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

Wednesday, 19 April 2017

Quantised Inertia from Fundamentals

The uncertainty principle of Heisenberg is usually written as dp.dx~hbar and it says that the uncertainty in momentum of a quantum object (dp) times its uncertainty in position (dx) is always a constant (hbar). If a quantum object knows well where it is (dx=small), then it loses the ability to know its speed (dp=big). Conversely, if it knows its speed very well (dp=small), it'll be lost in space (dx=big). This relation from quantum mechanics, and special relativity also, are two clues that physics is due to be reworked around the concept of information. This is what quantised inertia does, joining these two pillars of physics (QM and relativity) on the large scale.

Imagine a red mass (see diagram, top part, red circle). Suddenly you put another mass on the left of it (the black circle). The uncertainty of position of the red mass is shown by the black quadrilateral around it. The red mass can see a large amount of empty space up, down and rightwards (forgetting directions perpendicular to the page for now) so its uncertainty in position (dx) is large in those directions because it cannot position itself well in empty space. However, it can see less far into space to the left because the other mass blocks its view, so its uncertainty of position that way (dx) is lower. The quadrilateral represents dx in each direction. It is skewed outwards to the up, down and right where dx is large, and skewed in to the left where dx is small. Therefore, according to Heisenberg, the quadrilateral showing the uncertainty in momentum has to be the opposite: skewed out to the left and skewed in for the other directions (see the blue envelope). Since momentum involves speed, this predicts that it is statistically or quantum mechanically more likely that the object will move to the left. In a formal derivation I have shown this not only looks like gravity but predicts it (see reference below).

Now, as the red object approaches the black one (see lower panel) its uncertainty in position (dx) to the left gets ever smaller, so dp must increase and the red object must accelerate. "Aha!" Says the other great fundamental pillar of physics: relativity, "I now become relevant!". Since the red object is now accelerating away from the space to the right, information from far to the right cannot get to old Red, and a horizon forms (the black line) beyond which is unknowable space for Red. This Rindler horizon is like the black mass. It blocks Red's view and so Red's uncertainty in position to the right reduces (dx, see the black quadrilateral contract from the right) and so the uncertainty in momentum to the right increases (see the blue quadrilateral now extends further to the right). Red now has a chance of moving both left and right and this has the effect of cancelling some of its initial acceleration towards the black mass. This looks like inertia, and indeed it predicts quantised inertia (see reference below).

In this way, you can derive something that looks like quantised inertia (if you consider also the cosmic horizon) and gravity, just by allowing quantum mechanics and relativity to mix at large scales. The whole package could be called horizon mechanics. The word 'horizon' from relativity, the 'mechanics' from the quantum side. As a happy side effect, quantised inertia or horizon mechanics solves a lot of problems in physics that you may have heard of: it explains cosmic acceleration, predicts galaxy rotation without dark matter, and its redshift dependence, and predicts the emdrive. These successes should not be sneezed at, representing 96% of the cosmos, and with the emdrive practically offering a new kind of propulsion. Oddly enough, for a theory intended to replace general relativity, the behaviour I have just described looks quite tensor-ish..


McCulloch, M.E., 2016. Quantised inertia from relativity & the uncertainty principle, EPL, 115, 69001. ResearchGate preprintarXiv preprint

Wednesday, 12 April 2017

Easter Thank Yous

Rather than criticising theorists that in my opinion are doing things wrong, which is negative, exhausting and would take far too long :) it is more positive to thank those that I admire and who have inspired me in some technical way. I started this list a while ago and neglected to publish it. I have recently added to it, so here it is:

First of all: John Anderson, the co-discoverer of various spacecraft anomalies and more recently periodic variations in big G, without which I would have had far fewer anomalies to get me interested. I love his style because he publishes carefully analysed anomalous data and honestly points out that 'this is unexplained'. This is rare, and is a gift for a data-driven theorist like me.

Although the influence is not direct, I cannot not mention Stephen Fulling, Paul Davies, Bill Unruh and Stephen Hawking (with help from Zeldovitch, Starobinksy & Bekenstein). The discoverers of Hawking-Unruh radiation, without whom Quantised Inertia (QI) / MiHsC would not be possible.

Haisch, Rueda and Puthoff who in 1994 proposed the first model (stochastic electrodynamics) for how inertial mass might be caused by the zero point field (paper), a model that thrilled me when I first read it on a long train journey, like a chink of light would thrill someone lost in a cave. Later I decided it was the way to go, but wrong (it needs a arbitrary cutoff) and this inspired me towards QI/MiHsC and an asymmetric Casimir effect (aCe) which needs no cut-off. I am thrilled and honoured to now be in email contact with Hal Puthoff.

Mordehai Milgrom, who first suggested that physical laws might be wrong at low acceleration and invented MoND in 1983. Milgrom also speculated on a link between MoND and Unruh radiation but wasn't specific, and then discounted the possibility in 1999 saying Unruh radiation was isotropic so could not generate a force. Although MoND is a huge step up from dark matter, it is not as good as MiHsC because it lacks a specific model and needs a number to be input by hand (QI/MiHsC predicts this number by itself). However, Milgrom's papers on MoND were an inspiration to me, and he also kindly commented on (politely disagreed with) my first paper on MiHsC when I sent a draft to him.

Martin Tajmar who has the rare mix of being open-minded enough to test new anomalies while also being professional about it, and he brings much needed respectability to anomalous experiments. Also, like me, he is lucky enough to be married to a South Korean.

Scarpa et al. (2007) who wrote a brilliant paper on globular clusters (published at the first crisis in cosmology conference) that provided the first empirical evidence I was aware of that dark matter, which I didn't believe anyway, was wrong. The data also shows that QI/MiHsC, which depends on local accelerations, and not MoND which depends on external ones, was the answer.

