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/

The cosmos is a black hole?

When I was writing the first paper proposing MiHsC (a model for inertia) in 2006 I played around briefly in the discussion section with black holes. Hawking (1974) said that more massive black holes (mass=M) have a lower temperature (so T=K/M, where K is a constant). Wien (1893) said that an object of temperature T emits radiation of wavelength L, and T=k/L (k being another constant). These formulae mean that the more massive the black hole, the longer the wavelength of Hawking radiation it emits.

However, we can't see beyond the Hubble-scale so waves longer than this should not exist (following Ernst Mach). This means that a black hole can't be so massive that the Hawking radiation it emits is bigger than the observable universe. I showed that this predicts a maximum black hole mass of about 10^52 kg and put this into the paper as a curiosity. A year later I read that the mass of the observable universe is about 10^52 kg, with a large error bar. Does this agreement imply that the universe is a black hole? Later, I turned this model inside out and had the cosmos as a black hole emitting radiation inwards from its edge whose wavelengths had to fit exactly into the cosmos (in the same way as the Unruh waves in MiHsC have to) and a toy cosmology was born. I wrote a paper on it and went to the Cosmo-2008 conference in Wisconsin, funded by the Royal Astronomical Society and the Institute of Physics to present it (you can still find my Cosmo-08 .ppt slides on the web).

For six years I have been submitting this cosmology paper, having it rejected, and working to improve it, and I have gradually realised that the model predicts that the universe gains mass as it expands, like the old Steady State Theory of Sir Fred Hoyle. That theory was discredited when the Cosmic Microwave Background (CMB) showed that the early universe was hot. The Steady State Theory couldn't explain that and the rival Big Bang Theory could. The Hubble-scale Casimir effect model though, predicts that the universe must have been hotter when it was smaller, so it produces a Steady State Theory that predicts a Cosmic Microwave Background too.

Cosmology is notoriously data-poor so, since I like to stay close to the data, in the paper I also show that if you apply the dis-allowal of longer waves (the Hubble-scale Casimir effect of MiHsC) to patterns of variation in the cosmos, this predicts a drop-off of variation on the largest scales that agrees well with the 'low-l CMB anomaly' seen in the recent Planck satellite data.

In the paper I also describe an alternative way to think about the Hubble-scale Casimir effect, or 'cosmic seiche' of MiHsC that is more natural. Happily, the journal 'Galaxies' is open access, so a pdf of the paper can be found at the link below:

References

McCulloch, M.E., 2014. A toy cosmology using a Hubble-scale Casimir effect. Galaxies, 2(1), 81-88. Abstract and link to free pdf.

A diversity of ideas means faster progress.

There are many dull periods in history where the suppression of new ideas held up progress. The Inquisition burned books and drove science out of southern Europe to the benefit of northerners. Nowadays, I'd like to argue that a pointless conformity in western theoretical physics is suppressing badly-needed alternatives to standard physics.

As an example: four months ago I published a paper in the scientific literature that derives gravity in a new way from quantum mechanics (see reference below). Something very new. I'm not saying I'm right, I simply don't know yet, but what I would say is that it is interesting and unique, maybe useful, and crucially: already published. I uploaded this paper to the arXiv, hoping to stimulate some useful debate, which I badly need to further build on it, and four months later anonymous people are still mulling over whether to include or reject it, as if the arXiv is its own journal.

The arXiv is a kind of 'public library' that is supposed to reflect what goes on in the scientific community and make it freely available to all, a noble goal, unless it becomes hijacked by a anonymous group with a bias, in which case the arXiv becomes something else entirely: a way for a biased minority to steer the scientific community their way, circumventing the proper evidence-based scientific debate (this avoidance is useful if you have no evidence at all).

I doubt anyone from the arXiv understands the long-term negative impact of what they are doing, I'm sure they are content to be in the 'cool' crowd, but standard/current physics is provably wrong: it only predicts 4% of the cosmos, it is not even self-consistent, as Einstein knew way back in 1935. The suppression of un-cool alternatives simply delays progress, and game-changing technologies we might have had sooner will be lost, perhaps for decades.

On the other hand if the arXiv return to their job, and objectively reflect all the debates occuring in the scientific peer-reviewed literature then theoretical physics can only gain: it may even cease debating cool but untestable and useless subjects like the interior of black holes and will become evidence-based and scientific again. Inevitably this will make it more useful, practical and interesting.

My, maybe flawed, but interesting paper was published in Astrophysics and Space Science and is: here.

What's up with the gravity constant?

I'm looking into an interesting possible anomaly in the gravitational constant, the big G that appears in Newton's gravity law: F = GMm/r^2. Gravity is a tiny force, atom for atom, but it is cumulative unlike the electromagnetic (EM) force whose positive and negative components cancel themselves out, so for large masses (M and m) and close distances (r) gravity can dominate the EM force, for example causing chairs, held together by the EM force, to collapse when sat on.

In 1798, Cavendish worked out a way to measure G. He suspended known masses at both ends of a crossbar suspended by a wire, brought another known mass closer at an angle designed to cause a rotation and measured the twist in the wire. Since he know how much force was required to twist the wire, this told him the gravitational force F between the masses and since F = GMm/r^2, and he knew the mass and distances, he was able to find G. Over the centuries, this method has been refined so that the experimental uncertainty in the values they now get for G is smaller. The problem is, the values of G determined in different labs differ several times more than their expected uncertainty, so either the experimenters have underestimated their errors or a new physical process has been revealed.

Always on the lookout for anomalies, I've had a look at some of the values of G published in the third figure in a recent Physics World article (see the reference below) and noticed that there is a weak correlation with latitude. For example, the G that was measured in Birmingham, UK (at 52^o North) was 0.05% larger than the G measured in Boulder, Colorado (at 40^o North). Although the correlation between the various values for G and the latitude is 0.74, there were only 7 values given in this Figure to go on, so I wouldn't claim significance yet.

I do wonder whether MiHsC is causing this, since the acceleration of objects on the Earth with respect to the fixed stars is lower near the poles, but my initial calculations show that the MiHsC effect seems too small. It may be that I need to learn more about what these experiments are actually doing, so I'm going to a Royal Society Workshop on the uncertainties in G at the end of this month to learn a bit more about this problem.

Reference

Cartwright, J., 2014. "The lure of G". Physics World, Vol. 27, 2, 2nd February.