Galaxies further away from us, are moving away much faster than close ones, and therefore the light coming from them is red-shifted. So the redshift of star light is a measure of its distance, and of increasing age, since when we look far off we are also looking back in time since the light has taken aeons to reach us. Like an ice core in climatology, this gives us a record of the distant past.
The minimum acceleration predicted by Quantised Inertia / MiHsC is given by: a = 2c^2/CosmicDiameter, and 'CosmicDiameter' varies with time as the cosmos expands. This means that as we look at galaxies further away, and further back in time, the CosmicDiameter was smaller and the minimum acceleration was bigger (This might also explain the inflation of the early universe, but that's another story). The prediction then is that earlier galaxies, ones at higher redshift, have to rotate more rapidly, with the same visible mass, to remain above the minimum acceleration. I proposed this as a test in McCulloch (2007) (see paragraph 4 of the Discussion), but at the time the data did not seem to be good enough.
I was reminded of this test by various insightful people on my last blog entry and in a few emails (see the guilty names below). Thanks to them I've looked into it again and added it to the discussion of my latest paper (just submitted to MNRAS) which includes the plot below. Along the x-axis we have the log of the stellar acceleration expected given the visible matter and Newton's laws, and along the y-axis the log of the acceleration observed directly from the movement of the stars. Newton and Einstein would expect the results to lie on the dotted line. The observations, taken from McGaugh et al. (2016) are shown by the squares with their size indicating the uncertainty, and they are obviously at odds with dear Albert and Isaac. At low accelerations (on the left hand side) the stars orbit the galaxies far too fast. This is the famous galaxy rotation problem, that is usually solved by stuffing in huge amounts of dark matter wherever it's needed (the second worst hypothesis in history in my opinion, since it is unfalsifiable).
The black line shows the prediction of MoND which fits the data (the squares) and is much more falsifiable than dark matter, but despite the great respect I have for Milgrom's bold step, MoND has been adjusted to fit the data using its parameter a0, so it's not surprising that it fits. The MoND prediction also shows no dependence on time.
The coloured lines show the predictions of quantised inertia / MiHsC. Uniquely, among all the theories QI/MiHsC predicts the observations correctly without any adjustment, and, also uniquely, its prediction varies with redshift. The light blue line shows the curve for a redshift of Z=0 (nearby galaxies in this epoch). This agrees with McGaugh et al. (2016)'s data (which was for Z=0). The dark blue curve shows the prediction for Z=0.5, purple for Z=1 (for which the cosmos was half its present size) and the red curve for Z=2. As you can see the galaxy rotation problem is predicted by QI/MiHsC to have been worse when the cosmos was young (all other things being equal). If two galaxies have the same visible mass, then according to QI/MiHsC the one further away (earlier in time) should spin faster.
Does this prediction agree with the data? Well, the data still seems noisy, but earlier galaxies do seem to have faster spin, see for example Figure 6 in the Thomas et al. (2013) reference below (a paper found by airenatural). With a bit more data this could be the definitive proof that QI/MiHsC needs..
Thanks to S.S. McGaugh for sending his binned data, and R. Ludwick, T. Short, Magnus Ihse Bursie and J.A.M. Lizcano (airenatural), for advice ...and anyone else I may have forgotten.
McCulloch, M.E., 2007. The Pioneer anomaly as modified inertia. MNRAS, 376, 338-342. https://arxiv.org/abs/astro-ph/0612599
McGaugh, S., F. Lelli, J. Schombert, 2016. The radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett., (accepted).
Thomas, D., et al., 2013. Stellar velocity dispersions and emission line properties of SDSS-III/BOSS galaxies. MNRAS, 431, 2, 1383-1397. https://arxiv.org/abs/1207.6115