatan, dalam suatu intensitas perasaan yang tidak pernah meninggalkanku semenjak itu, tidak pernah hilang setelahnya (Carl Sagan seorang Ilmuwan Ateis) |
Meskipun merasa muak dengan konsepsi Tuhan dunia barat yaitu dari tradisi kristen dan yahudi yang membuat seolah tuhan itu hanyalah semacam dewa tinggi yang sangat mirip dengan manusia (kaum kafir Mujassimah) cuma lebih sempurna, yang bertentangan dengan pengalamannya tentang kemisterian teka-teki alam, Einstein tetap tidak kehilangan cita rasa religius ketika melihat keajaiban alam semesta, sebagaimana dinyatakannya dalam kutipan berikut
Isaac Newton juga sangat muak dengan konsepsi trinitas yang dianut barat kristen sehingga memutuskan menjadi seorang monoteis yang meyakini satu Tuhan, sebagai perintis sains kelaman modern, Isaac Newton juga disergap perasaan religius ketika merenungi alam semesta ini,
| Saya tidak tahu seperti apa gerangan saya tampak oleh dunia ini, namun bagi saya sendiri, saya hanyalah seorang anak kecil yang tengah bermain-main di pantai, dan terpukau oleh koral dan kerang-kerang yang indah, dan terus mencari koral dan kerang yang lebih baik, sedangkan lautan maha luas kebenaran membentang di hadapan saya tak terselami (Isaac Newton) |
Tulisan berikut adalah tulisan kapur tulis Dirac di Universitas Moscow di tahun 1956 yang hingga kini tidak pernah dihapus menjelaskan salah satu metode para Ilmuwan dalam menguak rahasia bagaimana hukum alam bekerja, yaitu selain tidak sekedar taat asas secara matematis, alam semesta juga harus mengandung ungkapan keindahan tertinggi.
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| Hukum Fisika seharusnya mengungkapkan keindahan matematis (P. Dirac) |
الَّذِي
خَلَقَ سَبْعَ سَمَاوَاتٍ طِبَاقًا ۖ مَا تَرَىٰ فِي خَلْقِ الرَّحْمَٰنِ مِنْ تَفَاوُتٍ ۖ فَارْجِعِ الْبَصَرَ هَلْ تَرَىٰ مِنْ فُطُورٍ
Artinya: “Yang telah
menciptakan tujuh langit berlapis-lapis. Kamu sekali-kali tidak melihat pada
ciptaan Tuhan Yang Maha Pemurah sesuatu yang tidak seimbang. Maka lihatlah
berulang-ulang, adakah kamu lihat sesuatu yang tidak seimbang?”Alam semesta yang bertingkat-tingkat ini, di mana alam syahadah yang dikenal oleh sains modern sebagai alam makrokosmos universum adalah salah satu dari alam tersebut. Masing-masing lapisan alam, alias masing-masing alam tegak dan berdiri kokoh dalam landasan kemahakuasaan Allah SWT, masing-masing mempunyai hukum tersendiri, dan setiap hukum yang berlaku pada masing-masing alam akan dipandu oleh keseimbangan, simetri-simetri indah dan jalinan hubungan matematis ruwet yang menyulam hikmah. Keseimbangan dan simetri matematis ini lah yang menjelaskan mengapa alam semesta mampu dijelaskan dalam sejumlah aspek oleh pendekatan matematika, problema ini dikenal sebagai "ketidakmasuka akalan efektifitas matematika" dalam menjelaskan alam semesta. Bagi kita kaum muslimin ini bukan problema, namun hanyalah hikmah yang ditemukan kembali dalam satu konteks dari kebenaran yang telah berulang disinyalir oleh Allah SWT dalam alqur'an. Berikut contoh Grup simetri yang memandu gaya fundamental
Kesimetrian dan keseimbangan tersebut selanjutnya diungkapkan lagi dalam "kerapian" relasi antara elemen-elemen yang saling berkaitan dalam satu kaitan. Ungkapan matematis yang menjelaskan kaitan-kaitan antara besaran-besaran fisis tersebut lebih lanjut membangun sebuah teori fisika. Efektivitas matematika dalam menjelaskan hukum alam sebenarnya sudah lama menjadi arena perdebatan di antara para Ilmuwan. Namun isyarat bahwa alam semesta telah dibentangkan dalam ukuran yang jelas telah diungkap dalam alQur'an sendiri,
الَّذِي لَهُ مُلْكُ السَّمَاوَاتِ وَالْأَرْضِ وَلَمْ يَتَّخِذْ وَلَدًا
وَلَمْ يَكُنْ لَهُ شَرِيكٌ فِي الْمُلْكِ وَخَلَقَ كُلَّ شَيْءٍ
فَقَدَّرَهُ تَقْدِيرًا
Artinya:yang kepunyaan-Nya-lah kerajaan langit dan bumi, dan Dia tidak mempunyai anak, dan tidak ada sekutu bagi-Nya dalam kekuasaan(Nya), dan dia telah menciptakan segala sesuatu, dan Dia menetapkan ukuran-ukurannya dengan serapi-rapinya.(alFurqan 2).
Dapatkah alQur'an menjadi sumber ilmu pengetahuan sains modern? tanpa terjebak dalam semangat Bucailisme dan latah untuk menyatakan bahwa setiap ada temuan sains modern lalu kita ikut-ikutan menyatakan bahwa itu semua telah ada dalam alqur'an, kita jawab dengan tegas ya, terutama dalam landasan metafisis yang ia bangun untuk menyiapakan semangat ilmiah dan penemuan. Meskipun demikian, secara prakstis ini benar-benar bisa terjadi. Salah seorang Ilmuwan Pakistan peraih hadiah Nobel Fisika adalah Abdus Salam. Beliau menemukan konsep yang menyatukan berbagai gaya di alam dalam satu kerangka tinjauan teoritis, dan beliau mengaku bahwa semua temuan itu di dorong dan di insfirasi oleh petunjuk alQur'an, berikut kutipan ungkapan beliau,
Salam was "known to be a devout Muslim",[30] and was a member of the Ahmadiyya Muslim Community who saw his religion as fundamental part of his scientific work. He once wrote:
"The Holy Qur'an enjoins us to reflect on the verities of Allah's created laws of nature; however, that our generation has been privileged to glimpse a part of His design is a bounty and a grace for which I render thanks with a humble heart."[30]During his acceptance speech for the Nobel Prize in Physics, Salam quoted the following verses from the Quran:
Thou seest not, in the creation of the All-merciful any imperfection, Return thy gaze, seest thou any fissure? Then Return thy gaze, again and again. Thy gaze, Comes back to thee dazzled, aweary.He then said:
This, in effect, is the faith of all physicists; the deeper we seek, the more is our wonder excited, the more is the dazzlement for our gaze.[99]
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| Abdus Salam di tahun 1987 |
Bagi seorang muslim beriman, semua alam raya ini, pada hakekatnya hanyalah perulangan terus menerus dari multifasetnya cermin Nama-Nama, jadi ketika kita mentafakkuri alam semesta, apakah itu dengan mengaktifkan potensi akal jasmani yang kita sebut "otak" atau "rasio" atau dengan mengaktifkan potensi "akal ruhani" yang kita sebut sebagai "hati atau qalbu" melaui zaugh cita rasa iman, kita hanyalah bagaikan "pezikir" dalam "suluknya" yang tenggelam dalam samudra Nama-Nama,yang terus menerus mengulang tasbihnya, dan melihat penampakan tak henti-hentinya dari panorama keindahan Nama-Nama yang bertajalli pada segala sesuatu.
