Classical mechanics vs. quantum mechanics

What is quantum mechanics and what does it do?
In very general terms, the basic problem that both classical Newtonian mechanics
and quantum mechanics seek to address can be stated very simply: if the state of a
dynamic system is known initially and something is done to it, how will the state of the
system change with time in response?
In this chapter, we will give a brief overview of, first, how Newtonian mechanics
goes about solving the problem for systems in the macroscopic world and, then, how
quantummechanics does it for systems on the atomic and subatomic scale.We will see
qualitatively what the differences and similarities of the two schemes are and what the
domain of applicability of each is.
Brief overview of classical mechanics
To answer the question posed above systematically, we must first give a more rigorous
formulation of the problem and introduce the special language and terminology (in
double quotation marks) that will be used in subsequent discussions. For the macro-
scopic world, common sense tells us that, to begin with, we should identify the
‘‘system’’ that we are dealing with in terms of a set of ‘‘static properties’’ that do not
change with time in the context of the problem. For example, the mass of an object
might be a static property. The change in the ‘‘state’’ of the systemis characterized by a
set of ‘‘dynamic variables.’’ Knowing the initial state of the system means that we can
specify the ‘‘initial conditions of these dynamic variables.’’What is done to the system
is represented by the ‘‘actions’’ on the system. How the state of the system changes
under the prescribed actions is then described by how the dynamic variables change
with time. This means that there must be an ‘‘equation of motion’’ that governs the
time-dependence of the state of the system. Themathematical solution of the equation
of motion for the dynamic variables of the system will then tell us precisely the state of
the system at a later time t>0; that is to say, everything about what happens to the
system after something is done to it.
For definiteness, let us start with the simplest possible ‘‘system’’: a single particle, or
a point system, that is characterized by a single static property, its mass m.We assume
that itsmotion is limited to a one-dimensional linear space (1-D, coordinate axis x, for
example). According to Newtonian mechanics, the state of the particle at any time t is
1completely specified in terms of the numerical values of its position x(t) and velocity
vx(t), which is the rate of change of its position with respect to time, or vx(t)¼dx(t)/dt.
All the other dynamic properties, such as linearmomentumpx(t)¼mvx, kinetic energy
T ¼ðmv2
xÞ=2, potential energy V(x), total energy E¼(TþV), etc. of this system
depend only on x and vx. ‘‘The state of the system is known initially’’ means that the
numerical values of x(0) and vx(0) are given. The key concept ofNewtonianmechanics
is that the action on the particle can be specified in terms of a ‘‘force’’, Fx, acting on the
particle, and this force is proportional to the acceleration, ax ¼d2
x /dt
2
, where the
proportionality constant is the mass, m, of the particle, or
Fx ¼ max ¼ md2
x
dt2
: (1:1)
This means that once the force acting on a particle of known mass is specified, the
second derivative of its position with respect to time, or the acceleration, is known
from (1.1).With the acceleration known, one will know the numerical value of vx(t)at
all times by simple integration. By further integrating vx(t), one will then also know the
numerical value of x(t), and hence what happens to the particle for all times. Thus, if
the initial conditions on x and vx are given and the action, or the force, on the particle
is specified, one can always predict the state of the particle for all times, and the
initially posed problem is solved.
The crucial point is that, because the state of the particle is specified by x and its first
time-derivative vx to begin with, in order to know how x and vx change with time, one
only has to know the second derivative of x with respect to time, or specify the force.
This is a basic concept in calculus which was, in fact, invented by Newton to deal with
the problems in mechanics.
A more complicated dynamic system is composed of many constituent parts, and
its motion is not necessarily limited to any one-dimensional space. Nevertheless, no
matter how complicated the system and the actions on the system are, the dynamics of
the system can, in principle, be understood or predicted on the basis of these same
principles. In the macroscopic world, the validity of these principles can be tested
experimentally by direct measurements. Indeed, they have been verified in countless
cases. The principles ofNewtonianmechanics, therefore, describe the ‘‘laws ofNature’’
in the macroscopic world

Tim Indonesia kembali mempersembahkan Emas di APhO X dan ICYS ke-16

2 Emas, 4 Perak dan 2 Perunggu dari APhO X, Thailand


Sesuai dengan prediksi awal sebelum keberangkatan tim, Hendra Kwee, Ph.D. menargetkan perolehan medali minimal 2 medali emas. Ternyata target tersebut terpenuhi dengan merebut 2 Emas, 4 Perak dan 2 Perunggu, bahkan tanpa diduga sebelumnya salah satu anggota tim juga merebut predikat "The best experiment". Dengan demikian seluruh anggota tim APhO X Bangkok, 24 April - 2 Mei 2009 berhasil membawa pulang medali. Terlihat dalam foto dari kiri : Fernaldo Richtia Winnerdy SMAK BPK Penabur Gading Serpong, Banten (Perak); Paul Zakharia Fajar Hanakata SMAN 1 Denpasar, Bali (Perak); Muhammad Sohibul Maromi SMAN 1 Pamekasan, Jawa Timur (Perunggu): Hendra Kwee, Ph.D (Leader); Winson Tanputraman SMAK 1 BPK Penabur, DKI Jakarta (Emas dan "The best experiment"); Kamsul Abraha, Ph.D (Leader); Brigitta Septriani SMA Santu Petrus Pontianak, Kalimantan Barat (Perunggu); Sandoko Kosen SMA Sutomo 1 Medan, Sumatera Utara (Perak); Dzuhri Radityo Utomo SMAN 1 Yogyakarta, DIY (Emas) dan Andri Pradana SMAK 1 BPK Penabur, DKI Jakarta (perak).



