Symmetry Definition and 958 Threads

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. 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...
  2. 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...
  3. D

    About symmetry operation and a corresponding unitary transformation

    For each symmetry operation R acting on a physical system,there is a corresponding unitary transformation U(R). But what is the principle for such relation? an example is that : for a continuous symmetry ,we can choose R infinitesimally close to the identity ,R=I+eT ,and the U is close to I...
  4. marcus

    Particle cartoons by Roz Chast in Symmetry mag

    http://www.symmetrymagazine.org/cms/?pid=1000475 click to enlarge---portraits of the fundamental particles http://www.symmetrymagazine.org/cms/?pid=1000480 Roz Chast did the cover of May issue of Symmetry (a joint SLAC/Fermilab publication) and illustrated the article on Dark Energy She is a...
  5. F

    Does Time Reversal Symmetry Apply to All Interactions?

    Ok, so if you have two electrons near one another, they will start to repel one another and separate as time goes on. Now if you reverse time, they will move towards one another. But it is said that antimatter can be viewed as matter going backwards through time. Now if this is true, this would...
  6. N

    Proving Symmetry of (A)(A^T) Matrix w/ Tensor Notation

    Homework Statement We are to show that (A)(A^T) is a symmetric matrix using tensor notation. Where ^T denotes TRANSPOSE Homework Equations The Attempt at a Solution I did it in the following way: Let P=(A)(A^T) Then, p_ik=(a_ij)(a_jk) Where A=a_ij and A^T=a_jk =(a_jk^T)(a_ji)...
  7. D

    Strings Chan-Paton U(N) gauge symmetry fractional winding number

    I understand why in the presence of a constant vector potential A=-\frac{\theta}{2 \pi R} along a compactified dimension (radius R) the canonical momentum of a -e charged particle changes to P=p-eA. Due to the single valuedness of the wavefunction [itex]\propto e^{iPX}[/tex] P should be...
  8. N

    Why do conservation laws in mechanics lead to symmetry principles?

    I do not know the Lagrangian or Hamiltonian principles of mechanics. However,I came to know that conservation of linear momentum,angular momentum and conservaton of energy lead to homogeneity of space,isotropy of space and homogeneity of time.Can anyone show why it is in purely Newtonian terms?I...
  9. R

    How Critical Are Symmetry Theories to Modern Engineering and Technology?

    If there were no symmetry theories in physics would our practical understanding of the world be worse - is there any everyday device/machine that would not have been thought up and invented without symmetry theories?
  10. S

    Exploring Symmetry: Understanding the Differences in Triangles and Squares

    Hi all, I was thinking of symmetries today and this kept bugging me. I wonder if anyone can help me with this. Consider the symmetries of a triangle. You can do 3 rotations and 3 reflections to get them all. Number the vertices, create an ordered set with 3 elements that contain the...
  11. M

    Proving Symmetry of Solutions in 1D Potential

    Hi! I read that in an 1D potential, the solution for the Schrödinger equation is always either symmetric or antisymmetric if the potential is a symmetric function: V(x) = V(-x). How can I proof this? Thanks, for ur answers!
  12. F

    Higher dimensions and symmetry

    I can't quite remember where I got this idea, but once my brain remembered one point about higher dimensions(that of how each higher dimension, at least in terms of the first three dimensions, is at 90 degrees from one another. Well, actually how can you say the first dimension is 90 degrees...
  13. T

    Gauge symmetry and symmetry breaking

    How would one know in general, whether an original gauge symmetry in the theory is still gauge symmetrical after symmetry breaking? I mean is there a theorem or something like that? And the other way around, is there a general way of knowing whether there is the possibility of a hidden, i.e...
  14. wolram

    Imaginary Engine: Dark Matter & Super Symmetry Needed

    My dream engine, needs a dark matter governor to prevent it exceeding its designed rpm limit, unfortunately no one makes them yet. It will produce dark energy as the motive power, but alas the formula for its production, or its existence is not known. It will, hypothetically, if it runs...
  15. T

