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Sabtu, 26 September 2015

Temuan Baru di Pluto

'Snakeskin' Pluto revealed in planetary close-up

Intriguing ridges add to dwarf planet's geological mysteries.

Alexandra Witze

24 September 2015

“What is that?” planetary scientist Barbara Cohen gasped, marvelling at the latest images of Pluto released on 24 September.
Cohen, of NASA's Marshall Space Flight Center in Huntsville, Alabama, is not alone. It is a question nearly every planetary specialist is asking with each release of pictures from NASA's New Horizons spacecraft, which flew past Pluto and its moons in July. The latest images — the most-detailed colour shots yet downlinked to Earth — show a bizarre 'snakeskin' terrain, wrinkled with ridges and smudged with rust-coloured material.

NASA/JHUAPL/SWRI

Ridges cover a mountain range known informally as Tartarus Dorsa.

Many of the ridges run in parallel directions, suggesting that they were formed by some sort of overarching geological influence — perhaps wind. The corrugated ridges seem to be tens of kilometres long. “These aren't little ripples — these are giant features,” says Alex Parker, a member of the New Horizons science team at the Southwest Research Institute in Boulder, Colorado.

Nature Special: Pluto and Ceres

The photos come from the colour camera aboard New Horizons's Ralph instrument, and are enhanced to bring out compositional differences between materials on the dwarf planet's surface.
So far, Pluto has turned out to be strikingly active for an icy world 5 billion kilometres from the Sun. Nitrogen glaciers swirl around the base of towering mountains, which are held up by the sheer rigidity of ice frozen at about −235 °C, 38 degrees above absolute zero.
Another image reveals Pluto's surface in the greatest detail yet, with resolutions down to 250 metres. Chunks of mountain blocks, coated with what are probably dark-red hydrocarbon molecules, are surrounded by ice that flows through a basin known as Sputnik Planum.

NASA/JHUAPL/SWRI

Blocky structures seen here may be mountains — or icebergs.

Seen from above, the ice seems to close in around the jagged mountains, resembling the embayments in the sea ice that surrounds Antarctica. But some of these 'mountains' might in fact be icebergs decoupled from the bedrock beneath.
And viewed at close range, even the smoothest ice surfaces turn out to be remarkably complex, with a pitted or dimpled texture that could reflect ices subliming away into the atmosphere. These vast plains might represent the tops of thick layers of ice that flow and churn from within, tracing polygonal structures on the surface.

NASA/JHUAPL/SWRI

Pebbled plains surround ice mountains in this patch of Pluto's surface.

Some of the mountain ranges seem to show darker layers of material in the sides of steep cliffs. Elsewhere, material piles up between the peaks, including a spot that looks like an icy pond.
“This is all bizarre,” says Parker. “There are a lot of new questions we're going to be able to ask because of these images, and we're going to be able to answer some of them.”
Next month, New Horizons will burn its engines in a series of manoeuvres to set it on course to fly past a second, even more distant world in 2019.

Nature

doi:10.1038/nature.2015.18433

Sabtu, 18 April 2015

Pengamatan Resolusi Tinggi

ALMA debuts its high-resolution results

Apr 17, 2015 1 comment

Ring-like image of the gravitationally lensed galaxy SDP.81

Cincin Api: Pengamatan dengan Resolusi Tertinggi ALMA

Scientific results of the highest resolution observations yet attempted by the Atacama Large Millimeter/submillimeter Array (ALMA) telescope are described in four papers to be published this month in Astrophysical Journal Letters. The observations were part of a campaign to test ALMA's capabilities when run in its long-baseline configuration, and the result is stunning images and data for five astronomical objects. These include the planet-forming disc of HL Tau, the tumbling asteroid Juno, and a lensed galaxy 12 billion light-years away. These results are not only rich with new insights, but they also give us a sense of the incredible capabilities that ALMA will provide in the future.

ALMA is an array of 12 m- and 7 m-diameter antennas that observe the cosmos at millimetre/submillimetre wavelengths. The antennas work together to function as an interferometer, and this allows the signals from each of the antennas to be combined to simulate a telescope the size of the distance between the individual units. The array works like a zoom lens on a camera: the antennas can be repositioned so that the baseline of the simulated telescope is as small as 150 m or as large as 15 km across.

Expecting the unexpected

ALMA's capabilities in its wavelength regime are revolutionary. The array is the largest and most sensitive millimetre/submillimetre instrument in the world, and its resolution is 10 times better than even the Hubble Space Telescope. As Anneila Sargent, chair of the ALMA board while the array was being built, predicted in 2008, "We know that every time in the past that a new wavelength region has been opened up, as ALMA will do, we have been surprised by entirely unexpected discoveries that significantly changed our understanding of the universe. We also expect the unexpected from ALMA."
In its smaller configurations, ALMA can study the large-scale structure of cold gas and dust in the universe – and this is how the array has been used since it began its first early-science operations in 2011. But now, ALMA is beginning to test its long-baseline configuration, in which it is able to make its highest resolution observations and study the small-scale structure of objects in detail.
ALMA's Long Baseline Campaign, which ran in late 2014, observed five targets using 22–36 antennas arranged with a baseline of up to the maximum 15 km. The targets were specifically selected to push the limits of ALMA's capabilities: each target has a small angular size (less than two arcseconds) with a fine-scale structure that had been largely unresolved in previous observations made with other telescopes. Two of the targets, the variable star Mira and the active galaxy 3C138, were primarily used for calibration and comparisons of ALMA data with those of other telescopes. The remaining three targets not only demonstrated ALMA's capabilities, but also resulted in new science discoveries.

Image of the protoplanetary disc surrounding the star HL Tau

Possible planets: this protoplanetary disc surrounds HL Tau

The first discovery involves HL Tau, which is a young star surrounded by a protoplanetary disc – a disc of gas and dust from which planets can be born. ALMA's detailed observations of this region revealed a remarkable structure within the disc: a series of light and dark concentric rings indicative of planets caught in the act of formation. Studying this system is allowing scientists to better understand how multi-planet solar systems, like our own, form and evolve.
Juno, which is one of the largest asteroids in our solar system's main asteroid belt, is the subject of the second discovery. ALMA's observations of Juno were made when the asteroid was approximately 295 million kilometres from Earth. The 10 images ALMA took have been stitched together into the brief animation shown below, which shows the asteroid tumbling through space as it orbits the Sun. ALMA's observations are not of reflected light, but rather of the millimetre-wavelength light emitted by the asteroid itself. The resolution of these images is good enough to study the shape and even some surface features of the asteroid – something that is unprecedented for this wavelength.
The final discovery concerns the star-forming galaxy SDP.81, which is so far from Earth that the light we see was emitted when the universe was only 15% of its current age. The galaxy is only visible because of a fortuitous alignment between it and a nearby foreground galaxy. The gravity of the foreground galaxy acts as a lens and bends the light from SDP.81 into a highly magnified cosmic ring. The combination of this lucky alignment and ALMA's high resolution gives scientists a spectacularly detailed view of this distant galaxy, allowing them to study the actual shape of the galaxy and motion within it. This is ALMA's highest resolution observation so far, and is described by Alma astronomers as being "about the same as seeing the rim of a basketball hoop atop the Eiffel Tower from the observing deck of the Empire State Building".
The observations from ALMA's first test of its long baseline clearly demonstrate that exciting times are ahead as scientists gear-up for the next cycle of observations. "It takes a combination of ALMA's high resolution and high sensitivity to unlock these otherwise hidden details of the early universe," says ALMA director Pierre Cox. "These results open a new frontier in astronomy, and prove that ALMA can indeed deliver on its promise of transformational science."

About the author

Susanna Kohler is Science Highlights editor at the American Astronomical Society

Minggu, 09 November 2014

Public Lecture Sang Peraih Nobel Fisika

Masih Banyak Misteri di Alam Semesta

Adalah pemenang hadiah Nobel Fisika tahun 2011 Prof. Brian Schmidt berkenan datang ke Indonesia menghadiri perhelatan ilmiah ICMNS yang diadakan di ITB setiap tahun. Beliau datang selaku qey note speaker serta berkenan juga memberikan kuliah umum yang diperuntukkan untuk para audiens umum seperti para guru dan siswa sekolah menengah serta siswa dan masyarakat umum pemerhati fisika dan astronomi modern.

Alhamdulillah Bloger berhasil menghadiri acara tersebut yang berlangsung pada hari minggu 2 November 2014 jam 3.30 sore yang di langsungkan di Aula Barat ITB yang memang biasa digunakan untuk tempat tampilnya sejumlah tokoh penting membicarakan berbagai topik aktual di ITB. Meskipun semenjak hari Jum'at 2 hari sebelumnya kondisi fisik bloger kurang fit dan mengalami demam panas, namun bloger tetap bela-belain hadir di seminar tersebut. Bahkan tepat di hari acara seminar berlangsung panas dalam tersebut berubah menjadi radang tenggorokan yang cukup serius sehingga Blogger tidak dapat menelan nasi sehingga hanya bisa memakan makanan yang berkuah serta minum susu.

Salah satu kebahagiaan yang Blogger rasakan meskipun hanya selaku guru di sekolah menengah ini adalah Blogger sering punya kesempatan untuk dapat melihat secara langsung dan bahkan dapat bertatap muka dan berkenalan dengan para Ilmuwan Fisika yang memang keseharian mereka bertungkus lumus dengan riset ilmiah di tapal batas terakhir perkembangan fisika kontemporer. Kesempatan seperti ini jelas jarang di miliki oleh rekan-rekan penulis yang mengajar sains di sekolah menengah. Beberapa di antara mereka penulis kenal secara pribadi serta pernah duduk dibangku kuliah mengikuti kuliah mereka, di antaranya Dr. rear. nat. M. Farchani Rosyid, Mirza Satriawan PhD, Prof. Dr. Bobby Eka Gunara, Prof. Dr. Freddy Zen, Prof. Dr. Triyanta, Dr. Husin al Attas, dan lain-lain. Lain kesempatan Blogger akan mengulas sedikit soal para Ilmuwan dan Guru Besar Fisika ini. Yang jelas para Ilmuwan ini mempunyai banyak kelebihan dan sisi positif yang menurut Blogger sangat penting di ambil untuk menjadi bahan pertimbangan bagaimanakah selayaknya sebuah kurikulum dan pembelajaran fisika dibangun agar menghasilkan tokoh-tokoh seperti mereka. Bagaimana menciptakan siswa-siswa yang punya mentalitas dan kecendrungan "pembelajar" serta "periset seperti mereka".

Artinya dengan merasakan secara langsung semangat, kegairahan dan visi mereka soal sains kita akan memperoleh suatu materi yang sangat banyak soal pendidikan sains di sekolah menengah ketimbang kita duduk di bangku kuliah yang berkutat dengan teori pendidikan. Karena kita tahu persis cara dan metode mereka berhasil sedangkan metode dan teori didaktik yang terkadang sangat rumit dan serba berbau formalitas kebijakan sangat sulit diuji validitas keberhasilannya. Penulis teringat dengan saran guru penulis waktu di UGM Dr. rear. nat M. Farchani Rosyid bahwa untuk mengerti cara buat patung, kita sebaiknya belajar kepada seorang pembuat patung sejati, jangan belajar kepada, katakanlah misalkan pada penjual patung. Boleh jadi sang penjual patung tampak mengesankan argumentasinya soal patung tersebut, namun membuat patung yang sebenarnya belum tentu mereka bisa. Salah satu kesempatan cukup langka juga untuk lebih merasakan "aura" saintifik sejati adalah hadir di perkuliahan yang dibawakan langsung oleh seorang pemenang hadiah Nobel.

Brian Paul Schmidt AC, FRS (lahir 24 Februari 1967) adalah a Distinguished Professor, Australian Research Council Laureate Fellow and astrophysicist di The Australian National University Mount Stromlo Observatory dan Research School of Astronomy and Astrophysics dan beliau dikenal dengan risetnya soal supernova (supernovae) yang dimanfaatkan sebagai perunut kosmologis. Baru-baru ini beliau menjabat Australia Research Council Federation Fellowship dan dipilih dalam keanggotaan Royal Society di tahun 2012.^[2] Schmidt berbagi Shaw Prize in Astronomy 2006 dan Nobel Prize in Physics 2011 dengan Saul Perlmutter dan Adam Riess yang berhasil memberikan bukti bahwa pengembangan alam semesta berlangsung dipercepat (expansion of the universe is accelerating).

