System of Information
||The term symmetry derives from the Greek words sun (meaning with or together) and metron (measure), yielding summetria, and originally indicated a relation of commensurability. It quickly acquired a further, more general, meaning: that of a proportion relation, grounded on integration of numbers. From the outset, then, symmetry was closely related to beauty and unity, and this was to prove decisive for its role in theories of nature. In Plato's Timaeus, for example, the regular polyhedra are afforded a central place in the doctrine of natural elements for the proportions they contain and the beauty of their forms: fire has the form of the tetrahedron, earth the form of the cube, air the form of the octahedron, water the form of the icosahedron, while the dodecahedron is used for the form of the entire universe.
From a modern perspective, the regular figures used in Plato's and Kepler's physics for the mathematical proportions they contain (and the related properties and beauty of their form) are symmetric in another sense that does not have to do with proportions. In the language of modern science, the symmetry of geometrical figures such as the regular polygons and polyhedra is defined in terms of their invariance under specified groups of rotations and reflections. Where does this definition stem from? In addition to the ancient notion of symmetry used by the Greeks and Romans (current until the end of the Renaissance), a different notion of symmetry emerged in the seventeenth century, grounded not on proportions but on an equality relation between elements that are opposed, such as the left and right parts of a figure. Crucially, the parts are interchangeable with respect to the whole. They can be exchanged with one another while preserving the original figure. This latter notion of symmetry developed, via several steps, into the concept found today in modern science.
The first explicit study of the invariance properties of equations in physics is connected with the introduction, in the first half of the nineteenth century, of the transformational approach to the problem of motion in the framework of analytical mechanics. Using the formulation of the dynamical equations of mechanics due to W. R. Hamilton (known as the Hamiltonian or canonical formulation), C. G. Jacobi developed a procedure for arriving at the solution of the equations of motion based on the strategy of applying transformations of the variables that leave the Hamiltonian equations invariant, thereby transforming step by step the original problem into new ones that are simpler but perfectly equivalent , Jacobi's canonical transformation theory, although introduced for the “merely instrumental” purpose of solving dynamical problems, led to a very important line of research: the general study of physical theories in terms of their transformation properties.
The application of the theory of groups and their representations for the exploitation of symmetries in the quantum mechanics of the 1920s undoubtedly represents the second turning point in the twentieth-century history of physical symmetries. It is, in fact, in the quantum context that symmetry principles are at their most effective. Wigner and Weyl were among the first to recognize the great relevance of symmetry groups to quantum physics and the first to reflect on the meaning of this. As Wigner emphasized on many occasions, one essential reason for the increased effectiveness of invariance principles in quantum theory is the linear nature of the state space of a quantum physical system, corresponding to the possibility of superposing quantum states. This gives rise to, among other things, the possibility of defining states with particularly simple transformation properties in the presence of symmetries.
The first non-spatiotemporal symmetry to be introduced into microphysics, and also the first symmetry to be treated with the techniques of group theory in the context of quantum mechanics, was permutation symmetry (or invariance under the transformations of the permutation group). This symmetry, discovered by W. Heisenberg in 1926 in relation to the indistinguishability of the identical electrons of an atomic system is the discrete symmetry (i.e. based upon groups with a discrete set of elements) at the core of the so-called quantum statistics (the Bose-Einstein and Fermi-Dirac statistics), governing the statistical behavior of ensembles of certain types of indistinguishable quantum particles (bosons and fermions).
The permutation symmetry principle states that if such an ensemble is invariant under a permutation of its constituent particles then one doesn't count those permutations which merely exchange indistinguishable particles, that is the exchanged state is identified with the original state.
The starting point for the idea of continuous internal symmetries was the interpretation of the presence of particles with approximately the same value of mass as the components (states) of a single physical system, connected to each other by the transformations of an underlying symmetry group. This idea emerged by analogy with what happened in the case of permutation symmetry, and was in fact due to Heisenberg (the discoverer of permutation symmetry), who in a 1932 paper introduced the SU symmetry connecting the proton and the neutron (interpreted as the two states of a single system).
Symmetry can be exact, approximate, or broken. Exact means unconditionally valid; approximate means valid under certain conditions; broken can mean different things, depending on the object considered and its context. Symmetry breaking was first explicitly studied in physics with respect to physical objects and phenomena. This follows naturally from the developments of the theory of symmetry, at the origin of which are the visible symmetry properties of familiar spatial figures and everyday objects. There are two different types of symmetry breaking of the laws: explicit and “spontaneous”.