Sebagaimana semua objek dan entitas di alam raya ini, baik alam nyata maupun alam ghaib, masing-masing berzikir serta mempunyai lokus tempat mereka thawaf dalam menyambut seruan Allah untuk mengagungkanNya, maka kita selaku hamba Allah juga bertawaf dan berzikir mengagungkanNya
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| Sebuah supergugus di mana segala komponennya bertawaf mengagungkan Tuhan dalam zikir Kosmik, perhatikan ukuran dari supergugus ini meliputi volume ruang dengan ukuran sisi 60 juta tahun cahaya, yaitu perjalanan yang ditempuh cahaya selama 60 juta tahun, setiap detik cahaya menempuh jarak 300.000 KM, bayangkan ukuran raksasa yang dahsyat dari materi dan energi ini ditarik oleh sebuah kekuatan yang maha hebat pula, bayangkan aspek Jalaliah dan keperkasaan Allah SWT di sini, ingat juga alam semesta terdiri dari tidak berhingga supergugus seperti ini, dan bayangkan ya akhi, ini baru untuk alam syahadah, belum alam lainnya yang jauh lebih dahsyat dan mengagumkan |
| Gugus Virgo di mana himpunan Galaxi sedang Thawaf mengelilingi sebuah pusat dalam rangka mengagungkan Allah SWT dalam keadaan patuh dan takut |
| Pada tiap Galaxi tersebut di atas terdapat Bintang-Bintang Thawaf mengelilingi suatu pusat di Galaxi |
| Sistem Planet yang tengah Bertawaf dengan pusat Tawafnya Matahari dalam rangka mematuhi "Piqh" mereka yaitu hukum Gravitasi Universal |
| Sistem Peredaran Darah manusia, di mana Jantung sebagai "Ka'bah" dari sel-sel darah merah yang bersirkulasi untuk menegakkan Zikir "biologis" manusia |
| Thawaf Hamba Allah |
Ya Allah, ampunilah dosa-dosa kami yang hina dina ini,...tegakkanlah kami di medan Tauhid dengan kokoh, jadikanlah jasad kami berzikir, akal jasmani kami berzikir, akal ruhani kami berzikir, setiap atom dan entitas kami berzikir dan gabungkanlah kami dalam "simponi" agung semesta yang tengah sibuk berzikir menyebut-nyebut keagunganMu ini,..jangan Engkau tolak kami dari pintu ke pintu, jangan Engkau usir kami karena kebodohan dan kelalaian kami, jangan engkau biarkan kami tenggelam dalam kesombongan dan ketidaktahuan diri ini, Shalawat beserta salam kita haturkan buat junjungan kita Nabiyyina wa Habibina Muhammad, dengan shalawat dan salam yang mencegah kami terusir dari pintunNya, yang tidak membiarkan kami tenggelam dalam samudra Nama-NamaNya dalam keadaan bingung dan tersesat. Sebagaimana banyak mereka yang tersesat dengan ilmuNya.
Sebagaimana seorang arifbillah telah bertutur dalam munajahnya
Ya Allah, jadikanlah kesalahan-kesalahan kami sebagai kesalahan-kesalahan dari orang yang Kau cintai. Dan jangan Kau jadikan kebaikan-kebaikan kami sebagai kebaikan dari orang yang Kau benci.
Amm Ba'du
Teori String saat ini dikatakan sebagai salah satu teori fisika yang paling ultimat yang menjadi kandidat dari teori medan terpadu yang disebut-sebut akan menjelaskan semua gaya fundamental alam . Usaha penuh pergumulan yang keras dari manusia dalam memahami alam syahadah ini telah berlangsung ribuan tahun. Teori ini belum sepenuhnya tuntas, masih banyak upaya yang harus dilakukan untuk menyempurnakannya sehingga makin baik dalam menjelaskan hukum-hukum alam semesta. Namun meskipun demikian, segera dikenali dari teori ini bahwa untuk mengapresiasi dengan selayaknya kebijaksanaan Allah SWT dan IlmuNya yang maha luas, dibutuhkan sofistikasi nalar dan kompleksitas matematika yang tinggi, namun disaat yang sama juga memancarkan kesederhanaan dan kesatuan gagasan yang disemburkan dari sumber terdalam akal tercerdas dan keindahan paling murni dari medan Tauhid yang sempurna. Jika pun para praktisinya yang mengembangkan ilmu ini banyak yang agnostik atau ateistik, namun sebagai kaum mulimin yang beriman kita pandang bahwa semua itu hanyalah "bagaikan laron yang melihat cahaya sangat terang dan terbutakan" sehingga berkesimpulan tidak ada lampu disitu yang menarik mereka kepusat cahaya atau bagaikan perahu kecil yang "dicampakkan disamudra Asma Wa Sifat" daripada kebesaran Allah SWT sehingga terombang ambing dan bingung ditengah samudra Nama-Nama yang tak terperikan dalam dan misterinya.
Betapa banyak tanda-tanda Allah telah dilalaikan bukan karena tumpulnya rasio namun lebih karena butanya mata hati.
Dan betapa banyat ayat-ayat Kami di langit dan di bumi yang mereka lalui, namun mereka berpaling daripadanya (Surat Yusuf 105)
Betapa banyak tanda-tanda Allah telah dilalaikan bukan karena tumpulnya rasio namun lebih karena butanya mata hati.
فَإِنَّهَا لَا تَعْمَى الْأَبْصَارُ وَلَٰكِنْ
تَعْمَى الْقُلُوبُ الَّتِي فِي الصُّدُورِ
“Karena sesungguhnya bukanlah mata itu yang buta,
tetapi yang buta ialah hati yang di dalam dada.” (QS.Al Hajj: 46)[10]Oleh karena itu sikap mental para praktisi dan teoriwan fisika modern sama sekali tidak mempengaruhi keimanan kita, dan hikmah dimanapun ditemukan, baik itu di "comberan" kekafiran sekalipun, akan kita pungut dan kita beri wewangian tauhid, karena kita yang paling berhak atas hikmah tersebut, dibanding orang yang menemukannya lalu mensia-siakannya. Ini sesuai dengan petunjuk nabi Muhammad SAW, bahwa
“Hikmah itu adalah barang yang hilang milik orang yang beriman. Di mana saja ia menemukannya, maka ambillah” (HR. Tirmidzi).