Berdasarkan amatan mereka, semenjak alam semesta mengembang setelah BigBang, pengembangan berlangsung dipercepat. Sebelum temuan tersebut, para Fisikawan memperkirakan bahwa semestinya laju pengembangan akan diperlambat.

Temuan ini mengarahkan kepada penerimaan luas akan teori energi gelap (dark energy), yaitu suatu teori yang memprediksikan adanya gaya misterius yang menolak gravitasi. Pengukuran astrofisika memperkirakan bahwa energi gelap 74 persen dari semua kandungan alam semesta.

Namun lebih dari satu dekade sesudah temuan bernilai hadiah Nobel ini, para ilmuwan masih berkutat dengan kajian apakah energi gelap itu sejatinya dan berusaha memecahkan persoalan yang disebut-sebut para ahli sebagai "persoalan paling penting" dalam sejarah fisika modern.

Astrofisikawan Saul Perlmutter menganalisis kecerlangan yang berasal dari supernova, seperti yang ditunjukkan oleh gambar ini, untuk mengukur seberapa cepat alam semesta mengembang.

Berikut penjelasan Physics World

Mengembang Melawan Gravitasi

Hanya 25 tahun yang lalu sebagian besar ilmuwan percaya bahwa alam semesta dapat digambarkan oleh model yang sederhana dan elegan dari Albert Einstein dan Willem de Sitter tahun 1932 pada mana gravitasi lambat laun akan menghentikan laju pengembangan ruang.

Meskipun demikian, semenjak pertengahan tahun 1980an sederetan pengamatan telah dilakukan yang mana hasilnya nampaknya tidak sesuai dengan teori standar. Hal ini menyebabkan sejumlah orang mengusulkan membangkitkan kembali konsep lama yang di sesali Einstein yaitu Konstanta Kosmologi agar supaya menjelaskan data baru ini lebih baik.

Konstanta ini pertama kali diperkenalkan oleh Einstein di tahun 1917 untuk mengimbangi gaya tarik gravitasi, karena beliau percaya akan alam semesta yang bersifat statik. He considered it a property of space itself, but it can also be interpreted as a form of energy that uniformly fills all of space; if lambda is greater than zero, the uniform energy has negative pressure and creates a bizarre, repulsive form of gravity. However, Einstein grew disillusioned with the term and finally abandoned it in 1931 after Edwin Hubble and Milton Humason discovered that the universe is expanding.

In 1987 physicists at the Lawrence Berkeley National Laboratory and the University of California at Berkeley initiated the Supernova Cosmology Project (SCP) to hunt for certain distant exploding stars, known as type Ia supernovae. They hoped to use these stars to calculate, among other things, the rate at which the expansion of the universe was slowing down.

Adam Riess and Brian Schmidt

Deceleration was expected because in the absence of lambda, many people thought that "ΩM", which is the amount of observable matter in the universe today as a fraction of the critical density, was sufficient to slow the universe's expansion forever, if not to bring it to an eventual halt.
In 1998, after years of observations, two rival groups of supernova hunters – the High-Z Supernovae Search Team led by Schmidt and Riess and the SCP led by Perlmutter – came to the conclusion that the cosmic expansion is actually accelerating and not slowing under the influence of gravity as might be expected.
The two teams came to this conclusion by studying type Ia supernova where they found that the light from over 50 distant supernovae was weaker than expected. This was a sign that the expansion of the universe was accelerating.
In order to account for the acceleration, about 75% of the mass-energy content of the universe had to be made up of some gravitationally repulsive substance that nobody had ever seen before. This substance, which would determine the fate of the universe, was dubbed dark energy.
It is now thought that dark energy constitutes around 75% of the current universe, with around 21% being dark matter and the rest ordinary matter and energy making up the Earth, planets and stars.
"The findings of the 2011 Nobel Laureates in Physics have helped to unveil a universe that to a large extent is unknown to science," stated the Academy. "And everything is possible again."
"My involvement in the discovery of the accelerating universe and its implications for the presence of dark energy has been an incredibly exciting adventure," says Riess. "I have also been fortunate to work with tremendous colleagues and powerful facilities. I am deeply honored that this work has been recognized."

New problems

Cosmologist Michael Turner from the University of Chicago says that the award to Perlmutter, Riess and Schmidt is "well deserved". "The two competing teams is a wonderful story in science – the physicists vs the astronomers," says Turner. "The biggest surprise to both teams was that the other team got the same answer. Each team believed the other didn't know what they were doing."
Turner adds that before the discovery, cosmology was in some disarray with astronomers having a model of the universe based on cold dark matter and inflation, but with not enough matter to make the universe flat – a key prediction of inflation.
"Dark energy and cosmic acceleration was the missing piece of the puzzle," says Turner. "Moreover, in solving one problem, it gave us a new problem – what is dark energy? I think that is the most profound mystery in all of science."
Robert Kirshner from Harvard University who supervised both Schmidt and Riess when they were PhD students says the decision by the Nobel committee is "great" as it will mean "no more waiting". "We did a lot of foundational work at Harvard and my postdocs and students made up a hefty chunk of the High-Z Team," says Kirshner. "[Riess] did a lot after the initial result to show that there was no sneaky effect due to dust absorption and that, if you look far enough into the past, you could see that the universe was slowing down before the dark energy got the upper hand, about five billion years ago."
Kirshner adds that Perlmutter is also "very deserving" of the prize. "[Perlmutter] was persistent even when his programme was moving slowly and, despite getting a contrary result in 1997, was convinced of cosmic acceleration during 1998 by comparing his own extensive data set of distant supernovae with the nearby supernovae measured by the group in Chile."
Peter Knight, president of the Institute of Physics, which publishes physicsworld.com says the work has "triggered an enormous amount of research" on the nature of dark energy. "These researchers have opened our eyes to the true nature of our universe. They are very well-deserved recipients," says Knight.

Leading lights

Born in Champaign-Urbana, Illinois, in 1959, Perlmutter graduated from Harvard University in 1981 receiving his PhD from the University of California, Berkeley in 1986 where he worked on robotic methods of searching nearby supernovae. He then moved to the Lawrence Berkeley National Laboratory and the University of California, Berkeley. Perlmutter now heads the SCP based at Lawrence Berkeley National Laboratory.
Schmidt was born in Missoula, Montana, in 1967. He graduated from the University of Arizona in 1989 and received his PhD from Harvard University in 1993 on using type II Supernovae to measure the Hubble Constant. During postdocs at Harvard, Schmidt, together with Nicholas Suntzeff from the Cerro Tololo Inter-American Observatory in Chile, formed the High-Z Supernovae Search Team. In 1993 Schmidt then went to the Harvard-Smithsonian Center for Astrophysics for a year before moving to the Australian National University where he is currently based.
Riess is also a former member of the High-Z Supernovae Search Team where he lead the 1998 study that reported evidence that the universe's expansion rate is now accelerating. He was born in Washington, D.C in 1969 and graduated from The Massachusetts Institute of Technology in 1992. Riess received his PhD from Harvard University in 1996 researching ways to make type Ia supernovae into accurate distance indicators. In 1999 he moved to the Space Telescope Science Institute at Johns Hopkins University.

Kamis, 09 Oktober 2014

Konsepsi Sains Menurut Prof. Bobby Eka Gunara

Artikel berikut penulis kutip serta merupakan sebuah ulasan atas pemikiran dan konsepsi seorang Ilmuwan Muslim Indonesia kontemporer prof. Bobby Eka Gunara tentang sains dan kewajiban bagi kaum muslimin menguasainya, Prof. Bobby adalah seorang Ilmuwan fisika Teoretis di ITB yang aktif melakukan riset frontier di berbagai bidang kajian sains fisika teoretis.

Islam Wajibkan Umatnya Belajar Sains

Posted on 2 Juli 2014 by DioN Erbe

Rabu, 02/07/2014 14:24 WIB

Masruri – detikRamadan

Ilmuwan Muslim (Foto:Ilustrasi)

Jakarta – Persatuan Pelajar Indonesia (PPI) di Italia mengadakan kajian online setiap dua pekan dengan pembicara dari Italia ataupun dari Negara Eropa lain bahkan dari Arab Saudi . Tujuan kajian ini untuk memfasilitasi dahaga ilmu keislaman dan menambah persaudaraan.Kajian kali ini mengambil tema Kewajiban Belajar Sains dalam Islam dengan pembicara Prof. Dr. rer. nat. Bobby Eka Gunara, profesor Fisika Matematika ITB (lulus PhD dari Halle University, German) yang sedang kunjungan riset atas fasilitas (award) the Abdus Salam international centre for theoretical physics (ICTP), Trieste. Sebagai moderator adalah Dr. Abdul Muizz Pradipto, PostDoc di CNR (Consiglio Nazionale delle Ricerche, semacam LIPI) di Chietti. Para peserta tersebar di berbagai kota di Italia seperti tercatat dari Torino, beberapa mahasiswa dari Bolzano, Trento, Pisa, Chietti, Trieste, dan masyarakat Indonesia di Parma dan Brescia. Setelah pemaparan materi, mahasiswa dan masyarakat Indonesia dipandu moderator antusias berdiskusi mengenai materi yang disampaikan oleh pembicara.
Dalam pemaparannya, Prof. Bobby menyampaikan bahwa pada zaman keemasan, umat Islam hampir 7 abad menjadi superpower dala segala bidang termasuk dalam ilmu pengetahuan. Karena dalam Islam ketika mengamalkan dengan benar maka diperlukan pengetahuan, misalnya dalam menentukan waktu salat dan puasa kita dituntut mengetahui peredaran bulan.
Bagaimana pun dalam ibadah yang kita lakukan baik salat ataupun puasa ternyata kita harus mempelajari tanda-tanda alam. Oleh karena itu Islam menganjurkan kita untuk memperhatikan dan mempelajari tanda-tanda alam seperti perputaran matahari, perputaran bulan, orbit matahari, orbit bulan, dan lain-lain. Menurut Prof. Agus Purwanto, penulis “Ayat-ayat Semesta” beliau mengatakan bahwa ada sekitar 800 ayat dalam Al Quran yang berkaitan dengan alam semester.
Ayat-ayat tentang alam semesta yaitu ayat-ayat yang menggambarkan bumi langit beserta isinya. Sedangkan ayat-ayat tentang salat dan puasa hanya beberapa. Alam semesta dalam hal ini kita belajar Sains secara luas, alam semesta dan isinya, termasuk juga manusia baik dari sisi penciptaannya maupun dari sisi sosiologinya. Salah satu mengapa Islam mewajibkan belajar alam semesta karena dalam penciptaannya meliputi penciptaan langit dan bumi, silih bergantian malam dan siang, bahkan penciptaan manusia itu sendiri merupakan tanda-tanda bagi orang yang berfikir. Orang orang yang berpikir, berarti dia harus menggunakan akalnya.
Ada 5 aspek dari manusia yaitu: akal, ruh (QS 17:85), qolbu, nafsu, jasad (QS 38:71, 25:54). Jasad ini terkait dengan penciptaan manusia yang berasal dari tanah atau air mani. Dalam Islam kita harus memenuhi atau memberikan makanan kelima unsur tersebut. Nafsu ada nafsu yang baik (mutmainnah) atau nafsu yang tidak baik (madzmumah). Akal harus kita penuhi dengan ilmu, ruh harus diisi dengan mempelajari ayat-ayat Al Quran yang berkenaan dengan ketenangan jiwa. Jasad seperti kita ketahui harus dipenuhi kebutuhan nutrisi dengan makanan yang sehat dan halal. Ruh juga berkaitan dengan aspek sosial di mana manusia tidak bisa hidup sendiri tetapi membutuhkan kehadiran orang lain baik dalam keluarga (suami-istri) maupun dalam masyarakat.

