What is Symmetry: Definition and 956 Discussions

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music.This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry, which refers to the absence or a violation of symmetry.

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  1. B

    Does the Hamiltonian Symmetry Extend to All N Dimensions?

    Homework Statement I shall consider the Hamilton H(q,p)=1/2\sum{p_l^2}+1/2\sum{q_l^2}+\gamma(\sum{q_l^2})^2 all the sums if from l=1 to l=N. (gamma is bigger or equal to zero) I shall discuss the symmetry/asymmetry plus determine that the form of the qeneral solution is qualitative...
  2. M

    Symmetry with respect to a circle

    Homework Statement Could someone please just explain a step in a proof for me? Suppose x and y are symmetric with respect to a circle, and a,b and c are three points on the circle. This means that: (x,a,b,c) = (\bar{y},\bar{a},\bar{b},\bar{c}) The writer then says: "symmetry...
  3. P

    Baryon singlet representation for SU(3) flavour symmetry

    Hi there! As most people already might know, we can decompose the 27 dimensional representation for the baryons under SU(3) flavour symmetry as 27 = 10 + 8 + 8 + 1. I can find a lot of information about the particles that lie in the decuplet and in the octet, but nothing about which particle...
  4. S

    The inherent symmetry of time dilation

    Please pardon this very newbie question: I am ploughing through Mayer's "The Many Directions of Time." He seems to assume right at the outset that Relativity is correctly interpreted as meaning that BOTH observers moving in constant velocity relative motion would be entitled to claim that the...
  5. J

    Symmetry factors for Feynman diagrams

    Hello I have to calculate symmetry factors for the following feynman diagrams for my qft class, and would be hugely grateful if anyone could point out any mistakes (I'm sure there are lots!) that I've made. http://picasaweb.google.com/jessicagreerstanley/Physics#5259179071440262450"...
  6. J

    Entropy & Time Reversal Symmetry: Breaking Symmetry?

    Does the ever increasing nature of entropy violate time reversal symmetry?
  7. L

    Symmetry of Odd-Degree Polynomials: Conditions for Symmetry in the Plane

    Hi! Brief question: I wonder which conditions should a polynomial function of odd degree fulfill in order to be symmetric to some point in the plane. Are there such conditions?
  8. A

    Gauss' Law: Cylindrical Symmetry

    Say we are looking at a positively charged rod with uniform charge density and a radius of R. When using Gauss' law and taking a cylindrical surface we use the formula E = lambda/2*pi*epsilon*r When we derive this equation we are assuming R is significantly smaller than L and so we...
  9. S

    Finding High Symmetry Points for Wurtzite Structure with 12 Atoms

    hi, I have found a website in which it has described how to find high symmetry points for wurtzite structure. Here is its address: http://cmt.dur.ac.uk/sjc/thesis_mcg/node53.html But, as I know these points are being used for standard numbers of atoms for example in a wurtzite system we...
  10. F

    Are the W bosons charged before symmetry breaking?

    When the SU(2) symmetry is broken by the Higgs mechanism, the W bosons acquire mass and become the well-known W^+ and W^- bosons discovered at CERN. So before the breaking, the Ws had no mass. Did they have charge? If yes: No particle is known without mass but with charge. Are the W...
  11. E

    Symmetry, absorbtion and benzene

    Hey Is it right that high symmetry molecules does not absorb light as good as low symmetry molecules? let's take an example like benzene versus benzene+hydroxyl?
  12. G

    What is Spontaneous Symmetry Breaking?

    Hi: What is Spontaneous symmetry breking ? and when does it happen.? Regards
  13. K

    Does the uncertainty principle break symmetry?

    The classic physics problem example of symmetry breaking is a pencil sitting directly on its tip (pointed down), but it's possible for the pencil to balance on its tip if we reduce the thermal fluctuations to zero by cooling it to close zero degree. Quantum fluctuations require/mean that...
  14. C

    Time-reverse symmetry of the principle of relativity

    Please look at the attached diagram and let me know if there is a reason for the asymmetric dynamics due to the relative position of rest or, if I have incorrectly interpreted the mechanics. Kev, I haven't forgotten.
  15. djeitnstine

    Can Random Symmetry Breakings Explain Quantum Oddities?

    I was reading the book "New Theories of Everything" and I came across the term "random symmetry breakings" Let me explain a bit: This applies if there are more than 3 spatial dimensions. In our early universe when our universe was very small, hot and dense, it would be safe to say that at one...
  16. Y

    Why Does a Cork Float Horizontally Instead of Vertically?

