Chirality ( / k aɪ ˈ r æ l ɪ t i / ) is a property of asymmetry important in several branches of science. The word chirality is derived from the Greek χείρ ( kheir ), "hand", a familiar chiral object.
62-441: An object or a system is chiral if it is distinguishable from its mirror image ; that is, it cannot be superposed (not to be confused with superimposed ) onto it. Conversely, a mirror image of an achiral object, such as a sphere, cannot be distinguished from the object. A chiral object and its mirror image are called enantiomorphs (Greek, "opposite forms") or, when referring to molecules, enantiomers . A non-chiral object
124-432: A Rear Window Captioning System used to assist individuals with hearing impairments in watching films. In the case of two mirrors, in planes at an angle α, looking through both from the sector which is the intersection of the two halfspaces, is like looking at a version of the world rotated by an angle of 2α; the points of observations and directions of looking for which this applies correspond to those for looking through
186-465: A massless particle is the double cover of SE(2) . This has unitary representations which are invariant under the SE(2) "translations" and transform as e under a SE(2) rotation by θ . This is the helicity h representation. There is also another unitary representation which transforms non-trivially under the SE(2) translations. This is the continuous spin representation. In d + 1 dimensions,
248-462: A mirror or water . It is also a concept in geometry and can be used as a conceptualization process for 3D structures. In geometry , the mirror image of an object or two-dimensional figure is the virtual image formed by reflection in a plane mirror ; it is of the same size as the original object, yet different, unless the object or figure has reflection symmetry (also known as a P-symmetry ). Two-dimensional mirror images can be seen in
310-410: A center of inversion (i) or a mirror plane (σ). Only figures with a point group designation of C 1 , C n , D n , T, O, or I can be chiral. A knot is called achiral if it can be continuously deformed into its mirror image, otherwise it is called chiral. For example, the unknot and the figure-eight knot are achiral, whereas the trefoil knot is chiral. In physics, chirality may be found in
372-532: A chiral molecule, the plane of polarization, when viewed along the axis toward the source, will be rotated clockwise (to the right) or anticlockwise (to the left). A right handed rotation is dextrorotary (d); that to the left is levorotary (l). The d- and l-isomers are the same compound but are called enantiomers . An equimolar mixture of the two optical isomers, which is called a racemic mixture , will produce no net rotation of polarized light as it passes through. Left handed molecules have l- prefixed to their names; d-
434-442: A frame like that of the first mirror, and a frame at the mirror image with respect to the first plane, of the second mirror. If the mirrors have vertical edges then the left edge of the field of view is the plane through the right edge of the first mirror and the edge of the second mirror which is on the right when looked at directly, but on the left in the mirror image. In the case of two parallel mirrors, looking through both at once
496-400: A mirror in the y , z plane) has coordinates (− x , y , z ). Thus reflection is a reversal of the coordinate axis perpendicular ( normal ) to the mirror's surface. Although a plane mirror reverses an object only in the direction normal to the mirror surface, this turns the entire three-dimensional image seen in the mirror inside-out, so there is a perception of a left-right reversal. Hence,
558-403: A molecule, one a "mirror image" of the other, are called enantiomers if they are not "superposable" (the correct technical term, though the term "superimposable" is also used) on each other. That is an example of chirality . In general, an object and its mirror image are called enantiomorphs . If a point of an object has coordinates ( x , y , z ) then the image of this point (as reflected by
620-481: A perpendicular direction. The translated view can also be described by a translation of the observer in opposite direction. For example, with a vertical periscope , the shift of the world is away from the observer and down, both by the length of the periscope, but it is more practical to consider the equivalent shift of the observer: up, and backward. It is also possible to create a non-reversing mirror by placing two first surface mirrors at 90º to give an image which
682-513: A right hand. In mathematics, chirality is the property of a figure that is not identical to its mirror image. In mathematics , a figure is chiral (and said to have chirality) if it cannot be mapped to its mirror image by rotations and translations alone. For example, a right shoe is different from a left shoe, and clockwise is different from anticlockwise. See for a full mathematical definition. A chiral object and its mirror image are said to be enantiomorphs. The word enantiomorph stems from
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#1732787858113744-481: A single enantiomer drug for a better therapeutic value. [1] Such a switching from a racemic drug to an enantiopure drug is called a chiral switch . The naturally occurring plant form of alpha-tocopherol ( vitamin E ) is RRR-α-tocopherol whereas the synthetic form (all-racemic vitamin E, or dl-tocopherol) is equal parts of the stereoisomers RRR, RRS, RSS, SSS, RSR, SRS, SRR, and SSR with progressively decreasing biological equivalency, so that 1.36 mg of dl-tocopherol
