In this paper he attempts to explain 'anomalous' galaxy and cluster orbital speeds (at the outer ranges) by means of a modification to classical inertia. He says that when the gravitational acceleration is small, inertial mass also reduces and the tendency for galaxies to 'fly apart' can be avoided. This could remove the need for dark matter halos around galaxies.

The universe sports an event horizon just outside the Hubble radius, from where no information emitted today can ever reach us. The cosmic horizon is due to the present accelerating expansion. McCulloch postulates that this cosmic horizon irradiates us with Unruh waves

^{[a]}with the same intensity from all directions, so that any effects cancel out. That is, until we accelerate. The moment you accelerate, Unruh radiation is no longer the same from all directions and this causes a cosmic scale Casimir force

^{[b]}that works against the conventional force (F=ma) that causes the acceleration. This looks just like classical inertia, according to McCulloch.

On top of that, it is well known that a Rindler event horizon is formed behind any accelerating observer that can 'feel' the acceleration (proper acceleration). This could also have an influence on the inertia, if McCulloch is right.

The dotted line represents the Rindler event horizon, while the wordline of the accelerating object is a segment of a hyperbola. No signals can reach the accelerating observer from the left-side of the horizon. Due to the inverse function, the Rindler distance (1/a) increases for smaller accelerations and tends to infinity when acceleration becomes zero - the parabola gets straighter and farther to the right.

It is postulated that the Rindler horizon contributes a tiny bit to the Unruh pressure from the rear and hence reduces the imbalance in the Casimir forces. This reduces the apparent inertia of the accelerated object for small accelerations. When acceleration is extremely small, the Rindler horizon can exceed the cosmic horizon and and the effect disappears. Then there is again total cancellation - even if the acceleration is non-zero, but tiny. This is where "quantized inertia" slips in. Acceleration must exceed the value that makes the Rindler horizon equal or smaller than the cosmic horizon, before inertia 'kicks in'. And not smaller by any old amount - Unruh wavelengths must fit an integer umber of times into the diameter of the cosmic horizon. Hence, a form of quantized acceleration.

This is the effect that McCulloch offers as a possible explanation for the high orbital speed of stars at the outer regions of galaxies. Because of the size of galaxies, the gravitational acceleration is very low there, but still way too low for keeping the stars in orbit. That is unless we modify gravity, or add dark matter, or if the inertia of the outer stars are reduced according to McCulloch's modified inertia theory.

Newton and Einstein's gravity both assume that the the gravitational mass and inertial mass of an object are the same. McCulloch says they are not the same when the acceleration is tiny, for the reasons briefly discussed above. So the outer stars need less gravitational force to keep them in orbit, because they have less inertial mass. This is still relatively new and quite controversial. And it probably does not conform to all astro/cosmo observations. But, since it agrees with some observations for which we don't have clear answers, it is intriguing, to say the least.

Add to that that McCulloch used the same theory to offer explanations for the "Pioneer anomaly", the "Flyby anomaly"

^{[c]}and the EmDrive's anomalous propulsive force (apparently without throwing out any reaction mass). Needless to say, the scientific community is skeptical, but not to the point of ignoring McCulloch completely. There is some smoke, but nobody really understands what or where the fire is.

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[a]https://en.wikipedia.org/wiki/Unruh_effect. The effect is not disputed, but Unruh radiation is still controversial, although it is not ruled out. The problem is that it is extraordinarily tiny and McCulloch offers no explanation for how it could result in the large inertia that we observe. He essentially says: "If Unruh radiation is (somehow) responsible for inertia, then my modification, using the Cosmic and the Rindler horizons together, can account for a number of unexplained effects".

[b] http://math.ucr.edu/home/baez/physics/Quantum/casimir.html

[c] I think the Pioneer and Flyby 'anomalies' have both been solved by NASA scientists, but I have not checked up on the latest status.