Artikel berikut penulis kutip dari Wikipedia karena wiki telah cukup mapan sebagai sebuah ensiklopedia online yang memaparkan banyak topik secara semi populer. Sasaran penulis dalam blog ini lebih kepada pemaparan sains kontemporer dalam format tidak terlalu teknis dan semipopuler agar dimensi hikmah sains modern tidak menjadi tenggelam dan kabur oleh abstraksi dan jargon-jargon teknis para praktisinya. Sebagai amanat ilmu, penulis akan kutip penuh lalu diterjemahkan apa adanya, dan selanjutnya diberi komentar di mana perlu serta ditambah uraiannya jika dirasa kurang lengkap.
Overview
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.[1] String theory aims to explain all types of observed elementary particles using quantum states of these strings. In addition to the particles postulated by the standard model of particle physics, string theory naturally incorporates gravity, and so is a candidate for a theory of everything, a self-contained mathematical model that describes all fundamental forces and forms of matter. Besides this hypothesized role in particle physics, string theory is now widely used as a theoretical tool in physics, and has shed light on many aspects of quantum field theory and quantum gravity.[2](Dalam Ilmu Fisika, teori string adalah suatu kerangka teoretis pada mana partikel bak-titik dalam fisika partikel diganti oleh objek-objek satu dimensional yang disebut sebagai string atau Dawai. Sasaran teori String adalah untuk bisa menjelaskan semua tipe dari partikel elementer yang teramati dengan melihatnya sebagai keadaan kuantum dari string tersebut. Sebagai tambahan bagi partikel yang dipostulatkan dalam model standar fisika partikel, teori string secara alami menggabungkan gravitasi, sehingga teori ini menjadi kandidat bagi teori segala sesuatu, yaitu suatu teori yang melengkapi dirinya sendiri secara matematis (Blogger:tidak perlu asumsi ad hoc tambahan) yang menggambarkan semua bentuk gaya fundamental dan materi di alam. Di samping peranan hipotetisnya dalam fisika partikel, teori string sekarang digunakan secara luas sebagai sebuah perangkat teoritis, yang memberi jalan terang bagi berbagai aspek teori medan kuantum dan teori gravitasi kuantum.)
The earliest version of string theory, called bosonic string theory, incorporated only the class of particles known as bosons, although this theory developed into superstring theory, which posits that a connection (a "supersymmetry") exists between bosons and the class of particles called fermions. String theory requires the existence of extra spatial dimensions for its mathematical consistency. In realistic physical models constructed from string theory, these extra dimensions are typically compactified to extremely small scales.
(Versi paling awal dari teori string, yang disebut sebagai teori string bosonik, hanya menyatukan satu kelompok partikel yang dikenal sebagai Boson, meskipun teori ini selanjutnya berkembang menjadi teori Superstring, yang menyarankan adanya suatu kaitan (suatu supersimetri) yang eksis antara boson-boson dengan kelompok partikel lain yang dikenal sebagai fermion. Demi konsistensi matematisnya, ternyata teori String mensyaratkan adanya dimensi ruang ekstra. Dalam model fisis realistik teori string ini (Koment Bloger: karena nyatanya dimensi ekstra ini tidak teramati di fisis), dimensi ekstra tersebut secara khas di kompaktifikasi ke skala ukuran luarbiasa sangat kecil (Blogger: yang menjelaskan mengapa tidak teramati) )
String theory was first studied in the late 1960s[3] as a theory of the strong nuclear force before being abandoned in favor of the theory of quantum chromodynamics. Subsequently, it was realized that the very properties that made string theory unsuitable as a theory of nuclear physics made it an outstanding candidate for a quantum theory of gravity. After five consistent versions of string theory were developed, it was realized in the mid-1990s that these theories could be obtained as different limits of a conjectured 11-dimensional theory called M-theory.[4]
(Teori String pertama kali di kaji di akhir tahun 1960an sebagai sebuah teori yang menjelaskan gaya nuklir kuat sebelum teori ini ditinggalkan karena kajian yang lebih berkembang di Kromodinamika Kuantum. Lebih lanjut di sadari sifat khas teori string yang menyebabkannya tidak cocok sebagai sebuah teori dari fisika nuklir ternyata merupakan kandidat yang sangat sesuai bagi teori gravitasi kuantum. Setelah dikembangnya 5 versi dari teori String yang konsisten, disadari dipertengahan tahun 1990an bahwa teori ini harusnya merupakan berbagai limit berbeda dari sebuah prakiraan teori 11 dimensi yang dikenal sebagai teori-M. )
Many theoretical physicists (including Stephen Hawking, Edward Witten, and Juan Maldacena) believe that string theory is a step towards the correct fundamental description of nature. This is because string theory allows for the consistent combination of quantum field theory and general relativity, agrees with general insights in quantum gravity such as the holographic principle and black hole thermodynamics, and has passed many non-trivial checks of its internal consistency. According to Hawking, "M-theory is the only candidate for a complete theory of the universe."[5] Other physicists, such as Richard Feynman,[6][7] Roger Penrose,[8] and Sheldon Lee Glashow,[9] have criticized string theory for not providing novel experimental predictions at accessible energy scales and say that it is a failure as a theory of everything.
(Banyak fisikawan Teoretis (termasuk Stephen Hawking, Edward Witten, dan Juan Maldacena) percaya bahwa teori string adalah suatu langkah yang benar dalam penggambaran fundamental alam. Salah satu alasan adalah teori string mengizinkan kombinasi yang konsisten antara teori medan kuantum dan relativitas umum, bersesuaian dengan wawasan umum yang mendalam dari gravitasi kuantum seperti azas holografik dan termodinamika lubang hitam, dan telah banyak melalui uji non-trivial terhadap konsistensi internalnya. Menurut Hawking, "teori-M adalah satu-satunya kandidat bagi teori lengkap alam semesta." Fisikawan lainnya seperti Richard Feynmann, Roger Penrose, dan Sheldon Lee Glashow telah mengkritik teori string belum memberikan ramalan eksperimental yang penting di wilayah energi yang masih bisa diakses dan oleh karena itu mereka pandang masih gagal sebagai sebuah teori segala sesuatu. )
The starting point for string theory is the idea that the point-like particles of elementary particle physics can also be modeled as one-dimensional objects called strings. According to string theory, strings can oscillate in many ways. On distance scales larger than the string radius, each oscillation mode gives rise to a different species of particle, with its mass, charge, and other properties determined by the string's dynamics. Splitting and recombination of strings correspond to particle emission and absorption, giving rise to the interactions between particles. An analogy for strings' modes of vibration is a guitar string's production of multiple distinct musical notes. In this analogy, different notes correspond to different particles.
