Zwicky (1933) first noticed that the motion of galaxy clusters was too energetic to be held together by visible matter, assuming Newtonian or general relativistic physics, and proposed the existence of an invisible (dark) matter that provides the extra required gravitational pull. A similar problem in disc galaxy rotation was proven by the higher quality galaxy rotation curves obtained by Rubin et al. (1980). Dark matter is still the most popular explanation for the galaxy rotation problem, but, after decades of searching, dark matter has not been directly detected, though many efforts are ongoing, such as Ahmed et al. (2009) and the XENON10 Collaboration (2010).

Milgrom (1983) proposed an alternative explanation for galaxy rotation. He speculated that either (1) the force of gravity increases or (2) the inertial mass (\(M_{\mathrm{I}}\)) decreases for the low accelerations at a galaxy’s edge. His empirical scheme, called Modified Newtonian Dynamics (MoND), can fit galaxy rotation curves and has the advantage of being less tunable than dark matter. However, it does require tuning by one arbitrary parameter, the acceleration \(a_{0}\), it does not suggest a specific mechanism and it does not predict the dynamics of galaxy clusters.

A theory has been proposed, see McCulloch (2007, 2013, 2016), in which inertia arises solely from a push on objects by the quantum vacuum, which is made more intense by acceleration (Unruh radiation) and made non-uniform in space by relativistic acceleration-dependent Rindler horizons and able to push on matter. The theory predicts galaxy rotation without dark matter and without any adjustment, see McCulloch (2012, 2017a), and it implies that it is possible to produce new dynamics by artificially creating horizons, damping the quantum vacuum, making it inhomogeneous and able to push on objects, see McCulloch (2017b). In QI the inertial mass becomes

$$ M_{\mathrm{I}}=M_{\mathrm{g}} \biggl(1-\frac{2c^{2}}{A\varTheta } \biggr) $$ (1)

where \(m_{\mathrm{g}}\) is the gravitational mass, \(c\) is the speed of light, \(A\) is the total acceleration of the object relative to the fixed stars, and \(\varTheta \) is the distance to the co-moving cosmic diameter, \(8.8\times 10^{26}\) m. This is a generally-accepted estimate of the cosmic diameter assuming that inflation has pushed objects beyond the distance that we can now see (see Bars and Terning 2009). This represents the diameter as it is now and not when the light was emitted from the horizon. For the derivation of Eq. (1) see McCulloch (2007, 2016). QI successfully predicts galaxy rotation without dark matter, see McCulloch (2012, 2017a), and the interesting pattern noticed by Sanders and McGaugh (2002) that the anomalous behaviour in galaxies begins at the radius where the acceleration of the stars drops below the acceleration of \(a_{0}\sim 2\times 10^{-10}~\mbox{m}/\mbox{s}^{2}\). The problem is that galaxies do not provide a clean test since dark matter can be ‘fitted’ to also explain them.

The much simpler globular clusters were studied by Scarpa et al. (2007), who observed the same change in behaviour at the critical acceleration. Hernandez (2012), and later with better GAIA DR2 (Data Release 2) data, Hernandez (2019), provided a brilliantly simple crucial experiment: they looked at the behaviour of wide-orbit binary stars (for which the critical acceleration \(a_{0}\) occurs at a separation of about 7000 AU or 0.03 pc). Again, they found that the start of anomalous behaviour occurs at the critical acceleration, not at a distance, so it is difficult to explain the anomalies with dark matter. Since dark matter cannot be applied to them at these small scales, wide binary systems allow a purer comparison between competing theories of motion and, as shown here, quantised inertia predicts their behaviour better than MoND, without needing a tunable parameter (unlike MoND). As a caveat, it should be noted that other studies for example Banik (2019) claim that more wide binary data is needed to make the results of Hernandez (2019) conclusive.