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, 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.

Friday, 23 June 2017

Evidence from an early galaxy

The best way to move forward in science is to find specific anomalies, with numbers attached to them, that theories can be tested against, and this morning I'm very grateful to Frank Becker and John Dorman who tweeted to me about an exciting paper just published in Nature. I say it is exciting, but it's hidden behind a paywall. However, from what I can see from other sources the authors (see references below) have managed to look in detail at a very early galaxy, cleverly using gravitational lensing: using a foreground galaxy which bends the light from a galaxy far distant (and way in the past) in such a way that it magnifies the background image. Thus they have inspected an ancient galaxy at a redshift of Z=2.1478, ten billion years ago when the cosmos was only one third its present size. The only other details I have are that it is half the radius of the Milky Way and has a rotation rate at its edge of 350+/-150 km/s (error bars taken from their Fig. 2). They note that this is very odd and unexpected, why is it spinning so fast! Quantised inertia can explain it.

Quantised inertia predicts that there is a minimum acceleration in the cosmos, given by 2c^2/T, where c is the speed of light and T is the co-moving cosmic diameter. In the far distant past, at a redshift of 2.1478 when the universe was about a third the size it is today, T would be a third the size, so the minimum acceleration should have been three times what it is today. So quantised inertia forces ancient galaxies to spin fast. Do the numbers agree then?

To check this at first order all you have to do is say that the acceleration of this ancient galaxy at its edge (where it is slowest) must be above the QI minimum of 2c^2/T and since acceleration is given by v^2/r where r is the radius, we get v^2/r > 2c^2/T and so v=sqrt(2c^2r/T). If we take the very crude estimates in the secondary sources that this galaxy is half the radius of the Milky Way, then QI predicts a speed of v=538+/-75 km/s which agrees with the observed speed (given the error bars). Admittedly I haven't even read the paper yet (as I said, I can't access it for free), but high redshift data is providing great evidence for quantised inertia, because quantised inertia, alone among theories, predicts a specific change in dynamics with cosmic time and it is just now becoming possible with studies like this one, to check this out. I have been trying to publish a paper on this and it has been rejected six times but is now undergoing a more positive review at ApSS. The paper uses six other early galaxies, which also spin fast in agreement with QI. So thank goodness for the finite speed of light since it makes a very useful time portal out of the night sky.

"What seest thou else in the dark backward and abysm of time?" - Shakespeare, The Tempest.

PS: I now have a copy of the paper. Thank you to those kind folks who sent one.


Sune Toft, Johannes Zabl, Johan Richard, Anna Gallazzi, Stefano Zibetti, Moire Prescott, Claudio Grillo, Allison W. S. Man, Nicholas Y. Lee, Carlos Gómez-Guijarro, Mikkel Stockmann, Georgios Magdis, Charles L. Steinhardt. A massive, dead disk galaxy in the early Universe. Nature, 2017; 546 (7659): 510. https://www.nature.com/nature/journal/v546/n7659/full/nature22388.html

Wednesday, 14 June 2017

Funny Business at the ArXiv

Once, in childhood, I was playing one of my best friends at chess, and on this occasion I won. After a minute my friend reached over and cheekily pushed over my king. Of course, this was only a couple of kids playing a friendly game, and this fellow is still a great friend of mine, but I feel that some parts of physics are acting the same way.

This was brought home to me last month. For the third time, the arXiv, a freely-available central library for physicists, deleted my submission of my peer-reviewed and accepted paper (on quantised inertia and the emdrive). They say it is similar to a previous one I submitted, but it is a significant advance on that paper, otherwise the journal, which is a good one and which published the other one as well, would not have accepted it as a new paper. I've had a long running battle with the physics arXiv (this section of the arxiv has anonymous and therefore unaccountable referees, not good scientific practice). They refused to take any of my published papers between 2013 and 2015, and since 2015 they have shifted them from the section on astrophysics, where I need to post to get the attention of astrophysicists, to the section on general physics (a section for work they perceive as 'fringe') that virtually no-one looks at. This is censorship without a solid stated reason.

