What is "local" defined to be? Why don't larger systems affect smaller ones? ie. Don't we need to consider the gravitational pull from all other objects in the universe? Is this "canceled" out somehow or do other objects just play such a small effect we don't consider them?

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    $\begingroup$ Who says gravity is local? Please provide a reference for context. $\endgroup$ – G. Smith Jan 5 at 5:36
  • $\begingroup$ For any purposes on earth's surface, all those effects are negligible and never considered. They are too far way $\endgroup$ – Wolphram jonny Jan 5 at 5:45
  • $\begingroup$ It clearly says “in principle all sources of gravity from all over the universe matter.” $\endgroup$ – G. Smith Jan 5 at 5:52
  • $\begingroup$ @wolphram Jonny "In addition, MOND made a bold prediction: the internal motions of an object in the cosmos should not only depend on the mass of the object itself, but also the gravitational pull from all other masses in the universe--called "the external field effect" (EFE)." eurekalert.org/pub_releases/2020-12/cwru-upo121620.php ...so how come MOND takes this into account but Netopia gravity doesn't? I'm confused... $\endgroup$ – Astroturf Jan 5 at 5:55
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    $\begingroup$ Just use $GMm/r^2$ to calculate the force of the Earth, Moon, Sun, Jupiter, Alpha Centauri, and the Andromeda galaxy on your body to get a feel for how each contributes. $\endgroup$ – G. Smith Jan 5 at 5:56

It's a bit difficult to give an all-encompassing definition of locality which isn't hopelessly broad, but we can phrase it in terms of your example.

In particle mechanics, a theory is local if the time-evolution of a particle is determined entirely by influences in its immediate neighborhood. For example, if we say that every pair of particles in the universe exerts an attractive gravitational force on each other, then this is a non-local theory because the force on me cannot be deduced from my immediate surroundings.

However, we can modify this theory to make it local by introducing the concept of a gravitational field which exists at every point in space. Even though the value of that field is determined by masses which may be very far away, it is the gravitational field at my precise location which exerts the force on me, making the theory local.

The difference between the local and non-local theories are more than superficial - the tangible existence of this local gravitational field introduces the possibility that it could carry momentum and energy in a way which could not reasonably be explained by the non-local "action-at-a-distance" which characterizes the non-local model.

  • $\begingroup$ Why tip-toe around the locality definition? I think what you said there holds for any sane definition of locality, namely the an object is only effected by its immediate surrounding. In the case of gravity, the gravitational field at the location of the object is the only thing that changes its motion at some point in time, not the gravitational field some finite or infinite distance away. Also, I think OP is confusing locality with the fact that we get away with neglecting the forces of celestial bodies for the most part because they cause tiny accelerations and come from random directions. $\endgroup$ – Bobak Hashemi Jan 5 at 6:16
  • $\begingroup$ @BobakHashemi The tip-toeing is because I'm referring specifically to the classical dynamics of particles, and didn't want to labor over definitions of locality which would cover e.g. "operators with spacelike-separated regions of support must commute"-style definitions which crop up in QFT. $\endgroup$ – J. Murray Jan 5 at 6:20
  • $\begingroup$ @BobakHashemi As to your latter point, I agree that that's most likely the main area of confusion. $\endgroup$ – J. Murray Jan 5 at 6:21
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    $\begingroup$ @Astroturf A dedicated question about the EFE would likely get you better answers, so perhaps you should ask a new question about that. In short, though, the EFE implies that the gravitational influence of faraway objects actually alters how masses respond to the gravitational fields of their neighbors. For instance, the Earth would essentially feel a different force from the sun depending on how the two bodies were aligned with the center of the Milky Way. This doesn't occur in GR or Newtonian gravity. $\endgroup$ – J. Murray Jan 5 at 6:30
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    $\begingroup$ @Astroturf Yes, you'd need to know the contribution from every mass in the universe to know the value of the gravitational field exactly, but this is irrelevant; such precision is completely unnecessary, which is why we often (but not always) are perfectly content to consider only the most significant gravitational influences when modeling systems. $\endgroup$ – J. Murray Jan 5 at 6:31

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