Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Would someone care to elaborate

  1. Jan 26, 2012 #1

    dpa

    User Avatar

    a further difference concerns the tensorial character of gravitational waves, in contrast to electromagnetic waves, which are vectorial. This means that the intrinsic angular momentum carried by a gravitational wave is twice that carried by an electromagnetic wave of the same intensity.
    -the universe before the big bang.

    And further what is quadrupole moment.
     
  2. jcsd
  3. Jan 26, 2012 #2

    Mentz114

    User Avatar
    Gold Member

    I think that's a reference to the fact that a rank-2 tensor can have spin-2 symmetry, whereas EM has spin-1. It's eaiser to see that a grav wave takes 2 complete cycles (4∏ of angle) to return to its initial state, but EM wave takes only 1 cycle (2∏). This is because the transverse parts of the GW are exactly opposed, but the E and the M parts of EM radiation are in phase.


    For quadrupole mement, see the Wiki article

    http://en.wikipedia.org/wiki/Quadrupole
     
    Last edited: Jan 26, 2012
  4. Jan 26, 2012 #3
    Don't you mean a half cycle (∏ of angle)? It's the 1/2 spin electron that takes 4∏ rotation to return (a weird QM thing I don't fully understand).
     
  5. Jan 26, 2012 #4

    Mentz114

    User Avatar
    Gold Member

    The weird thing about GWs is that the second period is different from the first, but it is the same at 0, 2∏, 4∏ which is not quite what I said earlier.

    Quantum spin is related to the degrees of freedom in the field vectors and/or tensors. I don't know how classical angular momentum is related to spin.
     
    Last edited: Jan 26, 2012
  6. Jan 26, 2012 #5
    me either.....if the above descriptions are correct, these diagrams might lend some insight.....but I don't get it yet...


    Wikiepdia says:

    So the issue seems to be why a gravitational wave has twice the angular momementum of an electromagnetic wave of the same energy density.

    Also from wikipedia [also a diagram there]:

    http://en.wikipedia.org/wiki/Angular_momentum_of_light

    but these diagrams make it appear that the angular momentum of electromagnetic waves might vary widely:

    http://en.wikipedia.org/wiki/Plane_wave#Polarized_electromagnetic_plane_waves



    All I could find regarding gravitational waves:

    http://en.wikipedia.org/wiki/Gravit...gular_momentum_carried_by_gravitational_waves
     
  7. Jan 26, 2012 #6

    Bill_K

    User Avatar
    Science Advisor

    The statement that electromagnetic waves are vectorial means that they are described by vectors E and B transverse to the direction of propagation. Electromagnetic waves are generated by dipole motions in the source, and subsequently produce dipole motions in the receiver.

    Gravitational waves are tensor in nature. This means they are generated by quadrupole oscillations in the source, and produce quadrupole oscillations in the receiver. In the linearized theory they are described by two rank-2 traceless tensors E and B whose components are transverse to the direction of propagation.

    For linearly polarized electromagnetic waves the E vector has a constant direction. There are two possible linear polarization states oriented 90 degrees apart. Linearly polarized waves do not carry angular momentum. One can also have circularly polarized waves in which the E and B vectors rotate either clockwise or counterclockwise, once per cycle. A circularly polarized wave does carry angular momentum. The ratio of the angular momentum density L to the energy density U is (Jackson, problem 6-12) L/U = ± 1/ω. (Compare this to a photon, where L/U = ± 1ħ/ħω.)

    For linearly polarized gravitational waves the E tensor has a constant direction. That is, its eigenvectors are constant. There are two possible linear polarization state oriented 45 degrees apart. (If one state has eigenvectors along the x and y axes, the eigenvectors of the other are along the directions x + y and x - y.) Linearly polarized gravitational waves do not carry angular momentum. Circularly polarized gravitational waves do, and the ratio of the angular momentum density to the energy density is twice what it was in the electromagnetic case, L/U = ± 2/ω.
     
  8. Jan 26, 2012 #7
    There is a little discussed apparent paradox here not at all mentioned in the Wiki references given in #5. A truly plain circularly polarized EM wave carries zero angular momentum density, yet 'in practice' there is indeed a non-zero averaged value as per above - that requires interference fringes for explanation. The freely downloadable article at http://www.opticsinfobase.org/abstract.cfm?id=84895 goes into the details, complete with coloured diagrams. As to any parallels with GW's I would rather not venture an opinion.
     
  9. Jan 26, 2012 #8
    [1]Intuitively it makes sense that a linearly polarized wave would not carry angular momentum while a circularly polarized wave would.

    [2] What does this mean:
    What's the difference?

    [3] Seems like a gravitational source produces gravitational waves only when it is producing angular momentum....never thought about that. The last Wiki reference I posted in #5 suggests a rotating [spherically symmetrical] black hole would hardly produce any gravitational waves and if it did they would not have angular momentum.

    I wonder what a charged black hole radiates...not much gravitational energy, but now I wonder about electromagnetic angular momentum.
     
  10. Jan 26, 2012 #9

    Bill_K

    User Avatar
    Science Advisor

    I just meant that the classical calculation gives you the same result for L/U that you expect for a photon.

    Black holes can be rotating and/or charged, and don't radiate any gravitational or electromagnetic waves at all.
     
  11. Jan 27, 2012 #10
    phew!!!! I kept looking and thinking "but those are identical!!!!' (LOL)

    Senility is, therefore, still around the corner!!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook