Asymmetry

Last updated November 28, 2024

Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection).^[1] Symmetry is an important property of both physical and abstract systems and it may be displayed in precise terms or in more aesthetic terms.^[2] The absence of or violation of symmetry that are either expected or desired can have important consequences for a system.

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 processes are highlighted, it is known that there are fundamental physical asymmetries, starting with time.

Asymmetry in biology

Asymmetry is an important and widespread trait, having evolved numerous times in many organisms and at many levels of organisation (ranging from individual cells, through organs, to entire body-shapes). Benefits of asymmetry sometimes have to do with improved spatial arrangements, such as the left human lung being smaller, and having one fewer lobes than the right lung to make room for the asymmetrical heart. In other examples, division of function between the right and left half may have been beneficial and has driven the asymmetry to become stronger. Such an explanation is usually given for mammal hand or paw preference (handedness), an asymmetry in skill development in mammals. Training the neural pathways in a skill with one hand (or paw) may take less effort than doing the same with both hands.^[3]

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

Most snails, because of torsion during development, show remarkable asymmetry in the shell and in the internal organs.^[4]
Male fiddler crabs have one big claw and one small claw.^[5]
The narwhal's tusk is a left incisor which can grow up to 10 feet in length and forms a left-handed helix.^[6]
Flatfish have evolved to swim with one side upward, and as a result have both eyes on one side of their heads.^[7]
Several species of owls exhibit asymmetries in the size and positioning of their ears, which is thought to help locate prey.^[8]
Many animals (ranging from insects to mammals) have asymmetric male genitalia. The evolutionary cause behind this is, in most cases, still a mystery.^[9]

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. For example, a greater degree of facial symmetry is seen as more attractive in humans, especially in the context of mate selection. In general, there is a correlation between symmetry and fitness-related traits such as growth rate, fecundity and survivability for many species. This means that, through sexual selection, individuals with greater symmetry (and therefore fitness) tend to be preferred as mates, as they are more likely to produce healthy offspring.^[10]

In structures

Pre-modern architectural styles tended to place an emphasis on symmetry, except where extreme site conditions or historical developments lead away from this classical ideal. To the contrary, modernist and postmodern architects became much more free to use asymmetry as a design element.

While most bridges employ a symmetrical form due to intrinsic simplicities of design, analysis and fabrication and economical use of materials, a number of modern bridges have deliberately departed from this, either in response to site-specific considerations or to create a dramatic design statement.

Some asymmetrical structures

Eastern span replacement of the San Francisco – Oakland Bay Bridge
Puente de la Mujer
Auditorio de Tenerife
Blohm & Voss BV 141 aircraft
A proa, a form of outrigger canoe

In fire protection

In fire-resistance rated wall assemblies, used in passive fire protection, including, but not limited to, high-voltage transformer fire barriers, asymmetry is a crucial aspect of design. When designing a facility, it is not always certain, that in the event of fire, which side a fire may come from. Therefore, many building codes and fire test standards outline, that a symmetrical assembly, need only be tested from one side, because both sides are the same. However, as soon as an assembly is asymmetrical, both sides must be tested and the test report is required to state the results for each side. In practical use, the lowest result achieved is the one that turns up in certification listings. Neither the test sponsor, nor the laboratory can go by an opinion or deduction as to which side was in more peril as a result of contemplated testing and then test only one side. Both must be tested in order to be compliant with test standards and building codes.

In mathematics

In mathematics, asymmetry can arise in various ways. Examples include asymmetric relations, asymmetry of shapes in geometry, asymmetric graphs et cetera.

Lines of symmetry

When determining whether an object is asymmetrical, look for lines of symmetry. For instance, a square has four lines of symmetry, while a circle has infinite. If a shape has no lines of symmetry, then it is asymmetrical, but if an object has any lines of symmetry, it is symmetrical.