Crying 'Fringe' or 'Fake News' is not enough, evidence must always be provided, otherwise it is easy for aggressive people to control events to protect their power or funding streams. The only way to destroy this control is to say: "What is your evidence for that?". I have asked the arXiv for their reason many times, they told me to stop asking. Evidence is the light and I always test against evidence in my papers, whereas physicists working on dark matter, string theory or black holes do not. This is no small matter. It is the difference between science and the fluff they had in the middle ages. I can cite some evidence for this contempt of evidence in the mainstream. David Meritt (see ref below) recently showed that most cosmology books published since 2004 do not mention that dark matter has not been found. They do not now even mention the evidence that they have no evidence.

The frustration is that I have lots of evidence that quantised inertia is the best theory available (I have published 18 papers now). QI simply predicts all galaxy rotations, even at high redshift, the low-l CMB anomaly, cosmic acceleration, the flyby anomalies, the Tajmar effect, the emdrive, and many other things. It combines relativity and quantum mechanics and thereby explains inertial mass for the first time. The only difficulty is getting a fair hearing. Thank goodness for journal peer-review and also Research Gate which has no anonymous censorship. The arXiv can be a great asset for physics and I once loved it, I have accessed many papers there, it is free, but the physics section is now clearly biased in this way. I think it is essential that to ensure decisions are made on a scientific basis, it should at least accept everything that is published in a proper journal. Let proper journal peer reviewers decide, not the anonymous.


Merritt, David, 2017. Cosmology and convention. Studies in History and Philosophy of science, 57, 41-52. https://arxiv.org/abs/1703.02389

Friday, 9 June 2017

Announcing: the New Physics channel

So many television programmes are made about dark matter, black holes and string theory using computers to hide with fancy graphics what they completely lack in solid evidence. I don't have access to fancy graphics but I have made a powerpoint video based on my recent seminar at Exeter University. It explains how quantised inertia predicts galaxies without dark matter, and the emdrive thrusts as well. I hope it is at least clear:

Please do give me constructive feedback on this video, and tell me what you'd like to hear about, and I will try and produce some more of them.

Wednesday, 31 May 2017

Opinion on the UK Election

Apologies, but I cannot help but write something about the election since I am excited by the possibility that Jeremy Corbyn might get into No. 10. There has been since 1979 a huge increase in inequality in the UK. The Gini coeffient that measures inequality has risen from 0.23 in 1979 (the value egalitarian Norway now has) to about 0.4 now (close to the US) and the UK has become a less kind country with more homeless and foodbanks, where assets that everybody used to own collectively (Royal Mail, NHS) are being sold to the rich.

The only solution is to put someone in No. 10 who will listen to ordinary people and not corporations, and will not sell out. In its empirical wisdom, that is what the British democratic system has produced in the form of Jeremy Corbyn, who has stood by his present democratic socialist views consistently for 40 years.

It is very important in my view that, as Labour now propose, the essentials of life: NHS, railways, utilities, post office are owned in common, as they were after WW2. If not, the processes of the game of monopoly take over, capital concentrates in a few hands, and we will all be dependent on the super-rich for the essentials, and they'll raise the price to the maximum. It is also essential to avoid burdening students with debt, so when they graduate they can chose to work on their dreams, rather than aim to get rich quick to pay off their debt. Labour promise to end tuition fees. This, and the increased equality, should produce a more fulfilled and creative society. Hopefully also the general atmosphere will become less money-driven: for example it is also important that scientists are not judged on the amount of funding they bring in, so they will make decisions based on what is scientifically interesting rather than what brings in easy funding (eg: safe topics or expensive equipment).