    SU(3) Symmetry of QCD: Quarks vs. Gluons

    I find it awkward that quarks are in fundamental representation of SU(3) while gluons are in adjoint representation of SU(3). Is there a reason as to why this is the case? Why aren't they in the same representation or in the current specific representation?
  16. V

    Symmetry and conservation of momentum

    The law of conservation of momentum has never been observed to be violated.In quantum mechanics conservation laws relate to symmetries.So is the existence of the law of conservation of momentum due to the fact that a symmetry exists, or does a symmetry exist because the law of conservation of...
  17. Loren Booda

    Does an exact three-fold symmetry exist in physics?

    An isolated electron and positron depict an exact two-fold symmetry. Are there any examples in physics of a truly triplicate symmetry? If not, what constraints are there that prevent it?
  18. malawi_glenn

    Exploring Momentum Transfer: F(q)^2 Factor & Spherical Symmetry

    I have a form factor that only depends on the momentum transfer q, this is symbolised by writing the form factor as F(B]q[/B]^2). if i have a spherical symmetric distribution of charge, f only depends on the radius; r = | q| Then integration over all solid angels yields...
  19. Y

    Gauss' Law - Planar Symmetry HELP

    Homework Statement A square plate of edge length 9.0 cm and negligible thickness has a total charge of 6.3 x 10-6 C. (a) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.50 mm) by assuming that the charge is spread uniformly over the...
  20. A

    Understanding Quantum Symmetry Breaking

    Hi, I have done classical symmetry breaking and now want to understand the quantum one. I have seen the statement that the symmetry is broken if and only if Q|0> not 0. Where |0> is the vacuum and Q is the associated charge of the broken symmetry. Why does this imply symmetry breaking? The way...
  21. A

    Relation between symmetry, charges and one-particle states

    Hi, I recently saw an author make the following statement: If the symmetry leaves the 1-particle states invariant then its associated charge Q acts on the 1-particle states |p> such that Q|p> = 0 This statement is nontrivial to me, so if anybody could show me how it works please let me know.
  22. G

    Determining Symmetry Group of Cyclopentadienyl using Huckel Theory

    Hi, I have to determine the symmetry group of cyclopentadienyl(assumed to be planar and symmetrical) and I should use Huckel theory. Is there a systematic way to determine the symmetry group and is it possible to use software to determine the symmetry group. Thanks in advance
  23. X

    Can Conservation Laws be Derived from Symmetry and Newton's Laws?

    Is it possible to show directly from Newton's Laws that conservation of momentum and energy follow from principles of symmetry?
  24. Mentz114

    What Group Preserves the Invariance of E^2 - B^2 in Electromagnetic Fields?

    I understand that E^2 - B^2 is invariant under various transformations. If we consider the vector ( E, B ) as a column, then E^2 - B^2 is preserved after mutiplication by a matrix - | cosh( v) i.sinh(v) | | i.sinh(v) cosh(v) | I think this transformation belongs to a group...
  25. D

    Probability conservation and symmetry

    What symmetry gives probability conservation? Or, what symmetry does probability conservation give? I have been trying (unsuccessfully) to find an answer to this question. I think the question makes sense. That is, I can't see how the situation is different from, for example, that of spatial...
  26. H

    Solving Symmetry & Graph Sketching for Curve x=t^2+3, y=t(t^2+3)

    A curve is given by the parametric equations x=t^2+3, y=t(t^2+3) a)Show that the curve is symmetric about the x-axis. b)Show that there are no parts of this curve where x<3 c)Find dy/dx in terms of t, and show that (dy/dx)^2 greater or equals to 9. Sketch the curve by using the above...
  27. A

    Definition for the term gauge symmetry

    Could somebody please give me a definition for the term gauge symmetry in contrast to any other symmetry? Is the decisive difference that a gauge symmetry is local i.e. a function of the coordinates in contrast to being constant? I would also appreciate it if it could be pointed out how the...
  28. R