Shubungan dengan pemenuhan akal dengan ilmu, Allah Swt berfirman dalam QS Ali Imran: 190-191.“Sesungguhnya dalam penciptaan langit dan bumi, dan silih bergantinya malam dan siang terdapat tanda-tanda bagi orang-orang yang berakal (ulil albab), [yaitu] orang-orang yang mengingat Allah sambil berdiri atau duduk atau dalam keadaan 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. Ya Tuhan kami, sesungguhnya barangsiapa yang Engkau masukkan ke dalam neraka, maka sungguh telah Engkau hinakan ia, dan tidak ada bagi orang-orang yang zalim seorang penolongpun.” Dalam ayat 190 yang dimaksud ulil albab tidak sekedar orang yang berakal tetapi adalah orang-orang yang mempunyai daya analisis yang tajam. Agar supaya kita mempunyai hasil analisis yang tajam maka sebagaimana dijelaskan dalam ayat 191 kita dituntut untuk mengingat Allah baik sambil berdiri, duduk atau dalam berbaring. Berdiri, duduk dan berbaring merefleksikan seluruh kegiatan kita sehari-hari. Kegiatan berdiri dapat berupa berdiri sambil berjalan atau berdiri diam. Duduk misalnya ketika kita sedang belajar dengan serius.
Bagi pembicara yang bergulat dalam fisika teori (fisika matematika), duduk yang dilakukan adalah duduk untuk menghitung. Bagi yang bergulat dalam ekperimen aktifitasnya bisa meliputi berdiri atau duduk. Duduk juga berarti pada saat kita sedang makan. Berbaring ketika kita sedang tidur, meskipun pada umumnya tidur tidak untuk berpikir namun bagi para peneliti (mahasiswa PhD) yang sedang menyelesaikan problem-problem dalam penelitiannya (lab), terkadang masalah tesebut terbawa dalam mimpi. Di semua kegiatan dalam hidup kita itu, kita memikirkan tentang penciptaan langit dan bumi, atau apa yang terjadi di alam. Dan hal itu diperintahkan oleh Allah Swt.
Menurut pembicara, umat Islam itu wajib mempelajari mekanika kuantum, teori relativitas baik umum maupun khusus, dan ilmu yang berkaitan dengan penciptaan langit dan bumi. Sehingga segala aspek hidup kita baik berdiri, duduk dan berbaring benar2 akan seperti ini.
Jika kita cukup sampai di sini yaitu dalam kegiatan kita, kita dedikasikan untuk memikirkan penciptaan langit dan bumi dan menganalisis alam semesta, maka akan sama juga dengan yang dilakukan oleh para ilmuwan barat (Eropa, USA) dan jepang pada umumnya yang juga melakukan hal yang sama. Tetapi rata-rata dari mereka adalah atheis atau religionless, karena mungkin traumatis dengan ketuhanan pada gereja. Kita sebagai orang yang beriman tidak cukup sampai di sini, tetapi ketika kita mengingat penciptaan Allah kita akan kembali kepada Allah Swt dan mengingat-Nya. Jangan sampai kita disesatkan dengan apa yang kita pelajari. Dalam ayat 191 yang menjadi ciri keimanan seorang ilmuwan adalah ketika dia berdoa
“Rabbana maa kholaqta hadza baatila”

“Ya Tuhan kami, tiadalah Engkau menciptakan ini dengan sia-sia”

Hal ini menggambarkan perkawinan atau titik temu antara ilmu dan iman pada puncak, dan merupakan kesimpulan atas perenungan terhadap penciptaan alam semestayang Allah Swt ciptakan tidak dengan sia-sia. Ilmuwan yang atheis pada pandangan Allah Swt, segala apa yang dia lakukan baik dalam keadaan berdiri, duduk, berbaring akan sia-sia, tidak ada nilainya di hadapan Allah Swt.Dari sini kita melihat bahwa keimanan adalah hak prerogatif Allah semata, dia tidak memandang seseorang itu pinter atau bodoh. Belajar sains hendaknya akan menambah keimanan kita kepada Allah Swt. Tidak ada penciptaan oleh Allah Swt yang sia-sia, yang ada adalah karena keterbatasan kita dalam memahaminya. Contohnya, dulu orang tidak terlalu care masalah kegunaan galaksi. Tata surya kita terletak di pinggiran galaksi bima sakti (milky way). Mengapa Allah Swt tidak meletakkan tata surya kita sedikit ke tengah agar lebih terang. Pusat galaksi bima sakti lebih terang tetapi di pusat itu diduga ada lubang hitam yang bersifat menyerap materi. Jika misalnya tata surya terletak di tengah galaksi, bisa jadi tata surya itu menjadi tidak akan ada karena terserap lubang hitam. Di tengah galaksi, suhunya juga lebih tinggi sehingga bisa jadi tidak cocok untuk manusia hidup. Oleh karena Allah Swt menempatkan tata surya di pinggir galaksi bima sakti. Lebih jauh lagi mungkin kita bertanya apa sih kegunaan dari galaksi? Kan tata surya sudah cukup. Hal ini tentu saja Allah Swt yang tahu dan hal itu memerlukan penelitian. Secara teoritis (dugaan) bisa jadi hal-hal yang terjadi di pusat galaksi memiliki pengaruh terhadap kehidupan kita. Ilmuwan telah mengembangkan teori yang disebut teori nolocal di mana peristiwa di sana berpengaruh pada kehidupan kita di sini. Hanya saja kita masih punya keterbatasan sabagai manusia baik dari sisi peralatan maupun pengetahuan. Apalagi kalau kita perhatikan luasnya langit, bisa jadi luasnya langit itu keberadaaanya untuk menopang kehidupan di bumi, hanya saja kita tidak mengetahu efeknya. Betapa luasnya ilmu Allah Swt, kita manusia memiliki keterbatasan. Bahkan mengenai ilmu tentang diri kita sendiri, misalnya dokter spesialis jantung atau superspesialis bahkan sub spesialist bisa jadi tidak mengetahui bagaimana kinerja jantung, bagaimana jantung terbentuk. Kita masih belum tahu mengenai diri kita apalagi mengenai sesuatu di luar sana.
Kita harus terus belajar, jangan sampai ilmu yang tidak disertai dengan mengingat Allah Swt menjadikan manusia sombong. Kesombongan ibarat dalam grafis matematika sebagai maksimum global yang tidak ada lagi maksimum selain titik itu, sehingga setelah itu yang ada adalah jatuh karena labil.
Bagaimana Islam menghargai kita untuk belajar. Dalam Al Quran 2:23-24. Allah Swt berfirman:
“Dan jika kamu [tetap] dalam keraguan tentang Al Qur’an yang Kami wahyukan kepada hamba Kami [Muhammad], buatlah [6] satu surat [saja] yang semisal Al Qur’an itu dan ajaklah penolong-penolongmu selain Allah, jika kamu orang-orang yang benar. (23) Maka jika kamu tidak dapat membuat [nya] dan pasti kamu tidak akan dapat membuat [nya], peliharalah dirimu dari neraka yang bahan bakarnya manusia dan batu, yang disediakan bagi orang-orang kafir. (24)”.
Di ayat tersebut Allah Swt yang menciptakan Al Quran dan Allah Swt mengajak kita untuk menguji untuk membuat satu surat saja yang semisal dengan Al Quran dengan mengikut sertakan para pakar. Dalam ayat 24 adalah closingnya di mana, kita tidak mungkin membuat satu surat dan itu terbukti sampai sekarang yang merupakan tanda kemukjizatan Al Quran. Al Quran mengajak kita untuk menguji jika kita tidak ragu terhadap Al Quran dan itu tidak ditemui di kitab yang lain, hanya ditemui kata-kata tersebut di Al Quran.
*)penulis adalah anggota PPI Italia, koordinator Keluarga dan Komunitas Islam Indonesia (KeKita), dan mahasiswa S3 bidang Teknologi Informasi, University of Parma, Italia.

Sumber : http://ramadan.detik.com/read/2014/07/02/141928/2625651/626/3/islam-wajibkan-umatnya-belajar-sains

Senin, 01 September 2014

Kaluza-Klein

Teori Kaluza–Klein

From Wikipedia, the free encyclopedia

Beyond the Standard Model
Detektor data partikel CMS Simulated Large Hadron Collider menangkap gambar sebuah Higgs boson yang dihasilkan oleh tumbukan proton yang meluruh menjadi jet hadron dan elektron
Standard Model
Fakta[tunjukkan]
Teori[sembunyikan] Technicolor Kaluza–Klein theory Teori Penyatuan Akbar Teori segala sesuatu Teori String Teori Superfluida Vakum
Supersymmetry [show]
Quantum gravity [show]
Eksperimen[show]

Dalam Fisika, teori Kaluza-Klein (teori KK) adalah sebuah model yang berusaha mencari solusi bagi penyatuan dua gaya fundamental yaitu gaya gravitasi dan gaya elektromagnetisme. Teori ini pertama kali diumumkan pada tahun 1921 yang diusulkan oleh matematikawan Theodor Kaluza yang memperluas teori relativitas umum hingga dimensi-5 ruang-waktu. Persamaan yang dihasilkan dapat diuraikan lebih lanjut menjadi seperangkat persamaan, satu kelompok ekuivalen dengan persamaan medan Einstein, himpunan persamaan lainnya ekuivalen dengan persamaan Maxwell dan bagian terakhir mengandung suatu medan skalar ekstra yang disebut sebagai "radion".

Tinjauan

Ruang M × C dikompaktifikasi atas himpunan kompak C, dan sesudah dekomposisi Kaluza–Klein diperoleh sebuah teori medan efektif effective field theory atas M.

Penguraian ruangwaktu 5 dimensional five-dimensional spacetime menjadi persamaan Einstein Einstein equations dan persamaan Maxwell empat dimensi pertama kali ditemukan oleh Gunnar Nordström di 1914, dalam konteks teori beliau tentang gravitasi, namun selanjutnya teori tersebut dilupakan. Kaluza menerbitkan penurunannya pada 1921 sebagai sebuah upaya untuk menyatukan elektromagnetisme dengan relativitas Einstein.

Pada tahun 1926, Oskar Klein mengusulkan bahwa dimensi ruang spasial yang ke empat sejatinya mengkeriting dalam lingkaran yang jejarinya sangat kecil, sehingga sebuah partikel yang bergerak dalam jarak yang pendek sepanjang sumbu itu akan kembali di titik mana ia berangkat. Jarak tempuh partikel hingga kembali ke tempat semula ini dikatakan sebagai ukuran dari dimensi. Dimensi ekstra ini sebuah himpunan kompak, dan fenomena ruang-waktu dengan dimensi kompak ini disebut sebagai kompaktifikasi.

Dalam geometri modern, dimensi ekstra ke 5 ini dapat difahami sebagai sebuah grup lingkaran U(1)( circle group U(1)), sebagaimana elektromagnetisme (electromagnetism) dapat secara esensial diformulasikan sebagai sebuah teori gauge (gauge theory) pada sebuah fiberbundel ( fiber bundle, circle bundle, )dengan gauge group U(1). Dalam teori Kaluza–Klein grup ini menyarankan bahwa simetri gauge adalah simetri dimensi kompak sirkuler. Sekali interpretasi geometris ini difahami, relatif langsung untuk menggantikan U(1) oleh sebuah grup Lie umum (Lie group). Perumuman demikian sering juga disebut sebagai teori Yang-Mills (Yang–Mills theories). Jika sebuah pembedaan ditarik, maka teori Yang-Mills berlaku di ruang-waktu datar, sedangkan Kaluza-Klein berlaku di kasus lebih umum ruang-waktu lengkung. Ruang basis teori Kaluza-Klein tidak harus ruang-waktu 4 dimensional, dapat juga sebarang manifold (pseudo-)Riemannian, atau bahkan manifold supersimetrik atau orbifold atau bahkan ruang nonkomutatif.

Sebagai sebuah pendekatan bagi teori yang menyatukan gaya-gaya fundamental alam, adalah langsung untuk menerapkan teori Kaluza-Klein dalam usaha menyatukan gravitasi dengan gaya kuat dan elektroweak dengan menggunakan grup simetri model standar ( Standard Model), SU(3) × SU(2) × U(1). Meskipun demikian, sebuah usaha untuk mengkonversi konstruksi geometrik menarik ini menjadi sebuah model yang bonafid bagi realitas bertungkus lumus dengan sejumlah persoalan, termasuk kenyataan bahwa fermions harus diperkenalkan dalam suatu cara yang dibuat-buat (dalam sebuah model nonsupersimetrik). Meskipun demikian, KK, tetaplah suatu batu uji penting dalam fisika teoretik dan sering ditanamkan dalam teori yang lebih sempurna. Teori ini dikaji secara tersendiri sebagai sebuah objek geometri yang menarik dalam teori K (K-theory).