Siswa-siswi yang mewakili Indonesia di olimpiade ini dipilih melalui seleksi ketat yang diselenggarakan oleh Departemen Pendidikan Nasional. Seleksi dilakukan secara berlapis mulai dari level seleksi kabupaten/kota, provinsi, Olimpiade Sains Nasional, dan seleksi 30 besar yang merupakan seleksi tahap akhir. Siswa siswi yang lolos dari proses ini yang memperoleh hak untuk mewakili Indonesia di ajang APhO. Dari hasil APhO ini akan dipilih 5 siswa terbaik untuk mewakili Indonesia di ajang International Physics Olympiad (IPhO) ke-40 yang akan diselenggarakan di Merida, Yucatan, Mexico pada 11 - 19 Juli 2009. Dengan demikian 2 peraih emas sudah merebut kursi, sedangkan 3 kursi sisanya masih diperebutkan oleh 4 siswa peraih medali perak. Direncanakan proses seleksi dilakukan setelah mereka (5 siswa) mengikuti ujian UN susulan. Kelima siswa yang mengikuti ujian susulan UN tanggal 11 Mei - 15 Mei 2009 adalah : Paul, Brigitta, Sandoko, Dzuhri dan Andri. Semua kegiatan Tim Olimpiade Fisika Indonesia mulai dari proses seleksi, pembinaan hingga keberangkatan didanai oleh Departemen Pendidikan Nasional.


APhO tahun ini diselenggarakan dari tanggal 24 April 2009 - 2 Mei 2009. Olimpiade yang sempat dikhawatirkan terganggu oleh hangatnya suhu politik di Thailand terselenggara dengan tanpa gangguan sama sekali. Hampir semua negara yang menyatakan mau ikut di olimpiade akhirnya tetap mengirim tim untuk berkompetisi di APhO ini. Lima belas negara berkompetisi, antara lain: Brunei Darussalam, Sri Lanka, Tajikistan, Thailand, Turkmenistan dan Vietnam.

Mohon doa restu seluruh masyarakat Indonesia, agar tim dapat meraih sukses di IPhO ke-40 di Mexico, walaupun saat ini sedang dilanda flu babi. (www.tofi.or.id)

Subrahmanyan Chandrasekhar

Subrahmanyan Chandrasekhar, peraih nobel Fisika tahun 1983 dilahirkan di Lahore, India pada 19 Oktober 1910. Ayahnya, Chandrasekhara Subrahmanyan Ayyar adalah pegawai di departemen keuangan India. Sementara Ibunya, Sita (neé Balakrishnan) seorang ibu rumah tangga biasa namun berintelektual tinggi (ia mampu menerjemahan karya Henrik Ibsen, “A Doll House” ke bahasa Tamil). Kedua orangtuanya, menurut Chandrasekhar sangat menaruh perhatian pada pendidikan anak-anaknya. Orangtuanyalah yang langsung memberikan pendidikan dasar khusus baginya di rumah hingga ia berusia 12 tahun. Mereka mengharapkan Chandrasekhar terkenal seperti pamannya, Chandrasekhara V. Raman, orang India pertama yang meraih hadiah Nobel fisika. Pada tahun 1918, ayahnya dipindahtugaskan ke Madras dan di sanalah keluarganya kemudian hidup menetap. Di Madras, ia bersekolah di sekolah lanjutan Hindu dari 1922 hingga 1925.

Pendidikan tingginya (1925-30) ia peroleh pertama kali di Presidency College. Kemudian ketika hendak melanjutkan studinya ke Universitas Cambridge, ibunya jatuh sakit. Menurut tradisi India, ia harus tinggal di rumah merawat ibunya. Namun ibunya yang ingin anaknya sukses mendesak Chandra (nama kecil Chandrasekhar) untuk tetap pergi ke Cambridge, Inggris.

Selama perjalanan panjang dengan kapal laut ke Inggris, Chandra mencoba menggabungkan pengetahuannya tentang bintang Bajang putih (white dwarf) dengan teori relativistik spesial, ia terkejut sekali mendapatkan hasil bahwa suatu bintang bajang putih dapat terbentuk melalui evolusi bintang, asalkan massa bintang itu kurang dari 1,45 massa matahari. Jika bintang terlalu berat maka gaya tolak akibat larangan Pauli tidak mampu menahan gaya gravitasi bintang, akibatnya bintang akan kolaps menjadi bintang netron atau bahkan menjadi lubang hitam (black hole).

