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Insights Understanding the General Relativity view of gravity on Earth - Comments

  1. Jul 20, 2015 #1

    Dale

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    Last edited by a moderator: Jul 20, 2015
  2. jcsd
  3. Jul 20, 2015 #2

    PeterDonis

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    Great post, DaleSpam!
     
  4. Jul 20, 2015 #3

    vanhees71

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    Yes, very nice article. I'd only make sure to say once that gravity is not due to mass (energy) only (as in the Newtonian theory of gravity) but to all forms of energy-momentum distributions. This explains why light, which is described by massless spin-1 fields is affected by gravity (bending of light at the sun as one of the most important early tests of GR; red shift of light in gravitational field) and (in principle) is a source of gravity itself.
     
  5. Jul 20, 2015 #4
    [I could not find the two comments already posted]

    good write up....unsure of background education experience you are aiming at....

    accelerometer: maybe an explanation??....eg, it measures proper acceleration relative to free fall...

    Proper acceleration: "the acceleration measured by an ideal accelerometer" [consider adding: an acceleration an observer feels]

    Coordinate acceleration: "the 2nd derivative of position in some given coordinate system [add: an acceleration not felt]

    Inertial frame: a coordinate system where inertial objects have no coordinate acceleration [I thought an inertial frame had no proper acceleration.] [yes, you say this later:"So inertial objects (accelerometer reads 0).......

    How about equivalence principle...That helped me at first....

    Nice insight:
    "In Newtonian mechanics gravity is considered to be a real force, despite the fact that it shares the first two properties of fictitious forces listed. This makes Newtonian gravity a bit of a strange force. You cannot determine if a given reference frame is inertial or not simply by using accelerometers, you have to additionally know the distribution of mass nearby in order to correct your accelerometer readings for the presence of gravity.
     
  6. Jul 20, 2015 #5

    ShayanJ

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    I don't understand what it means that " 5° N line is constantly turning to the north and the 5° S line is constantly turning to the south".
    Could someone explain?
     
  7. Jul 20, 2015 #6

    Dale

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    If it is hard to see at first then consider the 89.9 degree latitude line. This is a tight little circle around the pole, so to stay on the latitude line you have to constantly turn towards the pole.

    The same thing happens on the 5 degree latitude line, it just is not as tight of a turn.
     
  8. Jul 20, 2015 #7

    ShayanJ

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    I get it now, thanks.
    And now I can thank you a lot for the insight article, because this was the only thing that was keeping me from understanding this issue. So thanks.
     
  9. Jul 20, 2015 #8

    Dale

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    That is a good idea, but I am not sure it is a good idea for an "everyday gravity" explanation. I also avoided any discussion of time dilation for the same reason.

    I will look back and see if there is a good place to put that in without much distraction.
     
  10. Jul 20, 2015 #9

    Dale

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    I like that. I will add that.

    You do "feel" coordinate acceleration in a GR local inertial frame (since it is equal to proper acceleration).

    I did think about wording similar to that, but the problem is that Newtonian and GR inertial frames are different. In GR inertial frames have no proper acceleration, but in Newtonian mechanics inertial frames have a proper acceleration of -g. I tried to word it in a way that is true for both.

    It could probably still use some improvement, but a theory-neutral explanation is difficult.

    Thanks. I appreciate the encouragement.
     
  11. Jul 21, 2015 #10
    Cool post! I really liked how you explained the geodesic and ground's upward acceleration parts. I just didn't get the "free-body diagram of a small section of the ground" part. Can you elaborate on this a bit?
     
  12. Jul 21, 2015 #11
    The good textbooks that I know clearly differentiate between "inertial motion" and "inertial frames" on the one hand, and "local inertial frames" on the other hand. Those mimic inertial frames for sufficiently local measurements. There is as a consequence a consistent use of terms throughout those textbooks, independent of theory.
    To avoid unnecessary confusion it is better to follow that example: the rest frame of the free-falling apple is a "LOCAL inertial frame" in GR, so that the apple can be considered as "inertial" locally.

    PS: Einstein had a subtly different view of GR than the view that you describe as "the GR view", and surely he also taught GR. And Lorentz again had a subtly different view, and he also taught GR. In fact GR is interpretation neutral, as it is foremost mathematical, making predictions of observations. What you describe is perhaps more correctly indicated as the geometric view of GR, or the Minkowskian view of GR.
     
    Last edited: Jul 21, 2015
  13. Jul 21, 2015 #12

    vanhees71

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    Lorentz had also a different view concerning SR. Fortunately this is overcome in the physics community, and there is a unique view about relativity. Unfortunately, one can't say this about QT, where in some niches of the scientific universe there coexist very different interpretations and metaphysics (reaching well into the realm of esoterics), and I'm not talking about obvious crackpots ;-)).
     
  14. Jul 21, 2015 #13

    Dale

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    The problem for this description is not that GR inertial frames are local and Newtonian inertial frames are global. The problem is that even locally they disagree. So stressing "local" doesn't avoid the reason that I chose that description.

    There are many equivalent ways of defining an inertial frame. I chose one that I thought fit best with the intention of the article.
     
  15. Jul 21, 2015 #14

    Dale

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    Sure. Consider a 1 cubic meter chunk of soil. If we draw a free-body diagram of that chunk of soil then we have real pressure forces on all 6 faces of the cube. The left and right and the front and back pressures all cancel out. However, the pressure force on the top is much less than the pressure force on the bottom, so they do not cancel out and there is a net pressure force upwards.

    In the Newtonian inertial frame, that upwards pressure force is exactly balanced by the downwards gravitational force.

    In the GR inertial frame, the downwards gravitational force does not exist, so the upwards pressure force is unbalanced and causes the ground to accelerate upwards.
     
  16. Jul 21, 2015 #15

    A.T.

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    You can approximate a small latitude range with a cone:

    https://en.wikipedia.org/wiki/Map_projection#Conic

    If you roll out the cone flat, you end up with this local picture:

     
  17. Jul 21, 2015 #16
    Ah, got it, thanks!
     
  18. Jul 22, 2015 #17
    Not really: even Newton's mechanics recognized local inertial frames as follows:

    "If bodies are moving in any way whatsoever with respect to one another and are urged by equal accelerative forces along parallel lines, they will all continue to move with respect to one another in the same way as they would if they were not acted on by those forces." (emphasis mine)

    The pertinent difference for physics (that is, leaving aside philosophy and nomenclature) is that GR postulates this equivalence not only for Newton's mechanics but for all physics.
     
  19. Jul 22, 2015 #18
    Why would it be "fortunate" if there is a unique metaphysical opinion in the physics community? Physics must be based on facts of observation. Consequently the situation with QT is perhaps better - except from the esoterical part! o0)
     
  20. Jul 22, 2015 #19

    A.T.

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    According to your interpretation of this definition, which frame is inertial:
    - A frame at rest to the surface of a non-rotating planet?
    - A frame free falling towards that planet?
    - Both?
     
  21. Jul 22, 2015 #20

    Dale

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    You are reading something into this that simply isn't there. Neither the word "local" nor "inertial" nor "frame" even appears.

    To me this quote seems to be describing the use of non-inertial frames to eliminate real forces and simplify an analysis, although it isn't using clear terminology so I cannot be certain. I see no mention of anything local.

    What is the source for this quote? I am guessing that it is something quite old, before the terminology became clarified. I believe that my presentation accurately reflects the modern usage, and it is not intended to be an historical treatise.
     
    Last edited: Jul 22, 2015
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