(Titik tolak dari teori string adalah ide bahwa partikel bak titik yang digambarkan di fisika partikel dapat juga dimodelkan oleh objek satu dimensi yang dikenal sebagai string. Menurut teori string, string dapat berosilasi dalam beragam cara. Untuk jarak yang lebih besar dari radius string, tiap-tiap ragam osilasi memberikan jenis partikel yang berbeda, yang mana massa, muatan dan berbagai properti lainnya ditentukan oleh dinamika string. String yang lepas atau bergabung terkait dengan emisi serta absorbsi partikel, yang memberikan interaksi antara partikel. Sebuah analogi bagi ragam getaran string adalah senar gitar yang dihasilkan oleh not-not musik yang berbeda secara rangkap. Dalam analogi ini, not yang berbeda terkait dengan partikel yang berbeda.)
In string theory, one of the modes of oscillation of the string corresponds to a massless, spin-2 particle. Such a particle is called a graviton since it mediates a force which has the properties of gravity. Since string theory is believed to be a mathematically consistent quantum mechanical theory, the existence of this graviton state implies that string theory is a theory of quantum gravity.
(Dalam teori string, salah satu ragam osilasi dari string terkait dengan suatu partikel berspin-2 yang tak bermassa. Partikel demikian disebut sebagai sebuah graviton karena ia memediasi sebuah gaya yang mempunyai sifat sebuah gravitasi. Karena teori string dipercaya sebagai teori yang konsisten dengan mekanika kuantum secara matematis, hadirnya keadaan graviton ini mengindikasikan bahwa teori string adalah sebuah teori tentang gravitasi kuantum. )
String theory includes both open strings, which have two distinct endpoints, and closed strings, which form a complete loop. The two types of string behave in slightly different ways, yielding different particle types. For example, all string theories have closed string graviton modes, but only open strings can correspond to the particles known as photons. Because the two ends of an open string can always meet and connect, forming a closed string, all string theories contain closed strings.
(Teori string mencakup string terbuka, yang mempunyai dua titik ujung berbeda, dan string tertutup, yang membentuk kumparan lengkap. Dua tipe string ini berlaku dengan cara agak berbeda, yang menghasilkan tipe partikel berbeda. Sebagai contoh, semua teori string menampung ragam string graviton tertutup, namun hanya string terbuka yang terkait dengan partikel yang dikenal sebagai foton. Karena dua ujung dari sebuah string terbuka dapat selalu bertemu dan tersambung, membentuk sebuah string tertutup, dan semua teori string juga menampung adanya string tertutup)
The earliest string model, the bosonic string, incorporated only the class of particles known as bosons. This model describes, at low enough energies, a quantum gravity theory, which also includes (if open strings are incorporated as well) gauge bosons such as the photon.
(Model string paling awal, string bosonik, hanya mampu menampung klas partikel yang dikenal sebagai boson. Model ini menggambarkan teori gravitasi kuantum untuk limit energi rendah, yang juga mencakup (jika string terbuka juga diikutkan) gauge boson seperti foton)
However, this model has problems. What is most significant is that the theory has a fundamental instability, believed to result in the decay (at least partially) of spacetime itself. In addition, as the name implies, the spectrum of particles contains only bosons, particles which, like the photon, obey particular rules of behavior. Roughly speaking, bosons are the constituents of radiation, but not of matter, which is made of fermions. Investigating how a string theory may include fermions led to the invention of supersymmetry, a mathematical relation between bosons and fermions. String theories that include fermionic vibrations are now known as superstring theories; several kinds have been described, but all are now thought to be different limits of a theory called M-theory.
(Meskipun demikian model ini menderita sejumlah problema. Yang paling mendasar di antaranya adalah ketidakstabilan fundamental yang dipercaya menghasilkan peluruhan (sekurangnya secara parsial) dari ruang-waktu itu sendiri)
 |
| Levels of magnification: 1. Macroscopic level: Matter 2. Molecular level
3. Atomic level: Protons, neutrons, and electrons
4. Subatomic level: Electron5. Subatomic level: Quarks
6. String level
|
One of the challenges of string theory is that the full theory does not yet have a satisfactory definition in all circumstances. The scattering of strings is most straightforwardly defined using the techniques of perturbation theory, but it is not known in general how to define string theory nonperturbatively. It is also not clear as to whether there is any principle by which string theory selects its vacuum state, the spacetime configuration that determines the properties of our universe (see string theory landscape).
Strings
The motion of a point-like particle can be described by drawing a graph of its position with respect to time. The resulting picture depicts the worldline of the particle in spacetime. In an analogous way, one can draw a graph depicting the progress of a string as time passes. The string, which looks like a small line by itself, will sweep out a two-dimensional surface known as the worldsheet. The different string modes (giving rise to different particles, such as the photon or graviton) appear as waves on this surface.A closed string looks like a small loop, so its worldsheet will look like a pipe. An open string looks like a segment with two endpoints, so its worldsheet will look like a strip. In a more mathematical language, these are both Riemann surfaces, the strip having a boundary and the pipe none.
 |
| Interaction in the subatomic world: world lines of point-like particles in the Standard Model or a world sheet swept up by closed strings in string theory |
In quantum mechanics, one computes the probability for a point particle to propagate from one point to another by summing certain quantities called probability amplitudes. Each amplitude is associated with a different worldline of the particle. This process of summing amplitudes over all possible worldlines is called path integration. In string theory, one computes probabilities in a similar way, by summing quantities associated with the worldsheets joining an initial string configuration to a final configuration. It is in this sense that string theory extends quantum field theory, replacing point particles by strings. As in quantum field theory, the classical behavior of fields is determined by an action functional, which in string theory can be either the Nambu–Goto action or the Polyakov action.
Branes
In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions.[10] For example, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher-dimensional branes. In dimension p, these are called p-branes. The word brane comes from the word "membrane" which refers to a two-dimensional brane.Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge. A p-brane sweeps out a (p+1)-dimensional volume in spacetime called its worldvolume. Physicists often study fields analogous to the electromagnetic field which live on the worldvolume of a brane.
In string theory, D-branes are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to the fact that we impose a certain mathematical condition on the system known as the Dirichlet boundary condition. The study of D-branes in string theory has led to important results such as the AdS/CFT correspondence, which has shed light on many problems in quantum field theory.
Branes are also frequently studied from a purely mathematical point of view[11] since they are related to subjects such as homological mirror symmetry and noncommutative geometry. Mathematically, branes may be represented as objects of certain categories, such as the derived category of coherent sheaves on a Calabi–Yau manifold, or the Fukaya category.
