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GR - Gravity versus light - acceleration of light?

  1. Nov 22, 2008 #1

    rcgldr

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    Homework Helper

    Another thought on the equivalency of gravity and acceleration and it's affect on light.

    If a beam of light was shot directly outwards from the moon, and partiallly reflected by a series of mirrors in it's path, would the apparent speed of light as observed by an external viewer (say earth based) change (accelerate or decelerate) as the leading edge of the beam moved away from the the moon due to gravity of the moon?
     
    Last edited: Nov 22, 2008
  2. jcsd
  3. Nov 25, 2008 #2
    This is somewhat obfuscated. A beam "partially reflected by a series of mirrors" would not be travelling "directly outwards from the moon".

    Regards,

    Bill
     
  4. Nov 26, 2008 #3

    Jonathan Scott

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    Gold Member

    I'm assuming that what you mean is that the mirrors are used to observe the progress of the beam by reflecting part of it out at some angle from the beam.

    When one is observing anything from a distance where gravity is involved, then the apparent size of rulers varies with location, and it is necessary to adopt some convention for mapping space to a flat coordinate system. This is similar to the way in which maps of the curved surface of the Earth need some convention to project them on to flat paper. This means that the answer depends to some extent on the coordinate system convention. Note also that "observing" things at relativistic speeds typically involves seeing things later and then calculating back to determine when and where they actually happened in the observer's frame of reference.

    If we use "isotropic coordinates" (where the x, y and z ruler size variation is assumed to be equal relative to the coordinate system) with the moon as the origin, then relative to the coordinate system rulers appear to be shrunk by a fraction GM/rc^2 at distance r from the center of the moon of mass M, and also local clocks run slower than distant ones by the same fraction. Since the locally observed speed of light is the same standard c value everywhere, this means that relative to the coordinate system, both effects reduce the coordinate speed of light at a location closer to the moon, so as the beam gets further from the moon it will effectively speed up so that a distance r it is only a fraction 2GM/rc^2 slower than "at infinity".

    This fractional reduction in c is however extremely tiny - about 6 times 10^-11 at the surface of the moon, according to a quick calculation using Google Calculator.
     
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