Keindahan Prinsip Simetri dalam Fisika

Malam ini salah satu dosen dan guru yang penulis kagumi Dr. rer. nat. Muhammad Farchani Rosyid, M.Sc. seorang pakar fisika matematika di Indonesia menautkan sebuah video lagu yang berjudul Titip Rindu Buat Ayah karya Ebiet G. Ade, juga seorang palantun lagu yang disukai oleh ayah saya. 

Bahasa Langit:
Salah satu bait sya'ir-nya:

"Ayah, dalam hening sepi kurindu 
untuk menuai padi milik kita 
Tapi kerinduan tinggal hanya kerinduan 
Anakmu sekarang banyak menanggung beban"

"Namun semangat tak pernah pudar 
meski langkahmu kadang gemetar
kau tetap setia"

Ingat keluarga, ingat kampung halaman, dan ingat salah satu materi dalam sebuah seminar yaitu:
Prinsip Simetri, semoga menjadi obat kerinduan untuk mu ayah dan ibuku.
 
Memahami keindahan pola penciptaan Alam Raya 

Apakah arti "simetri"? 

In physics, symmetry includes all features of a physical system that exhibit the property of symmetry—that is, under certain transformations, aspects of these systems are "unchanged", according to a particular observation. A symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is "preserved" under some change.

A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group). Symmetries are frequently amenable to mathematical formulations such as group representations and can be exploited to simplify many problems.

An important example of such symmetry is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations.

Simetri dalam Fisika

Secara formal, walaupun mungkin agak kabur, kita dapat mengatakan bahwa sejenis simetri tertentu ada jika terdapat operasi matematis tertentu yang tidak mengubahnya. Seorang wanita yang anggun memiliki simetri terhadap sumbu vertikal, karena bila wanita yang anggun itu diputar terhadap suatu sumbu, hal itu tak akan mengubah rupa dan keistimewaanya. 

Ada beberapa simetri utama yang membiarkan hukum fisika tak berubah terhadap setiap situasi, seolah memperlihatkan keajegannya dan kekokohan prinsip ini. Operasi simetri yang paling sederhana ialah translasi dalam ruang, ini berarti hukum fisika tidak bergantung terhadap tempat pemilihan titik asal sistem koordinat yang dipakai. 

Dengan metode yang lebih lanjut dari pada apa yang kita pelajari saat ini, kita bisa membuktikan bahwa invariansi pemerian alam semesta raya terhadap translasi dalam ruang yang mengakibatkan kelestarian suatu momentum linear. 

Operasi simetri sederhana lainnya ialah translasi dalam waktu; ini berarti hukum fisika tak bergantung dari orientasi sistem koordinat tempat hukum itu dinyatakan. 

Kelestarian muatan listrik misalnya berhubungan dengan transformasi gauge yang menggeser titik-nol potensial elektromagnetik skalar dan vektor V dan A. 

(Seperti dibahas lebih mendalam pada teori elektromagnetik, dimana medan elektromagnetik dapat diperiksa dalam potensial V dan A, alih-alih dalam E dan B, yang mana kedua pemerian itu berhubungan melalui rumus kalkulus vektor E = - div V dan B = div x A). 

Transformasi gauge memberikan E dan B tidak terpengaruh karena kuantitas itu diperoleh dengan mendiferensiasi potensial, dan invariansi ini mengakibatkan kelestarian muatan listrik. 

Supersymmetry

In particle physics, supersymmetry (often abbreviated SUSY) is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartner. In a theory with unbroken supersymmetry, for every type of boson there exists a corresponding type of fermion with the same mass and internal quantum numbers (other than spin), and vice-versa.

There is no direct evidence for the existence of supersymmetry. It is motivated by possible solutions to several theoretical problems. Since the superpartners of the Standard Model particles have not been observed, supersymmetry must be a broken symmetry if it is a true symmetry of nature. This would allow the superparticles to be heavier than the corresponding Standard Model particles.

If supersymmetry exists close to the TeV energy scale, it allows for a solution of the hierarchy problem of the Standard Model, i.e., the fact that the Higgs boson mass is subject to quantum corrections which — barring extremely fine-tuned cancellations among independent contributions — would make it so large as to undermine the internal consistency of the theory. 

