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

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), the recent NASA vacuum test (Bv), and last but not least I've just added Tajmar's (2015) vacuum test (T1).

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
T 1          20.3  700       1.44       10.62      7.5      10.08          0.02      0.019
Thanks to Dr J. Rodal for pointing out some errors in the NASA cavity's dimensions. I've now doubled the Tajmar dimensions too.

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).

Tajmar, M.,  G. Fielder, 2015. Direct thrust measurements of an emdrive and evaluation of possible side effects. 51st AIAA/SAE/ASEE Joint Propulsion Conference, Orlando, Florida.

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.