Stacy McGaugh, who I met at my first astrophysics conference on 'Alternative Gravities' in Edinburgh in 2006, and who was the only one at the workshop who seemed to consider MiHsC seriously. He has been kind enough to send me stellar data from time to time, and I hope he will actually cite me someday! He has recently also co-published important results that falsify dark matter.

Jaume Gine, with whom I published the first collaborative paper on QI/MiHsC in 2016. This joint-paper was submitted to so many journals over a couple of years that I'm grateful for both his input and perseverence. The first paper on QI/MiHsC by another person solo was also recently published by Keith Pickering, and takes a refreshingly modified approach (here). Also, Prof Jose Perez-Diaz, who came to see me last year for a few months, and I enjoyed our many discussions. He is now trying to detect QI/MiHsC using a LEMdrive arrangement.

John Dorman who wrote the first, and incisively entertaining, review of my book, a review that struck truer to home than may be apparent from outside, since I sometimes feel just like a boxer in the ring. I now have it blue-tacked on my study wall. He has been especially quick to understand the central importance of horizons and suggested a new name for the theory: 'horizon mechanics'. This name could be used in future if and when gravity is incorporated, since 'mechanics' implies a complete system.

Finally to go back in time again: I submitted my first paper on MiHsC to the prestigious journal MNRAS in 2006, and fully expected to be rejected since I'd never submitted on astrophysics before (only ocean physics up till then). The reviewer said they "didn't exactly believe MiHsC, but it was more plausible than many alternatives which had been published", so they let it pass, to my great joy. The reviewer was also amused by my use of the word 'forecast' instead of 'prediction' (I worked at the Met Office at the time). If this first paper had been rejected I may have given up.

These are only some of the inspiring folk and someday I'll make a complete list. Thanks to all. Happy Easter!

Thursday, 23 March 2017

New Evidence at High Redshift

One of the unique and testable predictions of MiHsC / quantised inertia is that the dynamics of galaxies should depend on the size of the observable universe. This is because it predicts a cosmic minimum allowed acceleration of 2c^2/Cosmicscale. Why is this? Well, the Unruh waves seen by an object and that (in QI) cause its inertial mass, lengthen as the object's acceleration reduces and you can't have an acceleration that gives you Unruh waves that are too big to resonate in the cosmos. So if you imagine running the cosmos backwards, as the cosmic scale shrinks, more Unruh waves would be disallowed (as in the narrow end of the emdrive), inertial mass goes down, centrifugal forces decrease and so galaxies need faster rotation to be dynamically balanced. Therefore, QI predicts that in the past galaxies should have been forced to spin faster (everything else being equal).

Many people online alerted me to a paper that has just been published in Nature (Genzel et al., 2017) that supports this prediction. The paper looked at six massive galaxies so far away from us that we are looking at them many billions of years ago when the observable universe was much less than its present size, and, sure enough, they spin faster! To compare QI with the data, I have plotted the preliminary graph below.

It shows along the x axis the observed acceleration of these ancient galaxies, determined from Doppler measurements of their stars' orbital speed (a=v^2/r) and along the y axis the minimum acceleration predicted by quantised inertia (a=2c^2/cosmicscale). The QI vs observation comparison for the six galaxies is shown by the black squares and the numbers next to them show the redshift of each galaxy. The redshift (denoted Z) is a measurement of distance. Erwin Hubble found that the further away galaxies are from us, the faster they are receding from us, and so their light is stretched in a Doppler sense and is redshifted. So redshift is proportional to distance. The redshifts of the galaxies in this study ranged from Z=0.854, bottom left in the plot, at which the cosmos was 54% its present size to Z = 2.383, centre right, for which the cosmos was pretty cramped at 30% its present size (the formula for the size of the cosmos at redshift Z is SizeThen=SizeNow/(1+Z).

Quantised inertia predicts clearly that the acceleration increases with redshift, just as observed. The diagonal line shows where the points should lie if agreement was exact. Although the points are slightly above the line this is not a huge worry since the data is so uncertain. The uncertainty in the observed acceleration is probably something like 40% (looking at the scatter plots in Genzel et al. I've assumed a 20% error in the velocities they measured, and a=v^2/r). I have not plotted error bars yet because it'll take time to work out properly what they are. The two highest redshift galaxies are obviously quite aberrant, and this shows that the data is not yet good enough to be conclusive.

So in a preliminary way, and error-bars pending, the graph shows that QI predicts the newly-observed increase in galaxy rotation in the distant past. Given the uncertainties, more data is urgently needed to confirm this. As far as I know, quantised inertia is the only theory that predicted this observed behaviour.


Genzel et al., 2017. Nature, 543, 397–401 (16 March 2017) http://www.nature.com/nature/journal/v543/n7645/abs/nature21685.html

Wednesday, 22 March 2017


Once upon a long time ago there was a land called Plutophysia and it was ruled by General R. Tivity. The General, in his salad days, had developed quite a reputation for predicting the weather, and indeed for some phenomena he had skill. When he had said "Today it will rain!" it always did. When he said "Go to the beach" everyone went.

Then one day a strange apparition appeared: a vast swirling column of wind and dust which knocked down a grain silo. The country folk came to the General and described the phenomenon. The General, with perfect confidence said
"Ah yes. It is caused by an invisible wind God: a Chindi!"
and he directed his scientists to look for these wind Gods. Egon, the lead scientist scratched his head, and then other parts of his body, as he tried to think. Nothing occurred to him. Eventually, some leaders of industry came to him and said
"We have a machine that can detect wind Gods, but it is very expensive".
"Never mind!" said Egon "I have the General's ear!"
"Having his purse would be better.." said the industrialists.
"The two are connected" said Egon and sure enough before long there was a fine industry building machines to detect the Wind Gods. This went on for some time, because invisible wind Gods are difficult to detect.