Bahkan dengan absennya kerangka fisika teoretis yang memuaskan, ide untuk mengeksplorasi dimensi ekstra yang terkompaktifikasi tetap menarik perhatian di kalangan komunitas astrofisikawan dan fisikawan eksperimental. Berbagai ramalan, dengan konsekuensi eksperimental real dapat dibuat (dalam kasus large extra dimensions/warped models). Sebagai contoh, dengan prinsip paling sederhana, dapat diharapkan diperoleh gelombang berdiri (standing waves) dalam dimensi ekstra terkompaktifikasi. Jika sebuah dimensi ekstra spasial berjari-jari R, massa invarian (mass) gelombang berdiri tersebut adalah M_n = nh/Rc dengan n suatu bilangan bulat (integer), h konstanta Planck (Planck's constant) dan c laju kecepatan cahaya (speed of light). Sehimpunan massa yang mungkin ini sering disebut sebagai Kaluza–Klein tower. Begitu juga dalam Similarly, Teori medan kuantum termal kompaktifikasi dimensi waktu euklidean mengarah kepada frekuensi Matsubara sehingga menghasilkan spektrum energi termal terdiskritkan.

Contoh pencaharian eksperimental termasuk usaha yang dilakukan kolaborasi CDF , yang telah menganalisis kembali data penumbuk partikel untuk mencari jejak efek yang terkait dengan dimensi ekstra luas/warped models.

Brandenberger dan Vafa telah berspekulasi bahwa pada masa alam semesta dini, inflasi kosmik menyebabkan tiga dimensi ruang mengembang ke ukuran kosmologis di mana dimensi ruang sisa lainnya tetap mikroskopik.

Space-time-matter theory

One particular variant of Kaluza–Klein theory is space-time-matter theory or induced matter theory, chiefly promulgated by Paul Wesson and other members of the so-called Space-Time-Matter Consortium.^[1] In this version of the theory, it is noted that solutions to the equation

R_{AB}=0\,

with R_AB the five-dimensional Ricci curvature, may be re-expressed so that in four dimensions, these solutions satisfy Einstein's equations

G_{\mu\nu} = 8\pi T_{\mu\nu}\,

with the precise form of the T_μν following from the Ricci-flat condition on the five-dimensional space. Since the energy–momentum tensor T_μν is normally understood to be due to concentrations of matter in four-dimensional space, the above result is interpreted as saying that four-dimensional matter is induced from geometry in five-dimensional space.
In particular, the soliton solutions of R_AB = 0 can be shown to contain the Friedmann–Lemaitre–Robertson–Walker metric in both radiation-dominated (early universe) and matter-dominated (later universe) forms. The general equations can be shown to be sufficiently consistent with classical tests of general relativity to be acceptable on physical principles, while still leaving considerable freedom to also provide interesting cosmological models.

Geometric interpretation

The Kaluza–Klein theory is striking because it has a particularly elegant presentation in terms of geometry. In a certain sense, it looks just like ordinary gravity in free space, except that it is phrased in five dimensions instead of four.

The Einstein equations

The equations governing ordinary gravity in free space can be obtained from an action, by applying the variational principle to a certain action. Let M be a (pseudo-)Riemannian manifold, which may be taken as the spacetime of general relativity. If g is the metric on this manifold, one defines the action S(g) as

S(g)=\int_M R(g) \mathrm{vol}(g)\,

where R(g) is the scalar curvature and vol(g) is the volume element. By applying the variational principle to the action

\frac{\delta S(g)}{\delta g} = 0

one obtains precisely the Einstein equations for free space:

R_{ij} - \frac{1}{2}g_{ij}R = 0

Here, R_ij is the Ricci tensor.

The Maxwell equations

By contrast, the Maxwell equations describing electromagnetism can be understood to be the Hodge equations of a principal U(1)-bundle or circle bundle π: P → M with fiber U(1). That is, the electromagnetic field F is a harmonic 2-form in the space Ω²(M) of differentiable 2-forms on the manifold M. In the absence of charges and currents, the free-field Maxwell equations are

dF = 0 and d*F = 0.

where * is the Hodge star.

The Kaluza–Klein geometry

To build the Kaluza–Klein theory, one picks an invariant metric on the circle S¹ that is the fiber of the U(1)-bundle of electromagnetism. In this discussion, an invariant metric is simply one that is invariant under rotations of the circle. Suppose this metric gives the circle a total length of Λ. One then considers metrics

\widehat{g}

on the bundle P that are consistent with both the fiber metric, and the metric on the underlying manifold M. The consistency conditions are:

The projection of $\widehat{g}$ to the vertical subspace $\mbox{Vert}_pP \subset T_pP$ needs to agree with metric on the fiber over a point in the manifold M.

The projection of $\widehat{g}$ to the horizontal subspace $\mbox{Hor}_pP \subset T_pP$ of the tangent space at point p ∈ P must be isomorphic to the metric g on M at π(p).

The Kaluza–Klein action for such a metric is given by

S(\widehat{g})=\int_P R(\widehat{g}) \;\mbox{vol}(\widehat{g})\,

The scalar curvature, written in components, then expands to

R(\widehat{g}) = \pi^*\left( R(g) - \frac{\Lambda^2}{2} \vert F \vert^2\right)

where π* is the pullback of the fiber bundle projection π: P → M. The connection A on the fiber bundle is related to the electromagnetic field strength as

\pi^*F = \mathrm{d}A

That there always exists such a connection, even for fiber bundles of arbitrarily complex topology, is a result from homology and specifically, K-theory. Applying Fubini's theorem and integrating on the fiber, one gets

S(\widehat{g})=\Lambda \int_M \left( R(g) - \frac{1}{\Lambda^2} \vert F \vert^2 \right) \;\mbox{vol}(g)

Varying the action with respect to the component A, one regains the Maxwell equations. Applying the variational principle to the base metric g, one gets the Einstein equations

R_{ij} - \frac{1}{2}g_{ij}R = \frac{1}{\Lambda^2} T_{ij}

with the stress–energy tensor being given by

T^{ij} = F^{ik}F^{jl}g_{kl} - \frac{1}{4}g^{ij} \vert F \vert^2,

sometimes called the Maxwell stress tensor.
The original theory identifies Λ with the fiber metric g₅₅, and allows Λ to vary from fiber to fiber. In this case, the coupling between gravity and the electromagnetic field is not constant, but has its own dynamical field, the radion.

Generalizations

In the above, the size of the loop Λ acts as a coupling constant between the gravitational field and the electromagnetic field. If the base manifold is four-dimensional, the Kaluza–Klein manifold P is five-dimensional. The fifth dimension is a compact space, and is called the compact dimension. The technique of introducing compact dimensions to obtain a higher-dimensional manifold is referred to as compactification. Compactification does not produce group actions on chiral fermions except in very specific cases: the dimension of the total space must be 2 mod 8 and the G-index of the Dirac operator of the compact space must be nonzero.^[2]
The above development generalizes in a more-or-less straightforward fashion to general principal G-bundles for some arbitrary Lie group G taking the place of U(1). In such a case, the theory is often referred to as a Yang–Mills theory, and is sometimes taken to be synonymous. If the underlying manifold is supersymmetric, the resulting theory is a super-symmetric Yang–Mills theory.

Empirical tests

Up to now, no experimental or observational signs of extra dimensions have been officially reported. Many theoretical search techniques for detecting Kaluza–Klein resonances have been proposed using the mass couplings of such resonances with the top quark, however until the Large Hadron Collider (LHC) reaches full operational power observation of such resonances are unlikely. An analysis of results from the LHC in December 2010 severely constrains theories with large extra dimensions.^[3]
The observation of a Higgs-like boson at the LHC puts a brand new empirical test in the search for Kaluza–Klein resonances and supersymmetric particles. The loop Feynman diagrams that exist in the Higgs Interactions allow any particle with electric charge and mass to run in such a loop. Standard Model particles besides the top quark and W boson do not make big contributions to the cross-section observed in the H → γγ decay, but if there are new particles beyond the Standard Model, they could potentially change the ratio of the predicted Standard Model H → γγ cross-section to the experimentally observed cross-section. Hence a measurement of any dramatic change to the H → γγ cross section predicted by the Standard Model is crucial in probing the physics beyond it.

Notes

5Dstm.org
L. Castellani et al., Supergravity and superstrings, Vol 2, chapter V.11
CMS Collaboration, "Search for Microscopic Black Hole Signatures at the Large Hadron Collider", http://arxiv.org/abs/1012.3375

References

Nordström, Gunnar (1914). "Über die Möglichkeit, das elektromagnetische Feld und das Gravitationsfeld zu vereinigen". Physikalische Zeitschrift 15: 504–506. OCLC 1762351.
Kaluza, Theodor (1921). "Zum Unitätsproblem in der Physik". Sitzungsber. Preuss. Akad. Wiss. Berlin. (Math. Phys.): 966–972. http://archive.org/details/sitzungsberichte1921preussi
Klein, Oskar (1926). "Quantentheorie und fünfdimensionale Relativitätstheorie". Zeitschrift für Physik A 37 (12): 895–906. Bibcode:1926ZPhy...37..895K. doi:10.1007/BF01397481.
Witten, Edward (1981). "Search for a realistic Kaluza–Klein theory". Nuclear Physics B 186 (3): 412–428. Bibcode:1981NuPhB.186..412W. doi:10.1016/0550-3213(81)90021-3.
Appelquist, Thomas; Chodos, Alan; Freund, Peter G. O. (1987). Modern Kaluza–Klein Theories. Menlo Park, Cal.: Addison–Wesley. ISBN 0-201-09829-6. (Includes reprints of the above articles as well as those of other important papers relating to Kaluza–Klein theory.)
Brandenberger, Robert; Vafa, Cumrun (1989). "Superstrings in the early universe". Nuclear Physics B 316 (2): 391–410. Bibcode:1989NuPhB.316..391B. doi:10.1016/0550-3213(89)90037-0.
Duff, M. J. (1994). "Kaluza–Klein Theory in Perspective". In Lindström, Ulf (ed.). Proceedings of the Symposium ‘The Oskar Klein Centenary’. Singapore: World Scientific. pp. 22–35. ISBN 981-02-2332-3.
Overduin, J. M.; Wesson, P. S. (1997). "Kaluza–Klein Gravity". Physics Reports 283 (5): 303–378. arXiv:gr-qc/9805018. Bibcode:1997PhR...283..303O. doi:10.1016/S0370-1573(96)00046-4.
Wesson, Paul S. (1999). Space-Time-Matter, Modern Kaluza-Klein Theory. Singapore: World Scientific. ISBN 981-02-3588-7.
Wesson, Paul S. (2006). Five-Dimensional Physics: Classical and Quantum Consequences of Kaluza-Klein Cosmology. Singapore: World Scientific. ISBN 981-256-661-9.

Minggu, 17 Agustus 2014

Tips Belajar Fisika

Bagaimana Belajar Fisika dan Matematika

John Baez

July 29, 2014

Pengantar

"Bagaimana belajar fisika dan matematika" - Judul artikel ini cukup menohok. Tentu saja setiap orang belajar sesuai dengan caranya sendiri-sendiri. Saya tidak tahu bagaimana seharusnya anda belajar matematika dan fisika. Namun saya anggap anda ke sini dalam rangka meminta nasehat, maka inilah sedikit nasehat dari saya soal bagaimana belajar matematika dan fisika.

Saran saya ini ditujukan buat mereka yang tertarik dengan kajian fisika teoretis fundamental dan matematika terpakai di dalamnya. (yang di maksud dengan Fisika "fundamental" di sini adalah pencaharian hukum dasar tentang materi dan energi di alam semesta). Jika anda ingin melakukan eksperimen alih-alih teori, atau jika fisika bidang lain semisal fisika material mampat dan astrofisika, atau matematika yang tidak ada kaitannya dengan fisika, maka nasehat saya di sini tidak akan terlalu bermanfaat. Meskipun demikian ada saran penting juga di sini yang selayaknya anda perhatikan, namun setelahnya anda harus mencari pendapat dan nasehat dari yang lain menyangkut bidang anda.