    Time Symmetry and Matter/Energy Conservation

    I recently posted a question on energy and matter and I got a very good answer to that one so I thought another one wouldn't hurt. I understand that time symmetry is what makes all conservation laws possible as is stated in Noether's theorem. Time symmetry is what explains the conservation of...
  29. Cincinnatus

    Exploring Groups & Symmetry: Deciphering the Connection

    I hear all the time people saying things like "groups are the algebraic equivalent to the notion of symmetry". Yet I don't think I've ever really understood what was meant by this. I'm familiar with groups of symmetries (like the dihedral groups), but in these cases, to me it just seems like...
  30. L

    Chemistry Stereochemistry, molecules, internal symmetry

    Homework Statement Does the molecule in the file attached have an enantiomer? Homework Equations The Attempt at a Solution I think I can draw an internal symmetry plane to divide the molecule into 2 equivalent parts, but then again, it doesn't seem quite right to me. Building...
  31. S

    Solving an Integral without Symmetry: A Challenge

    I'm trying to solve a special integral. \int{\frac{1}{1+[Tan(x)]^a}}dx So far I've tried constructing a function F(a) and differentitating to show that it is a 0, hence any a would result in the same answer. Thus chose a = 2, and solve it quite easily. Although, all my arguments rely on...
  32. D

    Rotational Symmetry & Gravitational Waves: Exploring the Connection

    Ok , during my study , I read that the bodies which are rotating spherically symmetrically do not emit GW;s as in don't dent the spacetime memberane...same is with the bodies moving with uniform velocity ...why is that??...has it something to do with conservation of angular momentum??:blushing:
  33. O

    Why Symmetry of Tides on Earth (influenced by moon, sun)

    I have been trying to understand how our ocean tides work and read about the effect of our moon's and sun's gravitation. I have learned there are diurnal, semi-durnal and mixed semi-diurnal tidal patterns When the moon is directly overhead equatorially (near side), I've seen illustrations...
  34. S

    Complex Inner Products: Skew Symmetry & Linearity

    Previously i learned from maths that the complex inner product satisfied skew symmetry and linearity in the first component, ie - <aA+bB,C> = a<A,C> +b<B,C> But after studying Shankar in quantum mechanics, he claims the linearity is in the ket vector, ie - <A,bB+cC> = b<A,B> +c<A,C> which...
  35. E

    Is the Stress Tensor Symmetric? Examining the Physical Meaning and Implications

    Hello ! I'm having trouble with the symmetry of the stress tensor. What it means physically? In the demostration of the symmetry my book applies the angular momentum equation to a third material volume (a cube, length L). In the final step we have: 0 = \mathop {\lim }\limits_{L \to 0}...
  36. D

    Book on tensor symmetry, geometries, surfaces

    I'm looking for a good tensor reference book that provides insights into the following areas of tensors: 1. Symmetries & how to extract them. 2. Full tensor visualisation eg. how to visualise the stress tensor in its 9 component form without resorting to a split into 3 simultaneous...
  37. W

    Why do symmetry and Hamiltonian operators commute?

    Why do operators representing some symmetry commute with the Hamiltonian?
  38. kakarukeys

    Conserved charge generates symmetry transformation in Hamiltonian Mechanics

    Q is a conserved charge if \{Q, H\} = 0 Show that q+\epsilon\delta q satisfies the equation of motion. \delta q = \{q, Q\} I couldn't find the proof. Anybody knows? My workings: \delta q = \{q, Q\} \delta\dot{q} = \{\{q,Q\},H\} = - \{\{Q,H\},q\} - \{\{H,q\},Q\} \delta\dot{q} = \{\{q,Q\},H\} =...
  39. Loren Booda

    Planck - stelactic - cosmological black hole symmetry?

