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Meaning of general covariance

  1. Jun 2, 2015 #1

    I am reading GR and got confused about the principle of General Covariance. The principle of General Covariance says that the laws of physics take the same form in all reference frames. Since the laws are same in all reference frames, any experiment performed should give identical results in all reference frames. But this is not true since if I release a ball in an inertial frame it remains stationary but if released in an accelerated frame it speeds up.

    Am i not understanding the meaning of General Covariance?
  2. jcsd
  3. Jun 2, 2015 #2


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    Yes, general covariance says that the laws of physics should take the same form in all reference frames. But it doesn't say that they should give the same results when applied to different situations!
  4. Jun 2, 2015 #3


    Staff: Mentor

    Here's what wikipedia has to say:


    Results will always vary between inertial and accelerated frames.

    However, if you are falling in a gravitational field then locally you have an inertial frame and the experiment should give the same results.
  5. Jun 2, 2015 #4


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    I forgot to mention. You're mixing two different things. One is general covariance which I explained.
    The other thing is the equivalence principle which says that the laws of physics should be that of SR in small patches of spacetime. It also means that locally, you can't distinguish between a uniformly accelerated motion and being in a gravitational field.
  6. Jun 3, 2015 #5
    Say you have an equation for your inertial frame that tells you how the ball is going to move. Call it the geodesic equation. When you change coordinate system [frame of reference] you still have this geodesic equation, but it's a tensor equation, and the elements of the equation transform as the coordinate system transforms.The geodesic equation, with it's transformed elements, now tell you that ball is accelerating.

    So we write the geodesic equation in a sufficiently ambiguous way, that it can be applied to any coordinate system, and identify it as being "generally covariant".
    Last edited: Jun 3, 2015
  7. Jun 5, 2015 #6
    Thanks Shyan, jedishrfu and stewards!!
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