Chirality (physics)

In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly if it cannot be mapped to its mirror image by rotations and translations alone. Such objects come in two forms, called enantiomorphs. The word chirality is derived from the Greek χειρ (cheir), the hand, the most familiar chiral object; the word enantiomorph stems from the Greek εναντιος (enantios) 'opposite' and μορφη (morphe) 'form'. A non-chiral figure is called Including:

• Chirality mathematics - Chirality and symmetry group
• Chirality mathematics - Chirality in three dimensions
• Chirality mathematics - Chirality in two dimensions
• Chirality mathematics - Knot theory

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In three dimensions, every figure which possesses a plane of symmetry or a center of symmetry is achiral. (A plane of symmetry of a figure F is a plane P, such that F is invariant under the mapping , when P is chosen to be the x-y-plane of the coordinate system. A center of symmetry of a figure See also:

Chirality mathematics, Chirality mathematics - Chirality and symmetry group, Chirality mathematics - Chirality in three dimensions, Chirality mathematics - Chirality in two dimensions, Chirality mathematics - Knot theory

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Vector - Physics. Chirality (physics), vector (field) theory Vector - Computer Science. A list or one-dimensional array Vector processor, a computer processor which works on arrays of several numbers at once Dope vector Vector graphics, computer graphics defined by geometric primitives instead of pixels Vector (computing), the method that malicious code (viruses, etc) uses to propagate itself Ve ...

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• Vector - Mathematics
• Vector - Physics
• Vector - Computer Science
• Vector - Biology
• Vector - Miscellaneous

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A clockwise motion is one that proceeds 'like the clock's hands': from the top to the right, then down and then to the left, and back to the top. In a mathematical sense, a circle defined parametrically by the equations x = r sin t and y = r cos t, where r is the radius of the circle, is traced clockwise as t increases in value. The opposite sense of rota ...

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In two dimensions, every figure which possesses an axis of symmetry is achiral, and it can be shown that every bounded achiral figure must have an axis of symmetry. (An axis of symmetry of a figure F is a line L, such that F is invariant under the mapping , when L is chosen to be the x-axis of the coordinate system.) Consider the following pattern: > > > > > > > ...

See also:

Chirality mathematics, Chirality mathematics - Chirality and symmetry group, Chirality mathematics - Chirality in three dimensions, Chirality mathematics - Chirality in two dimensions, Chirality mathematics - Knot theory

Read more here: » Chirality mathematics: Encyclopedia II - Chirality mathematics - Chirality in two dimensions

The question of how these masses arise has not been answered conclusively. In the Standard Model of particle physics, fermions ("matter particles") only have mass because of interactions with the Higgs field (see Higgs boson). These interactions involve both left- and right-handed versions of the fermion (see Chirality (physics)). Neutrinos are special, since as electrically-neutral particles they may have another source of mass, Majorana mass (which cannot work for electrically-charged particles since it would allow particles to turn into a ...

See also:

Neutrino oscillation, Neutrino oscillation - Evidence for neutrino oscillations, Neutrino oscillation - The effect of neutrino masses, Neutrino oscillation - Origins of neutrino mass, Neutrino oscillation - Neutrino Parameters and Their Values, Neutrino oscillation - Neutrino Experiments, Neutrino oscillation - Measuring Theta_{13}, Neutrino oscillation - See Also

Read more here: » Neutrino oscillation: Encyclopedia II - Neutrino oscillation - Origins of neutrino mass

Neutrino oscillation - Measuring Theta_{13}. the Double Chooz Experiment ...

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Neutrino oscillation, Neutrino oscillation - Evidence for neutrino oscillations, Neutrino oscillation - The effect of neutrino masses, Neutrino oscillation - Origins of neutrino mass, Neutrino oscillation - Neutrino Parameters and Their Values, Neutrino oscillation - Neutrino Experiments, Neutrino oscillation - Measuring Theta_{13}, Neutrino oscillation - See Also

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It is widely accepted in the particle physics community that the oscillations are due to the different flavors of neutrino having different masses. If a neutrino is produced as a flavor eigenstate, and flavor eigenstates are not mass eigenstates, then we should write the neutrino wavefunction as a superposition of various mass eigenstates: Here, is a neutrino with given flavor (a=electron, muon or tau), Uai are the coefficients of the neutrino mixing ma ...

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Neutrino oscillation, Neutrino oscillation - Evidence for neutrino oscillations, Neutrino oscillation - The effect of neutrino masses, Neutrino oscillation - Origins of neutrino mass, Neutrino oscillation - Neutrino Parameters and Their Values, Neutrino oscillation - Neutrino Experiments, Neutrino oscillation - Measuring Theta_{13}, Neutrino oscillation - See Also

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Solar neutrino experiments combined with KamLAND have measured the so-called solar parameters and sin2Θsol. Atmospheric neutrino experiments such as Super-Kamiokande together with the K2K first long baseline accelerator neutrino experiment have determined the so-called atmospheric parameters and sin2Θatm. An additional experiment MINOS is expected to reduce the experimental erros si ...

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Neutrino oscillation, Neutrino oscillation - Evidence for neutrino oscillations, Neutrino oscillation - The effect of neutrino masses, Neutrino oscillation - Origins of neutrino mass, Neutrino oscillation - Neutrino Parameters and Their Values, Neutrino oscillation - Neutrino Experiments, Neutrino oscillation - Measuring Theta_{13}, Neutrino oscillation - See Also

Read more here: » Neutrino oscillation: Encyclopedia II - Neutrino oscillation - Neutrino Parameters and Their Values