After several decades of waiting, the folk of Plutophysia became fed up since many farms had been torn apart by the phenomena. They were also tired of hearing the words 'wind God', and the scientists and industrialists were getting so fat that they had to carry them around in wheelbarrows. One day an unimpressive scruff from The Shire was brought in to see the old General and said
"General, I can predict these swirls of wind! They are caused by heating of air near the ground which rises".
The General said "What is this idiot babbling about? What are heat and air?".
But the scruff insisted
"I can predict they all occur at the hottest times. I have the data to prove it! Furthermore we can make flying machines based on this idea and move away to a better place..".
The General said "Enough!" and looked to his industrial advisors and top scientists.
"What say you to this young miscreant?".
They conferred "We would say sire that he is a dangerous lunatic and it would be best to lock him away from the general public lest your reputation for weather prediction be called into question."
The General decided quickly.
"Quite right. Guards! Put him in jail. Oh, and burn that data will you? Nasty profit-less stuff to have lying around".

Some wise people complained at this insult to free speech and scientific inquiry. Most eventually forgot about it so as not to lose their jobs in the wind-God detector machine factories. Some did not forget and also ended up in gaol. So Plutophysia spent all its money on the machines and was ruined. In the end all that was left was a huge ring of machines surrounding the broken farms, and a few old codgers living by the shattered remains of a prison, but building an air balloon..

Saturday, 18 March 2017

Horizon Drive 1.0

Horizons are a prediction of general relativity. The first theoretical example was the idea of a black hole in which the gravity is so strong that light and therefore information cannot escape. So the black holes are surrounded by an event horizon, a boundary between what can be seen and what can't: the inside. This horizon not been seen directly, but the matter spiraling in towards the horizon emits heat due to friction (the accretion disc) and emits radiation, and that has been seen. Another kind of horizon occurs at the edge of the cosmos, since beyond that edge stars are moving away from us at a speed faster than light and so information from them cannot get to us: a cosmic horizon.

Lest you think that horizons are difficult to get to, I can assure you that there's no need to take part in a kamikaze mission into a black hole or to travel to the cosmic edge. Horizons are everywhere. If you accelerate to the right, then information from far to the left, limited to the speed of light, can't catch up with you, so a so-called Rindler horizon forms to your left. You can make your own horizon, at home, just by moving your hand. Quantised inertia comes from assuming that this horizon damps the zero point field, making it non-uniform and pulling your hand back against its initial acceleration. Quantum mechanics (zpf) and relativity (horizons) co-operate here to make quantised inertia which predicts inertial mass and, by the way, the 96% of the cosmos that standard physics cannot (see the orange bit in the pie chart below: an unsubtle way to make the point, but mainstream physics ignores this).

A common feature of all these horizons is that they attract. Black holes do by definition, though the evidence for them is not direct. The cosmic horizon also attracts everything towards it. Evidence for that was found by Riess and Perlmutter (1999): the famous cosmic acceleration (quantised inertia shows why). The Rindler horizon pulls you back against any acceleration and in this way, quantised inertia predicts inertial mass.

So, the obvious "spread-mankind-thru-the-galaxy" question is, can we make synthetic horizons wherever we want and make spaceships move without fuel? I think so. The first evidence I can mention to back this up is the Casimir effect, which was first demonstrated practically in 1997 by Lamoreaux. Two parallel metal plates act as horizons, damping the zero point field (zpf) between them so there's less zpf pushing out and more zpf outside pushing them together. Energy and movement from what was supposed to be 'nothing'. In my opinion the emdrive is the second example. My evidence for that is that quantised inertia predicts it by assuming that the metal walls of the cavity damp the zero point field more at its narrow end, so the cavity moves that way, almost as if it is moving down a hill. Quantised inertia (QI, MiHsC) predicts the observed thrusts well.

It is important to note that you can't use any old cavity here. If you want to change the inertial mass, or move, an object, then the metal shape you use must be of a size that damps the wavelength of the Unruh waves that the object will see. The higher the acceleration, the shorter the waves. In the emdrive the photons are accelerating so fast that the Unruh waves they see are of similar size to the cavity. If you put a snail in there, or indeed anything travelling at sub-light speed, they'll see Unruh waves far longer than the cavity and there'll be no effect on their inertia or motion. Most accelerations we know about 'see' Unruh waves light years long (associated with horizons light-years away) so to make a horizon drive you need to have a part of the engine hyper-accelerated (the acceleration core, see circle on the right, in the schematic below) and a metal structure to damp Unruh waves asymmetrically. This 'damper' is the structure on the left and it could be fractal, as shown, to damp Unruh waves across a greater range of accelerations. The core is predicted by QI to move left:

The emdrive does this with photons resonating back and forth, but there are many other possible ways to make a hyper-accelerated core: spinning discs, photons in fibre-optic loops (LEMdrive), plasmons propagating round sharp corners, electron jumps at superconducting transitions (Podkletnov, Poher), even sonoluminescence. Practical physicists will know of many more possibilities. You then just need an asymmetrical metal structure of the right size to damp the Unruh field and the core will move anomalously.

Quantised inertia predicts a entirely new field of horizon engineering. Ultimately it may provide technology like the space-time engineering used to build The Way in Greg Bear's brilliant novel Eon. Nature in my view is not made of old-fashioned waves and particles, but of information and horizons and the evidence is pilling up that this is true (see my papers).


McCulloch, M.E., 2013. Inertia from an asymmetric Casimir effect. EPL, 101, 59001 (see discussion). https://arxiv.org/abs/1302.2775

Sunday, 12 March 2017

Strings, loops and quantised inertia

I've just read an interesting, but ultimately unsatisfying article in New Scientist about string theory and loop quantum gravity and how these two theories might agree with each other. This agreement may be a great mathematical achievement, but it is only that, because neither theory is testable.

