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Topic: Symmetry principles

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Acute triangle

	Symmetry
		Symmetry is a characteristic of geometrical shapes, equations and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it.
		Symmetry is used in the design of the overall floor plan of buildings as well as the design of individual building elements such as doors, windows, floors, frieze work, and ornamentation; many facades adhere to bilateral symmetry.
		Symmetry is also an important consideration in the formation of scales and chords, traditional or tonal music being made up of non-symmetrical groups of pitches, such as the diatonic scale or the major chord.
	www.wapipedia.org /wikipedia/mobiletopic.aspx?cur_title=symmetry_principles (1476 words)

	SYMMETRY,
		So-called symmetry operations are those mathematical transformations that produce a figure identical to the original or a mirror image of the original figure.
		Symmetry operations are defined with respect to a given point (center of symmetry), line (axis of symmetry), and plane (plane of symmetry).
		Such symmetries exist in the mathematical “space” of that realm and underlie the conservation of such quantities as charge, parity, baryon and lepton number, and total strangeness, even as certain particles are substituted for one another.
	www.history.com /encyclopedia.do?vendorId=FWNE.fw..sy224600.a (451 words)

	physics - Symmetry
		Pentamerism is a body symmetry exhibited primarily by starfish; it is rotational symmetry with respect to an angle of 72°.
		This has led to group theory being one of the areas of mathematics most studied by physicists; spontaneous symmetry breaking of transformations of symmetric groups appears to explain topics in particle physics (for example, the unification of electromagnetism and the weak force) and cosmology.
		Symmetrical scales or chords, such as the whole tone scale, augmented chord, or diminished seventh chord (diminished-diminished seventh), are said to lack direction or a sense of forward motion, are ambiguous as to the key or tonal center, and have a less specific diatonic functionality.
	www.physicsdaily.com /physics/Symmetry_principles (1745 words)

	MAW 1995: The Mass-Produced Universe (Site not responding. Last check: 2007-10-19)
		Mathematicians talk not just of "symmetry" in a general sense, but have given precise definitions in particular settings of what it means for objects to be "symmetric." Mathematical symmetry is a powerful concept that is used to analyze and classify structure, and to provide models to predict as-yet-unobserved physical structure.
		To mathematicians, symmetry is both an attribute of an object as well as a particular transformation of the object.
		Symmetry principles have already led to a unified theory of two of these forces -- electromagnetism and the weak force.
	www.mathaware.org /mam/95/massprod.html (619 words)

	ELEMENTARY PARTICLES,
		In physics, symmetry principles were applied almost exclusively to problems in fluid mechanics and crystallography until the beginning of the 20th century.
		Most symmetry principles state that a particular phenomenon is invariant (unchanged) when certain spatial coordinates are transformed, or changed in a certain way.
		The principle of space reflection symmetry, or parity (P) conservation, states that the laws of nature are invariant when the three spatial coordinates, x, y, and z, of all particles are reflected (that is, when their signs are changed).
	www.history.com /encyclopedia.do?vendorId=FWNE.fw..el028900.a (2390 words)

	Symmetry and Symmetry Breaking (Stanford Encyclopedia of Philosophy)
		Huygens took the relativity principle as his 3rd hypothesis or axiom, but in Newton's Principia it is demoted to a corollary to the laws of motion, its status in Newtonian physics therefore being that of a consequence of the laws, even though it remains, in fact, an independent assumption.
		The extension of the concept of continuous symmetry from “global” symmetries (such as the Galilean group of spacetime transformations) to “local” symmetries is one of the important developments in the concept of symmetry in physics that took place in the twentieth century.
		Symmetries may be used to explain (i) the form of the laws, and (ii) the occurrence (or non-occurrence) of certain events (this latter in a manner analogous to the way in which the laws explain why certain events occur and not others).
	plato.stanford.edu /entries/symmetry-breaking (9828 words)

	NationMaster - Encyclopedia: James Cronin (Site not responding. Last check: 2007-10-19)
		Specifically, they proved, by examining the decay of kaons, that a reaction run in reverse does not merely retrace the path of the original reaction, which showed that the interactions of subatomic particles are not indifferent to time.
		In physics, and specifically particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics.
		the discovery of violations of fundamental symmetry principles in the decay of neutral K-mesons.
	www.nationmaster.com /encyclopedia/James-Cronin (1187 words)

	Symmetry Principles of the Unified Field Theory (a "Theory of Everything")
		Note (3): The symmetries usually discussed in physics articles with regard to the four forces are highly technical and mathematical, often described as parameters or dimensions of an imaginary "phase space".
		Symmetry and charge conservation in obedience to Noether's theorem are the primary topics of Row 3.
		The distributional symmetry of light's energy within spacetime is therefore broken; mass is a concentrated lump of undistributed energy with a specific location in spacetime; this location is actually identified energetically in terms of both the quantity and concentration of bound energy by the warped metric produced by the gravitational field of mass.
	www.people.cornell.edu /pages/jag8/appendix.html (17486 words)

