asymmetry

Asymmetry is the absence of, or a violation of, a symmetry.

Asymmetry in organisms

Due to how cells divide in organisms, asymmetry in organisms is fairly usual in at least one dimension, with biological symmetry also being common in at least one dimension.

Louis Pasteur proposed that biological molecules are asymmetric because the cosmic [i.e. physical] forces that preside over their formation are themselves asymmetric. While at his time, and even now, the symmetry of physical processses are highlighted, it is known that there are fundamental physical asymmetries, starting with time. Further, truly fundamental left-right symmetry violation is now known in particle physics (see Parity violation below).

Asymmetries useful to the organism

• Essential asymmetry and important evolutionary traits, such as the left human lung being smaller than the right to make room for the asymmetrical heart.
• Handedness is an asymmetry in skill development in people and animals. Training the neural pathways in a skill with one hand (or paw) takes less effort than doing the same with both hands.^{[citation needed]}

Nature also provides several examples of handedness in traits that are usually symmetric. The following are examples of animals with obvious left-right asymmetries:

Fiddler crab, Uca pugnax

• Fiddler crabs have one big claw and one small claw.
• The narwhal's tusk is a left incisor which can grow up to 10 feet in length and forms a left-handed helix.
• Flatfish have evolved to swim with one side upward, and as a result have both eyes on one side of their heads.
• Several species of owls exhibit asymmetries in the size and positioning of their ears, which is thought to help locate prey.

Asymmetry as an indicator of unfitness

• Certain disturbances during the development of the organism, resulting in birth defects.
• Injuries after cell division that cannot be biologically repaired, such as a lost limb from an accident.

Since birth defects and injuries are likely to indicate poor health of the organism, defects resulting in asymmetry often put an animal at a disadvantage when it comes to finding a mate. In particular, a degree of facial symmetry is associated with physical attractiveness, but complete symmetry is both impossible and probably unattractve.

Asymmetry in chemistry

Certain molecules are chiral; that is, they cannot be superposed upon their mirror image.

Some sugars are chiral: glucose (also called dextrose) and fructose (sometimes called levulose or invert sugar) are chiral isomers of the same molecule, C₆H₁₂O₆. The word invert comes from the way that sugar syrups rotate plane-polarized light. A sucrose or glucose solution rotates the plane of polarization of the light to the right, while a fructose syrup rotates it strongly to the left.

Asymmetry in physics

Asymmetry arises in physics in a number of different realms.

Thermodynamics

Thermodynamics is asymmetrical in time: the entropy in a closed system can only increase with time. A consequence of this is Clausius' Second Law, which states that there is no thermodynamic process whose sole effect is to extract a quantity of heat from a colder reservoir and deliver it to a hotter reservoir.

Particle physics

Symmetry is one of the most powerful tools in particle physics, because it has become evident that practically all laws of nature originate in symmetries. Violations of symmetry therefore present theoretical and experimental puzzles that lead to a deeper understanding of nature. Asymmetries in experimental measurements also provide powerful handles that are often relatively free from background or systematic uncertainties.

Parity violation

Main article: parity (physics)

Until the 1950s, it was believed that fundamental physics was left-right symmetric; i.e., that interactions were invariant under parity. Although parity is conserved in electromagnetism, strong interactions and gravity, it turns out to be violated in weak interactions. The Standard Model incorporates parity violation by expressing the weak interaction as a chiral gauge interaction. Only the left-handed components of particles and right-handed components of antiparticles participate in weak interactions in the Standard Model. A consequence of parity violation in particle physics is that neutrinos have only been observed as left-handed particles (and antineutrinos as right-handed particles).

In 1956-1957 Chien-Shiung Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson found a clear violation of parity conservation in the beta decay of cobalt-60. Simultaneously, R. L. Garwin, Leon Lederman, and R. Weinrich modified an existing cyclotron experiment and immediately verified parity violation.

CP violation

Main article: CP-violation

After the discovery of the violation of parity in 1956-57, it was believed that the combined symmetry of parity (P) and simultaneous charge conjugation (C), called CP, was preserved. For example, CP transforms a left-handed neutrino into a right-handed antineutrino. In 1964, however, James Cronin and Val Fitch provided clear evidence that CP symmetry was also violated in an experiment with neutral kaons.

CP violation is one of the necessary conditions for the generation of a baryon asymmetry in the universe.