Dualities
In physics, the term duality refers to a situation where two seemingly different physical systems turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory. The two theories are then said to be dual to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena.In addition to providing a candidate for a theory of everything, string theory provides many examples of dualities between different physical theories and can therefore be used as a tool for understanding the relationships between these theories.[12]
S-, T-, and U-duality
These are dualities between string theories which relate seemingly different quantities. Large and small distance scales, as well as strong and weak coupling strengths, are quantities that have always marked very distinct limits of behavior of a physical system in both classical and quantum physics. But strings can obscure the difference between large and small, strong and weak, and this is how these five very different theories end up being related. T-duality relates the large and small distance scales between string theories, whereas S-duality relates strong and weak coupling strengths between string theories. U-duality links T-duality and S-duality.M-theory
Main article: M-theory
Before the 1990s, string theorists believed there were five distinct superstring theories: type I, type IIA, type IIB, and the two flavors of heterotic string theory (SO(32) and E8×E8). The thinking was that out of these five candidate theories, only one was the actual correct theory of everything, and that theory was the one whose low energy limit, with ten spacetime dimensions compactified
down to four, matched the physics observed in our world today. It is
now believed that this picture was incorrect and that the five
superstring theories are related to one another by the dualities
described above. The existence of these dualities suggests that the five
string theories are in fact special cases of a more fundamental theory
called M-theory.[13]| Type | Spacetime dimensions | Details |
|---|---|---|
| Bosonic | 26 | Only bosons, no fermions, meaning only forces, no matter, with both open and closed strings; major flaw: a particle with imaginary mass, called the tachyon, representing an instability in the theory. |
| I | 10 | Supersymmetry between forces and matter, with both open and closed strings; no tachyon; gauge group is SO(32) |
| IIA | 10 | Supersymmetry between forces and matter, with only closed strings; no tachyon; massless fermions are non-chiral |
| IIB | 10 | Supersymmetry between forces and matter, with only closed strings; no tachyon; massless fermions are chiral |
| HO | 10 | Supersymmetry between forces and matter, with closed strings only; no tachyon; heterotic, meaning right moving and left moving strings differ; gauge group is SO(32) |
| HE | 10 | Supersymmetry between forces and matter, with closed strings only; no tachyon; heterotic; gauge group is E8×E8 |
Extra dimensions
Number of dimensions
An intriguing feature of string theory is that it predicts extra dimensions. In classical string theory the number of dimensions is not fixed by any consistency criterion. However, to make a consistent quantum theory, string theory is required to live in a spacetime of the so-called "critical dimension": we must have 26 spacetime dimensions for the bosonic string and 10 for the superstring. This is necessary to ensure the vanishing of the conformal anomaly of the worldsheet conformal field theory. Modern understanding indicates that there exist less trivial ways of satisfying this criterion. Cosmological solutions exist in a wider variety of dimensionalities, and these different dimensions are related by dynamical transitions. The dimensions are more precisely different values of the "effective central charge", a count of degrees of freedom that reduces to dimensionality in weakly curved regimes.[14][15]One such theory is the 11-dimensional M-theory, which requires spacetime to have eleven dimensions,[16] as opposed to the usual three spatial dimensions and the fourth dimension of time. The original string theories from the 1980s describe special cases of M-theory where the eleventh dimension is a very small circle or a line, and if these formulations are considered as fundamental, then string theory requires ten dimensions. But the theory also describes universes like ours, with four observable spacetime dimensions, as well as universes with up to 10 flat space dimensions, and also cases where the position in some of the dimensions is described by a complex number rather than a real number. The notion of spacetime dimension is not fixed in string theory: it is best thought of as different in different circumstances.[17]
Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions manually and arbitrarily, and this number is fixed and independent of potential energy. String theory allows one to relate the number of dimensions to scalar potential energy. In technical terms, this happens because a gauge anomaly exists for every separate number of predicted dimensions, and the gauge anomaly can be counteracted by including nontrivial potential energy into equations to solve motion. Furthermore, the absence of potential energy in the "critical dimension" explains why flat spacetime solutions are possible.
This can be better understood by noting that a photon included in a consistent theory (technically, a particle carrying a force related to an unbroken gauge symmetry) must be massless. The mass of the photon that is predicted by string theory depends on the energy of the string mode that represents the photon. This energy includes a contribution from the Casimir effect, namely from quantum fluctuations in the string. The size of this contribution depends on the number of dimensions, since for a larger number of dimensions there are more possible fluctuations in the string position. Therefore, the photon in flat spacetime will be massless—and the theory consistent—only for a particular number of dimensions.[18] When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time). The subset of X is equal to the relation of photon fluctuations in a linear dimension. Flat space string theories are 26-dimensional in the bosonic case, while superstring and M-theories turn out to involve 10 or 11 dimensions for flat solutions. In bosonic string theories, the 26 dimensions come from the Polyakov equation.[19] Starting from any dimension greater than four, it is necessary to consider how these are reduced to four-dimensional spacetime.
Compact dimensions
Two ways have been proposed to resolve this apparent contradiction. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable by present-day experiments.
To retain a high degree of supersymmetry, these compactification spaces must be very special, as reflected in their holonomy. A 6-dimensional manifold must have SU(3) structure, a particular case (torsionless) of this being SU(3) holonomy, making it a Calabi–Yau space, and a 7-dimensional manifold must have G2 structure, with G2 holonomy again being a specific, simple, case. Such spaces have been studied in attempts to relate string theory to the 4-dimensional Standard Model, in part due to the computational simplicity afforded by the assumption of supersymmetry. More recently, progress has been made constructing more realistic compactifications without the degree of symmetry of Calabi–Yau or G2 manifolds.[citation needed]
A standard analogy for this is to consider multidimensional space as a garden hose. If the hose is viewed from sufficient distance, it appears to have only one dimension, its length. Indeed, think of a ball just small enough to enter the hose. Throwing such a ball inside the hose, the ball would move more or less in one dimension; in any experiment we make by throwing such balls in the hose, the only important movement will be one-dimensional, that is, along the hose. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions (and a fly flying in it would move in three dimensions). This "extra dimension" is only visible within a relatively close range to the hose, or if one "throws in" small enough objects. Similarly, the extra compact dimensions are only "visible" at extremely small distances, or by experimenting with particles with extremely small wavelengths (of the order of the compact dimension's radius), which in quantum mechanics means very high energies (see wave–particle duality).
Brane-world scenario
Another possibility is that we are "stuck" in a 3+1 dimensional (three spatial dimensions plus one time dimension) subspace of the full universe. Properly localized matter and Yang–Mills gauge fields will typically exist if the sub-spacetime is an exceptional set of the larger universe.[20] These "exceptional sets" are ubiquitous in Calabi–Yau n-folds and may be described as subspaces without local deformations, akin to a crease in a sheet of paper or a crack in a crystal, the neighborhood of which is markedly different from the exceptional subspace itself. However, until the work of Randall and Sundrum,[21] it was not known that gravity can be properly localized to a sub-spacetime. In addition, spacetime may be stratified, containing strata of various dimensions, allowing us to inhabit the 3+1-dimensional stratum—such geometries occur naturally in Calabi–Yau compactifications.[22] Such sub-spacetimes are D-branes, hence such models are known as brane-world scenarios.In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza's early work demonstrated that general relativity in five dimensions actually predicts the existence of electromagnetism. However, because of the nature of Calabi–Yau manifolds, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our four-dimensional universe. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions.
