I've suggested (& published in 18 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

Friday, 20 October 2017

The Joy of Anomalies

It is the fashion in mainstream physics today to always start from the existing theory. For example, general relativity is always assumed to be right. If you don't believe that, try questioning it and see what happens! As a result the mainstream need to work out what data they need to find to make it right. Hence the search for dark matter, dark energy, dark flows, which brings in lots of funding too. This is the process everywhere, but it is the opposite of the scientific method which puts data first and reigned between say 1660 (founding of the Royal Society, who said 'disregard theory and look at data') and 1988 (when data-driven Feynman died). If you want to be cheeky, you could call the post-1988 way the 'religious' method, but without the attached morality.

Probably because I was educated in a more grounded form of physics (BSc in physics, PhD in ocean physics) and loved reading Feynman, I am pre-1988. What I like to do, and have ever since my physics degree, is look for interesting anomalies (data that defies the theory). Actually, before my physics degree I was fond of theories and philosophy and did not bother much about data. I spent hours in the library reading about Spinoza, and trying to devise theories from beautiful thoughts alone, but something changed when I did my third year research project at York University: An analysis of a chaotic Duffing oscillator. I built such an oscillator in the university's metalworking lab. It was a beautiful thing and I wish I still had it! (see my schematic below). A metal pendulum with a magnet at its base, repelled from its equilibrium point by a magnet underneath. It had two side-arms with magnets attached pointing down. One arm was driven sinusoidally with a electromagnetic coil around the magnet, the motion of the magnet on the other side was sensed with another electromagnetic coil. The signal was fed to a BBC computer, that also by integration could work out from the measured speed, the position of the pendulum. I collected and plotted strange attractors of the chaotic motion - the pendulum oscillates between two stable positions chaotically.

When I started my PhD shortly after, I began reading Feynman's books. Also, I eventually focussed on a beautiful anomaly. Cruise data has shown that every summer, a thin cold, fresh surface layer spreads over the north Atlantic. Why? I built a simple layered computer model of it, showed the spreading was due to wind-driven (Ekman) flow blowing polar water south and showed that the air-sea interaction heated the cold surface as it went, but did not erase the freshness, so it becomes unexpectedly buoyant (being now warm and fresh, both properties reduce water density). It forms an insulating cap on the ocean that has implications for climate (paper).

Later when I worked at the Met Office I was tasked with looking at the output of the ocean model and I decided, being fond of data by now, to look at the output without the smooth interpolation that was being done. I pixelated the raw sea surface salinity data instead, and what immediately appeared were nice bands of fresh surface water underneath rainbands. So I developed a simple model of those as well, and that predicted consequences for weather too.

I've always been keen on fundamental physics & astronomy and so I couldn't help but notice anomalies like the galaxy rotation problem, the Pioneer anomaly and that they both involve the same odd acceleration 10^-10 m/s^2. I developed a simple model to explain those, called MiHsC or quantised inertia and it turns out it predicts a lot of other anomalies, such as the emdrive, and cosmic acceleration which I did not know existed till it heard about it on the car radio and thought "MiHsC predicts that!"

I do love looking for anomalies or mysteries. That is why mainstream physics now seems so dry because they are so confident that they know it all and anomalies are brushed under the carpet with arbitrary fudges like dark matter. In my latest attempt to fight back, I have started writing #AnomalyoftheDay on twitter, documenting all the well-observed anomalies that prove that physics is very incomplete (eg: it only predicts 4% of the cosmos). There are many anomalies now, from the proton radius being different depending on how you measure it, the gravitational constant not being constant (blog), tapered microwave ovens which thrust slightly without expelling propellent (emdrives), odd lights flying around in Hesdallen, Norway (link), galaxies rotating in violation of Einstein, and the Cosmic Microwave Background being aligned with the Solar system in a way that would make Copernicus weep! (paper, see Figs. 1 and 2). I have a list of 40 or so anomalies and it is growing.

The tendency I and some others are fighting in mainstream physics is a huge one, a combination of hero-worship, intellectual laziness, group-think and a bias in physics towards mega-expensive solutions like dark matter detectors since bringing in the most funding gets academics promotion. My hope is to get physicists to look up from old books and funding applications and look at real anomalies again (an act which requires little or no funding and repays you with fun), or at least get taxpayers to demand they do. Only then will the mainstream see the utility of quantised inertia.

Monday, 16 October 2017

The Allais Effect

I'm getting slightly respectable in my old age, being invited to talk at St Andrews University, but I always found that un-respectable anomalies (no real anomaly is respectable) are the essential signposts to new physics and to show that I have lost none of my radicalism I'm going to talk about the Allais effect and a possible way that quantised inertia might apply. Please note that this proposal is not yet solid and is just an exploration at this stage.

The Allais effect was discovered by Maurice Allais, a Frenchman who won the Nobel prize for economics. He was using a Foucault pendulum during a Solar eclipse in 1954. Usually these pendulums swing to and fro in the same plane of space because of their inertia, so that, to us on the spinning Earth, their plane of oscillation appears to turn with a period of a day (at the poles, see comments).

The first component of the Allais effect is that during a Solar eclipse the plane of rotation of the pendulum rotates more rapidly than expected during the eclipse moving through about 10 degrees and at the end of it, it rotates back into the expected orientation.

The second effect was found in 1961 by Gheorghe Jeverdan who noticed that during the eclipse the period of the pendulum also decreases by one part in 2000 or dT/T=0.0005, where T is period.

The third effect was seen by Mishra and Rao (1995) and involves a reduction of apparent gravity, and then an increase, both of about 0.5 microgals or 0.5x10^-8 m/s^2.

If confirmed, then these observations would be a useful clue in the development from quantised inertia into horizon mechanics (a new complete dynamical model). I noticed a few months ago that quantised inertia agrees with the second effect but in a manner that I hesitate to mention, because it sounds a little wacky, even to me, but here's to bold suggestions and freedom of speech.

Consider Allais' pendulum. It sees huge accelerations within the hot Sun. As you'll see, the actual acceleration doesn't matter, which is lucky since I don't know it. Lets just assume it is a big number. So according to quantised inertia the acceleration is big, the Unruh waves seen are short and a large proportion of them are 'allowed' since they fit inside the Hubble volume. Suddenly, the Sun gets covered up by the Moon, and the main acceleration the pendulum sees now is the acceleration of the Moon around the Earth which is 0.0024 m/s^2. The Unruh waves it sees are now longer, fewer fit inside the Hubble volume, and a greater proportion are disallowed so the inertial mass of the pendulum drops. The change of inertial mass predicted by QI is

dm/m = (2c^2/Theta)((1/a1-1/a2)

where c is the speed of light, Theta is the co-moving distance to the cosmic horizon and a1 and a2 are the accelerations in the Sun, and of the Moon around the Earth respectively. So putting in values

dm/m = 2x10^-10 x ((1/0.0024)-(1/bignumber))
dm/m = 2x10^-10 x ((1/0.0024)-0)
dm/m = 8.3x10^-8

The period of a pendulum (T) is given by

T = 2pi.sqrt(lm/gM)

where l is its length, m is the inertial mass of the pendulum bob, g is the gravitational acceleration and M is the gravitational mass of the bob (M .ne. m in QI). So the variation of the period will be the square root of the variation of the inertial mass, in other words

dT/T = sqrt(dm/m) = sqrt(8.3x10^-8)

dT/T = 0.0003

The observed variation in the pendulum's period (Duif, 2004, data from Saxl and Allen) was

dT/T = 0.0005

So quantised inertia (summarised here) predicts in the right ballpark. I have to say that, even to me, the process of Moon-shielding of Unruh radiation sounds quite wild at this stage, and it predicts that there should also be a diurnal effect as the Sun sets and goes behind the Earth (see second reference, far from conclusive), but I think it is important to get these edgy ideas out there, just in case someone else can add a little to it, and to avoid the descent into safe irrelevance.


