# What is Chirality: Definition and 67 Discussions

Chirality is a property of asymmetry important in several branches of science. The word chirality is derived from the Greek χειρ (kheir), "hand," a familiar chiral object.
An object or a system is chiral if it is distinguishable from its mirror image; that is, it cannot be 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 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 the most universally recognized example of chirality. The left hand is a non-superimposable 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 a right hand. In mathematics, chirality is the property of a figure that is not identical to its mirror image. A molecule is said to be chiral if its all valence is occupied by different atom or group of atoms.

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1. ### Writing: Input Wanted Alien chiral chemistry

A lot of terrestrial biology has specific chirality, the 'Other Hand' being bio-unavailable or toxic... As 'our' set is product of aeons of happenstance and evolution, alien biology probably differs. ( I'm thinking genuinely alien 'alien' rather than eg 'seeding' or panspermia...) Can...
2. ### I Chiral symmetries in E[SUP]^n[/SUP]

As a biochemist, I deal with chirality of molecules all the time. If you have a tetrahedral molecule, for example a carbon atom, and all 4 vertices are labeled differently, as in different atoms on each one, then that molecule has a mirror-symmetric one that cannot be superimposed on the...
3. ### B Photon Chirality: Left, Right & Beyond

Are photons left- and right-handed? If so, does the handedness change when a photon is reflected? Is there any other way the handedness can change? -- Jeff, in Minneapolis
4. ### I Is the Chirality Projection Operator Misused in This Scenario?

Hello everybody! I have a doubt in using the chiral projection operators. In principle, it should be ##P_L \psi = \psi_L##. $$P_L = \frac{1-\gamma^5}{2} = \frac{1}{2} \begin{pmatrix} \mathbb{I} & -\mathbb{I} \\ -\mathbb{I} & \mathbb{I} \end{pmatrix}$$ If I consider ##\psi = \begin{pmatrix}...
5. ### A Helicity and electron/positron annihilation

Hello everybody! I have a question regarding the process ##e^+ e^- \rightarrow Z/\gamma \rightarrow f \bar{f}##, where ##f## is a fermion and ##\bar{f}## is an antifermion. I am studying the process to understand LEP measurements. Supposing of being in ultrarelativistic regime, so helicity and...
6. ### B How to explain "the right hand rule" to an alien universe

Suppose we are in communication with aliens who live in a different universe. I know, that's impossible, communication requires the exchange of mass or energy, which implies that we live in the same universe. But suppose it is true. I am wondering, can we and the aliens, via this communication...
7. ### A Relation between chirality and spin

When learning about chirality I was very surprised to find that for QED and QCD the decay modes that would produce 2 particles with the same chirality had a Matrix Element of 0, which I took to mean that angular momentum was being conserved. Even the W only decay into RH antiparticles and LH...
8. ### A Why do we write that there are no right-handed neutrinos?

I'm puzzled why, now that we know that neutrinos have mass, we still read that there are only left-handed neutrinos, as far as we know. I understand that right-handed neutrinos do not interact by the weak force, so we would not detect them. My question is why we read that they might not /...
9. ### I Helicity vs Chirality: Understanding the Difference

So I heard on different occasions that chirality it's a very confusing concept and it is often mixed with helicity. I read some definitions and examples from a book and as far as I can tell (at least for QED), helicity it's an operator that gives the component of the spin along the direction of...
10. S

### Can Chirality Be Transferred from Chiral Molecules to Achiral Hosts?

How is chirality transferred from a chiral molecule to an achiral host?

Hello! I have some questions about helicity and chirality: So I understand how is helicity defined and that it has eigenvalues of 1 or -1. But can a particle (massless) have mixed helicity? Like the spin not to be along the direction of motion? (I assume it can but I want to make sure, because...
12. G

### L-Idose (configuration, chirality and stereocenters)?

I'm struggling with the following problem: Draw (using Haworth notation) the L-Idose Is it chiral? Nominate every functional group Mark every stereocenter Now, I tried doing the following, but I'm quite frankly confused: which one Idose is the correct (meaning the true L-) one?
13. ### I Does the Chirality match the helicity?