I have blogged about string theory before (here). It imagines every particle in nature is made of a string (in 11-dimensions) and the waves on the string determine the properties of the particle. I admire its ambition, since it tries to explain all the particles, including the graviton, the particle assumed to be responsible for gravity, and tries to be a theory of everything, but it is really a theory of nothing, since it has so many variations you can pick whatever version agrees with what you are looking at, and it makes no specific testable predictions. The one sort-of prediction made, supersymmetry, has now been falsified by the LHC (see here).

Loop quantum gravity is the other popular theory and it is simpler and bolder. A great simplification of Einstein was that he made space-time dependent on the mass within it. A bit like making the stage one of the actors in a play. He did this because space-time is something you cannot directly see anyway, so it's fair game for tweaking and this process means that general relativity is neatly 'background independent': the background space-time is determined by the mass. Loop quantum gravity continues this simplification by saying that spacetime is quantised and so, as in commercial airflight, there is a minimum distance you can travel. Loop quantum gravity is neat but has not yet made a good testable prediction. In the article they claim bouncing black holes might be a test, and there are a lot of 'may's and 'might's, but this is not the same as a controllable lab test: how can you be sure you are seeing a bouncing black hole from afar and not a million other possibilities?

Neither of these theories address the huge observations anomalies we can see including anomalous galaxy rotation and cosmic acceleration which are crying out for attention. Both theories focus on the big bang and distant black holes, as if they are afraid of a more down-to-Earth test. Common sense says we need to learn to fix the bathroom tap (eg: galaxy rotation, flybys, emdrive) before we tackle the plumbing on Pluto (eg: the big bang and black holes).

There is a theory that in some sense looks a bit like both these, but it has not come from a theoretical approach. It has come from paying attention to the anomalous observations that the mainstream ignore. This theory is MiHsC/quantised inertia/horizon mechanics (three names, take your pick!). In this theory, incomplete as yet, particle properties (inertial mass) depend on whether the Unruh waves they can see fit inside horizons. This is similar to string theory's waves on strings, but without needing to invent new waves and seven new dimensions! Quantised inertia also has the background independence of loop quantum gravity in that the behaviour of masses determines their space: an observer's acceleration creates horizons that determine what space is for that observer and that leads back to mass. Plus quantised inertia has no lack of tests, predicting galaxy rotation, its redshift dependence and cosmic acceleration perfectly and simply.

In summary, the New Scientist article is interesting and informative, but far too theoretical, as is all of mainstream physics. Too much theory is a mistake: history shows that new physics always comes from thinking about new observations, because the cosmos' imagination is far better than man's.


Cartright, J., 2017. When loops become strings. New Scientist, 11th March 2017. 

Monday, 27 February 2017

The Range of Quantised Inertia

I've just finished teaching my Space Exploration module at the University of Plymouth. The useful thing about teaching is that it renews knowledge and helps one to view the subject as a whole. Of course, I gave a research lecture on quantised inertia (QI) and made a useful new summary plot for it, just to show the range of anomalies or phenomena in physics that can be explained and predicted by quantised inertia, and not by standard physics. The plot below shows on the x axis the scale of the phenomenon (in a qualitative manner), from the sub-atomic proton radius anomaly on the left to the oddities at the cosmic scale on the right. The y axis shows the accelerations within the phenomena from the infinitesimal cosmic accelerations at the bottom to the emdrive full of resonating microwaves at the top. The text boxes show all the anomalies QI predicts. I have published all these agreements, apart from Proxima Centauri & the proton radius anomaly, in mainstream journals. This is not to say I can confirm all these anomalies, and some of my analyses are incomplete (eg: for the flybys), but taken together they build a very strong empirical argument for quantised inertia. What other coherent theory can do all this? None.

Poor old standard physics does not predict any of these phenomena without inventing arbitrary exotic matter and arbitrary new physics to go with it: like the awful dark matter hypothesis which has now been falsified, for example by this paper. The anomalies in the plot are not a small problem either: they represent 96% of the cosmos! QI needs only a relatively small, if fundamental, tweak to standard physics to predict them all. All you have to do is allow the horizons made by relativity to 'damp' the quantum vacuum, making inertial mass as a side product. This is very satisfying and goes some way to reuniting the bifurcation in physics produced by Einstein when he sent the subject off onto the contradictory quantum and relativistic trajectories. Most physicists prefer to add bits to existing physics rather than tweak the equations that already exist, but QI tweaks those equations very very slightly, and in a way that does not violate any data, and, as the plot shows, it predicts a lot more that way.


To see how quantised inertia explains these phenomena, follow these links to the published papers /preprints::

Emdrive, Tajmar effect, Pioneer anomaly, Flyby anomaly, dwarf galaxy rotation, galaxy/cluster rotation, cosmic acceleration, low-l CMB anomaly.

Tuesday, 21 February 2017

The Data's the Thing

Actors have a saying "The play's the thing", ie: the play comes before the ego. Similarly scientist's should say: "The data's the thing". History and common sense back up the importance of data. Scientific progress has never involved playing it safe and fudging 96% of the cosmos with invisible dark stuff to preserve egos or the status quo. Progress has always come from looking at controversial new data, and thinking anew.

Quantised inertia is the result of pondering new data from the cosmic scale to the atomic, and I have had empirical success at various scales (cosmic scale, galactic scale and Solar system scale), but the lab scale is particularly useful because a desktop experiment can be easily controlled and reproduced. This is why the emdrive has caused such a furore: it is forcing people (well, some!) to question familiar physics for the first time in nearly a century. Not bad for a little copper cone. I do not discount the possibility it might still be wrong, but those who claim it is wrong have to say what it otherwise is, and not just say "it's wrong" as if they have God's phone number.

In all this it is important to keep focused on the data so here is a table of all the emdrive results so far. We have to be cautious because some of these results have been published with varying degree of peer-review (shown in bold) and some have not. I have also included a new result from 'monomorphic' on the NSF forum, so there are now 11 data points, seven of them published in conferences and one (NASA2016) in a mainstream journal.

