I chose the title Physics from the Edge because the theory of inertia I have suggested (MiHsC) assumes that local inertia is affected by the far-off Hubble-edge. My webpage is here and I've written a book on inertia and MiHsC which is also called Physics from the Edge.

Sunday, 29 March 2015

Dark matter contradicts itself.

There has just been a study published in Science (Harvey et al., 2015) that is interesting because it forces the dark matter hypothesis to contradict itself.

Harvey et al. have looked at the light from familiar objects like galaxies as seen from behind galaxy clusters, and looked at the distortion in the images due to gravitational lensing. They know what a typical galaxy looks like: a disc, so if it looks like a U-bend instead when it's behind the galaxy cluster, then they can infer the bending of the light that must be occurring and assume this bending is due to dark (invisible) matter in the cluster. They looked at 72 galaxy cluster collisions, and have modeled the collisions using several kinds of dark matter, and have shown that the only kind of dark matter that fits the observations, is a kind that doesn't interact with itself. I'd like to point out here that this makes the dark matter hypothesis self-contradictory since it is well known it must repel itself to stay spread out in the halo of galaxies, and yet this study now shows it must not interact with itself. So dark matter dissappears in a puff of logic? Well, I'm sure someone will think of a way to make it more complex to save the hypothesis, but it gets ever more ridiculous.

In contrast MiHsC says that there is no dark matter (see my blog here and my paper here) and that the light is bending because its inertial mass varies due to the variation in acceleration within the cluster. I know the inertial mass of light is a controversial issue, but it has never been well understood, and MiHsC predicts galaxy rotation, cosmic acceleration, the flyby anomalies, the emdrive (light in a box) and many other anomalies quite well without invisible entities or contradictions.


Harvey D, Massey R, Kitching T, Taylor A, Tittley E. The non-gravitational interactions of dark matter in colliding galaxy clusters. Science 27 March 2015. Read more at Phys Org

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

Saturday, 21 March 2015

One-wave MiHsC and the EmDrive

MiHsC (see an introduction) assumes that inertia is caused by a radiation pressure from Unruh radiation, and that the waves of this radiation are only allowed to exist if they have nodes at information horizons like the Rindler (local) or Hubble (cosmic) horizon, because if they didn't have nodes there, we could infer what lies behind the horizon and it wouldn't be a horizon (logic/information affects local physics).

So far with MiHsC I've used an approximation, and assumed that as accelerations decrease, then the number of waves in the Unruh spectrum decreases linearly as they are disallowed by the horizon, and so the inertial mass decreases in a new way (predicting galaxy rotation without dark matter...etc). I can get away with this because the accelerations are rarely small enough that only one or two Unruh waves fit.

To apply MiHsC to the resonating emdrive (a truncated metal cone), and probably to very low cosmic accelerations too, I need to consider individual Unruh waves. So I have recently tried an alternative approximation of MiHsC that assumes that there is only one wave at the peak of the Unruh radiation spectrum and this wave either fits or doesn't within the horizon (which for the emdrive, is its walls). This leads to a prediction for the anomalous force on the emdrive (F) like this

F = -PQ/c * (|sin(pi*w_small/L)|-|sin(pi*w_big/L)|)

where P is the input power, Q is the quality factor, c is the speed of light, w_big and w_small are the diameters of the big and small end plates of the emdrive, and L is its length. As you can see I'm using the magnitude of a sin function to decide whether the Unruh wave (only one now) fits within the walls or not, at the wide end and the narrow end. This Table shows how the results differ from what I had before:

Experiment       Observed      MiHsC2d    OnewaveMiHsC
                                     ----  milliNewtons ----
Shawyer 1             16               4.1              7.7
Shawyer 2           147           148.9            54.7
Cannae drive           9               5.3              4.3
Juan et al. A         214           154               39
Juan et al. B         315            241              61
NASA B1                 0.09          0.26            0.07
NASA B2                 0.05          0.63            0.18
NASA B3                 0.06          0.12            0.03
NASA vacuum        0.03          0.70            0.20

As you can see, I've used the 2d (two-dimensional) version of spectrum-MiHsC to compare with the 2d one-wave MiHsC, for a fair comparison. I've shown the Cannae and Juan (2012) cases in red because I'm not confident I have the right geometry for them. MiHsC predicts that (usually) photons are more likely to see a resonating Unruh wave at the wide end, so the photons' inertia increases as they go towards the wide end and to conserve momentum the whole cone then has to move the other way. As you can see, the new formulation is much better for the NASA data but worse for the more powerful of the Shawyer experiments (I still don't know the uncertainties in the data).