    Suppose we drop a bottle cork on water. It has a shape similar to -rougly- a pyramid i.e. upper area A1 is smaller than bottom A2. Therefore it's vertically as well as horizontally symmetric. But as we drop it, it does not stay vertical but horizontal making upside and downside areas (A) equal...
  17. E

    A question of protein subunit symmetry and normal coordinate analysis

    Hey Im doing vibrational spectroscopy (Raman, nir, vis/uv) of a protein called C-reactive Protein. Its a symmetric molecule regarding the subunits http://en.wikipedia.org/wiki/C-reactive_protein Then i wondered if one can apply normal coordinate analysis (using symmetry and group theory) to...
  18. B

    Spontaneous symmetry breaking

    Was the early spontaneous symmetry breaking caused by exponential expansion in the first instant of standard theory? Is that the reason that the early Big Bang universe is thought to have contained equal amounts of matter and anti-matter (produced by spontaneous symmetry breaking)? Does...
  19. L

    Weak Interaction Invariance Under CPT Symmetry

    Is weak interaction invaraint under CPT Symmetry? Why?
  20. W

    What is the difference between dynamical symmetry and geometrical symmetry?

    i really can not understand it
  21. S

    Why does symmetry lead to a restoring force in precessional rotation?

    I know it's just a mental block - for some reason I can't get the phrase "restoring force" out of the ongoing debate in my noggin. But this is a question about symmetry specifically, and the notion of a force appearing because of an asymmetry, or "symmetry-breaking". The simplest notion I...
  22. J

    Inertial frames and Parity symmetry

    Do you think you could give me some helpful insight to a follow up question from the discussion of defining inertial frames: I'm still having trouble figuring out a good way of incorporating parity violation into my intuition. If it wasn't for experiment showing otherwise, I probably would...
  23. A

    Understanding Local Gauge Symmetry

    Local Gauge Symmetry ?? Trying to understand local gauge symmetry ================================ I have an undergraduate degree in physics, so I know basic quantum mechanics, but that's all. Still, I'm trying to understannd the concept of local gauge symmetry. I would appreciate if...
  24. A

    On spontaneous symmetry breaking and Higgs’s mechanism of mass production

    On spontaneous symmetry breaking and Higgs’s mechanism of mass production From lectures: L. Peak and K. Varvell. The Physics of the Standard Model. Full Lagrangian for fermion and photon Combine the gauge-invariant Lagrangian density describing a fermion field in the presence of an...
  25. M

    Supergravity and local symmetry

    In chapter 4 of Bailin & Love, Supersymmetric gauge field theory and string theory, the authors state that supersymmetry is considered a global symmetry, and we can separately consider it to be a local symmetry. Further, since the supersymmetry algebra contains P^\mu, the generator of...
  26. B

    Is the Graph of y=(x-3)^3 Symmetric About the Origin?

    Determine whether the graph of the relation is symmetric with respect to the y axis, x axis, or the origin. y=(x-3)^{3} I don't know how to produce a visual of the graph with this post but it is a graph of y=x^{3} moved 3 units to the right along the x axis. Visual examination of the graph...
  27. B

    What is R Symmetry in SUSY and why is it important?

    Is there a nice, cute way to see what R symmetry is? I mean, N=1 SUSY has a global U(1)_R symmetry, which is a charge carried by the supercharges, right? And a spontnaeously broken U(1)_R is a sufficient (but not necessary) condition for broken global SUSY. (Counter-example is O'Raifeartaigh...
  28. A

    Understanding Composition of Point Symmetry Generators in Lie Algebras

    I am taking a first course in Lie algebras and currently working with this problem (see attached file). I understand that the product of the two operators should be regarded as composition. How to explain the final expression? Regards Staffan
  29. S

    SU(3) symmetry and simple zeros of w. f.

    Can someone help me? It is correct at all to make the conection between the SU(3) symmetry and zeros of (radial) wave function? To make more clear: can I say that the fact that radial wave function has only the simple zeros automatically excludes the existence of SU(3) symmetry for given quantum...
  30. M

    Symmetry and Conservation of Charge

    I understand that all conservation laws have underlying symmetries and that all symmetries have corresponding conservation laws. From reading some popular science books (don't shoot me :P), I understand that conservation of energy, linear and angular momentum are a natural consequence of time...
  31. L

    Symmetry behind Laplace-Runge-Lenz vector conservation?

    For gravitation and any inverse-square forces, the Laplace-Runge-Lenz vector is conserved. (see http://en.wikipedia.org/wiki/Laplace-Runge-Lenz_vector" ) Any conserved quantity is associated with a symmetry of the Hamiltonian with respect to some coordinate, according to the Noether theorem...
  32. F

    Basic Electric Field and Symmetry Problem - help

    Homework Statement 24 identical positive charges, each has a magnitude 2.0 microCoulombs equally spaced along a circle with a radius of 0.4 m which lies in the y-z plane. a)determine the electric field at a point 1 meter away from the circle's center along the x-axis. b) Find the...
  33. K

    Feynmann diagrams interpretation and diagramm symmetry order

    I'm trying to understand Feynman diagrams interpretation in terms of virtual particles. What I still can't understand is how this interpretation is compatible with the fact that one should divide each diagram by its symmetry order. As far as I understand, diagram symmetry order means how many...
  34. R

