'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.
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 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, C
6H
12O
6. 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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