Interestingly, this approach predicts there can be a reverse mode for the emdrive (not a particularly bold prediction I admit since NASA may have seen a reverse already). MiHsC predicts this reverse occurs if you 'tune' the Unruh waves to fit better into the narrow end.

I've been trying to develop a one-wave version of MiHsC for application to cosmology for ages, the emdrive is useful (if real) because it provides data on which to test progress.

Thursday, 12 March 2015

Predicting Proxima Centauri's Orbit

The best way to persuade others to accept a new paradigm is to find an anomaly that embarrasses the old one. The galaxy rotation problem should be such a thing, but the old theory has been saved by dark matter which is flexible enough to fudge a solution.

The goal then is to find an anomaly for which dark matter cannot work. Its Achilles' heel is scale, since, to work for full-sized galaxies, dark matter must have a tendency to spread out smoothly to explain why it stays out in the galactic halo, so dark matter shouldn't effect dynamics on smaller scales. One possible test then is to use globular clusters, smaller bound collections of stars within galaxies. They do indeed show a very similar rotational anomaly (Scarpa et al., 2006) but they are not simple enough to provide a clean test. Smaller and simpler are wide binary stars and again, a similar, orbital, anomaly has been seen (Hernandez et al., 2011) but the data is still too noisy. Recently, I've become interested in a wide 'trinary' for which the data is a bit better: our closest neighbour: the Alpha Centauri system.

I've talked about this before: this triple star system is interesting because the first two stars orbit close together so their masses are well determined from their orbits, but the third star orbits far from them in a low acceleration regime where MiHsC should apply. Sure enough, there is an anomaly. The third star, Proxima, has an orbit that is so fast that it should spin off into deep space with the centrifugal force, since the known mass of the the other two stars is too small to gravitationally bind it. Yet, other data, for example the similar chemistry of the three stars and the fact that they all seem to move together in the sky suggest that Proxima is bound to the system, but according to Newton, it can't be with that fast orbit.

This makes a nice experiment because the mass of the central two stars can't be increased to bind Proxima (their masses are too well known) and dark matter can't be used either (too small a scale). MoND (Modified Newtonian Dynamics) can be applied here, and can be thought of either as an increase in the gravitational constant, or a decrease in the inertial mass, but MoND has no physical model (no reason) behind it and it needs an adjustable parameter called a0 to be set by hand, again with no apparent reason.

MiHsC can also be used to predict the orbit, and it has a clear reason, and no adjustable parameters are needed. It predicts that the low acceleration of Proxima reduces its inertial mass so it can more easily be bent into a bound orbit by the small observed mass of the central two stars. The observed orbital velocity of Proxima and the various predictions of it are as follows:

Observed = 0.53 +/- 0.14 km/s   (to be improved by new ESA GAIA data)

Newton    = 0.34 +/- 0.02 km/s   (no wriggle room)
MoND      = 0.42 +/- 0.2 km/s    (if a0 is set to 1.2*10^-10 m/s^2)
MiHsC     = 0.65 +/- 0.02 km/s   (no wriggle room)

Newton and Einstein disagree with the data (unless the assumed orbit is extreme, which it could be) and dark matter can't be applied to this case. Both MoND and MiHsC agree with the data, and so they reconcile the chemical, co-moving and orbital data, but MiHsC does it with a reason and without the need for an adjustable parameter. I have just submitted a paper on this, so a reviewer somewhere is having fun.