Tiba di Universitas Cambridge, dengan beasiswa penuh dari pemerintah India, Chandrasekhar menjadi mahasiswa peneliti di bawah bimbingan Profesor R.H. Fowler. Di tengah-tengah kesibukannya, Chandrasekhar masih ingat hasil perhitungannya di kapal laut itu. Ia mencoba menghitung ulang dan mendiskusikannya dengan para fisikawan di Cambridge, ternyata ia mendapatkan hasil yang sama bahwa ada batas atas massa bintang agar dapat berevolusi menjadi bintang bajang putih. Batas atas ini kemudian terkenal dengan nama “Chandrasekhar limit”. Karena hasil penelitian mengenai evolusi bintang inilah, 50 tahun kemudian Chandrasekhar dianugerahi hadiah nobel fisika (1983).

Chandrasekhar sempat menghabiskan tahun ketiga masa kuliahnya di institut fisika teori, Copenhagen atas saran P.A.M. Dirac (pelopor fisika kuantum) yang melihat kemampuannya yang cemerlang. Pada tahun 1933, ia memperoleh gelar Ph.D dari Cambridge. Hanya beberapa bulan berselang, ia bergabung dengan Trinity College hingga tahun 1937. Ketika melakukan kunjungan ke Universitas Harvard, atas undangan Dr. Harlow Shapley selama musim dingin (Januari-Maret 1936), ia ditawari posisi sebagai peneliti di Universitas Chicago dan memutuskan menerima tawaran itu pada Januari 1937. Saat berada di Chicago, iapun melengkapi teorinya dan mempublikasikannya dalam buku An Introduction to the Study of Stellar Structure (1939).

Riset bagi Chandrasekhar memang merupakan kerja berkesinambungan. Ia mencatat ada tujuh periode riset dalam hidupnya. Pertama, teori tentang struktur bintang, termasuk mengenai Bajang Putih (1929-39). Kedua, teori gerak Brownian yang merupakan bagian dari dinamika bintang (1938-43). Ketiga, teori tentang transfer energi, termasuk tentang atmosfer bintang dan teori kuantum ion negatif hidrogen, juga tentang atmosfer bintang (1943-50). Keempat, stabilitas hidrodinamika dan hidromagnetik (1953-61). Kelima, keseimbangan dan stabilitas bentuk elips, bagian dari kolaborasinya dengan Norman R Lebovitz (1961-8). Keenam, teori relativitas umum dan astrofisika relativitas (1962-71). Terakhir, teori matematika Black Holes (1974-83). Hasil penelitiannya itu dipublikasikan dalam berbagai monograf dan jurnal terkenal untuk astrofisika dan fisika..

Pimpinan Universitas Chicago, Hanna Gray pernah mengungkapkan kesannya terhadap Chandrasekhar. Profesor bidang astronomi dan astrofisika ini adalah ilmuwan yang penuh dedikasi, guru dari para guru, seseorang yang senantiasa membaktikan dirinya untuk kreativitas dunia ilmiah.

Disamping fisika, Chandrasekhar juga menyukai bahasa Inggris dan senang membaca karya-karya sastra terkenal tulisan Shakespeare. Orang sangat mengagumi bahasa inggrisnya yang sangat sempurna baik dalam tata bahasa maupun aksennya, sampai-sampai fisikawan terkenal Hans Bethe mengatakan: "Chandrasekhar was one of the great astrophysicists of our time. He was also the greatest master of the English language that I know”.

Isaac Newton

Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727 [OS: 25 December 1642 – 20 March 1727])[1] was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian and one of the most influential men in human history. His Philosophiæ Naturalis Principia Mathematica, published in 1687, is considered to be among the most influential books in the history of science, laying the groundwork for most of classical mechanics. In this work, Newton described universal gravitation and the three laws of motion which dominated the scientific view of the physical universe for the next three centuries. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the scientific revolution.

In mechanics, Newton enunciated the principles of conservation of both momentum and angular momentum. In optics, he built the first practical reflecting telescope[5] and developed a theory of colour based on the observation that a prism decomposes white light into the many colours which form the visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound.

In mathematics, Newton shares the credit with Gottfried Leibniz for the development of the differential and integral calculus. He also demonstrated the generalised binomial theorem, developed the so-called "Newton's method" for approximating the zeroes of a function, and contributed to the study of power series.

Newton's stature among scientists remains at the very top rank, as demonstrated by a 2005 survey of scientists in Britain's Royal Society asking who had the greater effect on the history of science, Newton or Albert Einstein. Newton was deemed the more influential.[6]

Newton was also highly religious (though unorthodox), producing more work on Biblical hermeneutics than the natural science he is remembered for today.