President Roosevelt's 1944 GI Bill in the US (free college) and the 1948 Labour victory in the UK when the NHS and welfare state were formed, produced a secure and well-educated generation and it is interesting that the GI Bill in the US was followed by its so-called 'greatest generation' (Moon landings, Dylan, Woodward & Bernstein). In contrast high inequality makes a nation weak since the poor become too poor to create, and the rich hide their money away so the economy shrinks. This is why over the millennia there has been a slow tendency away from rule by the rich (the Tory way) and towards democracy and socialism (Labour). Compare for example Ancient Egypt with modern states.

Two of my favourite parts of Star Trek are in The Voyage Home when Dr McCoy goes from the 23rd century back to the 20th Century and regrows a woman's kidney saying "Kidney dialysis? My God, what is this, the dark ages?", and in First Contact when Picard says there is no money in the future. The future can be better, but more advanced technology is not enough. The social system also needs to advance. Electing Corbyn would be a great step towards that. Please vote Labour.


Star Trek IV: Kidney Dialysis: https://www.youtube.com/watch?v=UtllgbUiTt0

Thursday, 11 May 2017

Emdrives and dielectrics

I am giving a seminar tomorrow to the Plymouth Astronomical Society, so here is a summary of the talk which is humbly titled: "How to predict the impossible". The impossible in this case is of course the emdrive, a truncated cone-shaped microwave oven that seems to move very, very slightly towards its narrow end as the microwaves resonate within it. This is causing a lot of incredulity in physics, since humanity has never before encountered a system that is able to move itself in one direction without apparently expelling reaction mass in the other direction. The usual rule is called the conservation of momentum and is a very well tested. The emdrive anomaly was first discovered by Roger Shawyer and has recently been reproduced by others, including NASA's Eagleworks Lab.

For many years I have been proposing a theory called quantised inertia, that states that the property of inertia (that which makes it hard to stop walking into lamp-posts) is caused by relativistic horizons damping the quantum vacuum. When you accelerate in one direction two things happen 1) the waves of the quantum vacuum that you see get shorter (Unruh radiation) and 2) a horizon (like a black hole horizon) appears in the opposite direction that damps those waves. Quantised inertia states that the resulting asymmetry in the quantum vacuum pulls you back against the initial acceleration and so it predicts inertia for the first time, but also predicts a new loss of inertia when accelerations are so low that the Unruh waves get damped symmetrically by the cosmic horizon, so it also predicts galaxy rotation, and its change with time, perfectly without dark matter.

How about the impossible emdrive then? Well, it is an asymmetrical cavity, so the idea is that in the narrow end the microwave photons lose some inertia because the Unruh waves don't fit so well (just like galactic edge stars lose inertia because the Unruh waves they see don't fit well inside the cosmic horizon, and so feel less centrifugal force). As a result the emdrive photons gain inertia every time they shuttle towards the wide end, and to conserve momentum the cavity has to move towards its narrow end. Quantised inertia predicts the emdrive thrust data quite well, as I showed in a previous paper. Further, quantised inertia predicts that if you happen to put a dielectric in the wide end, this will shorten the Unruh waves, so more will fit and the gain of inertia from the narrow to the wide end will be enhanced and the cavity will accelerate more. Considering the dielectrics too, quantised inertia predicts the emdrive thrusts extremely well. The Figure below shows the observed thrust on the y axis and the thrusts predicted by quantised inertia on the x-axis, both without considering the dielectrics (white squares) and considering the dielectrics (black diamonds).

The diagonal line marks perfect theory-data agreement. The effect of the dielectrics can be seen most clearly for the tests marked 'NASA2016' (the four white squares, lower centre) where quantised inertia over-predicted the thrusts (the values ideally should be on the diagonal line) until I noticed that NASA put dielectrics in the narrow end of the cavity, thus inadvertently reducing the thrust. When this is considered in quantised inertia, the white squares shift left to become the black diamonds, close to the diagonal line. It can also be seen for Shawyer1, who put a dielectric in the wide end, thus boosting the thrust (top right). This dielectric dependence is a good confirmation of quantised inertia.