Hernandez, X., M.A. Jimenez and C. Allen, 2011. Wide binaries as a critical test of classical gravity. Euro. Phys. J. C., 72, 1884. Preprint.

Scarpa, R., G. Marconi, R. Gilmozzi, 2006. Globular clusters as a test for gravity in the weak acceleration regime. Proceedings of the 1st crisis in cosmology conference. Am. Inst. Phys Proceedings series, Vol. 822. Preprint.

Monday, 23 February 2015

Debate on the facts.

Over the weekend I put up on wikipedia some lines on my peer-reviewed publications on MiHsC and how it can solve the galaxy rotation problem...etc. As has happened a few times before, it was all deleted by someone anonymous.

Instead of ranting about it, it's best to deal with things on the facts, so here is a summary of all the real problems MiHsC solves without needing any extra dimensions, huge amounts of invisible (dark) stuff, or any adjustable parameters either. MiHsC does it with a simple model for inertia, with a solid physical model behind it. A model that defines the inertial mass (mi) of an object to be

where m is the normal inertial mass, c is the speed of light, |a| is the magnitude of the acceleration of the object relative to other objects, and T is the Hubble scale. All these quantities are well defined and well known, so there is no scope in MiHsC for 'tuning' (adjustment) such as is done freely with dark matter, and even in MoND with the adjustable parameter a0, and yet without adjustment this MiHsC formula predicts the following anomalous observations, within their uncertainties:

The mass of the cosmos (solving the flatness problem), the low-l CMB anomaly (unexpected smoothness on cosmic scales, paper), the dynamics of galaxy clusters without dark matter (MoND cannot do this), galaxy rotation without dark matter (paper), the observed minimum mass of dwarf galaxies, the strange (un)bound orbit of Proxima Centauri, the Pioneer anomaly (far more simply than the 'accepted' Byzantine thermal solution) (paper), the flyby anomalies (paper), the Podkletnov (paper) and Tajmar anomalies (paper), the EmDrive, (paper) and it explains for the first time the phenomenon of inertial mass itself (only 0.1% of which is explained by the Higgs mechanism) (paper). An accessible introduction to MiHsC is here.

Mainstream theoretical (astro)physics, lost in Plato's realm, has lost the ability to debate issues on the facts, and has resorted to rearranging invisible entities and deleting new ideas online, but this is a symptom of its bankruptcy.

Friday, 13 February 2015

MiHsC vs EmDrive data: 3d

The EmDrive is a fascinating anomaly. It consists of a truncated metal cone (cavity) with a magnetron inside that inputs EM radiation with the same wavelength as the size of the cavity (it's just like a loudspeaker-shaped microwave oven). It has been shown by three different groups (UK, China, US) that when a resonance is achieved the cavity moves slightly towards its narrow end in apparent violation of the conservation of momentum, since there is no expelled mass to cause this. There was a suspicion that the movement was due to air currents, but NASA have just this last week shown that the same thing happens in vacuo.

In previous blogs I showed that MiHsC predicts the EmDrive thrust reasonably well, if it is assumed that photons have inertial mass which is caused by Unruh radiation whose wavelengths must fit inside the cone. MiHsC predicts that more Unruh waves fit in at the wide end of the EmDrive, so for photons traveling along the axis they always gain mass going towards the wide end and lose it going the other way. This is equivalent to expelling mass towards the wide end, so the cavity moves towards its narrow end to conserve momentum.

The equation I derived to apply MiHsC to the EmDrive setup (and published here) was extremely simple and didn't take account of the 3-dimensional nature of the cavity. I have now worked out a short-cut way to calculate the effect in 3-d, and I've re-derived the equation I had before for the thrust (F), which was

F = PQL/c * (1/wb - 1/ws)                                   (1)

so that in 3-d it is now

F = 6PQL/c * ( 1/(L+4wb) - 1/(L+4ws) )             (2)

where P is the power input (in Watts), Q is the Q-factor (number of bounces of a typical photon inside the cavity, L is the axial cavity length, c is the speed of light, ws and wb are the diameters of the small and big ends of the truncated cone. I have now applied Eq. 2 to the data I had before, and added the new vacuum result from NASA. I've put everything into Table 1 which shows results, row by row, for the two Shawyer (2008) tests (denoted Sa and Sb), the Cannae Drive test (Ca), the Chinese Juan et al. (2012) tests (J1 and J2), the NASA tests of Brady et al. (2014) (Ba, b, c) and the recent NASA vacuum test (Bv).