806-419: A small minority of species and genera are virtually always sinistral (left-handed). A very few species (for example Amphidromus perversus ) show an equal mixture of dextral and sinistral individuals. In humans, chirality (also referred to as handedness or laterality ) is an attribute of humans defined by their unequal distribution of fine motor skill between the left and right hands . An individual who
868-402: A two-dimensional space. Many other familiar objects exhibit the same chiral symmetry of the human body, such as gloves, glasses (sometimes), and shoes. A similar notion of chirality is considered in knot theory , as explained below. Some chiral three-dimensional objects, such as the helix, can be assigned a right or left handedness, according to the right-hand rule . In geometry , a figure
930-583: Is achiral if and only if its symmetry group contains at least one orientation-reversing isometry. In two dimensions, every figure that possesses an axis of symmetry is achiral, and it can be shown that every bounded achiral figure must have an axis of symmetry. In three dimensions, every figure that possesses a plane of symmetry or a center of symmetry is achiral. There are, however, achiral figures lacking both plane and center of symmetry. In terms of point groups , all chiral figures lack an improper axis of rotation (S n ). This means that they cannot contain
992-419: Is aligned with the direction of the pitch. It will have one helicity with respect to the point of view of the players on the field, but would appear to have a flipped helicity in any frame moving faster than the ball. In this sense, helicity can be contrasted to chirality , which is Lorentz invariant, but is not a constant of motion for massive particles. For massless particles, the two coincide: The helicity
1054-420: Is associated with 3d chirality and circular conversion is associated with 2d chirality, both effects have also been observed in structures that are not chiral by themselves. For the observation of these chiral electromagnetic effects, chirality does not have to be an intrinsic property of the material that interacts with the electromagnetic wave. Instead, both effects can also occur when the propagation direction of
1116-485: Is associated with directionally asymmetric transmission (reflection and absorption) of circularly polarized waves. 2D-chiral materials, which are also anisotropic and lossy exhibit different total transmission (reflection and absorption) levels for the same circularly polarized wave incident on their front and back. The asymmetric transmission phenomenon arises from different, e.g. left-to-right, circular polarization conversion efficiencies for opposite propagation directions of
1178-449: Is because of other contributing factors. Also, for artificial compounds, including medicines, in case of chiral drugs , the two enantiomers sometimes show remarkable difference in effect of their biological actions. Darvon ( dextropropoxyphene ) is a painkiller, whereas its enantiomer, Novrad ( levopropoxyphene ) is an anti-cough agent. In case of penicillamine , the ( S -isomer is used in the treatment of primary chronic arthritis, whereas
1240-571: Is called achiral (sometimes also amphichiral ) and can be superposed on its mirror image. The term was first used by Lord Kelvin in 1893 in the second Robert Boyle Lecture at the Oxford University Junior Scientific Club which was published in 1894: I call any geometrical figure, or group of points, 'chiral', and say that it has chirality if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself. Human hands are perhaps
1302-610: Is considered equivalent to 1.0 mg of d-tocopherol. Macroscopic examples of chirality are found in the plant kingdom, the animal kingdom and all other groups of organisms. A simple example is the coiling direction of any climber plant, which can grow to form either a left- or right-handed helix. In anatomy, chirality is found in the imperfect mirror image symmetry of many kinds of animal bodies. Organisms such as gastropods exhibit chirality in their coiled shells, resulting in an asymmetrical appearance. Over 90% of gastropod species have dextral (right-handed) shells in their coiling, but
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#17327878581131364-543: Is equal to the chirality, both are Lorentz invariant, and both are constants of motion. In quantum mechanics , angular momentum is quantized, and thus helicity is quantized as well. Because the eigenvalues of spin with respect to an axis have discrete values, the eigenvalues of helicity are also discrete. For a massive particle of spin S , the eigenvalues of helicity are S , S − 1 , S − 2 , ..., − S . For massless particles, not all of spin eigenvalues correspond to physically meaningful degrees of freedom: For example,
1426-400: Is like looking at a version of the world which is translated by twice the distance between the mirrors, in the direction perpendicular to them, away from the observer. Since the plane of the mirror in which one looks directly is beyond that of the other mirror, one always looks at an oblique angle, and the translation just mentioned has not only a component away from the observer, but also one in
1488-491: Is more dexterous with the right hand is called right-handed , and one who is more skilled with the left is said to be left-handed . Chirality is also seen in the study of facial asymmetry and is known as aurofacial asymmetry. According to the Axial Twist theory , vertebrate animals develop into a left-handed chirality. Due to this, the brain is turned around and the heart and bowels are turned by 90°. In