The table gives a identifier for the experiment on the left in chronological order from top-bottom. The second column shows the thrust observed in milli-Newtons (mN). The third column shows the thrust predicted by quantised inertia (MiHsC) including the effect of dielectrics (which reduce the speed of light in the cavity). I submitted a paper on this dielectric version of quantised inertia to EPL about a month ago so I should have the reviewers' comments soon. The new 11th data point from monomorphic is shown at the bottom. His power input was 1 Watt, his Q value was 8100 and his cavity had no dielectric and was 0.24m long, and had wide and small end of diameter 0.299m and 0.178m respectively (according to his NSF posts, please correct me if I am wrong). The thrust he measured was 13 microN and quantised inertia predicts 14 microN.

Given all the data surely you have to agree that quantised inertia predicts pretty well for a theory that can not be adjusted and is still an approximation. It ideally needs a computer model, like COMSOL, to do it justice, because my usual technique of scribbling maths on bits of paper is unable to capture em-modes and their complex interaction with horizons.

It would be useful to compare the predictability of quantised inertia with that of the other emdrive theories by looking at some ratio of how accurately they predict the data, over the number of arbitrary parameters they need to do it, but I have not seen any comparison plots showing observations and calculations from the other theories (I may have missed them). If the Plymouth-Emdrive workshop gets off the ground, I will make sure it is empirical. Ernest Hemingway once said: "If a writer stops observing, then they are finished". I think the same thing goes for physicists.

Saturday, 18 February 2017

My response to the Forbes article

A few days ago an article appeared in Forbes magazine directly criticising me and quantised inertia. I understand that after working for decades on dark matter, many find quantised inertia difficult to accept. I do hope to persuade them slowly, but a debate should be based on empirical evidence and this article did not present any. It also misexplained quantised inertia, and vaguely attacked my attitude, so I need to answer it.

For example, the article accuses me of not addressing criticism, but all the comments I have received from the mainstream say I am violating a theory that only predicts 4% of the cosmos (in some sense). What exam can you pass with a mark of 4%? What matters to me is whether I am violating empirical data. No-one has shown that. It is true that I need to show how quantised inertia might fit together with general relativity, but that is a far lower priority than comparison with data, and to compare QI with GR some communication between me and general relativists needs to begin, but it has been cut off, and not by me. I haven't been accepted at a physics conference since 2012 and most physicists have refused my attempts to engage by email.

The article claims I am on some sort of mad slide into pseudoscience, but if you look at the facts: in every one of my 17 published papers I have tested quantised inertia against real data, and it worked without adjustment. In contrast there has never been any direct evidence for the dark matter the mainstream believe in, and the hypothesis is nothing but adjustment. So you have to conclude that it is the dark matterists who have been on the slide into pseudoscience for decades and the only reason they haven't noticed is they are all happily going down together, so self-correction has become impossible.

The article claims that Unruh radiation is so small it is incapable of generating an inertial force, but the author has not understood my papers: I have shown quite simply that when it is made non-uniform in space by relativistic horizons, Unruh radiation does produce the right amount of force. Please see this paper: preprint and a later one where Dr Jaume Gine corrected an error I made to give better results: journal.

The emdrive thrust (which QI predicts) is not "within the noise" as the article claims. The NASA emdrive paper went through five reviewers before being published. Of course, they and all of us may have missed some mundane effect we don't know about yet, but to suggest that all five reviewers do not know noise when they see it is implausible. Noise does not usually pass peer review.

The article says “How strongly verified [mainstream] theories are”. I have received such comments from many reviewers, especially recently, and I can never understand how this can be said with a straight face: mainstream theories predict only 4% of what we see. If that is 'strongly verified' than those words must be in a different language.

The article claims “This hodge-podge is misapplied”. How easy it is to say something like that, but what data proves it is misapplied? It is not enough just to say it and hope that people won't bother to think. Words must be supported by data, but there is no supporting empirical evidence anywhere in the article.

The article says QI “Overturns basic/established physics”. Well, I realise the difficulty of doing it, and do not take it lightly, but it is absolutely fine to modify fundamental physics so long as experiments are still satisfied, and they are. Quantised inertia has only a tiny effect in normal regimes, but it changes things in very low acceleration regimes, which is exactly where normal physics fails. It allows us to predict not 4% of nature, but much closer to all of it, offering an explanation for anomalies at low accelerations such as galaxy rotation and cosmic acceleration. Basic physics is self-contradictory anyway. We know its two halves (GR and quantum mechanics) do not fit together either formally, or causally with Bell test experiments. Quantised inertia allows us to fit it together a little more since the whole point of it is that relativity and quantum mechanics work together to make inertia.

Towards the end, the article bizarrely seems to accuse quantised inertia of being too successful, since it explains so much. First of all, since when is empirical success a crime? That is taking scepticism too far, and that does no-one any good. Also, the reason QI fits these anomalies, as well as the standard data, is because I designed it after looking at new data with an open mind. In my opinion, and I think history shows, that is exactly the right way to advance science and it is what the dark matterists have forgotten.

Quantised inertia is far from complete. It is an approximation to a full theory that I do not have yet. I need the help of other physicists and their great skills to look for the phenomena it predicts (see here) and flesh out the theory. The problem I have is the excruciating one of trying to persuade extremely well-educated and driven people, that I have no desire to antagonise at all, that they are wrong in this one matter, and enlisting their help (which I need) at the same time! If they wanted evidence for my lunacy then they could cite my hopeless optimism in this social respect.

My crucial point remains empirical: quantised inertia agrees with the data more simply than MoND or dark matter (see here for example). There is no way to get away from that fact. They can claim I'm a lunatic with delusions of gradeur (maybe I am, it is not for me to say) but after it all the mass of data that support quantised inertia will not go away, and in the end it will save all of us.


