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Strain in an elastic medium

  1. Oct 8, 2008 #1
    as I understand it aether theory claims that fields are strain in an elastic medium. the elastic medium can be thought of as a system of springs and masses. (note that the springs store energy proportional to the square of their change in length)

    I can see how this probably works fine for the inverse square law of particles and the inverse first power law of an infinite line of charges. but how could it possibly explain the field of an infinite plane of charges?

    for me this puts the nail in the coffin of aether theory. (conventional aether theory at least. Dr Einstein said that spacetime itself becomes a 'kind' of aether/medium)
  2. jcsd
  3. Oct 9, 2008 #2

    Andy Resnick

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    Continuum mechanics uses the concept of 'stress' rather than force to describe motion. A consitutive relation is then invoked to relate the developed stress to material strain- that consitutive equation can be a "Hookean" solid ('masses and springs'), Newtonian fluid, or more complicated materials- viscoplastic materials, Maxwell viscoelastic fluids, etc. Adding charges to this picture is not conceptually difficult, but requires yet other types of constitutive equations. It's important to note thatspecific constitutive relations are not derivable from first principles, but are invented-for example using the principle of material frame indifference, principle of local action, attainibility, etc.

    It's a misunderstanding to call continuum mechanics an Aether theory.
  4. Oct 9, 2008 #3
    fields store energy. if the continuum is a system of masses and springs then that energy would be stored in the springs. therefore the field at any point is proportional to the change in length of each spring. the change in length of each spring is equal to the difference in net displacement of the 2 masses on each end.

    thinking 2 dimensionally, imagine in infinite 2 dimensional system of masses and springs. imagine a perfectly straight infinitely long one dimensional line of charges. these charges try to produce a field by producing strain in the continuum. but the continuum will simply move en masse and there will be no stain produced. and the net displacement will increase without limit
    Last edited: Oct 9, 2008
  5. Oct 9, 2008 #4

    Andy Resnick

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    I think you are using a conceptual model too literally. Matter is not made of point masses, springs, and dashpots (or combinations of the three),but those concepts serve to reduce the overall complexity to something which we can model with reasonable accuracy.
  6. Oct 9, 2008 #5
    I am aware that its a model but the model doesnt work.
  7. Oct 9, 2008 #6

    Andy Resnick

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    I think you mean the model doesn't work as certain limits are approached (discrete limit, for example); this is obviously true. Do you have a suggestion on how to improve the continuum model?

    Or are you inquiring about a specific phenomena, how that could be modeled in terms of continuous fields?
  8. Oct 9, 2008 #7
    I'm saying that the 3D model doesnt work for the case of in infinite sheet of charge.

    nor will a 2D model work for a 1D line of charge.
  9. Oct 9, 2008 #8

    Andy Resnick

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    Of course it doesn't. Why do you think it would?
  10. Oct 9, 2008 #9
    as I understand it aether theory claims that fields are strain in an elastic medium.
  11. Oct 9, 2008 #10
    even for a point particle, it only works if the field is proportional to the displacement. but that makes no sense. the energy in the springs is the square of the difference between the displacements of the masses on each end. that gives the wrong result.

    in the case of an infinite sheet of charge the whole aether is displaced by the same amount. again the field would hove to be proportional to the displacement but then there would be no energy in the springs at all.
    Last edited: Oct 9, 2008
  12. Oct 9, 2008 #11
    its as though the medium is made of 2 materials (like a dielectric). one of which gets pulled by the change and the other gets pushed away by the charge. the field at each point being proportional to the net change.

    this WOULD work even for an infinite sheet of charge.
    Last edited: Oct 9, 2008
  13. Oct 21, 2008 #12
    that wont work either for a magnetic field from an infinite plane of uniform current density. the field should be constant (proportional to d^0) but an elastic medium would shear so the field would decrease as one went further away.

    as best I can figure its all just quantum mechanical. it does what it does because thats what quantum mechanics tells it to do.
  14. Oct 22, 2008 #13
    the elastic medium would have to resist compression (divergence) like a liquid and resist curl like a solid but unlike a solid it would not resist shear

    not exactly a liquid. not exactly a solid.
    Last edited: Oct 22, 2008
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