Belajar matematika dan fisika itu tidak akan pernah cukup bahkan jika sepanjang hayat. Asyiknya, belajar fisika dan matematika penuh dengan hal-hal yang menarik....tentu jika anda orang yang mempunyai cukup kesabaran. Banyak orang membaca buku populer tentang mekanika kuantum, lubang hitam, dan teorema Godel, dan sangat ingin segera mempelajarinya. Tanpa latar belakang yang memadai, mereka segera frustasi mempelajarinya---atau lebih buruk lagi menjadi patah semangat.

Bahkan lebih bahaya lagi jika anda langsung ingin menerjunkan diri ke teori medan terpadu, superstring, atau M-teori. Tak ada juga orang yang bisa memastikan bahwa teori ini benar! dan sangat sulit membuktikan klaim-klaim teori tersebut hingga anda tahu apa sebenarnya yang diketahui orang lain.

Jadi, khususnya ketika anda hendak belajar fisika, saya sarankan anda mulai dengan hal-hal yang lebih tidak wah yang kita tahu itu benar--sekurangnya sebagai sebuah pendekatan yang berguna, dan kemudian dengan latar belakang yang solid, pelan-pelan pengetahuan anda akan sampai ke frontier. Bahkan jika pada akhirnya anda menyerah di suatu titik anda setidaknya telah belajar beberapa hal.

Web ini tidak mempunyai banyak link. Website ini (tempat penulis artikel menuangkan tulisannya) tidak menampilkan materi lanjut semacam matematika dan fisika lanjut--setidaknya hingga saat ini. Untuk mempelajari topik-topik ini anda mesti membaca banyak buku. Beberapa akan saya daftarkan di sini dan sebagian lagi dapat anda peroleh secara on line.

Namun anda tidak dapat belajar fisika hanya dari baca buku-buku belaka! anda harus melakukan banyak perhitungan sendiri--atau melakukan eksperimen, tentu jika anda ingin melakukan fisika eksperimen. Buku Daras biasanya penuh dengan soal-soal, dan alangkah baiknya anda mengerjakan ini semua. Penting juga bagi anda untuk melakukan riset pribadi dan mengerjakannya sungguh-sungguh. Jika anda tidak mampu melakukan ini semua, tidak ada jalan melainkan harus mengambil kuliah di bidang fisika dan matematika. Keuntungan dari perkuliahan adalah anda dapat mendengar langsung perkuliahan, menemui mahasiswa dan profesor, dan melakukan hal-hal yang biasanya tidak akan anda lakukan--Misalkan akan lebih bekerja keras lagi dalam belajarnya.

Sangatlah penting bagi anda untuk bertanya pada yang lain serta menjelaskannya sendiri--dua cara ini adalah besar sekali sumbangannya bagi pemahaman anda. Tak ada yang lebih merangsang belajar selain duduk bersama dengan teman di sebuah cafe, dengan buku catatan yang terbuka, serta bekerja bersama-sama secara teratur. Dua pikiran tentu lebih baik dari pada hanya satu pikiran.

Namun jika anda tidak menemukan seorang teman di kota anda, ada cara lain untuk berdiskusi dengan orang lain yaitu secara on line. Dalam semua situasi, tentu penting bagi anda untuk memahami kebiasaan di situs tersebut sebelum terjun dalam diskusi. Sebagai contoh, langsung mencoba untuk memulai diskusi secara sporadis di sebuah website tanya jawab tidaklah bagus. Di sini ada beberapa pilihan web:

Question-and-Answer Websites - If you've got physics questions, try Physics Stack Exchange. Untuk pertanyaan-pertanyaan level riset fisika teoretik, silahkan di Theoretical Physics Stack Exchange. Untuk pertanyaan matematika Math Stack Exchange, atau pertanyaan matematika level riset, Math Overflow.
Forum Diskusi - Untuk mendiskusikan fisika, silahkan coba sci.physics.research. Untuk Matematika silahkan di sci.math atau, untuk pertanyaan-pertanyaan level riset, sci.math.research. Saya juga merokemndasikan Physics Forums untuk diskusi matematika maupun Fisika. Setidaknya beberapa dari question-and-answer websites yang di daftar di atas juga mempunyai forum-forum dan komunitas tempat anda mendiskusikan hal-hal penting.

Juga ada banyak Blog menarik, serta banyak buku matematika on line gratis free math books online.

Akhirnya penting sekali untuk mengakui ketika anda berbuat kesalahan. Semua kita melakukan begitu banyak kesalahan ketika kita mempelajari sesuatu. Jika anda tidak bisa menerima ini, lambat laun anda akan menjadi seorang yang dungu, yang menelorkan teori-teori bodoh, meskipun semua orang bisa melihat itu adalah kesalahan. Suatu tragedi jika anda sendiri tidak menyadarinya. Bahkan seorang profesor terkenal sekalipun dapat menjadi dungu ketika mereka berhenti mengakui kesalahan-kesalahannya.

Untuk menghindari hal ini sangatlah baik jika anda menjelaskan sejelas mungkin apakah anda memang memahami sesuatu atau pengetahuan anda hanya perkiraan belaka, tidaklah terlalu buruk jika salah mengira bahwa anda sebenarnya kurang yakin dari awal. Namun jika anda begitu percaya diri dan terbukti belakangan anda keliru, maka anda akan terlihat tolol.

Pungkas kata: stay humble, keep studying, and you'll keep making progress. Don't give up - the fun is in the process.

Bagaimana caranya Belajar Fisika

Ada 5 topik penting yang seyogyanya seorang fisikawan menguasainya:

Mekanika Klasik

Mekanika Statistik

Elektromagnetism

Relativitas Khusus

dan

Mekanika Kuantum

dalam urutan yang tak tentu. Sekali ilmu ini dikuasai, anda punya latar belakang untuk mempelajari dua teori terbaik:

Relativitas Umum (mengarahkan lebih lanjut ke kosmologi model Big Bang)

dan

Teori Medan Kuantum (mengarahkan lebih lanjut ke Model Standar fisika partikel)

Dan sekali anda memahami ini, anda siap untuk mengkaji usaha dewasa ini dalam menyatukan teori medan kuantum dan relativitas umum. Tampak ini usaha yang keras... memang demikian! Namun penuh juga dengan hal-hal yang menarik, terkadang juga melelahkan. Oleh karena itu bagus juga jika anda membaca buku sejarah fisika. . They're a nice change of pace, they're inspiring, and they can show you the "big picture" that sometimes gets hidden behind the thicket of equations. These are some of my favorites histories:

Emilio Segre, From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries, W. H. Freeman, New York, 1984.
Emilio Segre, From X-Rays to Quarks: Modern Physicists and Their Discoveries, W. H. Freeman, San Francisco, 1980.
Robert P. Crease and Charles C. Mann, The Second Creation: Makers of the Revolution in Twentieth-Century Physics, Rutgers University Press, New Brunswick, NJ, 1996.
Abraham Pais, Inward Bound: of Matter and Forces in the Physical World, Clarendon Press, New York, 1986. (More technical.)

Next, here are some good books to learn "the real stuff". These aren't "easy" books, but they're my favorites.
First, some very good general textbooks:

M. S. Longair, Theoretical Concepts in Physics, Cambridge U. Press, Cambrdige, 1986.
Richard Feynman, Robert B. Leighton and Matthew Sands, The Feynman Lectures on Physics, 3 volumes, Addison-Wesley, 1989. All three volumes are now free online.
Ian D. Lawrie, A Unified Grand Tour of Theoretical Physics, Adam Hilger, Bristol, 1990.

Then, books that specialize on the 5 cornerstone topics I listed above: Classical mechanics:

Herbert Goldstein, Charles Poole, and John Safko, Classical Mechanics, Addison Wesley, San Francisco, 2002.

Statistical mechanics:

F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw Hill, New York, 1965.

Electromagnetism:

John David Jackson, Classical Electrodynamics, Wiley, New York, 1975.

Special relativity:

Edwin F. Taylor, John A. Wheeler, Spacetime Physics: Introduction to Special Relativity, W. H. Freeman Press, 1992.

Quantum mechanics:

Anthony Sudbery, Quantum Mechanics and the Particles of Nature: an Outline for Mathematicians, Cambridge University Press, Cambridge, 1986. (Not just for mathematicians!)

Claude Cohen-Tannoudji, Bernard Diu und Franck Laloë, Quantum Mechanics (2 volumes), Wiley-Interscience, 1992. (I haven't actually read this, but it's widely respected for its systematic approach.)

These should be supplemented by the general textbooks above, which cover all these topics. In particular, Feynman's Lectures on Physics are incredibly valuable.
After you know this stuff well, you're ready for general relativity (which gets applied to cosmology) and quantum field theory (which gets applied to particle physics). General relativity - to get intuition for the subject before tackling the details:

Kip S. Thorne, Black Holes and Time Warps: Einstein's Outrageous Legacy, W. W. Norton, New York, 1994.

Robert M. Wald, Space, Time, and Gravity: the Theory of the Big Bang and Black Holes, University of Chicago Press, Chicago, 1977.

Robert Geroch, General Relativity from A to B, University of Chicago Press, Chicago, 1978.

General relativity - for when you get serious:

R. A. D'Inverno, Introducing Einstein's Relativity, Oxford University Press, Oxford, 1992.

J. B. Hartle, Gravity: An Introduction to Einstein's General Relativity, Addison-Wesley, New York, 2002.

B. F. Schutz, A First Course in General Relativity, Cambridge University Press, Cambridge, 1985.

General relativity - for when you get really serious:

Charles W. Misner, Kip S. Thorne and John Archibald Wheeler, Gravitation, W. H. Freeman Press, San Francisco, 1973.

Robert M. Wald, General Relativity, University of Chicago Press, Chicago, 1984.

Cosmology:

Edward R. Harrison, Cosmology, the Science of the Universe, Cambridge University Press, Cambridge, 1981.

M. Berry, Cosmology and Gravitation, Adam Hilger, Bristol, 1986.

John A. Peacock, Cosmological Physics, Cambridge University Press, Cambridge, 1999. (More technical.)

Quantum field theory - to get intuition for the subject before tackling the details:

Richard Feynman, QED: the Strange Theory of Light and Matter, Princeton University Press, Princeton, 1985.

Quantum field theory - for when you get serious:

Michael E. Peskin and Daniel V. Schroeder, An Introduction to Quantum Field Theory, Addison-Wesley, New York, 1995. (The best modern textbook, in my opinion.)

A. Zee, Quantum Field Theory in a Nutshell, Princeton University Press, Princeton, 2003. (Packed with wisdom told in a charmingly informal manner; not the best way to learn how to calculate stuff.)

Warren Siegel, Fields, available for free at the arXiv.
Mark Srednicki, Quantum Field Theory, available free on his website. (It's good to snag free textbooks while you can, if they're not on the arXiv!)
Sidney Coleman, Physics 253: Quantum Field Theory, 1975-1976. (Not a book - it's a class! You can download free videos of this course at Harvard, taught by a brash and witty young genius.)

Quantum field theory - two classic older texts that cover a lot of material not found in Peskin and Schroeder's streamlined modern presentation:

James D. Bjorken and Sidney D. Drell, Relativistic Quantum Mechanics, New York, McGraw-Hill, 1964.
James D. Bjorken and Sidney D. Drell, Relativistic Quantum Fields, New York, McGraw-Hill, 1965.

Quantum field theory - for when you get really serious:

Sidney Coleman, Aspects of Symmetry, Cambridge U. Press, 1989. (A joy to read.)
Rudolf Haag, Local Quantum Physics: Fields, Particles, Algebras, Springer-Verlag, 1992.

Quantum field theory - so even mathematicians can understand it:

Robin Ticciati, Quantum Field Theory for Mathematicians, Cambridge University Press, Cambridge, 1999.
Richard Borcherds and Alex Barnard, Lectures On Quantum Field Theory.

Particle physics:

Kerson Huang, Quarks, Leptons & Gauge Fields, World Scientific, Singapore, 1982.
L. B. Okun, Leptons and Quarks, translated from Russian by V. I. Kisin, North-Holland, 1982. (Huang's book is better on mathematical aspects of gauge theory and topology; Okun's book is better on what we actually observe particles to do.)
T. D. Lee, Particle Physics and Introduction to Field Theory, Harwood, 1981.
K. Grotz and H. V. Klapdor, The Weak Interaction in Nuclear, Particle, and Astrophysics, Hilger, Bristol, 1990.

While studying general relativity and quantum field theory, you should take a break now and then and dip into this book: it's a wonderful guided tour of the world of math and physics:

Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, Knopf, New York, 2005.

And then, some books on more advanced topics... The interpretation of quantum mechanics:

Roland Omnes, Interpretation of Quantum Mechanics, Princeton U. Press, Princeton, 1994.

This is a reasonable treatment of an important but incredibly controversial topic. Warning: there's no way to understand the interpretation of quantum mechanics without also being able to solve quantum mechanics problems - to understand the theory, you need to be able to use it (and vice versa). If you don't heed this advice, you'll fall prey to all sorts of nonsense that's floating around out there. The mathematical foundations of quantum physics:

Josef M. Jauch, Foundations of Quantum Mechanics, Addison-Wesley, 1968. (Very thoughtful and literate. Get a taste of quantum logic.)
George Mackey, The Mathematical Foundations of Quantum Mechanics, Dover, New York, 1963. (Especially good for mathematicians who only know a little physics.)

Loop quantum gravity and spin foams:

Carlo Rovelli, Quantum Gravity, Cambridge University Press, Cambridge, 2004.

String theory:

Barton Zwiebach, A First Course in String Theory, Cambridge U. Press, Cambridge, 2004. (The best easy introduction.)
Michael B. Green, John H. Schwarz and Edward Witten, Superstring Theory (2 volumes), Cambridge U. Press, Cambridge, 1987. (The old testament.)
Joseph Polchinski, String Theory (2 volumes), Cambridge U. Press, Cambridge, 1998. (The new testament - he's got branes.)

How to Learn Math

Math is a much more diverse subject than physics, in a way: there are lots of branches you can learn without needing to know other branches first... though you only deeply understand a subject after you see how it relates to all the others! After basic schooling, the customary track through math starts with a bit of:

Finite mathematics (combinatorics)

Calculus

Multivariable calculus

Linear algebra

Ordinary differential equations

Partial differential equations

Complex analysis

Real analysis

Topology

Set theory and logic

and

Abstract algebra

not necessarily in exactly this order. (For example, you need to know a little set theory and logic to really understand what a proof is.) Then, the study of math branches out into a dizzying variety of more advanced topics! It's hard to get the "big picture" of mathematics until you've gone fairly far into it; indeed, the more I learn, the more I laugh at my previous pathetically naive ideas of what math is "all about". But if you want a glimpse, try these books:

F. William Lawvere and Stephen H. Schanuel, Conceptual Mathematics: a First Introduction to Categories, Cambridge University Press, 1997. (A great place to start.)
Saunders Mac Lane, Mathematics, Form and Function, Springer-Verlag, New York, 1986. (More advanced.)
Jean Dieudonne, A Panorama of Pure Mathematics, as seen by N. Bourbaki, translated by I.G. Macdonald, Academic Press, 1982. (Very advanced - best if you know a lot of math already. Beware: many people disagree with Bourbaki's outlook.)

I haven't decided on my favorite books on all the basic math topics, but here are a few. In this list I'm trying to pick the clearest books I know, not the deepest ones - you'll want to dig deeper later: Finite mathematics (combinatorics):

Ronald L. Graham, Donald Knuth, and Oren Patshnik, Concrete Mathematics, Addison-Wesley, Reading, Massachusetts, 1994. (Too advanced for a first course in finite mathematics, but this book is fun - quirky, full of jokes, it'll teach you tricks for counting stuff that will blow your friends minds!)

Calculus:

Silvanus P. Thompson, Calculus Made Easy, St. Martin's Press, 1914. Also available free online at http://www.gutenberg.org/ebooks/33283. (Most college calculus texts weigh a ton; this one does not - it just gets to the point. This is how I learned calculus: my uncle gave me a copy.)
Gilbert Strang, Calculus, Wellesley-Cambridge Press, Cambridge, 1991. Also available free online at http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm. (Another classic, with lots of applications to real-world problems.)

Multivariable calculus:

James Nearing, Mathematical Tools for Physics, available at http://www.physics.miami.edu/~nearing/mathmethods/. See especially the sections on multvariable calculus, vector calculus 1, and vector calculus 2. (Very nice explanations!)
George Cain and James Herod, Multivariable Calculus. Available free online at http://www.math.gatech.edu/~cain/notes/calculus.html

Linear algebra:
I don't have any favorite linear algebra books, so I'll just list some free ones:

Keith Matthews, Elementary Linear Algebra, available free online at http://www.numbertheory.org/book/.
Jim Hefferon, Linear Algebra, available free online at http://joshua.smcvt.edu/linalg.html/.
Robert A. Beezer, A First Course in Linear Algebra, available free online at http://linear.ups.edu/.

Ordinary differential equations - some free online books:

Bob Terrell, Notes on Differential Equations, available free online at http://www.math.cornell.edu/~bterrell/dn.pdf. (Does both ordinary and partial differential equations.)
James Nearing, Mathematical Tools for Physics, available at http://www.physics.miami.edu/~nearing/mathmethods/. See especially the sections on ordinary differential equations and Fourier series (which are good for solving such equations).

Partial differential equations - some free online books:

Bob Terrell, Notes on Differential Equations, available free online at http://www.math.cornell.edu/~bterrell/dn.pdf. (Does both ordinary and partial differential equations.)
James Nearing, Mathematical Tools for Physics, available at http://www.physics.miami.edu/~nearing/mathmethods/. See especially the section on partial differential equations.

Complex analysis:

George Cain, Complex Analysis, available free online at http://www.math.gatech.edu/~cain/winter99/complex.html. (How can you not like free online?)
James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, McGraw-Hill, New York, 2003. (A practical introduction to complex analysis.)
Serge Lang, Complex Analysis, Springer, Berlin, 1999. (More advanced.)

Real analysis:

Richard R. Goldberg, Methods of Real Analysis, Wiley, New York, 1976. (A gentle introduction.)

Halsey L. Royden, Real Analysis, Prentice Hall, New York, 1988. (A bit more deep; here you get Lebesgue integration and measure spaces.)

Topology:

James R. Munkres, Topology, James R. Munkres, Prentice Hall, New York, 1999.

Lynn Arthur Steen and J. Arthur Seebach, Jr., Counterexamples in Topology, Dover, New York, 1995. (It's fun to see how crazy topological spaces can get: also, counterexamples help you understand definitions and theorems. But, don't get fooled into thinking this stuff is the point of topology!)

Set theory and logic:

Herbert B. Enderton, Elements of Set Theory, Academic Press, New York, 1977.

Herbert B. Enderton, A Mathematical Introduction to Logic, Academic Press, New York, 2000.

F. William Lawvere and Robert Rosebrugh, Sets for Mathematics, Cambridge U. Press, Cambridge, 2002. (An unorthodox choice, since this book takes an approach based on category theory instead of the old-fashioned Zermelo-Fraenkel axioms. But this is the wave of the future, so you might as well hop on now!)

Abstract algebra:
I didn't like abstract algebra as an undergrad. Now I love it! Textbooks that seem pleasant now seemed dry as dust back then. So, I'm not confident that I could recommend an all-around textbook on algebra that my earlier self would have enjoyed. But, I would have liked these:

Hermann Weyl, Symmetry, Princeton University Press, Princeton, New Jersey, 1983. (Before diving into group theory, find out why it's fun.)

Ian Stewart, Galois Theory, 3rd edition, Chapman and Hall, New York, 2004. (A fun-filled introduction to a wonderful application of group theory that's often explained very badly.)

Next, here are some books on topics related to mathematical physics. Out of laziness, I'll assume you're already somewhat comfortable with the topics listed above - yes, I know that requires about 4 years of full-time work! - and I'll pick up from there. Here's a good place to start:

Paul Bamberg and Shlomo Sternberg, A Course of Mathematics for Students of Physics, Cambridge University, Cambridge, 1982. (A good basic introduction to modern math, actually.)

It's also good to get ahold of these books and keep referring to them as needed:

Robert Geroch, Mathematical Physics, University of Chicago Press, Chicago, 1985.

Yvonne Choquet-Bruhat, Cecile DeWitt-Morette, and Margaret Dillard-Bleick, Analysis, Manifolds, and Physics (2 volumes), North-Holland, 1982 and 1989.

Here's a free online reference book that's 787 pages long:

Jean Claude Dutailly, Mathematics for Theoretical Physics, 2012.

Here are my favorite books on various special topics:
Group theory in physics:

Shlomo Sternberg, Group Theory and Physics, Cambridge University Press, 1994.
Robert Hermann, Lie Groups for Physicists, Benjamin-Cummings, 1966.
George Mackey, Unitary Group Representations in Physics, Probability, and Number Theory, Addison-Wesley, Redwood City, California, 1989.

Lie groups, Lie algebras and their representations - in rough order of increasing sophistication:

Brian Hall, Lie Groups, Lie Algebras, and Representations, Springer Verlag, Berlin, 2003.
William Fulton and Joe Harris, Representation Theory - a First Course, Springer Verlag, Berlin, 1991. (A friendly introduction to finite groups, Lie groups, Lie algebras and their representations, including the classification of simple Lie algebras. One great thing is that it has lots of pictures of root systems, and works slowly up a ladder of examples of these before blasting the reader with abstract generalities.)
J. Frank Adams, Lectures on Lie Groups, University of Chicago Press, Chicago, 2004. (A very elegant introduction to the theory of semisimple Lie groups and their representations, without the morass of notation that tends to plague this subject. But it's a bit terse, so you may need to look at other books to see what's really going on in here!)
Daniel Bump, Lie Groups, Springer Verlag, Berlin, 2004. (A friendly tour of the vast and fascinating panorama of mathematics surrounding groups, starting from really basic stuff and working on up to advanced topics. The nice thing is that it explains stuff without feeling the need to prove every statement, so it can cover more territory.)

Geometry and topology for physicists - in rough order of increasing sophistication:

Gregory L. Naber, Topology, Geometry and Gauge Fields: Foundations, Springer Verlag, Berlin, 1997.
Chris Isham, Modern Differential Geometry for Physicists, World Scientific Press, Singapore, 1999. (Isham is an expert on general relativity so this is especially good if you want to study that.)
Harley Flanders, Differential Forms with Applications to the Physical Sciences, Dover, New York, 1989. (Everyone has to learn differential forms eventually, and this is a pretty good place to do it.)
Charles Nash and Siddhartha Sen, Topology and Geometry for Physicists, Academic Press, 1983. (This emphasizes the physics motivations... it's not quite as precise at points.)
Mikio Nakahara, Geometry, Topology, and Physics, A. Hilger, New York, 1990. (More advanced.)
Charles Nash, Differential Topology and Quantum Field Theory, Academic Press, 1991. (Still more advanced - essential if you want to understand what Witten is up to.)

Geometry and topology, straight up:

Victor Guillemin and Alan Pollack, Differential Topology, Prentice-Hall, Englewood Cliffs, 1974.
B.A. Dubrovin, A.T. Fomenko, and S.P. Novikov, Modern Geometry - Methods and Applications, 3 volumes, Springer Verlag, Berlin, 1990. (Lots of examples, great for building intuition, some mistakes here and there. The third volume is an excellent course on algebraic topology from a geometrical viewpoint.)

Algebraic topology:

Allen Hatcher, Algebraic Topology, Cambridge U. Press, Cambridge, 2002. Also available free at http://www.math.cornell.edu/~hatcher/AT/ATpage.html. (An excellent modern introduction.)
Peter May, A Concise Course in Algebraic Topology, U. of Chicago Press, Chicago, 1999. Also available free at http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf. (More intense.)

