Edge rings?

One of the details of MiHsC that I have not as yet been able to model is subtle, but fairly unique, and so it might make a good test. MiHsC assumes that inertia is caused by Unruh radiation (a kind of wave in all the fields you can think of, including the electromagnetic and particle fields). This Unruh radiation is not made of just one wavelength but a broad Planck spectrum of radiation with a peak wavelength of ~8c^2/a, where a is the acceleration. MiHsC assumes that from this spectrum only wavelengths that fit exactly into the Hubble scale are allowed: a Hubble-scale Casimir effect (MiHsC = Modified inertia by a Hubble-scale Casimir effect). So far I have just assumed that this subsampling of this spectrum produces a 'linear' decrease in energy as acceleration reduces and less of the spectrum is allowed or sampled. I showed, in the paper below, that this 'linear-MiHsC' is a good approximation, but I haven't yet properly considered the smaller effect of the shape of the spectrum and where in the spectrum the allowed wavelengths are.

I discussed this a little in the discussion of the paper below. It means that when an object has such an acceleration that the peak wavelength of the Unruh spectrum it sees fits exactly into the Hubble scale (a 'resonant' one) then its inertia will be at a maximum according to MiHsC, and when the peak wavelength of Unruh radiation that it sees does not fit exactly into the Hubble scale then its inertia will be slightly less. This will not matter so much for high acceleration objects because so many of the wavelengths in the spectrum will be allowed so that wavelengths close to the peak wavelength will exist, and linear MiHsC will be a good approximation. For example, for Pluto or another object out at about 40 AU from the Sun there are still 4000 wavelengths within the Unruh spectrum allowed by MiHsC.

However, for extremely low accelerations only a few wavelengths will be allowed from the spectrum so it is not guaranteed that the sampled Unruh wavelengths will be close to the peak of the spectrum, so the difference in the inertial mass between an object with a 'resonant' acceleration and a non-resonant one will be larger: linear MiHsC will be inaccurate. Therefore as you go out from the centre of a rotating system like a galaxy, and sample lower and lower orbital accelerations, at certain radii this subtlety of MiHsC predicts that the inertial mass should be slightly greater so the extra centrifugal force will push matter outwards, and at other radii the inertial mass is predicted to be lower so the centripetal gravitational attraction produces more inwards acceleration. I have not modelled exactly what this would mean for the density distribution in a galaxy since this needs a full galaxy model, but this process should produce concentric patterns at larger galactic radii. To get acceleration low enough to see this in the Solar system you'd need to go out to about 1000 AU and be careful that you're not seeing other effects (eg: the orbital resonance that might produce the Titius-Bode law). Anyway, this is another way to look for MiHsC and the more ways the better.

McCulloch, M.E., 2007. Modelling the Pioneer anomaly as modified inertia. MNRAS, 376, 338-342. Link 

An abstract for NAM2014

I've just submitted the following abstract to the organiser of the cosmology section of the UK's National Astronomy Meeting (NAM2014). I hope he chooses it! (they didn't)

Title: A toy cosmology from a Hubble-scale Casimir effect.

A new cosmological model is presented here. The model proposes that inertia is caused as follows: as an object accelerates, for example, to the right, a Rindler horizon forms to its left allowing fewer Unruh wavelengths to exist between the object and the horizon. This can be thought of as a Rindler-scale Casimir effect or as ‘horizon wave censorship’ in which partial waves would provide information from behind the horizon so cannot be allowed. This effect suppresses Unruh radiation on the left side of the object causing a net radiative force that opposes its acceleration, predicting the standard inertial mass. In this model, very long wavelengths of Unruh radiation are also suppressed in the same way by a Hubble-scale Casimir effect (or a Hubble-scale censorship) causing a new detectable effect: a loss of inertia at very low accelerations. This effect predicts the cosmic acceleration, and galaxy rotation without dark matter, both without any adjustable parameters. The same model applied to Hawking radiation from the Hubble edge predicts the visible gravitational mass of the cosmos, that this mass increases as it expands, and that it had a hot start: a Cosmic Microwave Background (CMB). This model also predicts a suppression of variation on the largest scales in agreement with the low-l CMB anomaly recently seen by the Planck satellite. This cosmological model is preliminary, but is directly testable and a laboratory experiment will be proposed.

Reference: McCulloch, M.E., 2014. A toy cosmology using a Hubble-scale Casimir effect. Galaxies, 2, 81-88. link

MiHsC: no tuning required

One of the advantages that MiHsC (Modified inertia due to a Hubble-scale Casimir effect) has over other hypotheses like dark matter is that it makes successful predictions of galaxy rotation without any 'arbitrary tuning'. Consider dark matter, this is extra invisible matter added to galaxies to explain why, despite their fast rotation, they do not explode because of centrifugal forces. Dark matter is added specifically to make the predictions of Newton's gravity law (or GR) fit the observed galactic rotation, but dark matter requires a lot of tuning: it is added ad hoc where needed. This means as much information goes into setting up the hypothesis as is released by its predictions, so you gain no information (dark matter is not predictive).

