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Relativistic energy

  1. Sep 7, 2011 #1
    for an inverse square field the force is proportional to 1/r^2

    obviously we integrate over distance to get energy ≡ 1/r (where energy = 0 at infinity)

    but what happens when velocity becomes relativistic?
    is relativistic energy proportional to 1/r?


    if its any easier what I am really looking for is gamma as a function of r for an inverse square field and gamma = 1 at infinity
     
  2. jcsd
  3. Sep 7, 2011 #2

    BruceW

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    Yes, if the force is proportional to 1/r^2, then the energy of the particle is proportional to 1/r. (Even in relativity).
     
  4. Sep 7, 2011 #3
    wikipedia says that

    KE = m0(gamma - 1)

    so

    gamma = KE + 1 = 1/r + 1
     
  5. Sep 7, 2011 #4

    Dale

    Staff: Mentor

    Huh? How did you get this? Gamma is not a function of position.
     
  6. Sep 7, 2011 #5
    its for an inverse square field where gamma = 1 at infinity

    I'm assuming that KE = 1/r
     
  7. Sep 7, 2011 #6

    BruceW

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    Wikipedia are using the convention of setting c=1. If you want to include c, then the equation is:
    [tex] KE = m_0c^2(\gamma - 1) [/tex]
    So then you'd get:
    [tex]\gamma = \frac{KE}{m_0c^2} + 1 [/tex]
    And if we say gamma=1 when r=infinity, then KE=0 at r=infinity.
    We know 1/r gives the change in energy of the particle. And assuming the rest mass of the particle doesn't change, then 1/r is proportional to the KE.

    So then we have
    [tex]\gamma = \alpha \frac{1}{r} + 1 [/tex]
    Where I've left in the alpha as a constant of proportionality, since there is the rest mass, strength of the force and the speed of light which are all constants that must be taken in.
    (So yes, I agree, as long as the constants are kept in, which also provide the correct dimensions)
     
  8. Sep 7, 2011 #7

    Dale

    Staff: Mentor

    Oh, ok.
     
  9. Sep 7, 2011 #8
    I've been told that the gravitational time dilation at any point in a gravitational field is equal to the time dilation that a particle falling from infinity to that point would experience due to its velocity alone.

    Is that right?
     
  10. Sep 8, 2011 #9

    BruceW

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    I'm not sure, since I don't know much about general relativity.

    According to wikipedia, the gravitational time dilation of an object at rest in the vicinity of a non-rotating massive spherically-symmetric object is:
    [tex]\frac{1}{1-\frac{r_0}{r}}[/tex]
    Where r0 is the Schwarzchild radius of the massive object.
     
  11. Sep 26, 2011 #10
    Last edited: Sep 26, 2011
  12. Sep 27, 2011 #11
    Note that, if you want to talk about gravity in a relativistic manner, the 1/r potential is no longer a correct description.
     
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