I've suggested (& published in 21 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

Sunday, 7 April 2019

Models, Experiments & Theory

So much has happened over the last few months and thanks to my newly-funded collaborators, research into QI is now running on three cylinders instead of one: it was just theory, now the work includes models and experiments as well. My post doc, Dr Jesus Lucio is working very well. I asked him to write a matlab script that simulates wide binaries with ordinary Newtonian physics, and MoND and QI. His script has produced a very nice animation (see below) that shows that when you model a real wide binary, only quantised inertia (red) predicts the stars to be bound together (as they are in reality). Newton and MoND (blue and green) predict wrongly that the two stars should zoom off to infinity, and so they are falsified. He has extended this tool to also simulate the Solar system. It compares the predictions with the observed orbital trajectories. We are having fun simulating Oumuamua at the moment.

The other project I asked him to do is to develop a numerical COMSOL simulation of the asymmetric Casimir effect that underpins quantised inertia (reference 1). The process by which when you accelerate something to the right, say, relativity and the speed of light limit, implies there is a region of space to your left that you can no longer see and a horizon forms that damps the intensified (Unruh) quantum vacuum on the left side of the object leading to a net quantum force that resists the object's acceleration: inertia. Unfortunately COMSOL is having a hard time modelling a particle at the tiny Planck scale (10^-35 metres wide) moving within a cosmos approximately 8.8x10^26 metres wide. So, our first crude plan is to use a particle the size of a galaxy cluster, and then slightly smaller, and we will use the difference to extrapolate down to the Planck scale.

The two experimental teams I employed as part of my funded project are also getting started building light-emdrives. The Dresden team are building resonators, but the Madrid team are already experimenting and have seen some thrust of the hoped-for kind, that is over six sigma outside the noise. However, it will be a long struggle to show it is definitely The Big One. They are now slowly eliminating mundane effects that could also be causing it.

As well as thinking about thrust, I am trying to generalise and further extend QI to explain gravity. After reading a book by A. Unzicker (ref 2), it seems that Einstein may have been on a more QI-compatible course until 1911 when he was redirected into bent space by his geometer friend Marcel Grossman. The variable speed of light version of general relativity (VSL-GR) that Einstein published in 1911 had a flaw at the time, but that flaw was corrected by Dicke (1957) (ref 3) and this version is far simpler and agrees with all the predictions of standard general relativity. This VSL-GR is far more satisfactory to me than normal GR since it relies on a process (slowing photons) that can be measured directly, as opposed to standard GR which relies in bent space, which is an abstract thing that you cannot measure directly, except by virtue of the moving objects it was designed to predict anyway. I have had some success in building a mathematical bridge between quantised inertia and VSL-GR. I am still trying to decide whether the piles I built the bridge on (the assumptions) are solid or not. The best way to do this is to jump up and down on them a lot. I'll let you know if there is a splash.


McCulloch, M.E., 2013. Inertia from an asymmetric Casiir effect. EPL, 101, 59001. https://arxiv.org/abs/1302.2775

Unzicker, A., 2015. Einstein's Lost Key. https://www.amazon.co.uk/Einsteins-Lost-Key-Overlooked-Century/dp/1519473435

Dicke, R., 1957. Gravitation without a principle of equivalence. Review of Modern Physics, 29, 363-376.

Saturday, 9 February 2019

Wide Binaries 3.0

The best way to do incisive science is to find an empirical case that can discriminate between hypotheses, in this case dark matter, MoND and QI.

Galaxy rotation is not ideal in that respect. To recap: galaxies spin far too fast at their edges to be stable. They should fly apart, but they appear to be gravitationally bound. So astro-physicists have proposed that there is invisible dark matter in them to hold them together. One of the properties of this dark matter has to be that it stays spread out, otherwise it would collapse to the centre of the galaxy and not predict the rotation correctly. The problem is that although QI can predict galaxy rotation, dark matter can be 'fudged' to predict it too, and even MoND is tweakable (a0).

