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Inertial and non inertial frames

  1. Oct 26, 2012 #1


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    In the classical theory, there is an absolute rest frame, and every frame moving with constant velocity with respect to it is called inertial frame of reference. The frames that are accelerating with respect to it are called non inertial. To test whether a frame is an inertial, we test Newton's first law. Now in SR, there is no absolute rest frame, so why are there frames that are inertial while others not? In the absence of absolute rest frame, all frames should be completely equivalent.

    Just to clarify the point. Consider two frames where one of them is inertial, the other frame moves towards the first with an acceleration. Now both frames are completely symmetrical to each other, for each frame, the other is accelerating towards it, so what makes one of them preferable (inertial) over the other?
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  3. Oct 26, 2012 #2


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    One of them actually IS accelerating, and could be determined to be so by a measurement IN that frame. If you are in an accelerating elevator, you are in a non-inertial frame whereas a person on the floor of the same building is in an inertial frame. BOTH frames can be accelerating relative to some other frame, but that's irrelevant.
  4. Oct 26, 2012 #3


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    I know this, but when we say accelerating (and so non inertial), we mean accelerating with respect to a certain frame (According to both classical and special relativity). What is this frame?
    According to the classical theory, the answer is very clear: It is the absolute rest frame, but in SR it seems (to me) that there is something missing. It is not the issue how to test whether a frame is inertial or not, I know the whole story of this, but the issue is what initially makes some frames inertial and the others not? If we say that non inertial frames are those that are accelerating, this has no meaning unless we specify with respect to what frame.
  5. Oct 26, 2012 #4


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    No, we do not! Velocity is "relative" but "acceleration" is not. If you are accelerating you will feel an additional force that you do not feel when you are not accelerating.

  6. Oct 26, 2012 #5


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    If you stand on a (properly aligned) scale in an accelerating frame, the reading will get bigger and bigger, but if you stand on it in an inertial frame, it won't change over time. When a jet pilot gets launched off of an aircraft carrier, he knows damn good and well that he's in an accelerating frame, but the guy on the flight deck isn't.
  7. Oct 26, 2012 #6
    That seems to be exactly the point of the OP, a "relative" velocity implies treating all reference frames as equal, an absolute quantity on the contrary must define some absolute reference frame, so I'd say he is simply saying that if acceleration is considered "absolute" rather than "relative", what frame is it distinguishing as the absolute one?
  8. Oct 26, 2012 #7
    No, In galilean relativity every intertial frame is equivalent. None of them is an absolute rest frame.


    In SR there are a set of intertial frames miving with constant velocity with respect to eachother. All of them are equivalent, the same as in galilean relativity

    As newton laws only apply in inertial reference frames, SR laws only apply in inertial reference frames.

    Acceleration can be measured. It is not relative.

    Now, you might ask what determines this set of inertial frames. This question has not been addressed in galilean relativity and in SR. In GR, However, it turns out to be determined by the mass distribution in the universe. inertial frames are defined by free fall (geodesic motion)
    which is determined by the mass distribution
  9. Oct 26, 2012 #8
    I can't see right now the relation between the universe mass density and geodesics. Can you explain it?
  10. Oct 26, 2012 #9
    Oh, ok you must be referring to the critical density notion from cosmology, but notice that this is indeed determining a reference frame in FRW cosmology.
  11. Oct 26, 2012 #10

    Ben Niehoff

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    You distinguish inertial from non-inertial frames by the same test: whether Newton's first law holds.

    Acceleration is absolute, and locally-measurable, so these two frames are not equivalent.
  12. Oct 26, 2012 #11
    The OP refers to SR, Newton laws are set in an absolute space, that is not the case in SR.

    See my previous post before the last two.
  13. Oct 26, 2012 #12


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    Whaaat ? This logic is wrong. It's so wrong I can't think how to refute it.
  14. Oct 26, 2012 #13
    That's almost a self-defeating confession for a relativity forum, come on Mentz you know better than that :tongue2:, if it is so wrong it must be easy to pinpoint what exactly is wrong with that logic.
  15. Oct 26, 2012 #14
    By the way, for instance ofirg had no problem following that logic and he came to the right conclusion: this is not addressed in SR, and in GR is addressed by introducing coordinate conditions, like the FRW comoving frame.
  16. Oct 26, 2012 #15


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    What's wrong with

    "Some peas are white, some peas are not- therefore there must be an absolute pea"

    Translating your logic it seems to say

    "Some frames are inertial, some are not. Therefore there must be an absolute frame"
  17. Oct 26, 2012 #16


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    What absolute frame is defined by, for example, the proper mass of an electron?
  18. Oct 26, 2012 #17
    Hmmm, apparently you didn't understand what I wrote. Do you know the difference say, between saying that a quantity is relative as opposed to absolute?
  19. Oct 26, 2012 #18
    We are talking about rates of change either of position or of velocity, what's that got to do with the electron's invariant mass?
    Last edited: Oct 26, 2012
  20. Oct 26, 2012 #19


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    1) I really cannot see that acceleration is not relative. It is clear that every frame measures different acceleration, so we cannot say "accelerating" without considering a frame. For example: If two cars starts move at the same position with the same acceleration in the same direction, then each one sees the other non accelerating while both are accelerating with respect to the road.

    3) Consider two frames of reference approaching each other with a certain acceleration. Which one is inertial and which one is non inertial ?!
    The answer is simply we cannot know! There are missing information. It is possible that both are non inertial, and it is also possible that only one of them is inertial... My point is that physics here does not only depend on the relativity between the two objects as SR suggests. GR may be able to solve this problem, but I cannot figure how.

    3) Testing Newton's laws allow to identify inertial frames, but this is not my issue. I am looking for the reason that makes some frames inertial while others not. If acceleration is the reason that makes some frames non inertial, then we have to specify with respect to what.
  21. Oct 26, 2012 #20
    Let' see, there's atendency for some to get confused with the basics.
    SR, first postulate, yes, the relativity principle, it prescribes that there is no preferred reference frame for the laws of physics, that is all inertial frames are considered equal, it makes no difference wrt the principle between velocities and accelerations, the principle is clear. This didn't cause any problem in the first years of SR because acceleration was not usually dealt with in the SR context at that time (the twin paradox introduced by Einstein in 1905 was a notorious exception, but gave rise to multitude of heated debates, including Einstein himself saying in the 20's that the solution required GR, wich is not agreed by the majority of physicists nowadays), later it was found perfectly ok to work with acceleration in SR (Rindler coord., etc) as long as it was relative.
    If one wants to declare that acceleration is absolute, that is fine, but then you are either using a weaker form of the first postulate (like it is done in GR and the use of coordinate conditions), or you are using an absolute reference frame, otherwise don't call acceleration absolute.
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