Asymmetric Relation

An asymmetric relation is a binary relation $R$ defined on a set of elements such that if $aRb$ holds for elements $a$ and $b$ , then $bRa$ must be false. Stated differently, an asymmetric relation is characterized by a necessary absence of symmetry of the relation in the opposite direction.

Inequalities exemplify asymmetric relations. Consider elements $a$ and $b$ . If $a$ is less than $b$ ( $a<b$ ), then $a$ cannot be greater than $b$ ( $a\ngtr b$ ).^[11] This highlights how the relations "less than", and similarly "greater than", are not symmetric.

In contrast, if $a$ is equal to $b$ ( $a=b$ ), then $b$ is also equal to $a$ ( $b=a$ ). Thus the binary relation "equal to" is a symmetric one.

Asymmetric Tensors

In general an Asymmetric tensor is defined by the change of signs $(-/+)$ of its solution under the interchange of two indexes.

The Epsilon-tensor is an example of an asymmetric tensor. It is defined as: $\epsilon _{ijk}=\left\{{\begin{array}{cc}1&if\;(i,j,k)\in \{(123),(231),(312)\}\\-1&if\;(i,j,k)\in \{(213),(321),(132)\}\\0&else\end{array}}\right.$

,with $i,j,k\in \{1,2,3\}$ .^[12] For even or uneven permutations of the indexes the tensor is either 1 or -1.

In chemistry

Certain molecules are chiral; that is, they cannot be superposed upon their mirror image. Chemically identical molecules with different chirality are called enantiomers; this difference in orientation can lead to different properties in the way they react with biological systems.

In physics

Asymmetry arises in physics in a number of different realms.

Thermodynamics

The original non-statistical formulation of thermodynamics was asymmetrical in time: it claimed that the entropy in a closed system can only increase with time. This was derived from the Second Law (any of the two, Clausius' or Lord Kelvin's statement can be used since they are equivalent) and using the Clausius' Theorem (see Kerson Huang ISBN 978-0471815181). The later theory of statistical mechanics, however, is symmetric in time. Although it states that a system significantly below maximum entropy is very likely to evolve towards higher entropy, it also states that such a system is very likely to have evolved from higher entropy.

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

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.^{[ citation needed ]} Simultaneously, R. L. Garwin, Leon Lederman, and R. Weinrich modified an existing cyclotron experiment and immediately verified parity violation.^{[ citation needed ]}

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 early 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

The baryons (i.e., the protons and neutrons and the atoms that they comprise) observed so far 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 Eightfold 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.

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.

Related Research Articles

In particle physics, a baryon is a type of composite subatomic particle that contains an odd number of valence quarks, conventionally three. Protons and neutrons are examples of baryons; because baryons are composed of quarks, they belong to the hadron family of particles. Baryons are also classified as fermions because they have half-integer spin.

In particle physics, a meson is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, they have a meaningful physical size, a diameter of roughly one femtometre (10⁻¹⁵ m), which is about 0.6 times the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few tenths of a nanosecond. Heavier mesons decay to lighter mesons and ultimately to stable electrons, neutrinos and photons.

In nuclear physics and particle physics, the weak interaction, also called the weak force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation. It is the mechanism of interaction between subatomic particles that is responsible for the radioactive decay of atoms: The weak interaction participates in nuclear fission and nuclear fusion. The theory describing its behaviour and effects is sometimes called quantum flavordynamics (QFD); however, the term QFD is rarely used, because the weak force is better understood by electroweak theory (EWT).

The Standard Model of particle physics is the theory describing three of the four known fundamental forces in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.

In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are W⁺
, W⁻
, and Z⁰
. The W^±
bosons have either a positive or negative electric charge of 1 elementary charge and are each other's antiparticles. The Z⁰
boson is electrically neutral and is its own antiparticle. The three particles each have a spin of 1. The W^±
bosons have a magnetic moment, but the Z⁰
has none. All three of these particles are very short-lived, with a half-life of about 3×10⁻²⁵ s. Their experimental discovery was pivotal in establishing what is now called the Standard Model of particle physics.

