I've suggested (& published in 15 journal papers) a new theory called quantised inertia (or MiHsC) that assumes that inertia is caused by relativistic horizons damping quantum fields. It predicts galaxy rotation, cosmic acceleration & the emdrive without any dark stuff or adjustment.
My Plymouth University webpage is here, I've written a book called Physics from the Edge and I'm on twitter as @memcculloch

Tuesday, 18 October 2016

Strong evidence for MiHsC/QI

A few days ago Prof Stacy McGaugh kindly sent me the binned galaxy acceleration data they used in their paper (McGaugh, Lelli and Schomberg, 2016, see below) and I've been comparing MiHsC with it. The result is shown in the figure. To explain: the x-axis shows the log of the expected acceleration for stars within galaxies, g_bar. They looked at about 2693 stars, in 153 galaxies and calculated the expected acceleration using Newton's gravity law from the visible distribution of matter. Higher accelerations are shown to the right. The y-axis shows the acceleration of the stars derived from their observed motion, g_obs - a faster more curving path, means more acceleration. Higher accelerations are shown to the top. The data all lie between the two dashed lines, which represent the uncertainties in the values.

If Newtonian physics or general relativity were right without any fudging, then the two estimates of acceleration (g_bar and g_obs) would agree and you would expect all the data (between the two dashed lines) to lie along the dotted diagonal line. It doesn't. For low accelerations, at the edge of galaxies (on the left side of the plot) the observed acceleration is greater than Newton or Einstein predicted, which pushes the two dashed lines up away from the dotted line. This is the galaxy rotation problem. Stars at the edges of galaxies are moving so fast, they should escape from the galaxy, so dark matter is usually added to hold them in by gravity.

However, McGaugh et al.'s study showed that the acceleration is correlated with the distribution of 'visible' matter only, which implies there is no dark matter. Also, dark matter is an unscientific hypothesis because you have to add the stuff to galaxies just to make a theory (general relativity) fit the data and this is a bit like a cheat, especially since so much has to be added with no physical 'reason' for it (beyond saving a theory). Also it means you can't actually predict the motion of stars in a galaxy from its visible mass: you have to add the dark matter arbitrarily, and you can't double check you got it right because dark matter is invisible!

A slightly less fudged alternative is MoND (Modified Newtonian Dynamics) which is a empirical model that does not have an explanation, but fits the data if you set an adjustable parameter to be a0 = 1.2x10^-10 m/s^2. The MoND result is shown by the blue line in the plot. It works, but this is not surprising because the value of a0 is set manually to move the blue curve up and down on the plot so it fits the data.

The red line shows the prediction of quantised inertia (QI), otherwise known as MiHsC, which also fits the data (it is between the dashed lines). Now, this is surprising because MiHsC/QI fits the data without any adjustment. It predicts the observed galaxy rotation from just two numbers: the speed of light and the diameter of the cosmos. I should point out that in this work I am using the co-moving diameter of the cosmos 'now' which is 8.8x10^-10 m/s^2, see Got et al. (2005) and which I now think is correct, rather than the diameter when the light we see was emitted which is 2.6x10^-10 m/s^2. This latter is the value I used in my earlier papers, which means that the MiHsC flyby predictions will worsen, the predictions in my 2012 galaxy paper will improve and the MiHsC emdrive predictions are unaffected (there it depends on the cavity size). Nevertheless, this plot is evidence that MiHsC/QI is a very simple solution to the galaxy rotation problem (see also my 2012 paper). It also elegantly unifies quantum mechanics and relativity, predicts cosmic acceleration, and other MiHsCellaneous anomalies like the emdrive.


McGaugh, S.S, F. Lelli, J. Schombert, 2016. The radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett. (to be published). Preprint.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics and Space Science, 342, 342-575. Preprint

 Gott III, J. Richard; M. Jurić; D. Schlegel; F. Hoyle; et al. (2005). "A Map of the Universe". The Astrophysical Journal. 624 (2): 463–484.


qraal said...

There's still the question of galactic clusters. What does MiHsC predict there?

qraal said...

Ah... from your 2012 preprint, the answer to my question:

The model predicts the outer rotational velocity of dwarf and disk galaxies, and galaxy clusters, within error bars, without dark matter or adjustable parameters, and makes a prediction that local accelerations should remain above 2c^2/Theta at a galaxy's edge.

Jamie said...

Has anybody run a universe simulation using MiHsC yet? Are there any blockers to doing that?

jacob said...

...Then gravity is not a force after all? Instead mass, massive bodies (and whole galaxies) constitutes a "shade" for some radiation pressure that is otherwise nearly equally strong in all directions? that way of viewing "gravity" does seem intuitive to me when in comes to solar systems, galaxy rototion and why galaxies are generally "flat" and so on (I suppose the concept of gravity works well in most respects too).
Or am I getting QI wrong?

Mike McCulloch said...