Something un-fudge-able is needed and wide binaries are brilliant examples of unfudgeability. I have discussed them before. They are binary stars so far apart that their accelerations are as low as they are at the edges of galaxies. Hernandez et al. (2018) have shown in some brilliant papers, that wide binaries orbit each other far too fast, just as galaxies do. The data I have used here is from his latest paper which uses brand-new GAIA data. The data is shown by the crosses in the Figure below (prepared by my new post-doc Jesus Lucio). The x axis shows the separation of the stars in parsecs and the y axis shows their mutual speed in km/s. The grey area shows the uncertainty in the data, so it means that the orbital speed at each separation is somewhere in the grey area.
The dotted line shows the prediction of Newton or of general relativity (the same in this case). Just as in galaxies, although Newton/GR says the orbital speed should decrease with radius/separation (dotted line), the observed speeds stay much higher. Beyond a distance of 0.2 parsecs both Newton and general relativity are falsified. These theories disagree with the data and dark matter cannot be added to these wide binaries to save them, because to fit the larger galaxy it must stay diffuse. Unless they now come up with quantum dark matter that can be simultaneously spread out and clumpy!

The prediction of MoND is shown by the dashed line here with its fitting parameter set to a0 = 1.3x10^-10 m/s^2. It under-predicts the data at 1 parsec but if we set a0 = 2x10^-10 m/s^2 then it just about fits. However, the MoND prediction should probably be closer to the Newtonian/GR curve because it is subject to the External Field Effect (still under debate) which means that external accelerations bring it back towards Newtonian behaviour. These wide binaries are close to the Sun, and so accelerations due to the galaxy are still on the order of 8x10^-10 m/s^2. So, MoND is possibly also falsified by this data.

The prediction of quantised inertia is shown by the solid line, with the error shown by the two lighter solid lines above and below it. QI agrees with all the data (just). I submitted a paper on this to MNRAS a few weeks ago including a plot similar to this one, but in which QI did not quite agree. Well, a sincere thanks to my post-doc who recently spotted a factor of two error in my calculations which was making QI seem worse than it is, and he corrected it. So we will now resubmit with the new result.

In summary, QI predicts the orbits of these 83 pairs of wide binary stars better than other theories. Furthermore, QI does it without the need for any arbitrary fitting parameters (MoND needs one). QI needs just the observed mass, the observed speed of light and the observed cosmic scale. QI can only predict one outcome, and that turns out to agree with the data.


Hernandez, X., R.A.M. Cortes, C. Allen and R. Scarpa, 2018. Challenging a Newtonian prediction through Gaia wide binaries. https://arxiv.org/abs/1810.08696

McCulloch, M.E. and J.H. Lucio, 2019. Testing quantised inertia on wide binaries. Submitted to MNRAS.

Tuesday, 22 January 2019

New Collaborations

It has been a time of transition for me. Last year I was a part time lecturer. Now I am a full time research lecturer with no teaching duties, a post-doc and a hyper-ambitious project to manage. Projects don't come more ambitious than propellant-less propulsion. Anyway, I'm trying to seize the chance of a lifetime with both hands.

With my new funding, I have employed a post-doc in quantised inertia (QI). He started on January the 4th). He has already produced several toy models of basic QI-thrusters, treating QI mathematically as an external force which simplifies some things, and has just written a fascinating report on that, which may become a paper. I have also managed to get all parties, Plymouth University, TU-Dresden and Alcala, Madrid to agree to and sign the contract agreements - a new experience for me.

Last week I visited Airbus & told them how QI could be useful for satellite station-keeping since it predicts thrust without the need for propellant: the kind of thrust that does not run out. You just need energy for Solar sails, assuming it works. I'm now very confident about QI in the astrophysical arena (paper). The difficulty will be making it appear in a lab, but lab tests are still the most direct test and all roads in physics lead to the lab. My talk at Airbus was very popular - people were crowded into the lecture room - I suppose that is not surprising when you suggest to people in an aerospace company that they can ditch fuel!