Testability and experimental predictions
Although a great deal of recent work has focused on using string theory to construct realistic models of particle physics, several major difficulties complicate efforts to test models based on string theory. The most significant is the extremely small size of the Planck length, which is expected to be close to the string length (the characteristic size of a string, where strings become easily distinguishable from particles). Another issue is the huge number of metastable vacua of string theory, which might be sufficiently diverse to accommodate almost any phenomena we might observe at lower energies.String harmonics
One unique prediction of string theory is the existence of string harmonics. At sufficiently high energies, the string-like nature of particles would become obvious. There should be heavier copies of all particles, corresponding to higher vibrational harmonics of the string. It is not clear how high these energies are. In most conventional string models, they would be close to the Planck energy, which is 1014 times higher than the energies accessible in the newest particle accelerator, the LHC, making this prediction impossible to test with any particle accelerator in the near future. However, in models with large extra dimensions they could potentially be produced at the LHC, or at energies not far above its reach.Cosmology
String theory as currently understood makes a series of predictions for the structure of the universe at the largest scales. Many phases in string theory have very large, positive vacuum energy.[23] Regions of the universe that are in such a phase will inflate exponentially rapidly in a process known as eternal inflation. As such, the theory predicts that most of the universe is very rapidly expanding. However, these expanding phases are not stable, and can decay via the nucleation of bubbles of lower vacuum energy. Since our local region of the universe is not very rapidly expanding, string theory predicts we are inside such a bubble. The spatial curvature of the "universe" inside the bubbles that form by this process is negative, a testable prediction.[24] Moreover, other bubbles will eventually form in the parent vacuum outside the bubble and collide with it. These collisions lead to potentially observable imprints on cosmology.[25] However, it is possible that neither of these will be observed if the spatial curvature is too small and the collisions are too rare.Under certain circumstances, fundamental strings produced at or near the end of inflation can be "stretched" to astronomical proportions. These cosmic strings could be observed in various ways, for instance by their gravitational lensing effects. However, certain field theories also predict cosmic strings arising from topological defects in the field configuration.[26]
Supersymmetry
Main article: Supersymmetry
If confirmed experimentally, supersymmetry
could also be considered circumstantial evidence, because all
consistent string theories are supersymmetric. However, the absence of
supersymmetric particles at energies accessible to the LHC
would not necessarily disprove string theory, since the energy scale at
which supersymmetry is broken could be well above the accelerator's
range.AdS/CFT correspondence
Main article: AdS/CFT correspondence
The anti-de Sitter/conformal field theory (AdS/CFT) correspondence is
a relationship which says that string theory is in certain cases
equivalent to a quantum field theory. More precisely, one considers string or M-theory on an anti-de Sitter background. This means that the geometry of spacetime is obtained by perturbing a certain solution of Einstein's equation
in the vacuum. In this setting, it is possible to define a notion of
"boundary" of spacetime. The AdS/CFT correspondence states that this
boundary can be regarded as the "spacetime" for a quantum field theory,
and this field theory is equivalent to the bulk gravitational theory in
the sense that there is a "dictionary" for translating calculations in
one theory into calculations in the other.Examples of the correspondence
The most famous example of the AdS/CFT correspondence states that Type IIB string theory on the product AdS5 × S5 is equivalent to N = 4 super Yang–Mills theory on the four-dimensional conformal boundary.[27][28][29][30] Another realization of the correspondence states that M-theory on AdS4 × S7 is equivalent to the ABJM superconformal field theory in three dimensions.[31] Yet another realization states that M-theory on AdS7 × S4is equivalent to the so-called (2,0)-theory in six dimensions.[32]Applications to quantum chromodynamics
Main article: AdS/QCD
Since it relates string theory to ordinary quantum field theory, the
AdS/CFT correspondence can be used as a theoretical tool for doing
calculations in quantum field theory. For example, the correspondence
has been used to study the quark–gluon plasma, an exotic state of matter produced in particle accelerators.The physics of the quark–gluon plasma is governed by quantum chromodynamics, the fundamental theory of the strong nuclear force, but this theory is mathematically intractable in problems involving the quark–gluon plasma. In order to understand certain properties of the quark–gluon plasma, theorists have therefore made use of the AdS/CFT correspondence. One version of this correspondence relates string theory to a certain supersymmetric gauge theory called N = 4 super Yang–Mills theory. The latter theory provides a good approximation to quantum chromodynamics. One can thus translate problems involving the quark–gluon plasma into problems in string theory which are more tractable. Using these methods, theorists have computed the shear viscosity of the quark–gluon plasma.[33] In 2008, these predictions were confirmed at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory.[34]
Applications to condensed matter physics
In addition, string theory methods have been applied to problems in condensed matter physics. Certain condensed matter systems are difficult to understand using the usual methods of quantum field theory, and the AdS/CFT correspondence may allow physicists to better understand these systems by describing them in the language of string theory. Some success has been achieved in using string theory methods to describe the transition of a superfluid to an insulator.[35][36]Connections to mathematics
In addition to influencing research in theoretical physics, string theory has stimulated a number of major developments in pure mathematics. Like many developing ideas in theoretical physics, string theory does not at present have a mathematically rigorous formulation in which all of its concepts can be defined precisely. As a result, physicists who study string theory are often guided by physical intuition to conjecture relationships between the seemingly different mathematical structures that are used to formalize different parts of the theory. These conjectures are later proved by mathematicians, and in this way, string theory has served as a source of new ideas in pure mathematics.[37]Mirror symmetry
Main article: Mirror symmetry (string theory)
One of the ways in which string theory influenced mathematics was through the discovery of mirror symmetry. In string theory, the shape of the unobserved spatial dimensions is typically encoded in mathematical objects called Calabi–Yau manifolds.
These are of interest in pure mathematics, and they can be used to
construct realistic models of physics from string theory. In the late
1980s, it was noticed that given such a physical model, it is not
possible to uniquely reconstruct a corresponding Calabi–Yau manifold.
Instead, one finds that there are two Calabi–Yau manifolds that
give rise to the same physics. These manifolds are said to be "mirror"
to one another. The existence of this mirror symmetry relationship
between different Calabi–Yau manifolds has significant mathematical
consequences as it allows mathematicians to solve many problems in enumerative algebraic geometry.