Duif, C., 2004. A review of conventional explanations of anomalous observations during Solar eclipses. https://arxiv.org/abs/gr-qc/0408023

Saxl E.J., M. Allen, J. Burns, 1980. Torsion pendulum: peculiar diurnal variations in period. Letter submitted to Nature. https://www.researchgate.net/publication/284186911_AllaisBook_SAB1980

Monday, 9 October 2017

List of major QI papers

Here is a list of most of the peer-reviewed papers on MiHsC/quantised inertia (QI) so far, with brief summaries. The most conclusive ones are generally towards the end of the list:

McCulloch, M.E., 2007. Modelling the Pioneer anomaly as modified inertia. Mon. Not. Roy. Astro. Soc., 376, 338-342. https://arxiv.org/abs/astro-ph/0612599 The initial conceptual paper, explaining QI and showing that it predicts the Pioneer spacecraft anomaly, which also agrees with the cosmic acceleration and 2c^2/Cosmic_scale. Despite this clue the mainstream no longer considers it an anomaly having invented a computer-aided complex fudge for it. There are lots of other suggestions for tests of QI in the discussion.

McCulloch, M.E., 2008. Can the flyby anomalies be explained by a modification of inertia? J. British Interplanetary Soc., Vol. 61, 373-378. https://arxiv.org/abs/0712.3022. Most of this paper is now out of date, but I discuss 'how to modify inertia using metamaterials' in the discussion.

McCulloch, M.E., 2008. Modelling the flyby anomalies using a modification of inertia. Mon. Not. Royal. Astro. Soc., Letters, 389 (1), L57-60. https://arxiv.org/abs/0806.4159. Testing QI on the flyby anomalies, unexpected tiny boosts in the speed of spacecraft flying by Earth, which it predicts should be larger for slower-spinning bodies.

McCulloch, M.E., 2010. Minimum accelerations from quantised inertia. EPL, 90, 29001 https://arxiv.org/abs/1004.3303. QI explains cosmic acceleration and the minimum mass of dwarf galaxies. A test is also suggested using the LHC: accelerate particles so fast that the Unruh waves they see can be interfered with by long wave radiation.

McCulloch, M.E., 2011. The Tajmar effect from quantised inertia. EPL, 95, 39002.
https://arxiv.org/abs/1106.3266. QI predicts tiny dynamical anomalies observed by Tajmar close to super-cooled spinning rings.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics and Space Science, Vol. 342, No. 2, 575-578. https://arxiv.org/abs/1207.7007. My first attempt to properly model galaxy rotation. QI predicts well (within the wide error bars).

McCulloch, M.E., 2013. Inertia from an asymmetric Casimir effect. EPL, 101, 59001 https://arxiv.org/abs/1302.2775. A conceptual paper, to explain the origin of inertial mass from first principles. It is also suggested that inertia can be modified, and motion can be induced, by making an artificial horizon. ****

McCulloch, M.E., 2014. Gravity from the uncertainty principle. ApSS. 349, 957-959. https://link.springer.com/article/10.1007%2Fs10509-013-1686-9. How to derive Newton's gravity law, from quantum mechanics! (the derivation is flawed at the end as you will see, but this is sorted out in a later paper, see below)

McCulloch, M.E., 2014. A toy cosmology using a Hubble-scale Casimir effect. Galaxies, Vol. 2(1), 81-88. http://www.mdpi.com/2075-4434/2/1/81. My first attempt at a QI cosmology - are we inside a black hole? The low-l CMB anomaly (an unexpected smoothness in the CMB at large scales) is also predicted.

McCulloch, M.E., 2015. Testing quantised inertia on the emdrive, EPL, 111, 60005. https://arxiv.org/abs/1604.03449. Shows that QI predicts the anomalous thrust from asymmetric microwave cavities (emdrives).****

Gine, J. and M.E. McCulloch, 2016. Inertia from Unruh temperatures. Modern Physics Letters A, 31, 1650107. http://www.worldscientific.com/doi/abs/10.1142/S0217732316501078. The first collaborative paper - with a more thermodynamic theme.

McCulloch, M.E., 2016. Quantised inertia from relativity & the uncertainty principle, EPL, 115, 69001. https://arxiv.org/abs/1610.06787. Conceptual. A better attempt at deriving gravity & QI from Heisenberg's uncertainty principle by assuming that what is conserved is mass-energy and information/uncertainty ****

McCulloch, M.E., 2017. Low acceleration dwarf galaxies as tests of quantised inertia. Astrophys. Space Sci., 362, 57. http://rdcu.be/px8h. Quantised inertia predicts parts of the cosmos that other theories cannot, dwarf galaxies.

