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In my lecture notes on General Relativity, I have the following statements that are said to be wrong in Special Relativity:

  • Every physical observer measures a speed of light equal to $c$.
  • Every physical observer measures the same speed of light.
  • For every physical observer the speed of light is constant.

In a previous course I took, where some Special Relativity was covered, these three statements were assumed to be correct. I'm actually confused right now. Can someone please clarify what's going on?

Qmechanic
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1 Answers1

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1 SR assumes no gravity

2 SR assumes all observers are moving inertially.

If there is a gravitational field (eg light passing close to the sun so spacetime is distorted), or if observers are accelerating or rotating (an observer on rotating Earth will measure the "apparent" speed of distant galaxies to be much greater than c) then SR does not apply (unless modified in simple cases) and GR applies.

John
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  • I would argue with your point 2. Students are frequently given the impression that SR applies only to inertial observers but that isn't the case. SR is perfectly capable of dealing with acceleration as numerous posts on this site explain. The Lorentz transformations apply only to inertial frames, which is possibly how the confusion arises, but SR is far bigger than just the Lorentz ransformations. – John Rennie Jan 14 '17 at 06:02
  • I do not agree. SR can "deal with acceleration" when an inertial observer measures something which is accelerating. But SR requires that the observer him/herself is inertial. If you wish an accelerating observer to use SR then you need to restrict SR - eg Wuknitz' explanation of the Sagnac Effect states that SR applies for an observer on a rotating disk as long as the observer does not probe the radial direction. – John Jan 16 '17 at 10:33
  • Not true. See Rindler coordinates. – John Rennie Jan 16 '17 at 10:37
  • In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates: 
    The laws of physics are invariant (i.e. identical) in all inertial systems (non-accelerating frames of reference).
The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

    https://en.wikipedia.org/wiki/Special_relativity

     – John Jan 16 '17 at 10:47
  • I will have to read the Rindler reference to which you pointed me with some care! – John Jan 16 '17 at 10:49
  • I am digesting the Rindler reference. May I ask a question? If SR applies universally to any accelerated observer how does it cope with the case of an observer on a rotating disk, rotating at 1 rev/sec? If she probes r, she observes a "stationary" galaxy 1 light year away from her to be travelling at 2 x pi x 1 = 6.28 light years per second relative to her. She cannot synchronise clocks on the disk - those at different radii will run at different rates. However, if she does not probe r, she can set up a consistent SR system. – John Jan 16 '17 at 11:09
  • If SR applies for ANY accelerated observer, how does it cope with an observer on a rotating disk, rotating at 1 rev/sec? She is accelerating and she observes a galaxy 1 light year from her to be travelling at 2 x pi x 1 = 6.28 light-years/second. She cannot synchronise clocks on her disk as those at different radii run at different rates. If she does not probe r she can synchronise her clocks and set up a consistent SR environment on her circle. She cannot see the galaxy. Or is it that SR applies to accelerated observers in only special, restricted situations? – John Jan 16 '17 at 11:22
  • The coordinates of a rotating observer are described in Special Relativistic Time Dilation — A computer in a very fast centrifuge – John Rennie Jan 16 '17 at 11:27