In supersymmetric theories, on the other hand, the contributions to the quantum corrections coming from Standard Model are naturally canceled by the contributions of the corresponding superpartners. Other attractive features of TeV-scale supersymmetry are the fact that it allows for the high-energy unification of the weak interactions, the strong interactions and electromagnetism, and the fact that it provides a candidate for dark matter and a natural mechanism for electroweak symmetry breaking. Therefore, scenarios where supersymmetric partners appear with masses not much greater than 1 TeV are considered the most well-motivated by theorists.

These scenarios would imply that experimental traces of the superpartners should begin to emerge in high-energy collisions at the LHC relatively soon. As of September 2011, no meaningful signs of the superpartners have been observed,which is beginning to significantly constrain the most popular incarnations of supersymmetry. However, the total parameter space of consistent supersymmetric extensions of the Standard Model is extremely diverse and can not be definitively ruled out at the LHC.

Another theoretically appealing property of supersymmetry is that it offers the only "loophole" to the Coleman–Mandula theorem, which prohibits spacetime and internal symmetries from being combined in any nontrivial way, for quantum field theories like the Standard Model under very general assumptions. The Haag-Lopuszanski-Sohnius theorem demonstrates that supersymmetry is the only way spacetime and internal symmetries can be consistently combined.

In general, supersymmetric quantum field theory is often much easier to work with, as many more problems become exactly solvable. Supersymmetry is also a feature of most versions of string theory, though it may exist in nature even if string theories are not experimentally detected.

The Minimal Supersymmetric Standard Model is one of the best studied candidates for physics beyond the Standard Model. Theories of gravity that are also invariant under supersymmetry are known as supergravity theories.

Alam Semesta dan Simetri

Apakah alam semesta raya ini pun mempunyai keindahan simetri karena penciptaanya, ataukah terlahir hanya karena dampak dari fluktuasi-fluktuasi quantum yang acak tanpa adanya grand design? 

Atau Apakah alam raya ini pada hakikatnya simetri sehingga mempunyai tujuan dibalik kelahirannya? 

Wallohualam Bissawab. 

  Presentasi dari Prof. Satoshi Iso, Ph.D., mengenai Implikasi dari penemuan partikel Higgs

dalam Conference on Theoretical Physics and Nonlinear Phenomena

Sources: 

1. Modern Physics 

By: Prof. Arthur Beiser & Prof. Houw Liong Thee 

2. http://en.wikipedia.org/wiki/Symmetry_in_physics 

References:

General readers

• Leon Lederman and Christopher T. Hill (2005) Symmetry and the Beautiful Universe. Amherst NY: Prometheus Books.
• Schumm, Bruce (2004) Deep Down Things. Johns Hopkins Univ. Press.
• Victor J. Stenger (2000) Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Buffalo NY: Prometheus Books. Chpt. 12 is a gentle introduction to symmetry, invariance, and conservation laws.
• Anthony Zee (2007) Fearful Symmetry: The search for beauty in modern physics, 2nd ed. Princeton University Press. ISBN 978-0-691-00946-9. 1986 1st ed. published by Macmillan.

Technical

• Brading, K., and Castellani, E., eds. (2003) Symmetries in Physics: Philosophical Reflections. Cambridge Univ. Press.
• -------- (2007) "Symmetries and Invariances in Classical Physics" in Butterfield, J., and John Earman, eds., Philosophy of Physic Part B. North Holland: 1331-68.
• Debs, T. and Redhead, M. (2007) Objectivity, Invariance, and Convention: Symmetry in Physical Science. Harvard Univ. Press.
• John Earman (2002) "Laws, Symmetry, and Symmetry Breaking: Invariance, Conservations Principles, and Objectivity." Address to the 2002 meeting of the Philosophy of Science Association.
• Mainzer, K. (1996) Symmetries of nature. Berlin: De Gruyter.
• Thompson, William J. (1994) Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems. Wiley. ISBN 0-471-55264.
• Bas Van Fraassen (1989) Laws and symmetry. Oxford Univ. Press.
• Eugene Wigner (1967) Symmetries and Reflections. Indiana Univ. Press.

Thanks to: 

1. Mr. Iqbal Robiyana, S.Pd. 

Department of Physics Education, Indonesia University of Education and

Darul Qur'an International School 

2. Mr. Mirza Satriawan, M.Sc., Ph.D.
Doctor in Theoretical Physics, University of Illinois at Chicago. USA.

and to all my lovely friends
 

Oleh-oleh dari  Conference on Theoretical Physics and Nonlinear Phenomena