In trying to understand the Neutrino where it has mass and its chirality is the same as its helicity, I have always had trouble visualizing a particle. I recently ran into this particle. I believe the "the chirality is the same as helicity" as in one direction it would feed things through the...
14. ### I Chirality/Helicity difference?

I think these two words is most often used in high-energy physics. However, what are the differences between Chirality and Helicity The clock always turns "clockwisely", if you look in front of the clock. Is that chirality or helicity?
15. ### I Is chirality a conserved quantity?

From what I understand, there are 2 sets of fermions, one left-chiral and one right-chiral. Every electron in my body can be left-handed or right-handed. Do they stay the same forever or can they change chirality? Or is it more abstract property and a single electron can not be assigned...
16. ### I Question about Chirality and the Weak Interaction

Hello, From my understanding, the weak interaction only acts of Left-Handed Chiral Particles, and Right-Handed Chiral Anti Particles. There have been observed fermions (other than neutrinos, where all observed neutrinos are Left Handed Chiral) where some are left handed and some are right...
17. ### A Understanding the Use of Trace in QFT Lagrangian for Chiral Symmetry in QCD

I have a question about the use of trace in QFT in general - more specifically the use of trace in the lagrangian in the effective theory concerning chiral symmetry in QCD. I am slowly trying to get a hang of everything, and most things i am able to calculate, but i still have som very specific...
18. ### A Chirality of the electromagnetic force on atomic matter

It’s commonly held that left and right photons interact with matter in exactly the same way, because electromagnetism “conserves parity”. But we know that P-symmetry, in our world, is generally broken. Even according to the Standard Model, when light propagates through some media, it interacts...
19. ### I Zig-zag model illuminates helicity vs. chirality?

Can we use the Zig-Zag model of the electron to get an intuitive understanding of the difference between helicity and chirality? Suppose we have a long and narrow cylinder where the spin 1/2 massless zig and zag particles bounce between the top and bottom of the inside of the cylinder at the...
20. ### Yukawa interaction and chirality.

i still can't figure out how the higgs vev couples opposite chiral fermions(spinor components) to compose a physical electron/positron. (and actually in kurros 's thread it says that the yukawa interaction does not flip chirality nor helicity. what the hell does it mean for the yukawa...
21. ### I Understanding Anti-Positron Chirality: The Confusion Explained

please see the following conversaytion. he is saying in some point that the anti positron is right chiral and the says its left chiral... whats right ParoXoN • 4 years agoVery cool post! Thanks for that :) I'm a little confused though: You say towards the end: "The “anti-positron” (does not...
22. ### Understanding Electron Chirality and Scalar Conservation

(1) electron = left chiral . anti electron = right chiral. positron = left chiral. anti positron = right chiral. So scalar couples L and R chiral fermion fields. (2)electron = left chiral . anti electron = right chiral. positron = right chiral. anti positron = left chiral. So scalar...
23. ### Scalar interactions amd chirality

why do scalar interactions(for example the higgs vev or its components) reverse the chirality of the interacting particle?? i think this is the key for understanding the mass generation of fermions, but i can't think of a logical reason of the reversed chirality.
24. ### Chirality and charge - Could someone please check this

Hi, I was wondering if someone could please check this, my current understanding of electron chirality and charge, just to see if I'm wrong at all. Thanks a lot. All electrons have left-handed chirality. Helicity, in the other hand, is observer-dependent, the way you look at the chirality...
25. ### Exploring the Mystery of Sorbitol's 4 Chiral Centres

I wonder why the number of chiral centres in sorrbital is 4? Why isn't it 2? Is it because the H-C-OH bond cannot be rotated? Otherwise isn't the two chiral centres above identical to the 2 at the bottom?
26. ### Understanding Simple Chirality Equations with Dirac Spinors

Hi! Can anyone explain to me the math behind this simple step: $$P_L \psi = \psi P_R$$ where $$P_L = \frac{1}{2} ( 1 + \gamma_5 )$$ and $$P_R = \frac{1}{2} ( 1 - \gamma_5 )$$. And why is $$\bar{\psi }P_R \gamma^{\mu } \psi = \bar{\psi } \gamma^{\mu } P_L \psi ,$$ where $$\gamma_5$$ and...
27. ### Why chiral fermions don't exist in odd dimensions?

