Saturday, 6 August 2011

Einstein dan Relativitas Umum yang Legendaris



Dari mekanika klasik menuju relativitas umum Relativitas umum dapat dipahami dengan baik dengan mengevaluasi kemiripannya beserta perbedaannya dari fisika klasik. 

Langkah pertama adalah realisasi bahwa mekanika klasik dan hukum gravitasi Newton mengijinkan adanya deskripsi geometri. 

Kombinasi deskripsi ini dengan hukum-hukum relativitas khusus akan membawa kita kepada penurunan heuristik relativitas umum. 

Generalisasi relativistik

Geometri gravitasi Newton pada dasarnya didasarkan pada mekanika klasik. Ia hanyalah kasus khusus dari mekanika relativitas khusus.

Dalam bahasa simetri: ketika gravitasi dapat diabaikan, fisika yang berlaku bersifat invarian Lorentz pada relativitas khusus daripada invarian Galileo pada mekanika klasik. 

Perbedaan antara keduanya menjadi signifikan apabila kecepatan terlibat di dalamnya mendekati kecepatan cahaya dan berenergi tinggi.

Referensi:

Kunjungi Juga:

Relativitas Umum dan Ke Geniusan Einstein

Sumber:

The University of Cambridge

Wikipedia

The End

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Thursday, 4 August 2011

Mekanika Orbit: Bacaan Selanjutnya

Further reading

Many of the options, procedures, and supporting theory are covered in standard works such as:
  • Bate, R.R., Mueller, D.D., White, J.E., (1971). Fundamentals of Astrodynamics. Dover Publications, New York. ISBN 978-0486600611.
  • Vallado, D. A. (2001). Fundamentals of Astrodynamics and Applications, 2nd Edition. Springer. ISBN 978-0792369035.
  • Battin, R.H. (1999). An Introduction to the Mathematics and Methods of Astrodynamics. American Institute of Aeronautics & Ast, Washington, DC. ISBN 978-1563473425.
  • Chobotov, V.A. (ed.) (2002). Orbital Mechanics, 3rd Edition. American Institute of Aeronautics & Ast, Washington, DC. ISBN 978-1563475375.
  • Herrick, S. (1971). Astrodynamics: Orbit Determination, Space Navigation, Celestial Mechanics, Volume 1. Van Nostrand Reinhold, London. ISBN 978-0442033705.
  • Herrick, S. (1972). Astrodynamics: Orbit Correction, Perturbation Theory, Integration, Volume 2. Van Nostrand Reinhold, London. ISBN 978-0442033712.
  • Kaplan, M.H. (1976). Modern Spacecraft Dynamics and Controls. Wiley, New York. ISBN 978-0471457039.
  • Tom Logsdon (1997). Orbital Mechanics. Wiley-Interscience, New York. ISBN 978-0471146360.
  • John E. Prussing and Bruce A. Conway (1993). Orbital Mechanics. Oxford University Press, New York. ISBN 978-0195078343.
  • M.J. Sidi (2000). Spacecraft Dynamics and Control. Cambridge University Press, New York. ISBN 978-0521787802.
  • W.E. Wiesel (1996). Spaceflight Dynamics, 2nd edition. McGraw-Hill, New York. ISBN 978-0070701106.
  • J.P. Vinti (1998). Orbital and Celestial Mechanics. American Institute of Aeronautics & Ast, Reston, VA. ISBN 978-1563472565.
  • P. Gurfil (2006). Modern Astrodynamics. Butterworth-Heinemann. ISBN 978-0123735621.
The most elementary but very widely used reference is Bate, Mueller and White. It has several useful graphs off which one can read the rates of change of perigee and node due to earth oblateness, but there are typographical errors in a few equations. For example, in Eq. (9.7.5) the term in (3/2) J2 needs (re/r) squared and the term in J3 needs it cubed. The coefficient 315 in the J6 term, Eq.(9.7.6.) should be 245 (but the 315 in the J5 term is just fine). Battin's book may be too mathematical for many users.
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Monday, 1 August 2011

A Unified Physics By 2050 Part II


 

"Jika kita meninggalkan dunia ini, kita akan baik-baik saja karena kita yakin bahwa 
jiwa kita akan bertemu dengan-Nya"
~Arip~

  A Unified Physics by 2050?

Experiments at CERN and elsewhere should let us complete the Standard Model of particle physics, but a unified theory of all forces will probably require radically new ideas.

By: Prof. Steven Weinberg, Ph.D.

Beyond the Top

The heaviest known particle of the Standard Model is the top quark, with a mass equivalent to an energy of 175 gigaelectron volts (GeV). (One GeV is a little more than the energy contained in a proton mass.) [See "The Discovery of the Top Quark," by Tony M. Liss and Paul L. Tipton; Scientific American, September 1997.] The not yet discovered Higgs particles are expected to have similar masses, from 100 to several hundred GeV. But there is evidence of a much larger scale of masses that will appear in equations of the not yet formulated unified theory. The gluon, W, Z and photon fields of the Standard Model have interactions of rather different strengths with the other fields of this model; that is why the forces produced by exchange of gluons are about 100 times stronger than the others under ordinary conditions. Gravitation is vastly weaker: the gravitational force between the electron and proton in the hydrogen atom is about 10-39 the strength of the electric force.

To complete the Standard Model, we need to confirm the existence of these scalar fields and find out how many types there are. This is a matter of discovering new elementary particles, often called Higgs particles, that can be recognized as the quanta of these fields. We have every reason to expect that this task will be accomplished before 2020, when the accelerator called the Large Hadron Collider at CERN, the European laboratory for particle physics near Geneva, will have been operating for over a decade.