    Like nested dolls, these black holes appear coexisting concentrically where the central stelactic (stellar-galactic) black hole mediates a symmetry between the other two. For instance, consider how stelactic Hawking radiation manifests under inversion of its event horizon. The events within...
  40. N

    Reducing Symmetry from SU(2) to U(1) | Dear PF

    Dear PF, I don't know whether this is the right place for such question, but how to reduce symmetry suppose from SU(2) symmetric Lagrangian down to U(1)? Thank you
  41. A

    Unlocking Nature's Secrets Through Symmetry and Transformation

    These forums help me practice my communication skills, thank you to those who helped me reword the following little document. __________________________________________________________ I am going to try and deduce as much as I can about the nature of matter from symmetry and the galilean...
  42. E

    How Can Continuous Group Theory Be Applied to Solve a Differential Equation?

    Let be a differential equation : y^{(n)}=F(t,y,\dot y ,\ddot y , \dddot y,..., y^{n-1}) then if we propose a Lagrangian so its euler-Lagrange equation gives: \sum_{k=0}^{n}(-1)^{n}\frac{d^{2}}{dt^{2}}(\frac{\partial ^{n} L}{\partial \ y^{n} })=0 The differential equation can be...
  43. marcus

    Against Symmetry Smolin in Paris June 14

    "Against Symmetry" Smolin in Paris June 14 Prof. Smolin will be speaking at an amphitheater of the Ecole Polytechnique (Paris version of MIT). The talk is part of an historical controversy. Here is a short advance summary of the talk copied from Christine Dantas' blog...
  44. A

    Is the Shape Operator Always Symmetrical?

    :confused: Please, help me to solve that task related to Shape Operator. We have surface S and its normal N. Alse we have surface patch r : U -> S in local coordinates r_1, r_2, ..., r_n. Shape operator (Weingarten Linear Operator) is defined as follow: L_p : T_{r(p)}S -> T_{r(p)}S, where...
  45. Robert100

    Which books to read? Symmetry, Branes, LQG, etc.

    Ok, the problem is that I don't have enough time or money, so I want to be somewhat careful in what books I buy. I am looking to purchase a few books on modern physics that discuss new ideas in physics, and I've found many books with good reviews that cover the topics that I'm interested in...
  46. C

    Solving the Electrostatic Conundrum: Brute Force vs Symmetry

    Electrostatic conundrum: How "brute force" and symmetry arg. give different answers! Hello everyone, this is my first post -- and an interesting one (or so I think). **Note to Mods: this is NOT me asking for a solution to a HW type problem -- I know and have the solution already -- rather...
  47. D

    How Does Symmetry Impact Quantum Effects and Reality Transition?

    As someone returning to a study of physics after many years, I would appreciate any help and comments on my unresolved questions after reading “popular science” type information regarding quantum effects. In considering (that old chestnut!) the “twin slit” experiment to demonstrate the quantum...
  48. S

    Exchange symmetry splitting in Helium

    In Helium we find that each energy level specified by (n,l) splits into two sub levels, a singlet and a triplet (this triplet is supposed to be degenerate) I'm sure that this triplet does not turn out to be degenerate because of fine structure. But I'm not sure if the fine structure splitting...
  49. A

    Spontaneous symmetry breaking in the SM

    \mathcal{L} = \frac{1}{2}(\partial_{\mu}\underline{\phi}).(\partial^{\mu}\underline{\phi}) + \frac{1}{2}\mu^{2}\underline{\phi}.\underline{\phi} - \frac{\lambda}{4}(\underline{\phi}.\underline{\phi})^{2} + \bar{\psi}(i\gamma . \partial )\phi - g\bar{\psi}(\phi_{1}+i\gamma^{5}\phi_{2})\psi...
  50. N

    How Are Goldstone Bosons Formed in Chiral Symmetry Breaking?

    Dear PF, Could anyone help me to understand the following issue: I don't understand the formation of Goldston bosons in chiral symmmetry breaking. Namely - suppose there is only fermion fields Lagrangian and due to some reasons the fermion field obteins VEV - <0|psi^bar psi|0> is non...
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