Knot theory:

Louis Kauffman, On Knots, Princeton U. Press, Princeton, 1987.
Louis Kauffman, Knots and Physics, World Scientific, Singapore, 1991.
Dale Rolfsen, Knots and Links, Publish or Perish, Berkeley, 1976.

Geometrical aspects of classical mechanics:

V. I. Arnold, Mathematical Methods of Classical Mechanics, translated by K. Vogtmann and A. Weinstein, 2nd edition, Springer-Verlag, Berlin, 1989. (The appendices are somewhat more advanced and cover all sorts of nifty topics.)

Analysis and its applications to quantum physics:

Michael Reed and Barry Simon, Methods of Modern Mathematical Physics (4 volumes), Academic Press, 1980.

Homological algebra:

Joseph Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979. (A good introduction to an important but sometimes intimidating branch of math.)
Charles Weibel, An Introduction to Homological Algebra, Cambridge U. Press, Cambridge, 1994. (Despite having the same title as the previous book, this goes into many more advanced topics.)

I have always imagined that Paradise will be a kind of library. - Jorge Luis Borges

Berikut artikel yang juga bagus berisi saran dari Prof. T'hooft seorang nobelis fisika dari Belanda

How to become a
GOOD Theoretical Physicist

This is a web site (under construction) for young students - and anyone else - who are (like me) thrilled by the challenges posed by real science, and who are - like me - determined to use their brains to discover new things about the physical world that we are living in. In short, it is for all those who decided to study theoretical physics, in their own time.

It so often happens that I receive mail - well-intended but totally useless - by amateur physicists who believe to have solved the world. They believe this, only because they understand totally nothing about the real way problems are solved in Modern Physics. If you really want to contribute to our theoretical understanding of physical laws - and it is an exciting experience if you succeed! - there are many things you need to know. First of all, be serious about it. All necessary science courses are taught at Universities, so, naturally, the first thing you should do is have yourself admitted at a University and absorb everything you can. But what if you are still young, at School, and before being admitted at a University, you have to endure the childish anecdotes that they call science there? What if you are older, and you are not at all looking forward to join those noisy crowds of young students?

It should be possible, these days, to collect all knowledge you need from the internet. Problem then is, there is so much junk on the internet. Is it possible to weed out those very rare pages that may really be of use? I know exactly what should be taught to the beginning student. The names and topics of the absolutely necessary lecture courses are easy to list, and this is what I have done below. It is my intention to search on the web where the really useful papers and books are, preferably downloadable as well. This way, the costs of becoming a theoretical physicist should not exceed much the price of a computer with internet connection, a printer, and lots of paper and pens. Unfortunately, I still have to recommend to buy text books as well, but it is harder to advise you here; perhaps in a future site. Let’s first limit ourselves to the absolute minimum. The subjects listed below must be studied. Any omission will be punished: failure. Do get me right: you don’t have to believe anything you read on faith - check it. Try alternative approaches, as many as you can. You will discover, time and again, that really what those guys did indeed was the smartest thing possible. Amazing. the best of the texts come with exercises. Do them. find out that you can understand everything. Try to reach the stage that you discover the numerous misprints, tiny mistakes as well as more important errors, and imagine how you would write those texts in a smarter way.

I can tell you of my own experiences. I had the extreme luck of having excellent teachers around me. That helps one from running astray. It helped me all the way to earn a Nobel Prize. But I didn’t have internet. I am going to try to be your teacher. It is a formidable task. I am asking students, colleagues, teachers to help me improve this site. It is presently set up only for those who wish to become theoretical physicists, not just ordinary ones, but the very best, those who are fully determined to earn their own Nobel Prize. If you are more modest than that, well, finish those lousy schools first and follow the regular routes provided by educators and specialized -gogues who are so damn carefully chewing all those tiny portions before feeding them to you. This is a site for ambitious people. I am sure that anyone can do this, if one is gifted with a certain amount of intelligence, interest and determination. Now, here begins the serious stuff. Don’t complain that it looks like being a lot. You won’t get your Nobel Prize for free, and remember, all of this together takes our students at least 5 years of intense study (at least one reader was surprised at this statement, saying that (s)he would never master this in 5 years; indeed, I am addressing people who plan to spend most of their time to this study). More than rudimentary intelligence is assumed to be present, because ordinary students can master this material only when assisted by patient teachers. It is necessary to do exercises. Some of the texts come with exercises. Do them, or better, invent your own exercises. Try to outsmart the authors, but please refrain from mailing to me your alternative theories until you have studied the entire lot; if you do this well you will discover that many of these authors were not so stupid after all.

Theoretical Physics is like a sky scraper. It has solid foundations in elementary mathematics and notions of classical (pre-20th century) physics. Don’t think that pre-20th century physics is “irrelevant” since now we have so much more. In those days, the solid foundations were laid of the knowledge that we enjoy now. Don’t try to construct your sky scraper without first reconstructing these foundations yourself. The first few floors of our skyscraper consist of advanced mathematical formalisms that turn the Classical Physics theories into beauties of their own. They are needed if you want to go higher than that. So, next come many of the other subjects listed below. Finally, if you are mad enough that you want to solve those tremendously perplexing problems of reconciling gravitational physics with the quantum world, you end up studying general relativity, superstring theory, M-theory, Calabi-Yau compactification and so on. That’s presently the top of the sky scraper. There are other peaks such as Bose-Einstein condensation, fractional Hall effect, and more. Also good for Nobel Prizes, as the past years have shown. A warning is called for: even if you are extremely smart, you are still likely to get stuck somewhere. Surf the net yourself. Find more. Tell me about what you found. If this site has been of any help to someone while preparing for a University study, if this has motivated someone, helped someone along the way, and smoothened his or her path towards science, then I call this site successful. Please let me know. Here is the list.

Note that this site NOT meant to be very pedagogical. I avoid texts with lots of colorful but distracting pictures from authors who try hard to be funny. Also, the subjects included are somewhat focused towards my own interests.

LIST OF SUBJECTS, IN LOGICAL ORDER ARE ON THE SIDE. (Not everything has to be done in this order, but this approximately indicates the logical coherence of the various subjects. Some notes are at a higher level than others).

Languages

English is a prerequisite. If you haven’t mastered it yet, learn it. You must be able to read, write, speak and understand English, but you don’t have to be perfect here. The lousy English used in this text is mine. That’s enough. All publications are in English. Note the importance of being able to write in English. Sooner or later you will wish to publish your results. People must be able to read and understand your stuff.

French, German, Spanish and Italian may be useful too, but they are not at all necessary. They are nowhere near the foundations of our sky-scraper, so don’t worry. You do need the Greek alphabet. Greek letters are used a lot. Learn their names, otherwise you make a fool of yourself when giving an oral presentation.

If you have managed to read and follow this webpage so far, you probably don't need a first course in English. However, you want to be precise in your academic publications. You never want to be misunderstood, after all. Below, you will find several resources that are intended to be helpful for readers of various levels and with various requirements.

Dictionaries Grammar Vocabulary Punctuation Writing Pronunciation

Primary Mathematics

Now, first things first. Are you comfortable with numbers, adding, subtracting, square roots, etc.?

Natural numbers: 1, 2, 3, …
Integers: …, -3, -2, -1, 0, 1, 2, …
Rational numbers (fractions): 12, 14, 34, 23791773, …
Real numbers: Sqrt(2) = 1.4142135… , π = 3.14159265… , e = 2.7182818…, …
Complex numbers: 2+3i, e^ia= cos(a) + i sin( a), … they are very important!
Set theory: open sets, compact spaces. Topology.You may be surprised to learn that they do play a role indeed in physics!
Algebraic equations. Approximation techniques. Series expansions: the Taylor series.
Solving equations with complex numbers. Trigonometry: sin(2x)=2sin x cos x, etc.
Infinitesimals. Differentiation. Differentiate basic functions (sin, cos, exp).
Integration. Integrate basic functions, when possible. Differential equations. Linear equations.
The Fourier transformation. The use of complex numbers. Convergence of series.
The complex plane. Cauchy theorems and contour integration (now this is fun).
The Gamma function (enjoy studying its properties).
Gaussian integrals. Probability theory.
Partial differential equations. Dirichlet and Neumann boundary conditions.

This is for starters. Some of these topics actually come as entire lecture courses. Much of those are essential ingredients of theories in Physics. You don’t have to finish it all before beginning with what follows next, but remember to return to those subjects skipped during the first round.

Classical Mechanics

Static mechanics (forces, tension); hydrostatics. Newton’s Laws
The elliptical orbits of planets. The many-body system
The action principle. Hamilton’s equations. The Lagrangean. (Don’t skip - extremely important!)
The harmonic oscillator. The pendulum
Poisson’s brackets
Wave equations. Liquids and gases. The Navier-Stokes equations. Viscosity and friction

Optics

Fraction and reflection
Lenses and mirrors
The telescope and the microscope
Introduction to wave propagation
Doppler effect
Huijgens’ principle of wave superposition
Wave fronts
Caustics

Statistical Mechanics & Thermodynamics

The first, second and third laws of thermodynamics
The Boltzmann distribution
The Carnot cycle. Entropy. Heat engines
Phase transitions. Thermodynamical models
The Ising Model (postpone techniques to solve the 2-dimensional Ising Model to later)
Planck’s radiation law (as a prelude to Quantum Mechanics)

Electronics

(Only some very basic things about electronic circuits)

Ohm’s law, capacitors, inductors, using complex numbers to calculate their effects
Transistors, diodes (how these actually work comes later)

Lessons In Electric Circuits by T. R. Kuphaldt

Electromagnetism

Maxwell’s Theory for electromagnetism:

Homogeneous and inhomogeneous
Maxwell’s laws in a medium. Boundaries. Solving the equations in:

The vector potential and gauge invariance (extremely important)
Emission and absorption on EM waves (antenna)
Light scattering against objects

Electromagnetism by James Sparks
Notes on Classical Electromagnetism by R. Fritzpatrick
Bo Thide’s EM Field theory text(advanced)
Worked out exercises from Jackson’s book: Selection 1 / Selection 2

Computational Physics

Even the pure sang theorist may be interested in some aspects of Computational physics.

Quantum Mechanics (Non-relativistic)

Bohr’s atom
DeBroglie’s relations (Energy-frequency, momentum-wave number)
Schrödinger’s equation (with electric potential and magnetic field)
Ehrenfest’s theorem
A particle in a box
The hydrogen atom, solved systematically. The Zeeman effect. Stark effect
The quantum harmonic oscillator
Operators: energy, momentum, angular momentum, creation and annihilation operators
Their commutation rules
Introduction to quantum mechanical scattering. The S-matrix. Radio-active decay

Introduction to QM and special relativity: Michael Fowler
Niels Walet lecture course on QM (Manchester)
Lecture Notes on QM from MIT: Undergraduate / Graduate
James Branson, Quantum Physics (UCSD)

Atoms & Molecules

Chemical binding
Orbitals
Atomic and molecular spectra
Emission and absorption of light
Quantum selection rules
Magnetic moments

Solid State Physics

Crystal groups
Bragg reflection
Dielectric and diamagnetic constants
Bloch spectra
Fermi level
Conductors, semiconductors and insulators
Specific heat
Electrons and holes
The transistor
Supraconductivity
Hall effect

Nuclear Physics

Isotopes
Radio-activity
Fission and fusion
Droplet model
Nuclear quantum numbers
Magic nuclei
Isospin
Yukawa theory

Plasma Physics

Magneto-hydrodynamics
Alfvén waves

Introduction to plasma physics by R. Fritzpatrick

Advanced Mathematics

Group theory, and the linear representations of groups
Lie group theory
Vectors and tensors
More techniques to solve (partial) differential and integral equations
Extremum principle and approximation techniques based on that
Difference equations
Generating functions
Hilbert space
Introduction to the functional integral

See John Heinbockel, Virginia.
See Chr. Pope: Methods2.
Mathematics textbooks list. (Link not working; working on finding an alternative)
G.’t Hooft: Lie groups in Physics, (now also in English) + exercises.
For Lie Groups, see also the last section of Chr. Pope’s lectures (under “General Relativity”).
The special functions and polynomials(PDF) (just understand the principles).