    Proving Circle Symmetry through Rotation: Understanding the Equations

    Homework Statement http://tng.trekcore.com/1.JPG I'm trying to prove that the circle is symmetrical by showing that x² + y² = a² holds when the circle rotates. I know that this is proved given the following two formulae: x = x'cosθ - y'sinθ y = x'sinθ + y'cosθ but I don't know...
  35. P

    Spurion & Symmetry: Meaning, Breaking & Explanations

    What is the meaning of "spurion"? How can it break the symmetry? Which book give some good explanations about this theory? Thanks!
  36. M

    Symmetry of mass distribution producing radial gravitational force field

    I conjecture that only spherical symmetric mass distribution can produce radial gravitational force field (according Newton's law of gravitation). Can anybody prove or disprove this conjecture?
  37. F

    Orbital Symmetry Controlled Reactions

    Homework Statement http://avogadro.chem.iastate.edu/CHEM332/332Fall06Exam5Key.pdf Please go to page 5. Homework Equations No equations, just concepts. The Attempt at a Solution I tried the first problem (A), and got the solution wrong. I thought I'd check the concepts before attempting any...
  38. S

    Determining the Line of Symmetry of a Reciprocal Equation.

    Problem: How do you determine the line of symmetry of a reciprocal equation? Solution: For example, I'll graph the reciprocal function Y=1/(x+2) ^Just a quick sketch And the equation of the line of symmetry is simply -(x+2), which can be seen here: ^Also a quick sketch By adding a...
  39. N

    Understanding Chiral Symmetry in QCD for Heavy Ion Collisions

    Homework Statement I'm doing a dissertation on heavy ion collisions and one of the things they look for in the collisions is chiral symmetry resolution - what is it? Homework Equations The Attempt at a Solution I understand that it is a type of symmetry that is usually broken...
  40. V

    What are symmetry and symmetry breaking?

    hi What is symmetry? hi explain symmetry and symmetry breaking in details with example Regards Ryan
  41. pellman

    Symmetry and conserved probability current for wave functions

    Noether's theorem relates symmetries and conserved quantities, eg. if the Lagrangian is invariant under a spatial translation, you have have conservation of momentum. For continuous systems, the conserved quantities become conserved "currents". Anyone know what symmetry is associated with...
  42. A

    Electroweak symmetry breaking without a Higgs

    Interesting new paper from John Moffat: http://arxiv.org/abs/0709.4269 Introduces a non-local, finite QFT that dynamically generates boson and fermion masses as loop corrections. Experimental evidence for the theory will be visible in WW scattering at the LHC (coupling goes to zero, which...
  43. E

    Could chirality in LQG break the electroweak symmetry without the higgs?

    One difference between GR and LQG is that LQG is chiral, whereas GR is not. In order to break the electroweak symmetry, a higgs field needs to be introduced by hand. Einstein's understanding of inertia implies a strong EP as gravitational mass and inertia are identical, while a higgs...
  44. G

    Symmetry in Travel and Time Dilation

    -Is it possible for two objects to have symmetrical geodesics in which each accelerate with equal magnitude but in opposite directions? If not why not? -If so, how can both see each others clocks run slow? Would one have aged less than the other when then they reunite? Which? If not what...
  45. B

    Symmetry groups and Caley tables

    Homework Statement I have a shape about the origin. It has rotational symmetry but not reflectional symmetry (its an odd star shape!). I have to write down in standard notation the elements of the symmetry group and I have to construct a caley table under composition of symmetries. I...
  46. C

    Is Super Symmetry Real: String Theory Predictions

    is super symmetry real or has been predicted by string theory?
  47. P

    Symmetry and shape of elementary particles

    Hi! Although nobody can see the shape of elementary particles, we always assume that their shapes are symmetrical, for example, sphere. Why? Is the symmetry a law? Otherwise, are there any other reasons? Patrick
  48. L

    Testing Symmetry: X-Axis, Y-Axis, and Origin Explained

    I know there are 3 kinds of symmetry: x-axis, y-axis, and origin. So, if you test the function for symmetry and it turns that it has one of these, does it mean that it cannot have the others? Therefore, one function has one type of symmetry only?
  49. G

    Interpreting IR/Raman Spectra Using Character Tables

    hi, I am trying to interpret some data which have been calculated for IR/Raman but I don't know how to interpret them exactly. The schema says mode \nu 1 b_u 82 1 a_g 216 2 b_g 239 I presume that the u/g are gerade/ungerade from the bonding/antibonding wave functions but how to...
  50. M

    Understanding Pi: its Role in Symmetry and How it Was Found

    Hi all In almost all the formulae related with symmetry, we use pi. For example, in case of circle, we use pi, and in case of sphere we use 4*pi. e.g. E (electric field)= (q * qo) * 1/(4*pi*eps* r^2) A (circle)= pi*r^2 A (sphere)=4*pi*r^2 My question is: How does pi signify...
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