In physical cosmology, baryogenesis is the physical process that is hypothesized to have taken place during the early universe to produce baryonic asymmetry, i.e. the imbalance of matter (baryons) and antimatter (antibaryons) in the observed universe.

In nuclear physics and particle physics, isospin (I) is a quantum number related to the up- and down quark content of the particle. Isospin is also known as isobaric spin or isotopic spin. Isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons.

A chiral phenomenon is one that is not identical to its mirror image. The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry.

In the Standard Model of electroweak interactions of particle physics, the weak hypercharge is a quantum number relating the electric charge and the third component of weak isospin. It is frequently denoted $and corresponds to the gauge symmetry U(1).$

In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the $W \pm$ bosons; particles with zero weak isospin do not. Weak isospin is a construct parallel to the idea of isospin under the strong interaction. Weak isospin is usually given the symbol $T$ or $I$ , with the third component written as $T$ ₃ or $I$ ₃. $T$ ₃ is more important than $T$ ; typically "weak isospin" is used as short form of the proper term "3rd component of weak isospin". It can be understood as the eigenvalue of a charge operator.

In particle physics, flavour or flavor refers to the species of an elementary particle. The Standard Model counts six flavours of quarks and six flavours of leptons. They are conventionally parameterized with flavour quantum numbers that are assigned to all subatomic particles. They can also be described by some of the family symmetries proposed for the quark-lepton generations.

This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group $SU(3) \times SU(2) \times U(1)$ . The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.

<span class="mw-page-title-main">Baryon asymmetry</span> Imbalance of matter and antimatter in the observable universe

In physical cosmology, the baryon asymmetry problem, also known as the matter asymmetry problem or the matter–antimatter asymmetry problem, is the observed imbalance in baryonic matter and antibaryonic matter in the observable universe. Neither the standard model of particle physics nor the theory of general relativity provides a known explanation for why this should be so, and it is a natural assumption that the universe is neutral with all conserved charges. The Big Bang should have produced equal amounts of matter and antimatter. Since this does not seem to have been the case, it is likely some physical laws must have acted differently or did not exist for matter and/or antimatter. Several competing hypotheses exist to explain the imbalance of matter and antimatter that resulted in baryogenesis. However, there is as of yet no consensus theory to explain the phenomenon, which has been described as "one of the great mysteries in physics".

In particle physics, chiral symmetry breaking generally refers to the dynamical spontaneous breaking of a chiral symmetry associated with massless fermions. This is usually associated with a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction, and it also occurs through the Brout-Englert-Higgs mechanism in the electroweak interactions of the standard model. This phenomenon is analogous to magnetization and superconductivity in condensed matter physics. The basic idea was introduced to particle physics by Yoichiro Nambu, in particular, in the Nambu–Jona-Lasinio model, which is a solvable theory of composite bosons that exhibits dynamical spontaneous chiral symmetry when a 4-fermion coupling constant becomes sufficiently large. Nambu was awarded the 2008 Nobel prize in physics "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics".

In particle physics, the X and Y bosons are hypothetical elementary particles analogous to the W and Z bosons, but corresponding to a unified force predicted by the Georgi–Glashow model, a grand unified theory (GUT).

In particle physics, the X charge is a conserved quantum number associated with the SO(10) grand unification theory. It is thought to be conserved in strong, weak, electromagnetic, gravitational, and Higgs interactions. Because the X charge is related to the weak hypercharge, it varies depending on the helicity of a particle. For example, a left-handed quark has an X charge of +1, whereas a right-handed quark can have either an X charge of −1, or −3.

In nuclear physics and atomic physics, weak charge, or rarely neutral weak charge, refers to the Standard Model weak interaction coupling of a particle to the Z boson. For example, for any given nuclear isotope, the total weak charge is approximately −0.99 per neutron, and +0.07 per proton. It also shows an effect of parity violation during electron scattering.

This page is a glossary of terms in string theory, including related areas such as supergravity, supersymmetry, and high energy physics.

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