Today mathematicians are still working to develop a mathematical
understanding of mirror symmetry based on physicists' intuition.[38]Vertex operator algebras
Main articles: Vertex operator algebra and Monstrous moonshine
In addition to mirror symmetry, applications of string theory to pure mathematics include results in the theory of vertex operator algebras. For example, ideas from string theory were used by Richard Borcherds in 1992 to prove the monstrous moonshine conjecture relating the monster group (a construction arising in group theory, a branch of algebra) and modular functions (a class of functions which are important in number theory).[39]Early results
Some of the structures reintroduced by string theory arose for the first time much earlier as part of the program of classical unification started by Albert Einstein. The first person to add a fifth dimension to general relativity was German mathematician Theodor Kaluza in 1919, who noted that gravity in five dimensions describes both gravity and electromagnetism in four. In 1926, the Swedish physicist Oskar Klein gave a physical interpretation of the unobservable extra dimension—it is wrapped into a small circle. Einstein introduced a non-symmetric metric tensor, while much later Brans and Dicke added a scalar component to gravity. These ideas would be revived within string theory, where they are demanded by consistency conditions.String theory was originally developed during the late 1960s and early 1970s as a never completely successful theory of hadrons, the subatomic particles like the proton and neutron that feel the strong interaction. In the 1960s, Geoffrey Chew and Steven Frautschi discovered that the mesons make families called Regge trajectories with masses related to spins in a way that was later understood by Yoichiro Nambu, Holger Bech Nielsen and Leonard Susskind to be the relationship expected from rotating strings. Chew advocated making a theory for the interactions of these trajectories that did not presume that they were composed of any fundamental particles, but would construct their interactions from self-consistency conditions on the S-matrix. The S-matrix approach was started by Werner Heisenberg in the 1940s as a way of constructing a theory that did not rely on the local notions of space and time, which Heisenberg believed break down at the nuclear scale. While the scale was off by many orders of magnitude, the approach he advocated was ideally suited for a theory of quantum gravity.
Working with experimental data, R. Dolen, D. Horn and C. Schmid[40] developed some sum rules for hadron exchange. When a particle and antiparticle scatter, virtual particles can be exchanged in two qualitatively different ways. In the s-channel, the two particles annihilate to make temporary intermediate states that fall apart into the final state particles. In the t-channel, the particles exchange intermediate states by emission and absorption. In field theory, the two contributions add together, one giving a continuous background contribution, the other giving peaks at certain energies. In the data, it was clear that the peaks were stealing from the background—the authors interpreted this as saying that the t-channel contribution was dual to the s-channel one, meaning both described the whole amplitude and included the other.
The result was widely advertised by Murray Gell-Mann, leading Gabriele Veneziano to construct a scattering amplitude that had the property of Dolen-Horn-Schmid duality, later renamed world-sheet duality. The amplitude needed poles where the particles appear, on straight line trajectories, and there is a special mathematical function whose poles are evenly spaced on half the real line— the Gamma function— which was widely used in Regge theory. By manipulating combinations of Gamma functions, Veneziano was able to find a consistent scattering amplitude with poles on straight lines, with mostly positive residues, which obeyed duality and had the appropriate Regge scaling at high energy. The amplitude could fit near-beam scattering data as well as other Regge type fits, and had a suggestive integral representation that could be used for generalization.
Over the next years, hundreds of physicists worked to complete the bootstrap program for this model, with many surprises. Veneziano himself discovered that for the scattering amplitude to describe the scattering of a particle that appears in the theory, an obvious self-consistency condition, the lightest particle must be a tachyon. Miguel Virasoro and Joel Shapiro found a different amplitude now understood to be that of closed strings, while Ziro Koba and Holger Nielsen generalized Veneziano's integral representation to multiparticle scattering. Veneziano and Sergio Fubini introduced an operator formalism for computing the scattering amplitudes that was a forerunner of world-sheet conformal theory, while Virasoro understood how to remove the poles with wrong-sign residues using a constraint on the states. Claud Lovelace calculated a loop amplitude, and noted that there is an inconsistency unless the dimension of the theory is 26. Charles Thorn, Peter Goddard and Richard Brower went on to prove that there are no wrong-sign propagating states in dimensions less than or equal to 26.
In 1969, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind recognized that the theory could be given a description in space and time in terms of strings. The scattering amplitudes were derived systematically from the action principle by Peter Goddard, Jeffrey Goldstone, Claudio Rebbi, and Charles Thorn, giving a space-time picture to the vertex operators introduced by Veneziano and Fubini and a geometrical interpretation to the Virasoro conditions.
In 1970, Pierre Ramond added fermions to the model, which led him to formulate a two-dimensional supersymmetry to cancel the wrong-sign states. John Schwarz and André Neveu added another sector to the fermi theory a short time later. In the fermion theories, the critical dimension was 10. Stanley Mandelstam formulated a world sheet conformal theory for both the bose and fermi case, giving a two-dimensional field theoretic path-integral to generate the operator formalism. Michio Kaku and Keiji Kikkawa gave a different formulation of the bosonic string, as a string field theory, with infinitely many particle types and with fields taking values not on points, but on loops and curves.
In 1974, Tamiaki Yoneya discovered that all the known string theories included a massless spin-two particle that obeyed the correct Ward identities to be a graviton. John Schwarz and Joel Scherk came to the same conclusion and made the bold leap to suggest that string theory was a theory of gravity, not a theory of hadrons. They reintroduced Kaluza–Klein theory as a way of making sense of the extra dimensions. At the same time, quantum chromodynamics was recognized as the correct theory of hadrons, shifting the attention of physicists and apparently leaving the bootstrap program in the dustbin of history.
String theory eventually made it out of the dustbin, but for the following decade all work on the theory was completely ignored. Still, the theory continued to develop at a steady pace thanks to the work of a handful of devotees. Ferdinando Gliozzi, Joel Scherk, and David Olive realized in 1976 that the original Ramond and Neveu Schwarz-strings were separately inconsistent and needed to be combined. The resulting theory did not have a tachyon, and was proven to have space-time supersymmetry by John Schwarz and Michael Green in 1981. The same year, Alexander Polyakov gave the theory a modern path integral formulation, and went on to develop conformal field theory extensively. In 1979, Daniel Friedan showed that the equations of motions of string theory, which are generalizations of the Einstein equations of General Relativity, emerge from the Renormalization group equations for the two-dimensional field theory. Schwarz and Green discovered T-duality, and constructed two superstring theories—IIA and IIB related by T-duality, and type I theories with open strings. The consistency conditions had been so strong, that the entire theory was nearly uniquely determined, with only a few discrete choices.
First superstring revolution
In the early 1980s, Edward Witten discovered that most theories of quantum gravity could not accommodate chiral fermions like the neutrino. This led him, in collaboration with Luis Alvarez-Gaumé to study violations of the conservation laws in gravity theories with anomalies, concluding that type I string theories were inconsistent. Green and Schwarz discovered a contribution to the anomaly that Witten and Alvarez-Gaumé had missed, which restricted the gauge group of the type I string theory to be SO(32). In coming to understand this calculation, Edward Witten became convinced that string theory was truly a consistent theory of gravity, and he became a high-profile advocate. Following Witten's lead, between 1984 and 1986, hundreds of physicists started to work in this field, and this is sometimes called the first superstring revolution.During this period, David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm discovered heterotic strings. The gauge group of these closed strings was two copies of E8, and either copy could easily and naturally include the standard model. Philip Candelas, Gary Horowitz, Andrew Strominger and Edward Witten found that the Calabi–Yau manifolds are the compactifications that preserve a realistic amount of supersymmetry, while Lance Dixon and others worked out the physical properties of orbifolds, distinctive geometrical singularities allowed in string theory. Cumrun Vafa generalized T-duality from circles to arbitrary manifolds, creating the mathematical field of mirror symmetry. Daniel Friedan, Emil Martinec and Stephen Shenker further developed the covariant quantization of the superstring using conformal field theory techniques. David Gross and Vipul Periwal discovered that string perturbation theory was divergent. Stephen Shenker showed it diverged much faster than in field theory suggesting that new non-perturbative objects were missing.