The Forbes aticle:  http://www.forbes.com/sites/briankoberlein/2017/02/15/quantized-inertia-dark-matter-the-emdrive-and-how-to-do-science-wrong/#29792c8617f9

Sunday, 12 February 2017

Dwarfs as a crucial test

My latest paper has just been accepted by the journal Astrophysics and Space Science (journal website) and I have already posted a preprint on Research Gate here. I will also post it on arXiv, but the arXiv have demoted me to the general physics section so I get very few reads from arXiv anyway. In a previous paper (McCulloch, 2012, see references below) and a new paper I have been submitting to various journals with no luck so far, I have shown that quantised inertia (QI, MiHsC) predicts the rotation of dwarf galaxies, spiral galaxies and galaxy clusters without dark matter or adjustment, but in this accepted paper, in a sudden bout of strategic thinking, I deliberately selected more extreme objects that other models cannot predict well, or at least not without becoming ridiculous.

These objects are the Milky Way dwarf galaxies: about 20 tiny galaxies orbiting close to the Milky Way. They have very little mass and so the accelerations of the stars within them are tiny, and the effect of quantised inertia should be more obvious, and indeed they show huge anomalies. The Figure below plots data from 11 of these systems (those for which data on masses and speed is available) against their visible mass in Solar masses (on the x axis) and the spin velocity of their stars (y axis). The observed speeds are shown by the open squares, their names are also shown, and the errors in the speeds are shown by the vertical bars.

Given the visible mass in them, good old Newton would have predicted that the maximum speed the stars might achieve without breaking free should be the speed shown by the small crosses at the bottom of the plot. Newton would look at this data and say: "Bah! They should fly asunder! I shall have another crack at that." The dwarfs obviously don't fly apart since they look more or less round, so to make it all work out astrophysicists who don't wish to change the old theories (GR predicts similarly) add just enough invisible dark matter to these systems to hold them in. The trouble is that in these dwarf cases they have to add the dark stuff in amounts that make the actual laws of normal physics pretty irrelevant (amounts of dark mass several hundred times the amount of visible matter) so these systems are governed mostly by convenient dark 'magic'.

MoND is far more specific than dark matter, so it is a better hypothesis, but MoND also has the problem that it needs a 'little bit' of magic: an adjustable parameter which is set by trial and error to 'make' its predictions fit the data. Adjustable parameters are simply an admission that one does not know what the dingo's kidney is going on. Anyway, MoND underpredicts the speeds a bit, and the rms difference between the data and the predictions is 3.6 km/s (By the way, entropic gravity also cannot predict these dwarfs since it predicts the anomalies should be greatest at large scales, but these dwarfs show that galaxy rotation anomalies are greatest at low accelerations, rather than large scales).

The predictions of quantised inertia, QI/MiHsC, don't depend on scale, but depend, correctly, on low acceleration, and are shown in the plot by the black triangles. They are closer to the observations than MoND (the rms difference is 3.2 km/s) but the main point is that quantised inertia beats MoND (albeit slightly) WITHOUT an arbitrary adjustable parameter. Nothing is input to QI apart from the visible matter, the speed of light and the cosmic diameter (all quantities that can be observed). I now have the beginnings of the feeling you get in chess when you are approaching the end game with the advantage (I recognise this feeling, though I have not had it very often!) and I hope that physicists do not just try to throw the chess board out of the window, but show some interest in how it was done.


McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics and Space Science, Vol. 342, 2, 575-578. ResearchGate preprint, ArXiv preprint

McCulloch, M.E., 2017. Low-acceleration dwarf galaxies as tests of quantised inertia. Astrophysics and Space Science (accepted). Online

Saturday, 4 February 2017

Proxima Centauri or Bust

The fastest object launched by man so far is the New Horizons probe which was launched directly into a Sol escape trajectory and is traveling now beyond Pluto at 16.26 km/s. At this speed it would get from London to New York in about 6 minutes. Even so, it would get to our nearest stellar neighbour, Proxima Centauri, if it was heading that way, in 78,600 years. This is the state of our space propulsion at the present time. Pretty weenie!

What we need to do is to get close enough to the speed of light so that relativistic time dilation slows time down from those on the ship (and keep the acceleration time short, because it does the opposite) so that physics gives us a kind of built-in suspended animation. Slo-time for those on the ship, but not for those back on Earth. In this way, say at half light speed you could get to Proxima Centauri in 8 years (measured from the Earth) and 4 years as measured on the ship. A four year trip to explore/settle another Solar system is not that bad! It is theoretically possible, but the big problem, and it's a pretty big one as problems go, is that to get a ship of similar size as the Space Station (400 tonnes) to 0.5c would take about 27 times the entire energy output of our civilisation per year. Another way of looking at it is that that you'd need to carry a planet-sized amount of fuel.

But, in my opinion, and I believe I now have enough evidence for quantised inertia / MiHsC / horizon dynamics to say this boldly, there is another way. The zero point field predicted by Einstein and Stern (1913) is all around us and we have been mostly oblivious to it. It is like air pressure: an intense 100,000 Newtons per metre. We don't notice it because it is uniform, but if you try to make it non-uniform (ie: make a vacuum) you suddenly notice it, because if you don't build a tough vacuum chamber then it would implode violently.

A kind of 'vacuum' can be made in the zero point field using two metal plates placed very close to each other (the Casimir effect) and this also makes a force as has been confirmed experimentally. Quantised inertia says that whenever a metal plate, or an object's acceleration, or a limit-to-what-we-can-view makes a 'horizon', then this damps the zero point field making it non-uniform and able to push on the objects. In this way quantised inertia simply explains the previously unexplained phenomenon of inertia, galaxy rotation without dark matter, cosmic acceleration without dark energy, and the emdrive.