Pickering, K.,  2017. The universe as a resonant cavity: a small step towards unification of MoND and MiHsC. Adv. Astro., Vol. 2, No.1: http://www.isaacpub.org/images/PaperPDF/AdAp_100063_2017021413572668843.pdf. Models the cosmos with a better cavity model and has an interesting take on the cosmic boundary.

McCulloch, M.E., 2017. Testing quantised inertia on emdrives with dielectrics. EPL, 118, 34003. http://iopscience.iop.org/article/10.1209/0295-5075/118/34003. A further test of QI using the emdrive, taking account of the dielectrics in them.

McCulloch, M.E., 2017. Galaxy rotations from quantised inertia and visible matter only. Astrophys. & Space Sci., 362,149. https://link.springer.com/article/10.1007/s10509-017-3128-6. Shows QI predicts galaxy rotation perfectly without the need for dark matter. It also predicts that galaxies at high redshift should spin faster for the same apparent mass: a good test of QI since no other theory predicts that, and observations now tentatively show this is the case. ****

McCulloch, M.E. and J. Gine, 2017. Modified inertial mass from information loss. Mod. Phys. Lett. A., 1750148. http://www.worldscientific.com/doi/abs/10.1142/S0217732317501486. An attempt to derive QI from a conservation of information (an improved sequel is coming..).

Wednesday, 4 October 2017

LIGO: New data, too many assumptions

The award yesterday of the Nobel prize to Weiss, Thorne and Barish (and the LIGO team) for gravitational waves is interesting because they have discovered a new phenomenon. It could be gravitational waves or something else, but it should be treated as an interesting observation for further open-minded study. What bothers me about it is the assumption that the anomaly was caused by the merger of a couple of black holes in a far off galaxy, which is unfalsifiable and apparently unquestioned (as I also said in a previous blog entry).

Imagine you're sat on a beach and a particular waveform rolls in from the deep ocean. You have a supercomputer at hand and a love of dolphins and because the computer is so powerful you manage to compute the exact action a nice old dolphin out to sea must take to produce that pattern of waves. Maybe he jumped out of the sea whistling "I'm a little teapot" (have you heard of Russell's Teapot?) and plunged in with a twist of its tail. The fact that you can post-dict a scenario that leads to that pattern of waves is not surprising these days because we have such powerful computers. It does not mean you have proved it was the dolphin. It is not a direct proof: other things could have caused it, since in the case of physics the prevailing framework is not as sure as people suppose (see below). The ability of computers to invent unfalsifiable facts to support a comforting conclusion is one of the great problems of 21st century physics. To explain here's a quote from Douglas Adams (Dirk Gently's.., p55):

"..there have been several programs written that help you to arrive at decisions by properly ordering and analysing all the relevent facts so that they point naturally toward the right decision, but the decision that all the properly ordered facts point to is not necessarily the one you want. .. Gordon's great insight was to design a program which allowed you to specify in advance what decision you wished it to reach, and only then to give it the facts. The program's task, which it was able to do with consummate ease, was simple to construct a plausible series of logical-sounding steps to connect the premises with the conclusion. Gordon was able to buy a Porsche almost immediately."

You may say that black holes are the only entities that can produce the chirp that was seen by LIGO, but in saying this you are relying on a theoretical framework (general relativity, GR) that has been falsified in thousands and thousands of cases (at very low accelerations, not at high ones where it is supported by Gravity Probe B). This may come as a surprise since GR is supposed to be the highest creation of the human intellect, but it was falsified in the 1930s and then again in the 1970s by galaxy rotations - low acceleration phenomena very far from our normal experience. GR failed to predict any galaxy's rotation speed, badly, and galaxies are a pretty huge chunk of the universe not to predict (almost all of its matter!). The old theoretical framework has been patched up by the addition, where needed, of a huge amount of invisible (dark) matter, but this is an arbitrary addition, a fudge. It means that GR still cannot predict any galaxy's rotation from directly-observed quantities. You have to observe both the visible matter, the lit stars, then the rotation of the stars (the answer), and then add the dark matter distribution by computer so that GR can predict the right answer - Gordon's program is post-dicting the facts that are needed to make GR right. This goes unchallenged because it is an unfalsifiable prediction because dark matter is invisible, so Gordon is still buying Porsches.