1550-488: Is most often the cause of chirality in molecules is the presence of an asymmetric carbon atom . The term "chiral" in general is used to describe the object that is non-superposable on its mirror image. In chemistry, chirality usually refers to molecules. Two mirror images of a chiral molecule are called enantiomers or optical isomers . Pairs of enantiomers are often designated as " right- ", "left-handed" or, if they have no bias, "achiral". As polarized light passes through
1612-445: Is not reversed. Helicity (particle physics) In physics , helicity is the projection of the spin onto the direction of momentum. Mathematically, helicity is the sign of the projection of the spin vector onto the momentum vector : "left" is negative, "right" is positive. The angular momentum J is the sum of an orbital angular momentum L and a spin S . The relationship between orbital angular momentum L ,
1674-446: Is prefixed to right handed molecules. However, this d- and l- notation of distinguishing enantiomers does not say anything about the actual spatial arrangement of the ligands/substituents around the stereogenic center, which is defined as configuration. Another nomenclature system employed to specify configuration is Fischer convention. This is also referred to as the D- and L-system. Here
1736-404: Is responsible for the smell of caraway seed oil, whereas (–)-carvone is responsible for smell of spearmint oil. However, it is a commonly held misconception that (+)-limonene is found in oranges (causing its smell), and (–)-limonene is found in lemons (causing its smell). In 2021, after rigorous experimentation, it was found that all citrus fruits contain only (+)-limonene and the odor difference
1798-521: Is reversed. If a person stands side-on to a mirror, left and right hands will be reversed directly by the mirror, because the person's left-right axis is then normal to the mirror plane. However, it is important to understand that there are always only two enantiomorphs, the object and its inside-out image. Therefore, no matter how the object is oriented towards the mirror, all the resulting images are fundamentally identical (as Corballis explains in his paper "Much ado about mirrors", mentioned above). In
1860-557: Is the property that describes the orientation , i.e., the time-varying direction and amplitude , of the electric field vector . For example, the electric field vectors of left-handed or right-handed circularly polarized waves form helices of opposite handedness in space. Circularly polarized waves of opposite handedness propagate through chiral media at different speeds ( circular birefringence ) and with different losses ( circular dichroism ). Both phenomena are jointly known as optical activity. Circular birefringence causes rotation of
1922-555: The photon is a massless spin 1 particle with helicity eigenvalues −1 and +1, but the eigenvalue 0 is not physically present. All known spin 1 / 2 particles have non-zero mass; however, for hypothetical massless spin 1 / 2 particles (the Weyl spinors ), helicity is equivalent to the chirality operator multiplied by 1 / 2 ħ . By contrast, for massive particles, distinct chirality states (e.g., as occur in
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1984-403: The spin of a particle, where the handedness of the object is determined by the direction in which the particle spins. Not to be confused with helicity , which is the projection of the spin along the linear momentum of a subatomic particle, chirality is an intrinsic quantum mechanical property, like spin. Although both chirality and helicity can have left-handed or right-handed properties, only in
2046-475: The weak interaction charges) have both positive and negative helicity components, in ratios proportional to the mass of the particle. A treatment of the helicity of gravitational waves can be found in Weinberg. In summary, they come in only two forms: +2 and −2, while the +1, 0 and −1 helicities are "non-dynamical" (they can be removed by a gauge transformation). In 3 + 1 dimensions, the little group for
2108-404: The ( R )-isomer has no therapeutic effect, as well as being highly toxic. In some cases, the less therapeutically active enantiomer can cause side effects. For example, ( S -naproxen is an analgesic but the ( R -isomer causes renal problems. In such situations where one of the enantiomers of a racemic drug is active and the other partner has undesirable or toxic effect one may switch from racemate to
2170-628: The E-Z notation. Molecular chirality is of interest because of its application to stereochemistry in inorganic chemistry , organic chemistry , physical chemistry , biochemistry , and supramolecular chemistry . More recent developments in chiral chemistry include the development of chiral inorganic nanoparticles that may have the similar tetrahedral geometry as chiral centers associated with sp3 carbon atoms traditionally associated with chiral compounds, but at larger scale. Helical and other symmetries of chiral nanomaterials were also obtained. All of
2232-465: The Greek ἐναντίος ( enantios ) 'opposite' + μορφή ( morphe ) 'form'. A non-chiral figure is called achiral or amphichiral. The helix (and by extension a spun string, a screw, a propeller, etc.) and Möbius strip are chiral two-dimensional objects in three-dimensional ambient space. The J, L, S and Z-shaped tetrominoes of the popular video game Tetris also exhibit chirality, but only in
2294-473: The case of the health condition situs inversus totalis , in which all the internal organs are flipped horizontally (i.e. the heart placed slightly to the right instead of the left), chirality poses some problems should the patient require a liver or heart transplant, as these organs are chiral, thus meaning that the blood vessels which supply these organs would need to be rearranged should a normal, non situs inversus ( situs solitus ) organ be required. In