Jamie: There are no obvious problems with putting MiHsC into a cosmological model. I wish someone who has the expertise would try it, but they are all playing with dark matter. MiHsC does still need refining in various ways, but trying it in the models will help to do this.

Mike McCulloch said...

Jacob: Yes, in the MiHsC paradigm gravity is not a fundamental force, just an emergent phenomenon. For example, gravity can be derived from the uncertainty principle, see my blog and paper here:


and maybe also as an Unruh sheltering, which I haven't managed to prove mathematically yet. I get maddeningly close, but it's not right yet.

jacob said...

Mike: so the universe is currently expanding due to (electromagnetic?) "heat" with cosmic wavelengths. (That would mean super low energy radiation with rather high density?) - and mass held together by mutual shading. That would imply no "gravity" in absolute 0 Kelvin. Should be testable even in an earth based laboratory...
Interestingly a "cold" universe will not collapse because of gravitational attraction, as there would be no such thing.
The relation between size, density, distance, etc. will be accounted for when defending an interpretation of gravity as a sort of shading. Should be hard!

jacob said...

to add to my previous comment: I think any new, old or revived theory of gravity will have to fit with Einsteins concept of curvature of spacetime.

qraal said...

Interesting preprint today:


Looking for dark matter trails in colliding galaxy clusters

David Harvey, Andrew Robertson, Richard Massey, Jean-Paul Kneib

(Submitted on 17 Oct 2016)

If dark matter interacts, even weakly, via non-gravitational forces, simulations predict that it will be preferentially scattered towards the trailing edge of the halo during collisions between galaxy clusters. This will temporarily create a non-symmetric mass profile, with a trailing over-density along the direction of motion. To test this hypothesis, we fit (and subtract) symmetric halos to the weak gravitational data of 72 merging galaxy clusters observed with the Hubble Space Telescope. We convert the shear directly into excess {\kappa} and project in to a one dimensional profile. We generate numerical simulations and find that the one dimensional profile is well described with simple Gaussian approximations. We detect the weak lensing signal of trailing gas at a 4{\sigma} confidence, finding a mean gas fraction of Mgas/Mdm = 0.13 +/- 0.035. We find no evidence for scattered dark matter particles with a estimated scattering fraction of f = 0.03 +/- 0.05. Finally we find that if we can reduce the statistical error on the positional estimate of a single dark matter halo to <2.5", then we will be able to detect a scattering fraction of 10% at the 3{\sigma} level with current surveys. This poten- tially interesting new method can provide an important independent test for other complimentary studies of the self-interaction cross-section of dark matter.

Mike McCulloch said...

Jacob: About your comment re gravity disappearing at 0K. MiHsC does not allow 0K because then the waves radiated would be larger than the cosmos and so unobservable. It predicts a minimum temperature, which is in the pK range.

Mike McCulloch said...

qraal: A good paper: they are testing the dark matter hypothesis a little, but dark matter is so vague that the mainstream will just invent a new type that can fit this null result as well and request millions in funding to go look for it. Nice setup. I wonder how many more millions must be spent on huge dark matter detectors to defend the old theory? MiHsC/QI predicts galaxy rotation just from the speed of light and the cosmic diameter, on a little piece of paper worth about 2 pence!

Czeko said...

Mike, you should use more expensive sheet of paper. :)

OOT, do MiHsC has something to say about highest temperature? If it defines a lower temperature in the pK range linked to minimal possible acceleration, there should be an upper bound. Any number?

Mike McCulloch said...

Czeko: What a great idea! I should apply for funding to use gold paper :) About the maximum temperature: good point. Assuming that waves of radiation shorter than a Planck length cannot be observed and therefore cannot exist, and using Wien's law, T=Beta.h.c/kL, gives a maximum temperature: T=1.8x10^32K. Hot!

Czeko said...

It agrees with Plank temperature which is about 1.41×10^32K. But no MiHsC involved here?

Mike McCulloch said...

Indeed, quantum mechanics already assumes waves are not valid at these tiny scales.

Tom Short said...

The following paper on early galaxies is interesting.


It shows a mismatch with MOND. If I'm reading it right, these galaxies show a bigger accelleration effect in the early universe as you predicted in another blog post. Might be worth more exploration...

(Hopefully, I'm not too off-topic.)

Magnus Ihse Bursie said...


I've been following your writings with quite some interest for some time. This is the first time I really see you addressing the issue that the Hubble diameter is changing with time, which means that MiHsC will produce different effects at different times since the Big Bang.

I've been thinking about fiddling around with your equations with a non-constant value for the Hubble horizon, to see what happens over time, but never gotten around to it. Have you written anything about this that I have missed?


Mike McCulloch said...

Tom: Many thanks. I'll look at this paper in detail, because MiHsC does indeed predict fast-spinning early galaxies, as they have seen. This could be something of an experimentum crucis.

Mike McCulloch said...