In four dimensions, left and right chiral fermion can be written as \psi_L= \begin{pmatrix} \psi_+\\ 0 \end{pmatrix},\qquad \psi_R= \begin{pmatrix} 0\\ \psi_- \end{pmatrix}, respectively, where \psi_+ and \psi_- are some two components spinors(Weyl spinors?). In this representation, the...
28. ### How Does Chirality Affect the Dirac Adjoint in Quantum Mechanics?

I have a question about chirality. When a spinor \psi have plus chirality, namely \gamma_5\psi=+\psi, how can I write this condition for the Dirac adjoint \bar{\psi}=\psi^\dagger i\gamma^0? Let me choose the signature as \eta_{\mu\nu}=\mathrm{diag}(-,+,+,+) and define \gamma_5\equiv...
29. ### Does charge conjugation affect parity?

"Notice that these transformations do not alter the chirality of particles. A left-handed neutrino would be taken by charge conjugation into a left-handed antineutrino, which does not interact in the Standard Model." --https://en.wikipedia.org/wiki/C-symmetry The excerpt above seems to...
30. ### Weak Isospin, Chirality and Helicity

Could someone please help me to understand the difference between the concepts of Weak Isospin, Chirality and Helicity. In particular, I have the following questions to which I was unable to find answers so far: 1. Since both spin direction and momentum are vectors, would not their apparent...
31. ### Chirality for massive neutrinos - right neutrinos - Majorana

My question concerns the chirality vs helicity for massive neutrinos. I know that as the mass is really light we can usually approximate helicity = chirality. But I would like to consider the exact case with the mass : i.e left handed (chirality )neutrino propagates with both left and right...
32. ### Is Chirality Necessary in Theories of Physics?

I would like to ask, to make it clearer to me, what does chirality means? and how can someone see whether his theory can be chiral or not? I think chirality in the standard model appears due to the fact that the left and right handed components are transformed not identically under the Lorentz...
33. ### Biot–Savart law: the origin of chirality?

As we know Biot-Savart law follows right-hand rule, like this: ...so the question is why right-hand rule, why not left? I suppose it must have something to do with electron's magnetic dipole moment or "spin", as that's the only source of asymmetry I am aware of in this scenario. It...
34. ### Chirality of Naproxen: Explaining With CIP Rules

Homework Statement determine and explain its chirality using the CIP rule *see attached image* Homework Equations CIP rules The Attempt at a Solution Hello I've determined that the stereocenter of this molecule is at the carbon where the carboxyl group meets the two benzene...
35. ### Empirical verification of massive Chirality

I want to ask someone here with a good practical background about the intrinsic quantum mechanical chirality (not helicty)...of say, a beta particle...Namely, What is the experimental proof of the existence of two distinct chiralities (not helicities) of the electron? IOWs, how can it be it...
36. ### Why are heilicty and chirality equivalent for massless particles?

Salutations, question: ~wikipedia. I'm assuming that's because (correct me if I'm wrong) those particles would travel at c and you could not overtake them so their chirality and helicity are equal.But if a photon was coming towards you then zoomed past you surely the chirality would change...
37. ### Is chirality dependent on the representation of the gamma matrices?

