The empirical MOND explanation of galactic rotation curves involves switching over in the low acceleration regime from the Newtonian acceleration Gm/r^2 to the MOND acceleration term sqrt(Gm a_0)/r.(adsbygoogle = window.adsbygoogle || []).push({});

This is normally achieved using an "interpolation function" which effectively switches off one term and switches on the other when the Newtonian acceleration decreases past the MOND acceleration parameter a_0.

MOND is of course normally applied only on the scale of galaxies. However, if we consider a Cavendish-style laboratory experiment involving a mass of 1kg at a distance of 1m, the resulting acceleration Gm/r^2 = 6.67e-11 ms^-2 is less than the MOND acceleration parameter a_0 = 1.2e-10 ms^-2, so the MOND effect should be significant.

As the mass is increased and the distance is decreased, making the acceleration more easily measurable, the acceleration moves from the MOND regime into the Newtonian regime, but one would still expect a partial MOND acceleration effect if MOND were really related to acceleration thresholds. Such an acceleration would be proportional to sqrt(m)/r instead of the usual m/r^2.

Have such effects been ruled out by laboratory experiments? If so, this would prove that MOND could not work without taking into account additional physical effects in addition to the gravitational acceleration; for example, it might depend only on the total gravitational acceleration relative to some background space.

Another oddity with the MOND idea is that particles of a star experience accelerations orders of magnitude higher than the overall acceleration of the star, which might appear to mean that they should not exhibit the MOND acceleration. I think that if the MOND extrapolation function is chosen to simply give a linear sum of the MOND and Newtonian accelerations, this theoretical problem does not arise, although this would then also rule out the "total gravitational acceleration" explanation for why MOND does not affect laboratory experiments. If my maths is correct, the extrapolation function which achieves this effect is as follows:

mu(x) = (sqrt(1+1/4x) - sqrt(1/4x))^2

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# Can MOND be ruled out at laboratory scale?

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