Magnus: As you know, the minimum acceleration predicted by MiHsC is 2c^2/cosmicscale, predicting higher, earlier accelerations. You may be interested to read my paper here:


where the 'apparent' dark mass (what appears to be dark mass, but is actually an effect of MiHsC) is inversely correlated with the cosmic scale, so early galaxies should spin faster (as seen in the data, see the paper mentioned in Tom Short's comment). One uncertainty here is whether 'c' should be a constant, or should also accelerate from t=0. I also wrote a 'toy cosmology' paper which is here


Max Kargl said...

not quite the same track, but also interesting regarding the "standard model"

qraal said...

Hi Mike,
I noticed you got past the gate-keepers of Orthodoxy at the arXiv too...


Hopefully it'll invite discussion of your ideas.

airenatural said...

Hi Mike,
This article https://arxiv.org/pdf/1610.06183v1.pdf is dealing with the same idea of the other one that Tom Short is citing in this post and also questions MOND, saying that the parameter of minimum acceleration is different for older galaxies. Check please inside the figure 2 where you can see the original McGaugh curve but for redshifts up to z = 2.
I suggest checking the data in this figure 2 against MiHsC, by estimating the radius of the universe at epochs where redshifts seen from our point of observation are z = 0.5, z=1 and z=2. Or you can apply your fitting formulae to McGaugh data, separating the 2693 points if they have the z parameter and check. If it works, Eureka!
Congratulations for your blog.

Mike McCulloch said...

airenatural: Eureka! MiHsC fits! Thanks for pointing out Fig 2.

qraal said...

Holy Cow! A whole new scientific discovery in a blog conversation!

airenatural said...

Hi Mike, I'm desperate to read your new post... Can not stand waiting!!!

Mike McCulloch said...

airenatural: I need to look into this more, because the Fig 2 in the paper you pointed out is actually model data. However, I suspect the model has been tuned to reflect some real data. I just need the real data.. Never easy is it?

qraal said...

As I noted in another context, when it comes to models the GIGO Principle applies!

airenatural said...

Hi Mike, searching for real data, not just model data, seems the most reliable source is SDSS database in


They have stellar kinematics up to redshifts z=2 and based on this data there are works like this one:


In this reference we can see in Figure 6 (composed of 6 subgraphs) that in the upper bin 0.75 < z < 2.00 the average velocity is clearly higher than in the lower bin 0.00 < z < 0.15. In the intermediate bins the velocity is around 240 km/sec with some good confidence.

Maybe an experimental work could be testing if this data fits well with predicted MiHsC formulae. A simple calculation to convert redshifts in universe diameter yields the following dimensions ( http://home.fnal.gov/~gnedin/cc/ )

Redshift z = 0.15 is 86% of the age of the universe today, scale factor 0.87
Redshift z = 0.45 is 65% of the age of the universe today, scale factor 0.69
Redshift z = 0.75 is 51% of the age of the universe today, scale factor 0.571

So effects of MiHsC in the sense of an increased average stellar velocity for a smaller universe radius can be noticed in principle for redshifts higher than 0.45. This completely rules out MOND and goes clearly in favour of MiHsC (of course a dark-matter enthusiast will propose a tweaked explanation saying that there was a bigger amount of dark matter in the early universe… or that the dark matter was concentrated in so precise way to make fits this data).

Further conclusions could be extracted by processing the 3829 objects of the subgraph that lies in the bin 0.75 < z < 2.00 and splitting it in two bins, let`s say centred in

Redshift z = 1 is 43% of the age of the universe today, scale factor 0.50
Redshift z = 1.75 is 27% of the age of the universe today, scale factor 0.364

To do it properly I think is necessary to first determine the MiHsC relation that links redshift_z versus universe_diameter versus minimum_MiHsC_acceleration_parameter versus stellar_velocity and do statistical processing on the full SDSS database:


If the resulting average star velocities fit well in your prediction, something big is really in your hand!!!

qraal said...

An alternative red-shift cosmic scale relationship comes from the R_h=c.t cosmology, studied by Fulvio Melia over the past few years. It's a standard FRW cosmology, but flat at all times (until the very early Universe) rather than for just the coincidental period when we happen to be observing. Thus the cosmic radius (or Hubble radius) is the product of speed of light and the current cosmic time - so at present it's 13.8 giga-lightyears. The radius scales to the red-shift by R = Ro/(1+z) with Ro being the radius right now. Thus at z = 1, the cosmos is half its current size.

Melia has a whole bunch of papers and preprints on the theory, linked from his page:


airenatural said...

Another article very recent supports your prediction:


“The residuals are again small (inset panel), but show evidence of a slight but systematic redshift dependence (the mean residual increases slightly with redshift, but remains within the observational error)”.

Now there are four findings that confirm one of the most key predictions of MiHsC, that further back in time the minimum acceleration, a_min=2c^2/(Hubble scale), was higher, since the Hubble scale was smaller, so ancient (high redshift) galaxies should have greater spin for less visible mass:


Seems the fight done by dark-matterists against McGaugh article about MoND is confirming MiHsC!!!