Hi, In QFT we define the projection operators: $$P_{\pm} = \frac{1}{2} ( 1 \pm \gamma^5)$$ and define the left- and right-handed parts of the Dirac spinor as: \begin{align} \psi_R & = P_+ \psi \\ \psi_L & = P_- \psi \end{align} I was wondering if the left- and...
38. ### Is it possible to change the chirality of an atom like this?

Heres the chiral center: I want to change the chirality of the amino group. I was wondering if I can do it through some kind of nucleuphilic addition to the carbonyl group, while adding something to adding a metal that will coordinate the amino group and drag it back or force it to change...
39. ### Chemistry Chirality: why these molecules are not chiral?

Homework Statement Look at the image please. The image shows 3 pairs of compounds. Explain why the first two are not chiral but the last one is chiral. Homework Equations Ar means Aromatic ring Aquirais means aquiral Quirais means chiral The Attempt at a Solution...
40. ### A question on particle-antiparticle chirality.

Concerning chirality, I recently read that matter is left-handed and that antimatter is right-handed. Are matter particles left- handed as seen from in front or behind? As an electron can have spin up or spin down and a positron has opposite spin up and opposite spin down. So I was thinking that...
41. ### Changing the chirality of fermions in interactions with Higgs

Am i correct when i say that the fermions get a mass and interaction term with the Higgs from the SU(2)_{L}\times U(1)_{Y} invariant Yukawa interaction -g_{y}\bar\psi_{L}\phi\psi_{R} - g_{y}\bar\psi_{R}\bar\phi\psi_{L} where \psi is the fermion field and \phi the Higgs field. My...
42. ### Is there a general test for chirality?

I have been wondering: Given an arbitrary geometric shape is there a sequence of tests I can perform on individual parts of the shape to determine whether or not it is achiral? I was hoping for something a little less trivial that simply seeing if the mirror image could be adjusted to...
43. ### Lorentz invariance of chirality

Hi folks, I've been reading into the concepts of chirality & helicity and often I find a statement that chirality is Lorentz invariant in contrast to helicity (which of course depends on the frame). BUT I don't see in which way chirality IS Lorentz invariant. For massless particles things...
44. ### Direct Determination of Chirality: Explained for Non-Chemists

Is it possible these days to directly determine the chirality of your molecule without the need of a chiral auxiliary? http://www.sciencedirect.com/science/article/pii/S0301010405004970 This would be extremely useful if this technology ever came to fruition. Can anyone explain how this...
45. ### Massive particle has a specific chirality

What does the author mean here when he says How does a massive particle have a specific chirality? I learned that the only massive single chiral fields are the ones with Majorana mass. Dirac fields are a mix of left-chiral and right chiral fields, they do not have a specific chirality. Is...
46. ### Organic reaction and chirality

There is a compound 1-fluoro,1-chloro,1-bromo, propanone (a substituted ketone). If we react it with an alkali, we know alkali will attack carbonyl carbon and chloro-fluoro-bromo- methyl carbanion will be the leaving group, finally acetic acid and chloro-fluoro-bromo- methane will be formed...
47. ### How chirality helps in polarsing?

I have learned that molecules whose mirror images are not superimposable are chiral and it rotates the plane of polarisation by some degrees. But i don't understand how How does unsymmetry help in rotating the plane of polarisation?
48. ### Chirality, helicity, and electron-photon vertices, and polarised electron beams

I am having some conceptual difficulties here. Let's start with the electron-photon vertex piece of the QED Lagrangian: -e\overline{\psi}\gamma^\mu\psi A_\mu Now we can write this in the chiral representation as -e\overline{\psi}_L\sigma^\mu\psi_R A_\mu -...
49. ### Unraveling the Mystery of Drug Chirality

Hi Everyone! I am having a little trouble understanding the concept of drug chirality... I know what they are, but am unsure about how they are formed in the first place (is it a random chance that one enantinomer will be formed over the other, can the be specifically created...?). Also, how...
50. ### Help with finding chirality centres

I am having a lot of trouble with this. Does anyone know how to identify the chiral centres in the following attached molecule?