Explicit symmetry breaking indicates a situation where the dynamical equations are not manifestly invariant under the symmetry group considered. This means, in the Lagrangian (Hamiltonian) formulation, that the Lagrangian (Hamiltonian) of the system contains one or more terms explicitly breaking the symmetry.
Spontaneous symmetry breaking, occurs in a situation where, given a symmetry of the equations of motion, solutions exist which are not invariant under the action of this symmetry without any explicit asymmetric input (whence the attribute “spontaneous”). A situation of this type can be first illustrated by means of simple cases taken from classical physics.
In quantum physics SSB actually does not occur in the case of finite systems: tunneling takes place between the various degenerate states, and the true lowest energy state or “ground state” turns out to be a unique linear superposition of the degenerate states.
The SSB prototype case, is Heisenberg's theory of the ferro-magnet as an infinite array of spin with 1/2 magnetic dipoles, with spin-spin interacts between the nearest neighbors in such a way that neighboring dipoles tend to align.
The concept of SSB was transferred from condensed matter physics to QFT (Quantum field theory) in the early 1960s, the application of SSB to particle physics in the 1960s; and successive years led to profound physical consequences and played a fundamental role in the edification of the current Standard Model of elementary particles.
According to a “mechanism” established in a general way in 1964, in the case that the internal symmetry is promoted to a local one, the Goldstone bosons “disappear” and the gauge bosons acquire a mass. The Goldstone bosons are “eaten up” to give mass to the gauge bosons, and this happens without (explicitly) breaking the gauge invariance of the theory.
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Irregularity (High-Entropy) - lowest energy (use)
Regularity (low-Entropy) - Highest energy (use)
- Decreasing Entropy > Lowest Bit.
- Increasing Entropy > Highest Bit.
Causality Sequence (non-accidental) means a sequence with probability of 1, has lowest Bits.
Non-Causality Sequence (accidental) means a sequence with unknown probability has highest numbers of Bits.
More information means powerful Structure. It means Harmony comes from chaos.
It is the fact of Nature to be chaotic.
It is reality.
It is nature.
The total state can be obtained by adding the spatial state the particles which could also be symmetric Or anti-symmetric But in the case of Bosons the spatial part of the wave function HAS TO be Anti-Symmetric...
(Bosons are particles of force transmission.)
"Bell-State Analyser"
Wave function can explain exactly about two particles while spatial states be symmetrical, that can be unequal zero, So spin states must be Asymmetrical.
- It means symmetrical universe cannot exist.
Universe can be symmetrical But just in spatial states as virtual parameter, not about reality.
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Asymmetric Supernovae: Not All Stellar Explosions Expand Spherically;
http://www.sciencedaily.com/releases/2011/02/110224145803.htm
Surprising New Evidence for Asymmetry Between Matter and Antimatter;
http://www.sciencedaily.com/releases/2010/05/100524161338.htm
Using Chaos to Model Geophysical Phenomena;
http://www.sciencedaily.com/releases/2010/12/101207091811.htm
Physicists propose mechanism that explains the origins of both dark matter and 'normal' matter;
http://www.physorg.com/news/2010-12-physicists-mechanism-dark.html
Dark Matter Could Transfer Energy in the Sun;
http://www.sciencedaily.com/releases/2010/12/101201095822.htm
& …
If laws of nature were symmetrical Now we couldn’t observe any Asymmetrical that be basis of Chaos.
- Wave function can explain two particles while spatial state be symmetrical that it can be not equal Zero, So Spin MUST be Asymmetrical.
Several Frame in one Frame.
§ Laws must be symmetrical?
NO.
But we suppose at first that laws always symmetrical. (And suppose this supposition as principle!)
- For everyFrame & everyTime laws are symmetrical But if you suppose several frame in a frame
It becomes impossible to have symmetry for primal frame. You walk on floor, other one walks on wall and I walk on roof…
All of us measure our walk-side as floor!
So easy you can understand it. Just be careful when see your LCD/LED.
Angles are important for measuring (to get information).
(However LCD/LED s not exact and complete example!)
Well we understand here about Angle of Effect.
Laws are effecting with pi/2 (R) on frame But if the frame has angle proportion to primal frame laws will effect on with |pi/2 + a|.
So from another frame will measure sth different.
Now we can understand concepts of HyperCube better, And can explain about HyperCube (Tesseract) and its events in it and they wont be exotic & marvelous for us.
But we can see symmetry in nature sometimes. What is it?
- Yes. It s exactly symmetry But in some coordinates for some viewpoint.
Sometimes in some special frame for some observer we have Symmetry.
- - To be continue…