Applications of this are to be found in any form of terrestrial of space transport, and one advantage of the explanation from quantised inertia is that it suggests that dielectrics can be used to enhance the effect, which has been too small to be useful as yet. My latest paper on this is just about to appear in EPL (see the reference below).

To change the subject for a bit, it would be fascinating to go to another star in a human lifetime, but for that you need to travel close to the speed of light so that relativistic time dilation gives you an Einsteinian version of suspended animation. For example, if you accelerate at 9.8 m/s^2 for one year, travel at 90% the speed of light (c) for 10 years and then decelerate for one year at 9.8 m/s^2 you could make the 25 light-year trip to Gliese 667 in 12 years (the duration for those on the ship). Unfortunately, although theoretically possible, engineering gets in the way. To get a habitable normal spaceship to 90% of c you would need more energy than can be produced by our civilisation, or as much fuel as a small planet. The emdrive, though, as quantised inertia suggests, uses 'nothing' as its fuel and nothing is readily available everywhere in space (of course, a power source would need to be included).


McCulloch, M.E., 2017. Testing quantised inertia on emdrives with dielectrics. EPL.. Preprint

Sunday, 30 April 2017

What is an electron?

What is an electron? This is the title of a jem of an article written in Wireless World back in 1979 by Prof Roger C. Jennison (see references). Someone sent me the pdf a year or so ago and I have been dipping into it from time to time, increasingly excited and amazed by it.

Roger Jennison made the fascinating point that electrons look very much like photons locked in a self made trap (somehow). For example, when an electron and a positron collide, they annihilate cleanly and out come two oppositely-polarised photons. Also, if you fire photons of slowly-decreasing wavelength at the vicinity of something like a heavy nucleus, suddenly, when the photon wavelength reaches 2.4x10^-12 metres, out comes a positron and an electron (pair production). Why this particular wavelength? See below!

The obvious conclusion is that electrons are made of photons and Jennison took this further by modelling an electron as a photon trapped in a cavity, as shown in the schematic below.

Imagine the photon bounces around inside (the blue waves) pushing the cavity plates (black lines) outwards, and you charge the plates positively and negatively so they attract electrostatically to balance the outward push. This is now a stable, static system.

Now imagine you push the cavity externally from the left to the right (black arrow). Now the photon that is just bouncing off the left wall (the light blue wave) is given more energy by the wall pushing it, and the super-energetic wave then pushes the right wall, so it moves too. As the photon bounces back (dark blue wave) it has lost energy so it has less energy when it gets back to the left hand wall and so pulls that wall rightwards. Now if you take away the initial push, this process continues so that the cavity continues to move rightwards, and so this predicts inertia: the cavity keeps going at constant speed unless pushed on. Jennison's model predicts a lot of other photon properties as well, for example its half classical spin, and it predicts a new effect: changes in speed occur in discrete jumps and that when you use photons of wavelength 2.4x10^-12m then the size of the jumps is Planck's constant, which may explain why that wavelength is crucial.

The model is not complete however, because it is unclear what the cavity walls are made of. They're not likely to be made of a conductive shell. The new point I'd like to make is that quantised inertia might be able to answer this: the cavity walls might be the relativistic horizons seen by the photon as it orbits. For objects like photons (if they are objects) an acceleration towards a centre causes the creation of a cylindrical relativistic horizon, from the electrons' point of view, rather like a wall outside the orbit. Could this complete Jennison's electron model? This also makes me think of course of the origin of other particles (higher modes?), the emdrive cavity and also ball lightning..


Thanks to Michael C. Fidler who sent me the Jennison paper last year, and to John Dorman and others for online discussions on this matter.


Jennison, R.C., 1979. What is a electron? Wireless World, June (Link to pdf, thanks to Tom Short).

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.