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MOND is the idea that Gravity either behaves differently at extremely large scales or that our understanding of acceleration must be modified for extremely low acceleration rates. Some versions of MOND propose that at extremely large scales Gravity does not follow an inverse square law but instead follows something more like an inverse law, while others propose that at extremely low accelerations our equations for acceleration break down and need to be modified.

How would Modified Gravity influence the rest of physics? How would MOND affect Gravitational Waves for instance? If the equations involving acceleration were modified for low acceleration rates would this influence the equations involving momentum?

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    $\begingroup$ MOND has to be designed so that it affects virtually nothing else than the motion at very low accelerations etc. in the galaxies - simply because the existing theories have been tested at all the sub-galactic scales and higher-than-galactic accelerations. So it would be extremely hard to see a MOND effect in the lab. If such effects existed and were accessible to experiments, we would have probably already seen them. $\endgroup$ – Luboš Motl Dec 3 '15 at 18:00
  • $\begingroup$ The effect on gravitational waves depend on the precise MOND theory one considers. There are MOND theories trying hard to be modern extensions of general relativity. Jacob Bekenstein, who recently died, kickstarted the TeVeS MOND theories with extra vectors and scalars. So they still have gravitational waves and the extra effects of MOND would probably be too tiny to measure. Grav. waves come from some astrophysical events which are much more dramatic but shorter-scale than the galactic rotation, so the effect of MOND has to be small. $\endgroup$ – Luboš Motl Dec 3 '15 at 18:02
  • $\begingroup$ More on MOND. $\endgroup$ – Qmechanic Dec 3 '15 at 18:03
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    $\begingroup$ But MOND is a somewhat more general phrase that also includes models and their proponents that deny general relativity at a much deeper way than just by adding new scalars and vectors. Some of the MOND proponents almost certainly believe that GR is so wrong that the prediction of gravitational waves is wrong, too. This particular possibility is somewhat alive now - the waves have been seen indirectly (the pulsar) but not directly - but it's likely that those claims will look ludicrous in a year or two. There are different degrees of "denial of GR". $\endgroup$ – Luboš Motl Dec 3 '15 at 18:04

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