	Principles of Virus Architecture
		A body with cubic symmetry possesses a number of axes about which it may be rotated to give a number of identical appearances.
		With the advent of negative staining, it became obvious that the myxo- and paramyxo-viruses consisted of an inner nucleo-protein component with helical symmetry surrounded by an envelope of characteristic morphology.
		This realization of the helical symmetry of the myxoviruses laid the foundation for the understanding of the symmetry of other complex groups of viruses such as rabies virus and granulosis virus.
	www.uct.ac.za /depts/mmi/stannard/virarch.html (1262 words)

	Introduction to the Symmetry Principles of the Unified Field theory (Site not responding. Last check: 2007-10-19)
		The fourth force is the weak force, responsible for breaking the symmetry of the particle-antiparticle pairs formed in column three, and by this action plunging the Universe into the asymmetric state of matter and bound energy we are all familiar with.
		These charges represent the symmetry debts of light, and are conservation consequences of the breaking of the symmetric energy state of light by the weak force in row 1, a conservation required by "Noether's Theorem".
		The interrelationship of these 4 principles and corollaries constitutes a further expression of unification, at a level of abstraction anterior to the level of the four forces, and is extensively discussed in the section on the Tetrahedron Models of the conservation laws of energy.
	home.earthlink.net /~johngowan/sect1.html (1314 words)

	Symmetry Principles in Solid State and Molecular Physics by Melvin J. Lax (Site not responding. Last check: 2007-10-19)
		Unique features of this volume include use of subgroup techniques, consideration of the influence of time reversal on selection rules, use of shell theorems and invariance techniques to construct the form of tensors, and use of broken symmetry to relate the symmetry of valence and molecular orbitals to the symmetry of electron molecular wave functions.
		Symmetry Principles in Solid State and M : High-level text applies group theory to solid st...
		Symmetry in Chemistry by Hans H. Jaffe, : Symmetry arguments are a powerful tool in teachi...
	www.china-manufactory.com /524334.html (454 words)

	JOT: Journal of Object Technology -Understanding Symmetry in Object-Oriented Languages, Zhao, Coplien
		This law derives from the symmetry principle that physical laws are invariant with respect to time; that is, the amount of energy present before any physical interaction must equal the amount available after the interaction.
		In algebra [15], symmetry is characterised as a group of transformations that are closed, associative and invertible under a given law of composition.
		Symmetry has found to be most successful in assisting the search of solutions for combinatorial design problems in constraint programming [24].
	www.jot.fm /issues/issue_2003_09/article3 (3701 words)

	ZPEnergy.com - Unity of Spacetime and Matter (Site not responding. Last check: 2007-10-19)
		When the coin stops spinning, it hits the table and the symmetry is broken as it becomes either heads or tails; the coin enters a lower energy[broken symmetry] state.
		That is to say, the elegant symmetry principles specify what sort of dice were rolled to produce our world.
		It appears that spontaneous symmetry breaking only works for infinite spaces; basically because in a finite[compact] space, there exists a finite probability for the multiplicity of differently oriented would-be vacua to tunnel into one another and thus, the true vacuum is a linear superposition of them all.
	www.zpenergy.com /modules.php?name=News&file=print&sid=1053 (362 words)

	elementary particles: Conservation Laws and Symmetry — FactMonster.com (Site not responding. Last check: 2007-10-19)
		principles that apply to changing the total circumstances of an event rather than changing a particular quantity.
		The three symmetry operations associated with these principles are: charge conjugation (C), which is equivalent to exchanging particles and antiparticles; parity (P), which is a kind of mirror-image symmetry involving the exchange of left and right; and time-reversal (T), which reverses the order in which events occur.
		According to the symmetry principles (or invariance principles), performing one of these symmetry operations on a possible particle reaction should result in a second reaction that is also possible.
	www.factmonster.com /ce6/sci/A0920748.html (477 words)

	No Special Creation - Hypothesis Text - Physics Forums Library
		When the coin hits the floor the symmetry is broken (its either heads or tails) and energy is released in the process (the noise the coin makes as it hits the ground).
		Symmetry and randomness are inseparable, the way the symmetry between heads and tails is essential to the randomness of a coin flip.
		Symmetry itself, does not need a "creator", since, one can describe nothingness, or "non-existence" to be a condition of perfect indistinguishability and therefore it becomes a perfect symmetry.
	www.physicsforums.com /archive/index.php/t-55243.html (519 words)

	Digital Web Magazine - The Principles of Design
		For this article, the principles of design are the overarching truths of the profession.
		When symmetry occurs with similar, but not identical, forms it is called approximate symmetry.
		The principles of design are the guiding truths of our profession, the basic concepts of balance, rhythm, proportion, dominance and unity.
	www.digital-web.com /articles/principles_of_design (1912 words)