Next month I will be meeting the great Roger Shawyer, and that will be fascinating. It could be that some polite disagreements will occur because we have different interpretations of what may or may not be going on in those hot copper cones. I'll be asking him about the recent null tests of the emdrive and trying to dig down a little to his comments that the emdrive needs a little resistance to push against. Who doesn't? It would also be great to meet Hawking (but sadly too late!), Milgrom, John Anderson, Paul Davies, Bill  Unruh & Hal Puthoff (I have met the latter by email).

I have submitted a paper to MNRAS showing that quantised inertia predicts wide binary orbits well. To summarise: co-orbiting binary stars far apart show the same sort of anomaly that galaxies do at their edges (too high an orbital speed), but in the binaries' case you cannot add dark matter, because it must stay spread out smoothly if you want to continue to predict the whole galaxy. They can't have it both ways! I've now shown that quantised inertia predicts wide binaries' orbital speeds (orbital speed data from Hernandez et al, 2018) just as well as MoND, and without needing MoND's adjustable parameter or, of course, dark matter, see the plot. There is a discrepancy around one parsec separation where both MoND and QI underpredict the data.

I've submitted a paper to EPL on the Allais effect, and although I realise this is controversial data, it is true that any observation that disagrees with the standard model is going to be controversial, and yet the only observations that will help us build a new physics will have to disagree with the standard model, and so they will be controversial. In other words, the quickest way to build new physics is to look for trouble. I would not say that is how I work, but it may appear that way to some! The Allais effect is also less than ideal since it has not been seen in some experiments, which bothers me, but I enjoyed writing the paper since it involves QI working elegantly in quite a different situation.

I've submitted a paper with Jaume Gine improving the way I derived quantised inertia before from the uncertainty principle, so we can now derive QI exactly that way. He is also helping me to resubmit the paper on EPR and time that I've been trying to get published for years. We are just ironing out our differences now and then Foundation of Physics might be the lucky target.

I've also started a paper that was inspired by my son. I'd just been fiddling around with QI formulae while I was waiting for him to finished a school tutorial, and as I was driving him home he asked me a question about schoolwork "Dad. What's Pi?". I said "3.14.." and immediately realised that the odd number that dropped out of QI onto paper half an hour ago was close (within 0.5%) to Pi. In haste I hadn't made the connection. This result may be a coincidence or it may have given me a huge new handle on nature. It rings true to me, and is very simple. I'll spill the beans when I'm sure it's not a circular argument..

Wednesday, 19 December 2018

Towards Propellant-less Propulsion

The Journal of Space Exploration has just accepted my latest paper in which I focus far more on applying quantised inertia to propulsion, and which also shows an even simpler way to derive and understand QI, just from the uncertainty principle and relativity. This is a path I've been tending towards for a long time (see references). Werner Heisenberg showed, for a quantum object, the uncertainty in its momentum (dp) times the uncertainty in its position (dx) always has to be larger then Planck's constant divided by two Pi (hbar), over two (aka hbar/2). So: dpdx > hbar/2.

The assumption of quantised inertia is that you can apply quantum mechanics on the macroscale, if you take account of relativistic horizons. So, imagine we have a highly-accelerated system that excites the quantum vacuum (another way to say that is to say it sees Unruh radiation). For example, this might be a cavity with microwaves or a discharge spark inside. Imagine we now increase 'hbar' to represent the energy in this macroscopic system - bringing quantum mechanics to the macroscale. Now make the cavity asymmetrical so that the Unruh waves on the left side are blocked by a shield but those on the right side are not. Since you are blocking information from the left from getting to the system you are decreasing dx on the left side (the uncertainty in position in space is decreased because so far as the system knows there is no space beyond your shield), and so dp must increase to the left. This means that the normal quantum jitter (dp) usually very weak, is now magnified by the large accelerations (Unruh radiation) and also must be larger towards the left hand side. The system on a statistical average will move towards the left. As I show in the new paper, this predicts, to the right order of magnitude, the thrusts seen in the emdrive, the Woodward drive and also some intriguing results from asymmetrical capacitors.