Please note that, forgetting far off black holes for a minute the LIGO team still have discovered a real and very interesting effect, but it is the connection of that to a specific unfalsifiable scenario (two merging black holes) that I believe is unscientific and stops healthy debate. This is due to an unfortunate blind spot that the mainstream has, caused by the over-use of computer programs and it is serious perverting the progress of science. Note that in quantised inertia, a new framework that I am proposing, all the inputs are observed parameters, so Gordon's program is powerless.

Friday, 22 September 2017

Horizon Drive 1.1

The best option now, both in order to convince people, and to get to applications and change the world, is to work out how to unambiguously demonstrate quantised inertia in the lab. Since experiments are already underway I have to somehow tread the fine line of talking about how this might be done so that other experimenters can join in, with their own practical insights, but not give the game away for people who are already doing these experiments. So wish me good luck with that!

As most of you know by now, quantised inertia (QI) attributes the property of inertia to a mechanism involving Unruh radiation: a radiation seen only by an accelerating object. The Unruh wavelength seen shortens as acceleration increases. The way to reveal QI in the lab is to accelerate something so fast that the Unruh waves it sees shorten so they can be controlled by our technology. The wavelength of Unruh waves seen by a body with acceleration 'a' is L=8c^2/a, so for an apple falling on someone's head the acceleration is 9.8 m/s^2 and the waves are a light year long. No wonder Newton didn't spot them. Visible Unruh waves would need an acceleration of around 10^24 m/s^2.

Most objects are too heavy to be accelerated that much, but light is an exception, being, well, light! Light going round a desktop fibre-optic loop would produce Unruh waves of a few decimetres length that may be damp-able by metal plates. Just as in the Casimir effect when quantum fields are damped between parallel metal plates, similarly here, a metal plate placed on one side of the light-loop should damp the Unruh field on that side. The other side will be undamped so just as the Casimir plates are pushed together by the loss of the fields between them, so the light-loop here will be pushed to one side, just as a boat is pushed to one side when more water waves hit it from one side than the other (see the references below for discussions).

I have done my usual back-of-the-envelope calculations, and the force you get out will depend on the efficiency of damping, but for complete damping would be of the order F ~ PQ/c where P is the power input, Q is the quality factor of the system constraining the light (eg: the loop), and c is the speed of light. The emdrive is similar to this, but uses contained microwaves instead, and quantised inertia predicts it quite well. There are still many unresolved questions. Can we damp Unruh waves with metal plates? (the agreement between QI and the emdrive data suggests 'yes'). But, let the discussion begin. As for learning a language, the best way to make progress is to try to apply it. Nature may first laugh, but if we pay attention it will eventually co-operate.

References (see the discussion section of these papers)

McCulloch, M.E., 2008. Can the flyby anomalies be explained by a modification of inertia? J. British Interplanetary Soc., 61, 373. Preprint

McCulloch, M.E., 2013. Inertia from an asymmetric Casimir effect. EPL, 101, 59001. Preprint

Friday, 15 September 2017

Evidence and Applications

I'm back! Sorry for the gap in blogs, but it was a natural time to pause. In my opinion I have now provided enough evidence that physicists should be excited about quantised inertia. Also I've reached the stage where I need to develop more collaborations with galaxy modellers and lab experimenters (some are already in place). So, here is an attempt to convince others to join in:


We're all familiar with the idea of inertia, that objects in deep space once pushed keep going, but no-one has ever explained why it happens. Quantised inertia explains it for the first time by saying that if an object accelerates one way, then relativity makes a horizon appear in the other direction since information finds it harder to get to the object from that direction. This horizon damps the quantum vacuum (Unruh radiation) on that side of the object, causing a net push by radiation from the other side. This predicts inertia very well (see the 1st reference). Note that this is an elegant collaboration between relativity and quantum mechanics, and is amusing because for over 100 years people have assumed that relativity doesn't talk to quantum mechanics, and here they are cheekily in cahoots behind the scenes.