We can apply all this to our travel problem. Imagine a spaceship with a horizon in front of it (see Figure). The horizon would damp the zero point field in front of the ship, making something like a virtual vacuum there. Suddenly there would be a force (analogous to the force caused by the air-vacuum) that would pull the ship forwards. Note that no heavy fuel is required, just a horizon/shield. The emdrive, in my opinion, is doing just this, and quantised inertia predicts the emdrive's thrust very well (see recent post).

Mainwhile mainstream physics is, in my opinion, wasting millions searching for dark matter that quantised inertia has shown is not needed, and other studies have also falsified. The mainstream should really start to pay attention to quantised inertia. They could help immensely: there is a lot of scope for improvement and extension of the theory. The bonuses would be a unification of physics (quantised inertia combines quantum mechanics and relativity), an explanation for astrophysical anomalies like galaxy rotation, and cosmic acceleration, and the opening up of entire new kind of horizon-engineering (which amounts to an manipulation of space-time, for lifting, transport and launching). We could also stop messing around in space weenie-town and start thinking of galactic settlement. No other planet in our Solar system is pleasantly habitable, but many other Solar systems will have their 'Earths' at just the right distance from their sun.  There's a possibly habitable planet orbiting Proxima Centauri. Wouldn't it be fascinating to visit?

"Really mankind, the plans for demolition have been available on Alpha Centauri which is only 4 light years away you know. I'm sorry, but if you can't be bothered with local affairs than it's your own fault..." - Prostetnic Vogon Jeltz' comments on the demolition of Earth to make way for a new hyperspace bypass (Douglas Adams).

Saturday, 28 January 2017

The Proton Radius Anomaly

Imagine you are in a little rowing boat, rowing round an island and you notice that your boat always gets washed towards the shore. There is no surprise, since there are likely to be more ocean waves hitting you from the open sea than from the direction of the island.

On a not entirely unrelated subject, many recent experiments (Pohl, 2010, 2016) have shown that muons (heavy electrons) in a close orbit around the proton in so-called 'muonic hydrogen' appear to be bound to the proton a more than expected, a bit like the boat is to the island. This can also be interpreted as a 'proton radius anomaly' where the proton appears to have gone on a diet, and this is what this anomaly is usually called, but an extra binding energy can just as well explain the data. Both possibilities are far too big to be explained by the standard model of physics which has no mechanism by which the proton can go on a diet or suddenly become more attractive to muons (see previous blog).

So, to cut to the chase, can Unruh radiation explain it? I have found that it can explain roughly 55% of it. If you calculate how much Unruh radiation is seen by the orbiting muon and how much of that is blocked by the central proton, just like the island blocks waves from the point of view of the boat, then this predicts that more Unruh radiation hits the muon from outside the atom than from the centre, pushing the muon closer to the proton. The predicted extra binding energy is about 55% of the observed extra binding energy. The normal proton-electron atom does not show an anomaly because an electron orbits 200 times further out than the muon and so the solid angle of the central proton is tiny and the sheltering is negligible (see the reference below for details, McCulloch, 2017).

To go further, this attraction looks a little bit like gravity, which also tends to pull matter together. Wouldn't it be funny if Fatio / Le Sage were right about gravity after all, but instead of it being due to a sheltering of electromagnetic radiation, which has been falsified, it is due to a sheltering of Unruh radiation by protons?

I recently saw an episode of Friends (The One Where Heckles Dies). It amused me because the character Phoebe declares "Gravity seems to be to be not so much pulling me down, as pushing". Maybe the writers here had something, and although Phoebe should listen to Ross about the solid evidence for evolution, her 'scientific arrogance' speech later on in the episode was brilliant: "There was a time when the greatest minds on the planet thought that the world was flat! Are you telling me that there is not the slightest chance that you might be wrong about this?". A plea for humility that is much needed in physics.

Evidence from galaxies and all other low acceleration systems shows something big and deep is rotten in the state of physics. I've managed to show that quantised inertia can clear up some of the mess. What about gravity? It has never sat well with quantum mechanics. In my recent (2016) EPL paper I managed to derive part of gravity as well as quantised inertia from the uncertainty principle. This proton radius anomaly might represent a better line of attack since, as I always prefer, there is some direct data to show the way.


Pohl, R. et al., 2010. Nature, 466, 213. http://www.nature.com/nature/journal/v466/n7303/full/nature09250.html

Pohl, R. et al., 2016. Science, 353, 6300. http://science.sciencemag.org/content/353/6300/669

McCulloch, M.E., 2017. The proton radius anomaly from the sheltering of Unruh radiation, Progress in Physics, Vol. 13, 2, 101-102. http://www.ptep-online.com/index_files/2017/PP-49-05.PDF

Wednesday, 18 January 2017

How Unruh radiation makes inertia

The core of MiHsC / quantised inertia / horizon mechanics*, is the idea that the property known for centuries as inertia is caused by an asymmetry in Unruh radiation (an asymmetric Casimir effect). I have already discussed the evidence for Unruh radiation itself here (Fulling-Davies-Unruh radiation), and how quantised inertia (introduced here) predicts galaxy rotation exactly, and cosmic acceleration, without any dark stuff, but many people have asked how can a process based on the zero point field, so weak in the Casimir effect, could have such a large effect on matter that it produces inertia. How can it be?

Well, it can be. This can be shown with simple maths and the schematic below. The black circle is a Planck mass. Let us say that for some reason it is accelerating to the left (purple arrow), so a combination of quantum mechanics and relativity says that it sees a warm bath of Unruh radiation (orange colour). Relativity then says that information from far to the right (from the black zone) is limited to the speed of light and so cannot reach the mass, so this is its 'unknowable space'. A Rindler horizon forms to separate that space from the known space. Now as far as the mass is concerned, there is no space beyond the horizon and waves need space to wiggle in. So this horizon damps the Unruh waves on the right, creating a colder Unruh bath there (blue area). The gradient in the Unruh radiation means that more thermal energy bangs into the Planck mass from the left than from the right and so it is pushed back against its initial acceleration. Another way to think about this is that energy is now extractable from the difference in (virtual) heat.

