A question on the Graviton

Discussion in 'Physics & Math' started by Green Destiny, Aug 4, 2010.

  1. Green Destiny Banned Banned

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    I am ultimately unsure why the graviton ''must'' be massless. I know the basics of fundamental field theory, so i am quite aware of the graviton being a massless entity moving at the speed of light.

    Is the reason part of the field source of matter, since the graviton \(h_{\mu \nu}\) vanishes on the background vacuum \(g_{\mu \nu}=\bar{g}_{\mu \nu} + h_{\mu \nu}\), because of the identity:

    \(\delta I/ \delta_{g \mu} = \phi_{\mu \nu}(g,R, \nabla R...) = k \tau_{\mu \nu}\)

    So the term \(h_{\mu \nu}\) vanishes and is this a concurrent reason also why the graviton must have no connection to the source mass field \(\tau_{\mu \nu}\)?

    Indeed, i am looking for a mathematical reason. I know conceptually that if the graviton was travelling at less than \(c\) then it would not be able to have the effects they would on long-scale terms.
     
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  3. AlphaNumeric Fully ionized Registered Senior Member

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    If memory serves it follows from the EFEs that \(\Square h_{\mu\nu}=0\) and since \(\Square = \partial^{2}_{t} - c^{2}\partial_{x}^{2}\) is the wave operator with wave velocity that of light it follows that the perturbations move at the speed of light.

    /edit

    Okay, I can't remember the LaTeX code for the D'Alembert operator, but the \Square is supposed to be a square (obviously) and is equal to \(\partial_{t}^{2} - c^{2}\Delta\).
     
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  5. temur man of no words Registered Senior Member

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    Yea, I think it is something like that.

    The latex code for the D'Alambertian is \ Box
     
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  7. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

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    AN: try \nabla and \Box

    Anyway, if the graviton were massive, gravity would be a short range force, which would give you problems with the galaxy formation data, I think.

    You'd break diffeomorphism invariance too, right?
     
  8. temur man of no words Registered Senior Member

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    I don't know what you mean by diffeomorphism invariance, but there are perfectly good massive gravity theories. One I know is topologically massive gravity, which I think you would say breaks "chirality invariance" or something, but not the diffeomorphism invariance.
     
  9. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

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    Hmm. Maybe I'm confusing my words here. I know you can treat gravity as a gauge theory, and giving a gauge boson a mass breaks the symmetry. This is like ``gauging'' GR, which is based on diffeomorphism invariance.

    So the prediction of these theories should be a breakdown of GR at long distances, which I think they use to explain dark matter/dark energy.

    Is this right?
     
  10. Green Destiny Banned Banned

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    This would be related to gauge transformations would it not?
     
  11. Green Destiny Banned Banned

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    Ah! Sorry, i should have read further. Then my question above has been answered.
     
  12. Green Destiny Banned Banned

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    As i understand, the field theory governing these are indeed from the Boson family - if it were massive, long range phenomena would not match our observations... howsoever, this strangely is in harmony with the defect that General Relativity breaks down on large scales, hence we have resorted to the messier model of dark negative matter and energy.
     
  13. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

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  14. Green Destiny Banned Banned

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    I've not seen this i must admit.

    I'll read it right now.
     
  15. Green Destiny Banned Banned

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    I'm sorry, but i'm about to probably make quite a negative appearance here at the forum. I read this, and as i went to the part;

    ''This provides support for the idea that most of the mass in the cluster pair is in the form of collisionless dark matter.''

    It kind of seems like a quantum jump in idea's!!! We are inexorably assuming the dark matter as a correction to the equations. However, the logic inside me is telling me that this is more of a fudge-factor than actual evidence.
     
  16. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

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    No.

    I can go into detail about why dark matter is a completely generic prediction of particle physics, irrespective of the gravitational evidence we have for its existence.

    Basically what happened was that two galaxies collided, and the baryonic matter stopped. But most of the mass of the galaxies (which can be seen using gravitational lensing) kept going. This mass was not baryonic matter.

    So the conclusion is that the bulk of the matter in the galaxy was non-baryonic in nature, or (as we call it) dark matter.

    Or you can distrust gravitational lensing measurements, in which case you probably don't care about the bullet cluster

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    Even the proponents of modified gravity theories acknowledge that at least some dark matter must be present in the universe, to explain the bullet cluster.
     
  17. Green Destiny Banned Banned

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    That would certainly seem a reasonable analysis.
     
  18. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

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    But...
     
  19. temur man of no words Registered Senior Member

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    I don't know enough QFT to understand "gauging" and "giving a mass breaks symmetry", but let me think about it for a while on classical level a bit and get back.

    No, the topologically massive gravity is 3 dimensional so it is just a toy model. There seem to be other 4 dimensional theories like Lovelock and f(R) but I don't know if they are massive. Oh yea, there is something called New Massive Gravity.
     
  20. Green Destiny Banned Banned

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    I just don't know. Something seems fishy

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  21. Green Destiny Banned Banned

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    The more i have read papers on the subject now, i did come across a more elementary explanation ~ thank god, because the mathematics seems very difficult in the Massive Models ~ that it may retain the laws of Einsteins Theory, the so-called Diffeomorphism Invariance as i qoute:

    '' What he found was remarkable: the nonlinearities of the theory become stronger and stronger as the mass of the graviton shrinks. What this means is that when the graviton mass vanishes, the extra modes are completely frozen by their non-linearities, and the theory becomes compatible with general relativity after all! ''

    [ps] i cannot link -

    Now, i've read this to quite literally mean that it still preserves the diffemorphism restraints in the General Theory of Relativity - but i could be incorrect.
     
    Last edited: Aug 5, 2010
  22. Green Destiny Banned Banned

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    Massive.. i meant massive

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