Now consider MiHsC. This works by reducing the inertial mass in a new way for very low accelerations, reducing the inertial outward tendency of stars at the edges of galaxies. The MiHsC prediction for the orbital velocity of stars is derived from only four parameters; the gravitational constant G, the 'visible' mass M, the speed of light (c) and the Hubble scale (Theta). All these parameters are well observed (the worst known are M which depends on the stellar mass to light ratio and the Hubble scale with an error of 9 percent) so there is no arbitrary wriggle room and yet MiHsC predicts galaxies and galaxy clusters well (see the reference below).

There should be a quantitative way to assess theories based on a ratio of the accuracy of their predictions divided by the amount of initial ad hoc tuning you have to do. With this method the completely arbitrary dark matter would score very low, MoND (Modified Newtonian Dynamics) with its single arbitrary adjustable parameter (a0) would score a bit higher, but MiHsC with no arbitrary adjustable parameters at all would have an infinite score. Of course, there are other kinds of assumption in MiHsC, for example the existence of Unruh radiation, but none of these assumptions are arbitrary ones.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophys. Space Sci., 342, 2, 575-578. Journal / Preprint

How to solve a problem like big G.

I've just returned from a Royal Society meeting at their new Chicheley Hall (cunningly designed to get scientists to actually talk to each other) titled: "The Newtonian constant of gravitation: a constant too difficult to measure?" There was so much in the meeting that was fascinating and amusing that it will take a few blogs to cover it, but my overall impression was that, although I have no bias either way whether G is constant, the experimenters are limiting themselves by their assumption that it is.

G is difficult to measure because gravity is such a weak force, and it stands alone theoretically so you can't (yet) get to it from other parts of physics. Most of the experiments to find G are done using a torsion balance. This is made up of two test masses joined like a dumb-bell and suspended from the crossbar's centre by a wire. Source masses are held horizontally to one side of the test masses to avoid confusion with the Earth's gravity which operates vertically. Gravity pulls the test masses sideways and the angle of twist of the wire is measured. Since the force needed to twist the wire a given angle is known, the experimenters can find the gravitational force due to the source masses and using Newton's F=GMm/r^2 they can infer G (knowing F, M, m and r, which requires very careful measurement, surveying and planning).

It is very clear that all the experimental groups believe that they have measured the correct value of G and their uncertainty in their work is low (within 50 parts per million, ppm). However, their different values for G differ by 480 ppm (ten times the uncertainties)! No one knows what is causing these significant differences. The experimenters suspect overlooked mundane effects, others, eg: Prof Gibbons from Cambridge suggested at the meeting that perhaps G could vary in time. I wonder if inertial mass might vary in these experiments due to MiHsC, but the data to decide is not clear yet.

The experimenters themselves are a quality group: precise, tenacious, and also stressed, since they've spent the past decade measuring G, and there's been no closure since the true value is still unknown. It must be like training for 10 years for the Olympics, but at the end of the race it becomes clear that someone forgot to paint in the finish line and no-one knows who won. Dr Gundlach has given up on G and gone into biophysics and says he would never go back because of the sleepness nights (mind you, he smiles whenever he talks about his experiment, so he might). Dr Schlamminger (who seems to operate at twice the speed of everyone else) is young enough not to have run out of enthusiasm yet. Prof Clive Speake says that despite the huge import of this work he is finding it hard to engage the young in the classical-sounding physics of interacting balls. All the experimenters are keen to set up a new joint experiment that will solve all the (unknown) problems of the old ones and hope that the shared responsibility will mean less stress, but whatever new value for G they get is not going to agree with all the previous ones and may just add another data point to the menagerie.

In my view, a change of attitude is needed. One should look for patterns without presupposing a model. The obvious assumed model all the groups have is that G is constant. This means that they all take many measurements of G over, say, a month, and then average all these values to produce a precise G. What I think they should do, for old if possible, and new experiments is to publish time series of all the un-averaged data and all the environmental factors and experimental configurations in a data base online so others can look for patterns. The few plots I saw that did show the actual data (before averaging) showed large variations. What causes them? Are there any correlations? A compilation of old and new data like this would cost a tiny percentage of the cost of a brand new experiment, and curious scientists would then be able to search for patterns for free. Something like this was attempted by Dr Gillies at the meeting, but he only looked at variations in the source masses.

I don't know whether G is constant or not, but if it varies, or some other new physics is present they may never see it with their present averaging attitude. One should always test assumptions, and, in fact, that is the motto of the Royal Society: "Nullius in Verba: don't take anyone's word for it".

The webpage of the meeting is here:  http://royalsociety.org/events/2014/gravitation/