Expt     Q       Power     Freq'     wb        ws             L     Observed     MiHsC
                      Watts      GHz       cm        cm          cm     (----milliNewtons----)

S a      5900     850       2.45       16        12.750   15.6          16           3.84
S b    45000   1000       2.45       28        12.890   34.5      80-214   148
C a     1.1e7       10.5    1.047     22        20            3.0            9           7.34
J 1     32000   1000       2.45       28        12.89     34.5        214       106
J 2     50000   1000       2.45       28        12.89     34.5        315       165
B a      7320       16.9    1.933     27.94    15.88    22.86          0.09      0.23
B b    18100       16.7    1.937       "           "             "               0.05      0.57
B c    22000         2.6    1.88         "           "             "               0.06      0.11
B v      6730       50       1.937       "           "             "               0.03      0.64
Thanks to Dr J. Rodal for pointing out some errors in the NASA cavity's dimensions.

The results show a correlation between the observed thrusts (column 8) and the predictions of MiHsC (column 9), but with varying degrees of success: for the smaller NASA thrusts the error ratio is between 2 and 12, for the larger thrusts it is between 2 and 4. So, as usual, these results are interesting enough to record, but nothing yet to write to Nature about. Note that for J1 and J2 I've had to assume that their cavity dimensions were the same as those for Shawyer b, since their geometry was not documented. If anyone knows the dimensions, or notices any errors in the Table please do let me know! A summary of the Table is shown as a log-log plot below (I had to use a naughty log-log plot to separate the tiny NASA values).

Some of the discrepancy between MiHsC and the data could be due to an observation pointed out by Bob Ludwick that I read on a website somewhere: the Chinese noted that the correct parameter to use is not the Power P, but the power within the resonant bandwidth of the EmDrive, which is harder to calculate.

Some of my previous blog entries about MiHsC and the emdrive are here and here. My paper is here.


Brady, D., et al., 2014. Anomalous thrust production from an RF test device measured on a low-thrust torsion pendulum. Conference proceedings, see Table page 18. Link

Juan, W., 2012. Net thrust measurement of propellantless microwave thrusters. Acta Physica Sinica, 61, 11. 

McCulloch, M.E., 2015. Can the EmDrive be predicted by quantised inertia? Progress in Physics, 11, 1, 78-80. Link
Shawyer, R., 2008. Microwave propulsion - progress in the emdrive programme. Link. (see section 6, page 6).

Saturday, 7 February 2015

A shape is just a shape

I do not go looking for controversy, but the interesting areas that I get attracted to (anomalies) are often those areas where scientific taboos have put up warning signs. One example of breaking a different kind of taboo is the paper I have just published.

It all began at the end of 2004 when I went to South Korea and noticed that there were swastika signs next to the country roads. The swastika means Buddhist temple over there, proving that in some cases Bertrand Russell was right and 'Sin is geographical'. While Germany bans the swastika, Koreans associate it with Buddhism and peace. Travel broadens the mind, and we should remember that in physics, a shape is just a shape. Anyway, seeing all these signs, I had the idea for a new way of generating energy from ocean waves, using a swastika-rotor. This is illustrated by the Figure:

The swastika, or British fylfot if you wish, is centred on a axle (black circle) connected to a dynamo and sits in a random wave field. In the inner square areas (eg: A and B) there are fewer waves because of a sheltering effect, and because fewer wavelengths fit between the solid arms (to exist they need a node at the walls) so there is also a seiche effect. If we take the inner part of the southeast arm there is no net wave impact force on it because there are the same intensity of waves on both sides, but if we look at the outer part of the arm between areas B and C there are waves to the east of it banging into it and pushing it to the west, but no waves to the west of it pushing it east, so the net effect is a force (the arrow) pushing the arms of the swastika clockwise, and generating rotation and electricity with the dynamo.