2356-439: The electromagnetic wave together with the structure of an (achiral) material form a chiral experimental arrangement. This case, where the mutual arrangement of achiral components forms a chiral (experimental) arrangement, is known as extrinsic chirality. Chiral mirrors are a class of metamaterials that reflect circularly polarized light of a certain helicity in a handedness-preserving manner, while absorbing circular polarization of
2418-508: The fingers curl into the palm, representing the direction of rotation of the particle (i.e. clockwise and counterclockwise). Depending on the linear and rotational motion, the particle can either be defined by left-handedness or right-handedness. A symmetry transformation between the two is called parity . Invariance under parity by a Dirac fermion is called chiral symmetry . Electromagnetic waves can have handedness associated with their polarization . Polarization of an electromagnetic wave
2480-438: The genetic make up of the organism. From chemical level (molecular scale), biological systems show extreme stereospecificity in synthesis, uptake, sensing, metabolic processing. A living system usually deals with two enantiomers of the same compound in drastically different ways. In biology, homochirality is a common property of amino acids and carbohydrates . The chiral protein-making amino acids , which are translated through
2542-473: The helicity commutes with the Hamiltonian , and thus, in the absence of external forces, is time-invariant. It is also rotationally invariant, in that a rotation applied to the system leaves the helicity unchanged. Helicity, however, is not Lorentz invariant ; under the action of a Lorentz boost , the helicity may change sign. Consider, for example, a baseball, pitched as a gyroball , so that its spin axis
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2604-519: The incident wave and therefore the effect is referred to as circular conversion dichroism. Like the twist of a 2d-chiral pattern appears reversed for opposite directions of observation, 2d-chiral materials have interchanged properties for left-handed and right-handed circularly polarized waves that are incident on their front and back. In particular left-handed and right-handed circularly polarized waves experience opposite directional transmission (reflection and absorption) asymmetries. While optical activity
2666-470: The inside parts, even if they are not transparent . The term then relates to structural as well as visual aspects. A three-dimensional object is reversed in the direction perpendicular to the mirror surface. In physics, mirror images are investigated in the subject called geometrical optics . More fundamentally in geometry and mathematics they form the principal objects of Coxeter group theory and reflection groups . In chemistry, two versions ( isomers ) of
2728-452: The known life-forms show specific chiral properties in chemical structures as well as macroscopic anatomy, development and behavior. In any specific organism or evolutionarily related set thereof, individual compounds, organs, or behavior are found in the same single enantiomorphic form. Deviation (having the opposite form) could be found in a small number of chemical compounds, or certain organ or behavior but that variation strictly depends upon
2790-400: The massless case are they identical. In particular for a massless particle the helicity is the same as the chirality while for an antiparticle they have opposite sign. The handedness in both chirality and helicity relate to the rotation of a particle while it proceeds in linear motion with reference to the human hands. The thumb of the hand points towards the direction of linear motion whilst
2852-404: The mirror image of the halfspace before the mirror is relevant; if there is another mirror, the mirror image of the other halfspace is too. A mirror does not just produce an image of what would be there without it; it also changes the light distribution in the halfspace in front of and behind the mirror. A mirror hanging on the wall makes the room brighter because additional light sources appear in
2914-402: The mirror image. However, the appearance of additional light does not violate the conservation of energy principle, because some light no longer reaches behind the mirror, as the mirror simply re-directs the light energy. In terms of the light distribution, the virtual mirror image has the same appearance and the same effect as a real, symmetrically arranged half-space behind a window (instead of
2976-400: The mirror). Shadows may extend from the mirror into the halfspace before it, and vice versa. In mirror writing a text is deliberately displayed as its mirror image, in order to be read through a mirror. For example, emergency vehicles such as ambulances or fire engines use mirror images in order to be read from a vehicle's rear-view mirror . Some movie theaters also use mirror writing in
3038-401: The monocot bloodroot family , the species of the genera Wachendorfia and Barberetta have only individuals that either have the style points to the right or the style pointed to the left, with both morphs appearing within the same populations. This is thought to increase outcrossing and so boost genetic diversity, which in turn may help to survive in a changing environment. Remarkably,
3100-400: The most recognized example of chirality. The left hand is a non-superposable mirror image of the right hand; no matter how the two hands are oriented, it is impossible for all the major features of both hands to coincide across all axes. This difference in symmetry becomes obvious if someone attempts to shake the right hand of a person using their left hand, or if a left-handed glove is placed on