So where's the proof? Over the last ten years I have published 20 peer-reviewed papers on the theory including various bits of evidence. The most important piece of evidence is that quantised inertia predicts the rotation of galaxies without dark matter and without any adjustment (See the 2nd reference). It even predicts the behaviour of galaxies in the early universe, a part of the cosmos that no other theory can reach. It also predicts myriad interesting anomalies including the flyby anomaly, the cosmic acceleration, the low-l CMB anomaly, the Tajmar effect and the emdrive.


So how can we utilise quantised inertia? The most dramatic possibility is in the horizon drive (of which the emdrive is a weak example). The idea is simple. We can use the same trick that nature uses to produce inertia. Instead of relying on relativity to make horizons when objects accelerate away, instead make an object which makes its own horizon. Then we will have a fuel-less propulsion system. Where is the energy coming from? It is coming from Heisenberg's uncertainty principle dp.dx~hbar. Make an artificial horizon and you reduce the uncertainty in position, dx, so dp, new momentum and energy, appear (see the 3rd reference below). There is already evidence for the horizon drive since quantised inertia predicts the emdrive.


As you can see the evidence and applications for quantised inertia are coming together nicely now. The evidence for quantised inertia makes the horizon drive, which would open the galaxy to us, more than a speculation, and this application surely makes it worthwhile to look into the theory (which is admittedly still incomplete, please help!). The references below represent my most up to date summaries of the theory and the evidence.


McCulloch, M.E., 2013. Inertia from an asymmetric Casimir effect. EPL, 101, 59001. Link
McCulloch, M.E., 2017. Galaxy rotation from quantised inertia and visible matter only. Astrophys. & Space Sci., 362,149. Link
McCulloch, M.E., 2016. Quantised inertia from relativity & the uncertainty principle, EPL, 115, 69001. Link

Friday, 7 July 2017

QI and Emdrive: dc/dt=0.

I've had some complaints that my explanation for the emdrive violates a central tenet of special relativity: that the speed of light cannot change. Well, there were reasons not to be worried so much about that, but as it happens I've just published a paper in EPL that shows that the results I derived in 2016 do not imply a speed of light change in the cavity anyway. The new derivation is based on an insight I had one night when I was walking into the local TESCOs (not too often associated with scientific inspiration, but times change): what quantised inertia says is that more Unruh waves (assumed to cause inertia) can exist at the wide end of the cavity, and this simply shifts the centre of inertial mass of the input microwaves continually towards the wide end of the cavity. The cavity then has to move the opposite way, towards its narrow end. This more simply reproduced the same results I had before, but without the need for a change in light speed, so there is no possibility of relativistic violation.

In this new paper I also investigate what happens when you put a dielectric in the cavity. Dielectrics are insulators, so electrons do not move through them freely, but the electrons can shift slightly. So, like people in unions, who can organise to resist forces from above, the electrons can re-arrange en-masse to create a counter field to resist an applied electric field. Air is a dielectric, so are glass and all plastics. Dielectrics really do reduce the speed of light in a way that is well accepted, and since the frequency of light stays the same, the wavelength of the light has to shorten and this means that the Unruh waves can also be expected to shorten in the dielectric, meaning that more of them fit into the cavity at the end with the dielectric.

So, according to quantised inertia, adding a dielectric to a cavity end is rather like widening that end. If you add a dielectric to the wide end you can expect an enhanced emdrive thrust since it boosts the existing surplus of Unruh waves there. Conversely, if you add a dielectric to the narrow end, it should reduce the thrust since it reduces the effective 'taper'. As you can see in the paper, the best-documented NASA tests all used dielectrics, and considering them in the theory improves the predictions of QI considerably. Unfortunately for the first Shawyer test it worsens the prediction considerably, such that the thrust is now equal but opposite to that observed. The observed and predicted emdrive thrusts are shown in this table:


McCulloch, M.E., 2017. Testing quantised inertia on emdrives with dielectrics. EPL, Vol. 118, 34003. Journal paper, now open access! Full text also here.