This can be applied to ocean waves of course, but why not also to other kinds of waves or disturbances? For example: sound waves, Brownian motion and, last but definitely not least, the zero point field? Could we generate 'free' energy from the zpf this way? The rotors would have to be nano-scale though, so I don't see yet how this process could be scaled up..

After 8 years of procrastinating, and experiments with Lego, I wrote a paper and started submitting it to journals. I submitted it to three journals, and at all of them I had a long wait, and in each case the paper wasn't rejected, but it just never got reviewed so I had to withdraw it, and resubmit it to another journal. It was odd (I do wonder whether the politics stymied it?). Anyway, I have now published it in the fourth journal I sent it to (see the reference below). The next thing I intend to do is apply for funding to test this in Plymouth University's new wave tank and investigate the zpf angle theoretically.

Note the connection with MiHsC in that the arms of the shape are acting as a kind of horizon for the waves..


McCulloch, M.E., 2015. Energy from swastika-shaped rotors. Progress in Physics, 11, 2, 139-140. PDF

Monday, 2 February 2015

Empirical Falsification & Alpha Centauri

I strongly agree with Karl Popper's philosophy of empirical falsification: 'A theory in the empirical sciences can never be proven, but it can be falsified, meaning that it can and should be scrutinised by decisive experiments. If the outcome of an experiment contradicts the theory, one should refrain from ad hoc manoeuvres that evade the contradiction merely by making it less falsifiable'.

It's clear that much of modern physics, for example the search for gravitational waves and dark matter, are complete reversals of this sensible approach. The search for gravitational waves is an attempt to 'prove' general relativity, not to disprove it. Similarly for dark matter: when general relativity was first applied to other galaxies it was found to wrongly predict their rotation, so invisible dark matter was invented, huge amounts of it, to make general relativity fit. This is clearly an 'ad hoc manoeuvre to evade the contradiction that makes the whole system less falsifiable', since dark matter is added by hand and cannot be disproven. Since then, mind boggling sums of money have been spent building detectors to look for dark matter, in disregard of the sensible Popperian approach which would design decisive experiments that attack general relativity.

What would be a decisive experiment or observation? Torsion balance tests of the equivalence principle (the basis of general relativity, GR) are not decisive, because a theory now exists that explains galaxy rotation and violates equivalence, but would not show up in such experiments (MiHsC). One decisive way to attack GR would be to look at a very low acceleration system that cannot be explained by dark matter.

For example, I have discussed globular clusters, wide binary stars and the Alpha Centauri system before and I have now completed a nice paper on the latter (to be submitted). Alpha Centauri is the closest star system to us. It is a triple star system with two stars very close together and one extremely far away and in the 'low acceleration' regime. Sure enough, the far star (Proxima Centauri) is orbiting far too fast to be bound by the visible matter of the other two, and yet it is definitely bound because it has the same motion through the sky and the same chemistry as the others. This may sound oddly familiar! It is a decisive anomaly because it sounds just like the galaxy rotation problem, but dark matter cannot be applied on these small scales. One 'fix' that has been inevitably suggested is to increase the mass of the two central stars, by 3-sigma, a large increase over their mass uncertainty, so not ideal.

I've now shown that MiHsC predicts a loss of inertia for Proxima, so that it can be bent into a bound orbit with the observed fast speed. This means that MiHsC reconciles the chemical, co-moving and orbital data without the need for any 'fiddling', and dark matter and additions of normal matter can't work in this case.


McCulloch, M.E., 2015. Testing quantised inertia on the Alpha Centauri system (to be submitted).

Wertheimer, J.G., G. Laughlin, 2006. Are Proxima and Alpha Centauri gravitationally bound? Astronomical Journal, 132, 1995-1997.