Combining the CP symmetry with simultaneous time reversal (T) produces a combined symmetry called CPT symmetry. CPT symmetry must be preserved in any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian. As of 2006, no violations of CPT symmetry have been observed.

Baryon asymmetry of the universe

Main article: baryogenesis

The baryons (i.e., the protons and neutrons and the atoms that they comprise) observed in the universe are overwhelmingly matter as opposed to anti-matter. This asymmetry is called the baryon asymmetry of the universe.

Isospin violation

Isospin is the symmetry transformation of the weak interactions. The concept was first introduced by Werner Heisenberg in nuclear physics based on the observations that the masses of the neutron and the proton are almost identical and that the strength of the strong interaction between any pair of nucleons is the same, independent of whether they are protons or neutrons. This symmetry arises at a more fundamental level as a symmetry between up-type and down-type quarks. Isospin symmetry in the strong interactions can be considered as a subset of a larger flavor symmetry group, in which the strong interactions are invariant under interchange of different types of quarks. Including the strange quark in this scheme gives rise to the Eight-fold Way scheme for classifying mesons and baryons.

Isospin is violated by the fact that the masses of the up and down quarks are different, as well as by their different electric charges. Because this violation is only a small effect in most processes that involve the strong interactions, isospin symmetry remains a useful calculational tool, and its violation introduces corrections to the isospin-symmetric results.

Asymmetries in collider experiments

Because the weak interactions violate parity, collider processes that can involve the weak interactions typically exhibit asymmetries in the distributions of the final-state particles. These asymmetries are typically sensitive to the difference in the interaction between particles and antiparticles, or between left-handed and right-handed particles. They can thus be used as a sensitive measurement of differences in interaction strength and/or to distinguish a small asymmetric signal from a large but symmetric background.

• A forward-backward asymmetry is defined as A_FB=(N_F-N_B)/(N_F+N_B), where N_F is the number of events in which some particular final-state particle is moving "forward" with respect to some chosen direction (e.g., a final-state electron moving in the same direction as the initial-state electron beam in electron-positron collisions), while N_B is the number of events with the final-state particle moving "backward". Forward-backward asymmetries were used by the LEP experiments to measure the difference in the interaction strength of the Z boson between left-handed and right-handed fermions, which provides a precision measurement of the weak mixing angle.
• A left-right asymmetry is defined as A_LR=(N_L-N_R)/(N_L+N_R), where N_L is the number of events in which some initial- or final-state particle is left-polarized, while N_R is the corresponding number of right-polarized events. Left-right asymmetries in Z boson production and decay were measured at the Stanford Linear Collider using the event rates obtained with left-polarized versus right-polarized initial electron beams. Left-right asymmetries can also be defined as asymmetries in the polarization of final-state particles whose polarizations can be measured; e.g., tau leptons.
• A charge asymmetry or particle-antiparticle asymmetry is defined in a similar way. This type of asymmetry has been used to constrain the parton distribution functions of protons at the Tevatron from events in which a produced W boson decays to a charged lepton. The asymmetry between positively and negatively charged leptons as a function of the direction of the W boson relative to the proton beam provides information on the relative distributions of up and down quarks in the proton. Particle-antiparticle asymmetries are also used to extract measurements of CP violation from B meson and anti-B meson production at the BaBar and Belle experiments.

Lexical asymmetry

Asymmetry is also relevant to grammar and linguistics, especially in the contexts of lexical analysis and transformational grammar.

Enumeration example: In English, there are grammatical rules for specifying coordinate items in an enumeration or series. Similar rules exist for programming languages and mathematical notation. These rules vary, and some require lexical asymmetry to be considered grammatically correct.

For example in standard written English:

   We sell domesticated cats, dogs, and goldfish.        ### in-line asymmetric and grammatical
   We sell domesticated animals (cats, dogs, goldfish).  ### in-line symmetric and grammatical
   We sell domesticated animals (cats, dogs, goldfish,). ### in-line symmetric and ungrammatical
   We sell domesticated animals:                         ### outline symmetric and grammatical
     - cats
     - dogs
     - goldfish

References

• Yuh-Nung Jan and Lily Yeh Jan, 1999. Asymmetry across species. Nature Cell Biology 1, E42 - E44 PMID 10559895

Sabelli, H. Bios. A Study of Creation. World Scientific 2005

See also

• Information asymmetry

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