In the 1990s, Joseph Polchinski discovered that the theory requires higher-dimensional objects, called D-branes and identified these with the black-hole solutions of supergravity. These were understood to be the new objects suggested by the perturbative divergences, and they opened up a new field with rich mathematical structure. It quickly became clear that D-branes and other p-branes, not just strings, formed the matter content of the string theories, and the physical interpretation of the strings and branes was revealed—they are a type of black hole. Leonard Susskind had incorporated the holographic principle of Gerardus 't Hooft into string theory, identifying the long highly excited string states with ordinary thermal black hole states. As suggested by 't Hooft, the fluctuations of the black hole horizon, the world-sheet or world-volume theory, describes not only the degrees of freedom of the black hole, but all nearby objects too.
Second superstring revolution
In 1995, at the annual conference of string theorists at the University of Southern California (USC), Edward Witten gave a speech on string theory that in essence united the five string theories that existed at the time, and giving birth to a new 11-dimensional theory called M-theory. M-theory was also foreshadowed in the work of Paul Townsend at approximately the same time. The flurry of activity that began at this time is sometimes called the second superstring revolution.
During this period, Tom Banks, Willy Fischler, Stephen Shenker and Leonard Susskind formulated matrix theory, a full holographic description of M-theory using IIA D0 branes.[41] This was the first definition of string theory that was fully non-perturbative and a concrete mathematical realization of the holographic principle. It is an example of a gauge-gravity duality and is now understood to be a special case of the AdS/CFT correspondence. Andrew Strominger and Cumrun Vafa calculated the entropy of certain configurations of D-branes and found agreement with the semi-classical answer for extreme charged black holes. Petr Hořava and Witten found the eleven-dimensional formulation of the heterotic string theories, showing that orbifolds solve the chirality problem. Witten noted that the effective description of the physics of D-branes at low energies is by a supersymmetric gauge theory, and found geometrical interpretations of mathematical structures in gauge theory that he and Nathan Seiberg had earlier discovered in terms of the location of the branes.
In 1997, Juan Maldacena noted that the low energy excitations of a theory near a black hole consist of objects close to the horizon, which for extreme charged black holes looks like an anti-de Sitter space. He noted that in this limit the gauge theory describes the string excitations near the branes. So he hypothesized that string theory on a near-horizon extreme-charged black-hole geometry, an anti-deSitter space times a sphere with flux, is equally well described by the low-energy limiting gauge theory, the N = 4 supersymmetric Yang–Mills theory. This hypothesis, which is called the AdS/CFT correspondence, was further developed by Steven Gubser, Igor Klebanov and Alexander Polyakov, and by Edward Witten, and it is now well-accepted. It is a concrete realization of the holographic principle, which has far-reaching implications for black holes, locality and information in physics, as well as the nature of the gravitational interaction. Through this relationship, string theory has been shown to be related to gauge theories like quantum chromodynamics and this has led to more quantitative understanding of the behavior of hadrons, bringing string theory back to its roots.
Criticisms
Some critics of string theory say that it is a failure as a theory of everything.[42][43][44][45][46][47] Notable critics include Peter Woit, Lee Smolin, Philip Warren Anderson,[48] Sheldon Glashow,[49] Lawrence Krauss,[50] Carlo Rovelli[51] and Bert Schroer.[52] Some common criticisms include:- Very high energies needed to test quantum gravity.
- Lack of uniqueness of predictions due to the large number of solutions.
- Lack of background independence.
High energies
It is widely believed that any theory of quantum gravity would require extremely high energies to probe directly, higher by orders of magnitude than those that current experiments such as the Large Hadron Collider[53] can attain. This is because strings themselves are expected to be only slightly larger than the Planck length, which is twenty orders of magnitude smaller than the radius of a proton, and high energies are required to probe small length scales. Generally speaking, quantum gravity is difficult to test because gravity is much weaker than the other forces, and because quantum effects are controlled by Planck's constant h, a very small quantity. As a result, the effects of quantum gravity are extremely weak.Number of solutions
String theory as it is currently understood has a huge number of solutions, called string vacua,[23] and these vacua might be sufficiently diverse to accommodate almost any phenomena we might observe at lower energies.The vacuum structure of the theory, called the string theory landscape (or the anthropic portion of string theory vacua), is not well understood. String theory contains an infinite number of distinct meta-stable vacua, and perhaps 10520 of these or more correspond to a universe roughly similar to ours—with four dimensions, a high planck scale, gauge groups, and chiral fermions. Each of these corresponds to a different possible universe, with a different collection of particles and forces.[23] What principle, if any, can be used to select among these vacua is an open issue. While there are no continuous parameters in the theory, there is a very large set of possible universes, which may be radically different from each other. It is also suggested that the landscape is surrounded by an even more vast swampland of consistent-looking semiclassical effective field theories, which are actually inconsistent.[citation needed]
Some physicists believe this is a good thing, because it may allow a natural anthropic explanation of the observed values of physical constants, in particular the small value of the cosmological constant.[54][55] The argument is that most universes contain values for physical constants that do not lead to habitable universes (at least for humans), and so we happen to live in the "friendliest" universe. This principle is already employed to explain the existence of life on earth as the result of a life-friendly orbit around the medium-sized sun among an infinite number of possible orbits (as well as a relatively stable location in the galaxy).
Background independence
See also: Background independence
A separate and older criticism of string theory is that it is
background-dependent—string theory describes perturbative expansions
about fixed spacetime backgrounds which means that mathematical
calculations in the theory rely on preselecting a background as a
starting point. This is because, like many quantum field theories, much of string theory is still only formulated perturbatively, as a divergent series of approximations.[citation needed]Although the theory, defined as a perturbative expansion on a fixed background, is not background independent, it has some features that suggest non-perturbative approaches would be background-independent—topology change is an established process in string theory, and the exchange of gravitons is equivalent to a change in the background. Since there are dynamic corrections to the background spacetime in the perturbative theory, one would expect spacetime to be dynamic in the nonperturbative theory as well since they would have to predict the same spacetime.[citation needed]
This criticism has been addressed to some extent by the AdS/CFT duality, which is believed to provide a full, non-perturbative definition of string theory in spacetimes with anti-de Sitter space asymptotics. Nevertheless, a non-perturbative definition of the theory in arbitrary spacetime backgrounds is still lacking. Some hope that M-theory, or a non-perturbative treatment of string theory (such as "background independent open string field theory") will have a background-independent formulation.[citation nee
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