Profoundest advances in fundamental physics



The profoundest advances in fundamental physics tend to occur when the principles of different types of theories are reconciled within a single new framework. We do not yet know what guiding principle underlies the unification of quantum field theory, as embodied in the Standard Model, with general relativity.



The very least new thing that will be discovered is a single electrically neutral scalar particle. It would be a disaster if this were all that were discovered by 2020, though, because it would leave us without a clue to the solution of a formidable puzzle regarding the characteristic energies encountered in physics, known as the hierarchy problem.


The heaviest known particle of the Standard Model is the top quark, with a mass equivalent to an energy of 175 gigaelectron volts (GeV). (One GeV is a little more than the energy contained in a proton mass.) [See "The Discovery of the Top Quark," by Tony M. Liss and Paul L. Tipton; Scientific American,  September 1997.] The not yet discovered Higgs particles are expected to have similar masses, from 100 to several hundred GeV. 

But there is evidence of a much larger scale of masses that will appear in equations of the not yet formulated unified theory. The gluon, W, Z and photon fields of the Standard Model have interactions of rather different strengths with the other fields of this model; that is why the forces produced by exchange of gluons are about 100 times stronger than the others under ordinary conditions. Gravitation is vastly weaker: the gravitational force between the electron and proton in the hydrogen atom is about 10-39 the strength of the electric force.

But all these interaction strengths depend on the energy at which they are measured [see the "Coupling Strengths" illustration below]. It is striking that when the interactions of the fields of the Standard Model are extrapolated, they all become equal to one another at an energy of a little more than 1016 GeV, and the force of gravitation has the same strength at an energy not much higher, around 1018GeV. (Refinements to the theory of gravitation have been suggested that would even bring the strength of gravitation into equality with the other forces at about 1016 GeV.) We are used to some pretty big mass ratios in particle physics, like the 350,000 to 1 ratio of the top quark to the electron mass, but this is nothing compared with the enormous ratio of the fundamental unification energy scale of 1016GeV (or perhaps 1018 GeV) to the energy scale of about 100 GeV that is typical of the Standard Model [see the "Hierarchy Problem" illustration below].

The crux of the hierarchy problem is to understand this huge ratio, this vast jump from one level to the next in the hierarchy of energy scales, and to understand it not just by adjusting the constants in our theories to make the ratio come out right but as a natural consequence of fundamental principles.

Image: Slim Films


THE STANDARD MODEL of particle physics describes each particle of matter and each force with a quantum field. The fundamental particles of matter are fermions and come in three generations (a). Each generation of particles follows the same pattern of properties. The fundamental forces are caused by bosons (b), which are organized according to three closely related symmetries. In addition, one or more Higgs particles or fields (c) generate the masses of the other fields.


Theorists have proposed several interesting ideas for a natural solution to the hierarchy problem, incorporating a new symmetry principle known as supersymmetry (which also improves the accuracy with which the interaction strengths converge at 1016 GeV), or new strong forces known as technicolor, or both [see the illustration "What Comes Next" below]. All these theories contain additional forces that are unified with the strong, weak and electromagnetic forces at an energy of about 1016GeV. 

The new forces become strong at some energy far below 1016GeV, but we cannot observe them directly, because they do not act on the known particles of the Standard Model. Instead they act on other particles that are too massive to be created in our laboratories. These "very heavy" particles are nonetheless much lighter than 1016 GeV because they acquire their mass from the new forces, which are strong only far below 1016 GeV.

In this picture, the known particles of the Standard Model would interact with the very heavy particles, and their masses would arise as a secondary effect of this relatively weak interaction. This mechanism would solve the hierarchy problem, making the known particles lighter than the very heavy particles, which are themselves much lighter than 1016 GeV.


All these ideas share another common feature: they require the existence of a zoo of new particles with masses not much larger than 1,000 GeV. If there is any truth to these ideas, then these particles should be discovered before 2020 at the Large Hadron Collider, and some of them may even show up before then at Fermilab or CERN, although it may take further decades and new accelerators to explore their properties fully. When these particles have been discovered and their properties measured, we will be able to tell whether any of them would have survived the early moments of the big bang and could now furnish the "dark matter" in intergalactic space that is thought to make up most of the present mass of the universe. At any rate, it seems likely that by 2050 we will understand the reason for the enormous ratio of energy scales encountered in nature.

 Further Reading:

1. Unified Theories of Elementary-Particle Interaction. Steven Weinberg in Scientific American, Vol. 231, No. 1, pages 50-59; July 1974.

2. Dreams of a Final Theory. Steven Weinberg. Pantheon Books, 1992.

3. Reflections on the Fate of Spacetime. Edward Witten in Physics Today, Vol. 49, No. 4, pages 24-30; April 1996.

4. Duality, Spacetime and Quantum Mechanics. Edward Witten in Physics Today, Vol. 50, No. 5, pages 28-33; May 1997.

5. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. Brian Greene. W. W. Norton,1999.

http://hera.ph1.uni-koeln.de/~heintzma/Weinberg/Weinberg.htm 



The Author
 

STEVEN WEINBERG is head of the Theory Group at the University of Texas at Austin and a member of its physics and astronomy departments. His work in elementary particle physics has been honored with numerous prizes and awards, including the Nobel Prize for Physics in 1979 and the National Medal of Science in 1991. 
The third volume (Supersymmetry) of his treatise The Quantum Theory of Fields is out from Cambridge University Press. The second volume (Modern Applications) was hailed as being "unmatched by any other book on quantum field theory for its depth, generality and definitive character."



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