	Leon Lederman Interview -- page 5 / 8 -- Academy of Achievement
		Symmetry means what most artists, and people who appreciate Greek sculpture know about, something which looks the same on the left and the right side.
		Some of the apparatus that we needed was already there on the floor of the accelerator, being polished by a graduate student who was going to use this particular apparatus to do his thesis.
		That this symmetry idea that we had been working on was not a perfect symmetry, that there was an imperfection in the symmetry, a very important imperfection in the symmetry.
	www.achievement.org /autodoc/page/led0int-5 (1265 words)

	Spiritual and Scientific Principles of the Tetrahedron Energy Model
		The four principles of the "Tetrahedron Model of Energy and Conservation Law" are as much spiritual principles of "divine law" as they are scientific principles of "natural law".
		The principle of symmetry corresponds to the spiritual principle of beauty, and to the "Son", or 2nd person of the Christian Trinity.
		Together with raw energy conservation in the form of mass and momentum, entropy and charge conservation permit the transformation of free energy to bound energy in the form of atomic matter, which is the whole argument of the "Cosmic Tetrahedron" model.
	home.earthlink.net /~johngowan/principles.html (4293 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: 2007-10-19)
		He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles".
		Wigner is famous for laying the foundation for the theory of symmetries in quantum mechanics as well as for his research into atomic nuclei, and for his several theorems.
		He laid the foundation for the theory of symmetries in quantum mechanics and in 1927 introduced what is now known as the Wigner D-matrix.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Eugene_Wigner (1205 words)

	Analysis and Synthesis in Architectural Designs by Jin-Ho Park for the Nexus Network Journal vol.3 no.1 Winter 2001 (Site not responding. Last check: 2007-10-19)
		The underlying structure of their spatial logic may be discussed with regard to the use of symmetry principles in mathematics (Weyl, 1952).
		In architectural designs, the use of symmetry may sometimes be apparent immediately by just looking at designs, although the final design is seemingly asymmetrical; or various symmetries are manifested in the parts of the designs, yet not immediately recognizable despite an almost obsessive concern for symmetry.
		The symmetry groups of the square in the third row each have two elements, while the square in the bottom row has only the identity motion in its symmetry group, that is, the no rotation less than the full turn through 360°.
	www.nexusjournal.com /Park.html (4531 words)

	Symmetry - Mathematics and the Liberal Arts
		The author notes that many of the symmetries appear to be derived from the symmetries of the same base motif, which is merely translated; it is acknowledged that this distinction is not a mathematical one.
		Symmetry groups have already been used in discussing mathematical properties of textiles, but may not be appropriate for all kinds of fabrics.
		Next, he discusses appearances of symmetry and symmetry breaking in modern physics, in the theory of relativity, and in quantum mechanics and superstring theory.
	math.truman.edu /~thammond/history/Symmetry.html (6651 words)

	Charge, Parity, and Time Reversal (CPT) Symmetry
		The changes in symmetry properties can be thought of as "mirrors" in which some property of the nucleus (space, time, or charge) is reflected or reversed.
		Wu and her collaborators found that when a specific nucleus was placed in a magnetic field, electrons from the beta decay were preferentially emitted in the direction opposite that of the aligned angular momentum of the nucleus.
		If CPT symmetry is to be preserved, the CP violation must be compensated by a violation of time reversal invariance.
	www.lbl.gov /abc/wallchart/chapters/05/2.html (1109 words)

	PhilSci Archive - Symmetries and invariances in classical physics
		Symmetry, intended as invariance with respect to a transformation (more precisely, with respect to a transformation group), has acquired more and more importance in modern physics.
		The general topics include illustration of the distinctions between symmetries of objects and of laws, and between symmetry principles and symmetry arguments (such as Curie's principle), and reviewing the meaning and various types of symmetry that may be found in classical physics, along with different interpretative strategies that may be adopted.
		In bringing these diverse materials together in a single Chapter, we display the pervasive and powerful influence of symmetry in classical physics, and offer a possible framework for the further philosophical investigation of this topic.
	philsci-archive.pitt.edu /archive/00002569 (239 words)

	steelheadsite.com Books : Symmetries in Physics: Philosophical Reflections
		The contributors cover all the fundamental symmetries of modern physics, such as CPT and permutation symmetry, as well as discussing symmetry-breaking and general interpretational issues.
		This book brings together current philosophical discussions of symmetry in physics, highlighting the main issues and controversies, and providing an entry into the subject for both physicists and philosophers.
		It covers topical issues such as the significance of gauge symmetry, particle identity in quantum theory, how to make sense of parity violation, the role of symmetry-breaking, the empirical status of symmetry principles, and so forth, along with more traditional problems in the philosophy of science.
	www.steelheadsite.com /amz/amazon.pl?Operation=ItemLookup&ItemId=0521821371&templates=default&max_results=9 (287 words)

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