Maths helps us to be specific. The wavelength (L) of the Unruh radiation seen by a mass of acceleration 'a' is

L = 8c^2/a

The c is the speed of light, a huge number, so that the c^2 in the numerator makes the Unruh wavelength usually very long. A sperm whale falling in Earth's gravity would see Unruh waves a lightyear long, but probably wouldn't last long enough (a year) to measure one passing by. The energy in the Unruh field on the left is then

E1 = hc/L = hca/8c^2 = ha/8c

The energy in the Unruh field on the right is


Using normal physics, the force on the mass is the energy gradient from left to right across the diameter of the mass

F = dE/dx = ((E1-E2)/d = ((ha/8c)-(0))/d

F = ha/8cd

This looks suspiciously like Newton's second law: F=ma, and suggests that m=h/8cd

For a Planck mass d is the Planck length so the predicted mass is m=1.7x10^-8 kg. The accepted Planck mass is 2.2x10^-8 kg. In other words, at least in this case of the Planck mass, the Unruh effect is strong enough to produce inertia. It predicts the accepted numbers quite well even in this simple analysis which leaves out a lot of detail. As I said in my 2013 paper on this (see below): to make this process work for larger particles, you can't just put in a larger diameter d. You have to add up the effect of each Planck mass.


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

Horizon mechanics* = A new name suggested to me by J.M. Dorman.

Tuesday, 10 January 2017

A Taste of Kafka

Well, before I start I should say that most journals I have dealt with have been fair, but I'm having a bad month it seems, and every so often one is entitled to a rant. It's therapeutic for me and I think it is illuminating, maybe, for people to see the agonizing effort I'm making to try and squeeze my papers through peer review.

I've written a paper that gives good observational evidence that quantised inertia / MiHsC models 153 galaxies in the SPARC dataset without dark matter and without any adjustment of any kind. I've discussed this comparison on this blog too. I've submitted the paper on it to four journals so far. I've just received this frustrating reply from the editor of the 4th one:

Dear Dr. McCulloch:

I am writing to you with regard to your manuscript cited above, which you recently submitted to the (name of journal). I regret to tell you that we are not able to undertake further consideration of your submission for publication in the (name of journal group).

In case you are waiting for the scientific reason, that is the end of the message! This isn't the only meaningless response I've had in my career but surely science can do better! The whole point of science is that an empirical, or at least rational, reason has to be given for decisions. The Royal Society decided in about 1600 that science worked better this way. Otherwise, instead of rational progress you get hidden elites deciding whatever they want in their own interests. Recently, as I have written papers that show more and more clearly that quantised inertia works far better than dark matter, I have increasingly received vague responses like this. The editor clearly is unable to find any fault with quantised inertia, and yet is unwilling to even consider it. Why? I don't mind being rejected for a rational reason, but I get a mediaeval or Kafkaesque chill when my papers are rejected for no reason at all.

My reply to the editor was:

Dear Editor,

You have to give a reason, since you represent a scientific journal.


No response. If you have any advice on which journal I can next submit myself to, please let me know. Readers Digest? I always wanted to submit there..

Friday, 6 January 2017

Emdrives, dielectrics, & the Kaporin optimisation.

In the past I've presented many comparisons between quantised inertia (MiHsC, horizon mechanics) and the emdrive thrust data, and here is another one (see the graph below) updated with the new NASA 2016 data (White et al., 2016). The ten comparisons between the thrust predicted by MiHsC/QI (this way) along the x axis, and the thrust experimentally observed, along the y axis, are shown by the open squares. Ideally, they should all lie on the diagonal line, and they are close to it, but you'll notice that the NASA thrusts (NASA2014 and NASA2016) are overestimated (too far to the right ) by anything up to a factor of ten (the scales are logarithmic), and Shawyer's first test (Shawyer1) is too far to the left.

I wondered (see the NASA shift) if it could be because NASA put a thin dielectric at the narrow end of their emdrives (Paul March confirmed they did), and Shawyer put a dielectric at the wide end of his first emdrive (Shawyer1). So I have now calculated the change this makes to MiHsC/QI since a dielectric changes the speed of light. The amended thrusts are shown on the plot with the black diamonds, and they lie closer to the diagonal 'correct' line, which is encouraging and some evidence that MiHsC/QI is the right explanation (but let's see if the reviewers of my new paper, to be submitted, agree with the way I've calculated the effect of the dielectric). Here is the same data in table format:
I'm also very grateful that, just before Christmas, Professor Igor Kaporin of the Russian Academy of Science, Moscow, told me he'd taken equation 14 from my paper (see the first reference below), which predicts the emdrive thrust, and optimised it to predict the emdrive shape likely to give maximum thrust. It is silly I didn't do that, since I've done it many times in other contexts (eg: least squares matrix algebra) and it is quite easy to do. You differentiate the MiHsC thrust equation (eq. 14) with respect to L and set the result equal to zero and what comes out after a few lines of algebra is that the maximum thrust occurs when L=4*(ws*wb)^0.5, where L = cavity length, wb & ws are the big and small end widths. I should point out that eq. 14 is approximate and doesn't include the effects of cut-offs within the cavity or the effect of dielectrics, but I will publish the dielectric-capable formula soon, and I will be sure to optimise this time!


McCulloch, M.E., 2015. Testing quantised inertia on the emdrive. EPL, 111, 60005. Preprint

White, H., P. March, J. Lawrence, J. Vera, A. Sylvester, D. Brady, P. Bailey, 2016. Measurement of impulsive thrust from a closed rf cavity in vacuum. AIAA J. of Propulsion and Power.