Special Relativity

The Lorentz transformation
Lorentz contraction, time dilatation
E = mc2
4-vectors and 4-tensors
Transformation rules for the Maxwell field
Relativistic Doppler effect

Advanced Quantum Mechanics

Hilbert space
Atomic transitions
Emission and absorption of light
Stimulated emission
Density matrix
Interpretation of QM
The Bell inequalities
Towards relativistic QM: The Dirac equation, finestructure
Electrons and positrons
BCS theory for supraconductivity
Quantum Hall effect
Advanced scattering theory
Dispersion relations
Perturbation expansion
WKB approximation, Extremum principle
Bose-Einstein condensation
Superliquid helium

Phenomenology

Subatomic particles (mesons, baryons, photons, leptons, quarks) and cosmic rays; property of materials and chemistry; nuclear isotopes; phase transitions; astrophysics (planetary system, stars, galaxies, red shifts, supernovae); cosmology (cosmological models, inflationary universe theories, microwave background radiation); detection techniques.

General Relativity

The metric tensor
Space-time curvature
Einstein’s gravity equation
The Schwarzschild black hole
Reissner-Nordström black hole
Periastron shift
Gravitational lensing
Cosmological models
Gravitational radiation

Introduction + exercises by G. ‘t Hooft
Sean M. Carrol’s lecture notes on GR
Chr. Pope, Geometry and Group Theory, PDF

Cosmology

Cosmology and Astrophysics are relatively young branches of science where a lot is happening. It is recommended to take notice of these important subjects, and devote time on them according to your taste. Indeed you must know that there is feedback from cosmology, astrophysics and astroparticle physics in solving various physics questions. But I can go on this way: what about the physics of other special branches of science: biophysics, geophysics, the physics of music, ... I encourage you to search for other such subjects of interest on the web.

Astro-Physics & Astronomy

Quantum Field Theory

Classical fields: Scalar, Dirac-spinor, Yang-Mills vector fields.
Interactions, perturbation expansion. Spontaneous symmetry breaking, Goldstone mode, Higgs mechanism.
Particles and fields: Fock space. Antiparticles. Feynman rules. The Gell-Mann-Lévy sigma model for pions and nuclei. Loop diagrams. Unitarity, Causality and dispersion relations. Renormalization (Pauli-Villars; dimensional ren.) Quantum gauge theory: Gauge fixing, Faddeev-Popov determinant, Slavnov identities, BRST symmetry. The renormalization group. Asymptotic freedom.
Solitons, Skyrmions. Magnetic monopoles and instantons. Permanent quark confinement mechanism. The 1/N expansion. Operator product expansion. Bethe-Salpeter equation. Construction of the Standard Model. P and CP violation. The CPT theorem. Spin and statistics connection. Supersymmetry.

Pierre van Baal’s notes on QFT.

Supersymmetry & Supergravity

...

Astro Particle Physics

...

Super String Theory

Texts & Other Resources

There are many more lecture notes to be found on the web.

There are numerous good books on all sorts of topics in Theoretical Physics. Here are a few:

Classical Mechanics:

Classical Mechanics - 3rd ed. - Goldstein, Poole & Safko
Classical dynamics: a contemporary approach - Jorge V. José, Eugene J. Saletan
Classical Mechanics - Systems of Particles and Hamiltonian Dynamics - W. Greiner
Mathematical Methods of Classical Mechanics, 2nd ed. - V.I. Arnold
Mechanics 3rd ed. - L. Landau, E. Lifshitz

Statistical Mechanics:

L. E. Reichl: A Modern Course in Statistical Physics, 2nd ed.
R. K. Pathria: Statistical Mechanics
M. Plischke & B. Bergesen: Equilibrium Statistical Physics
L. D. Landau & E. M. Lifshitz: Statistical Physics, Part 1
S.-K. Ma, Statistical Mechanics, World Scientific

Quantum Mechanics:

Quantum Mechanics - an Introduction, 4th ed. - W. Greiner
R. Shankar, Principles of Quantum Mechanics, Plenum
Quantum Mechanics - Symmetries 2nd ed. - W. Greiner, B. Muller
Quantum Mechanics - Vol 1&2 - Cohen-TannoudjiJ.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley

Electrodynamics:

J.D. Jackson, Classical Electrodynamics, 3rd ed., Wiley & Sons.
Electromagnetic Fields And Waves - lorrain and corson
Classical Electrodynamics - W. Greiner
Introduction to Electrodynamics - D. Griffiths
Quantum Electrodynamics - 3rd ed., - W. Greiner, J. Reinhardt

Optics:

Principles of Optics - M.Born, E. Wolf
Principles Of Nonlinear Optics - Y. R. Shen

Thermodynamics:

Thermodynamics and an Introduction to Thermostatistics 2ed - H. Callen
Thermodynamics and statistical mechanics - Greiner, Neise, Stoecker

Solid State Physics:

Solid State Physics - Ashcroft, Neil W, Mermin, David N
Introduction to Solid State Physics 7th edition- Kittel, Charles

Special Relativity:

Classical Mechanics - Point Particles And Relativity - W. Greiner
Introduction to the theory of relativity and the principles of modern physics - H. Yilmaz

General Relativity:

J.B. Hartle, Gravity, An Introduction to Einstein’s General Relativity, Addison Wesley, 2003.
T.-P. Cheng, Relativity, Gravitation and Cosmology, A Basic Introduction, Oxford Univ. Press, 2005.

Particle Physics:

Introduction to Elementary Particles - D. Griffiths
Fundamentals in Nuclear Physics - From Nuclear Structure to Cosmology - Basdevant, Rich, Spiro

Field Theory:

B. de Wit & J. Smith, Field Theory in Particle Physics, North-Holland
C. Itzykson & J.-B. Zuber, Quantum Field Theory, McGraw-Hill.

String Theory:

Barton Zwiebach, A First Course in String Theory, Cambridge Univ. Press, 2004
M.B. Green, J.H. Schwarz & E. Witten, Superstring theory, Vols. I & II, Cambridge Univ. Press

Cosmology:

An Introduction to cosmology, 3rd Ed – Roos
Relativity, thermodynamics, and cosmology - Tolman R.C.

General:

J.B. Marion & W.F. Hornyak, Principles of Physics, Saunders College Publishing, 1984, ISBN 0-03-049481-8
H. Margenau and G.M. Murphy, The Mathematics of Physics and Chemistry, D. v.Nostrand Comp.
R. Baker, Linear Algebra, Rinton Press

Find lists of other useful textbooks here: Mathematics, Physics (most of these are rather for amusement than being essential for understanding the World), or a little bit more seriously: Physics.

Responses & Questions

Please direct any questions, comments or suggestions to Nava Gaddam (gaddam@uu.nl).

There already has been some response. I thank: Rob van Linden, Robert Tough, Thuy Nguyen, Tina Witham, Jerry Blair, Jonathan Martin, David Cuthbertson, Trent Strong, and many others.

Mr. Hisham Kotry came with an important question:

"… You sketch the path for potential students through the forest of college level physics… Two years ago I decided to self-study theoretical physics by following the syllabus of a renown university and the advice from your page and now I’m half-way through the journey but I was wondering about what happens next? Quoting you from the former page "In short, it is for all those who decided to study theoretical physics, in their own time.", Do you know of anyone who got tenure at a physics department or any research institute based on studies he did in his own time without holding a university degree?"

This is not so easy to answer, unfortunately. What I can say, is:
Eventually, whether you like it or not, you will have to obtain some University degree, if you wish a self-supporting career in theoretical Physics. One possibility is to follow a Master course such as the one offered by our University. I don’t know about your qualifications, but I suspect that, with enough determination, you may be able to comply.

This is not a burocratic argument but a very practical one. It is also advisable not to wait until you think your self-study is completed. You must allow your abilities to be tested, so that you get the recognition that you may well deserve. Also, I frequently meet people who get stuck at some point. Only by intense interactions with teachers and peers one can help oneself across such barriers. I have not yet met anyone who could do the entire study all by him/herself without any guidance. If you really think you have reached a professional level in your studies, you can try to get admitted to schools, conferences and workshops in topics of your interest.

3/04/06: Message received from John Glasscock, Bloomington, IN:
The only one I know of currently is John Moffatt at U Toronto, who was a student of Abdus Salam at Imperial College, London. He started life as a painter in Paris, had no undergraduate degree, taught himself, corresponded with Einstein, and was admitted, based on his demonstrated original work, at IC. (Source: João Magueijo, _Faster than the Speed of Light_. Perseus Publishing, Cambridge, MA. 2003.)

Suggestions for further lecture notes from Alvaro Véliz:

The archimedeans webpage: It has a lot of lecture notes in Physics and Mathematics from Part I and II from Cambridge.
David Tong’s (DAMTP) lectures in classical mechanics. I found these lectures fascinating.
Bo Thide’s (Uppsala) lectures in electromagnetic theory.
Angel Uranga’s lectures in String Theory.
I found also extremely helpful MIT’s OpenCourseWare: Lewin’s lectures in basic Physics are terrific (in video).
Michael Fowler’s (Virginia) lectures in Quantum Mechanics. (Not checked, G. ‘t H.)

Suggestions from Seth Strimas-Mackey:

James Binney's (Oxford) video lectures on Quantum Mechanics.
Shankar has two video lecture series that I imagine would be excellent (haven't watched them myself): Series 1 / Series 2. Both Shankar's and Binney's lectures can be found on iTunes for free.
A useful page of lecture notes on several topics in theoretical physics is that of Eric Poisson (U of Guelph).
A page with lecture notes for applied mathematics that is helpful (for example, for learning basic calculus of variations at the level good for physics).
For Quantum Field Theory, Mike Luke of U Toronto has an excellent page of references (including his own excellent notes, which are basically an abridged version of the famous Sidney Coleman ones). There are also problem sets on this website which are the best way to learn! Mike Luke
Finally, possibly the most amazing resource of all is the huge collection of lectures on a wide variety of (fairly advanced) topics in theoretical physics from the PSI program at Perimeter Institute: Perimeter Scholars

Suggestion from Daniel MacIsaac:

Feynman Lectures

Acknowledgements

The number of people who have helped build, maintain and improve this website is growing rather quickly. I would like to thank and acknowledge them here:

Several people have contributed to the website via feedback, responses and questions, etc.: Rob van Linden, Robert Tough, Thuy Nguyen, Tina Witham, Jerry Blair, Jonathan Martin, David Cuthbertson, Trent Strong, Hisham Kotry, John Glasscock, Alvaro Véliz, Seth Strimas-Mackey, Daniel MacIsaac, Adrian Belarr, James Melville, Aditya Thakkar, Niall Devlin, Hossam Halim, Kelly Ann Pawlak and many others.
Others have assisted extensively in updating, renewing and finding reliable resources for this website: Aldemar Torres Valderrama, Panos Betzios.

Please direct any questions, comments or suggestions to Nava Gaddam (gaddam@uu.nl).

Sabtu, 26 September 2015

'Snakeskin' Pluto revealed in planetary close-up

Article tools

Sabtu, 18 April 2015

ALMA debuts its high-resolution results

Expecting the unexpected

About the author

Minggu, 09 November 2014

Masih Banyak Misteri di Alam Semesta

Mengembang Melawan Gravitasi

New problems

Leading lights

Kamis, 09 Oktober 2014

Senin, 01 September 2014

Teori Kaluza–Klein

Tinjauan

Space-time-matter theory

Geometric interpretation

The Einstein equations

The Maxwell equations

The Kaluza–Klein geometry

Generalizations

Empirical tests

Notes

References

Further reading

Minggu, 17 Agustus 2014

Bagaimana Belajar Fisika dan Matematika

John Baez

July 29, 2014

Bagaimana caranya Belajar Fisika

Languages

Primary Mathematics

Classical Mechanics

Optics

Statistical Mechanics & Thermodynamics

Electronics

Electromagnetism

Computational Physics

Quantum Mechanics (Non-relativistic)

Atoms & Molecules

Solid State Physics

Nuclear Physics

Plasma Physics

Advanced Mathematics

Special Relativity

Advanced Quantum Mechanics

Phenomenology

General Relativity

Cosmology

Astro-Physics & Astronomy

Quantum Field Theory

Supersymmetry & Supergravity

Astro Particle Physics

Super String Theory

Texts & Other Resources

Responses & Questions

Acknowledgements