3162-472: The observed reversal. Another example is when we stand with our backs to the mirror and face an object that is in front of the mirror. Then we compare the object with its reflection by turning ourselves 180°, towards the mirror. Again we perceive a left-right reversal due to a change in our orientation. So, in these examples the mirror does not actually cause the observed reversals. The concept of reflection can be extended to three-dimensional objects, including
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#17327878581133224-440: The observer moves, or if the image is viewed using binocular vision . This is because the relative position of objects changes as the observer's perspective changes, or is differently viewed with each eye. Looking through a mirror from different positions (but necessarily with the point of observation restricted to the halfspace on one side of the mirror) is like looking at the 3D mirror image of space; without further mirrors only
3286-440: The opposite handedness. However, most absorbing chiral mirrors operate only in a narrow frequency band, as limited by the causality principle. Employing a different design methodology that allows undesired waves to pass through instead of absorbing the undesired waveform, chiral mirrors are able to show good broadband performance. A chiral molecule is a type of molecule that has a non-superposable mirror image . The feature that
3348-422: The perceived left-right reversal is discussed in "Much ado about mirrors" by Professor Michael Corballis (see "external links", below). Reflection in a mirror does result in a change in chirality , more specifically from a right-handed to a left-handed coordinate system (or vice versa). If one looks in a mirror two axes (up-down and left-right) coincide with those in the mirror, but the third axis (front-back)
3410-467: The picture of the mountain reflected in the lake (photograph top right), the reversal normal to the reflecting surface is obvious. Notice that there is no obvious front-back or left-right of the mountain. In the example of the urn and mirror (photograph to right), the urn is fairly symmetrical front-back (and left-right). Thus, no obvious reversal of any sort can be seen in the mirror image of the urn. A mirror image appears more obviously three-dimensional if
3472-507: The polarization state of electromagnetic waves in chiral media and can cause a negative index of refraction for waves of one handedness when the effect is sufficiently large. While optical activity occurs in structures that are chiral in three dimensions (such as helices), the concept of chirality can also be applied in two dimensions. 2D-chiral patterns, such as flat spirals, cannot be superposed with their mirror image by translation or rotation in two-dimensional space (a plane). 2D chirality
3534-422: The position operator r and the linear momentum (orbit part) p is so L' s component in the direction of p is zero. Thus, helicity is just the projection of the spin onto the direction of linear momentum. The helicity of a particle is positive (" right-handed") if the direction of its spin is the same as the direction of its motion and negative ("left-handed") if opposite. Helicity is conserved . That is,
3596-417: The reflections of mirrors or other reflecting surfaces, or on a printed surface seen inside-out. If we first look at an object that is effectively two-dimensional (such as the writing on a card) and then turn the card to face a mirror, the object turns through an angle of 180° and we see a left-right reversal in the mirror. In this example, it is the change in orientation rather than the mirror itself that causes
3658-525: The related genus Dilatris also has chirally dimorphic flowers, but here both morphs occur on the same plant. In flatfish , the summer flounder or fluke are left-eyed, while halibut are right-eyed. Mirror image A mirror image (in a plane mirror) is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface. As an optical effect , it results from specular reflection off from surfaces of lustrous materials, especially
3720-459: The relative configuration is assigned with reference to D-(+)-Glyceraldehyde and L-(−)-Glyceraldehyde, being taken as standard. Fischer convention is widely used in sugar chemistry and for α-amino acids. Due to the drawbacks of Fischer convention, it is almost entirely replaced by Cahn-Ingold-Prelog convention , also known as the sequence rule or R and S nomenclature. This was further extended to assign absolute configuration to cis-trans isomers with
3782-415: The reversal is somewhat misleadingly called a "lateral inversion". The perception of a left-right reversal is geometrically explained by the fact that a three-dimensional object seen in a mirror is an inside-out version of the actual object, like a glove stripped off the left hand and turned into a right-hand glove, but there is still some confusion about the explanation amongst psychologists. The psychology of
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#17327878581133844-480: The ribosome from genetic coding, occur in the L form. However, D -amino acids are also found in nature. The monosaccharides (carbohydrate-units) are commonly found in D -configuration. DNA double helix is chiral (as any kind of helix is chiral), and B-form of DNA shows a right-handed turn. Sometimes, when two enantiomers of a compound are found in organisms, they significantly differ in their taste, smell and other biological actions. For example,(+)- Carvone
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