The thrust of the argument :) is that quantum mechanics may not just apply to the small, and relativity to the fast: quantised inertia implies that at very high accelerations they join up to produce observable, and very useful, behaviour. Thrust without propellant means much lighter (cheaper) launch systems, and the possibility of interstellar travel in a human lifetime.


McCulloch, M.E., 2013. Gravity from the uncertainty principle. Astrophy & Space Science, 349, 957-959 Preprint

McCulloch, M.E., 2016. Quantised inertia from relativity and the uncertainty principle. EPL, 115, 69001 Preprint

McCulloch, M.E., 2018. Propellant-less propulsion from quantised inertia. J. of Space Exploration (in press). Preprint

Wednesday, 31 October 2018

Bozeman, Montana or TU-Dresden?

This is a summary of the visit I have just made to Prof Martin Tajmar's esteemed Institute fuer Raumfahrttechnik at the Technische-Universitat-Dresden (TU-Dresden). I arrived on time at 10am. One of his students met me and took me to his office and then after a short chat, I gave a one-hour talk on quantised inertia (QI) to him & his research group of 30 or so. Martin Tajmar asked a few questions, eg:
  1. How does the cosmic horizon interact with local dynamics in QI given the speed of light limit? (Answer: there is no relativistic speed limit for monochromatic waves).
  2. Your assumption of an average acceleration of photons in the emdrive is wrong, they accelerate only when they rebound (Answer: true, but my assumption now has more backing, see below).
  3. What is the degree of shielding of Unruh radiation by matter? Won't that introduce an adjustable parameter to QI? (Answer: Maybe).

After the talk we all went for a meal at the nearby canteen, and I made it clear, as I tried to do in my talk, that I am very confident about quantised inertia on a galactic scale, but I need Tajmar and his team's world-class experimental expertise to bring it down to the lab scale.

Then he gave me a tour of his labs, in which he seems to be testing most of the anomalies I have heard of. I saw the equipment he used for the 'Tajmar effect' that I tried to explain in a paper in 2011 (see refs). It is still embedded in its concrete well. I held his small emdrive. He also has a massive wind tunnel for more mundane aeronautical experiments. At one point he said "And here is my Stargate..". I looked through a window and saw a huge room in which he is building something that looks like the fictional stargate (it's not).

Back in his office, a student who has just started a PhD devoted to the emdrive gave a talk on recent progress. They have applied 3-10 Watts to an emdrive and measured a thrust of two microN, but it disappears when they subtract thermal changes due to an asymmetrical expansion of the cavity and the resulting changes in the centre of mass. Note that this is a thrust ten times smaller than the thrust NASA JPL was getting for a similar power and this work is still in progress.

We talked about Travis Taylor's mirror proposal. It may not be possible to build as originally proposed, due to the dielectric and mirrors not being able to fit together - manufacturing limitations. So they suggested a simpler arrangement where the dielectric and mirrors do not touch.

Martin then said "We are physicists, let's play" and started writing on a white board, asking me for the relevant QI formulas to put in, and this way, we derived the maximum acceleration of a photon of given frequency. The result was interesting because it means that for visible light bouncing off a mirror the Rindler horizon will be so close that a shield will not effect it, but it also shows that for microwaves the horizon is cavity-sized, so they can see the emdrive shape, or a shield.

The most unexpected thing that Martin said to me was in the evening while socialising (I had some delicious Saxische Sauerbraten and dumplings, and rather more than my usual amount of beer). He criticised most of the well-known lab anomalies as being debatable due to often sloppy technique, and yet showed some interest in an anomaly I thought had been wildly discredited: Hutchison's. I thought I'd had too much beer.. Good physics is of course predictive, but the profession itself is not!


McCulloch, M.E., 2011. The Tajmar effect from quantised inertia. EPL, 95, 3. http://iopscience.iop.org/article/10.1209/0295-5075/95/39002/pdf

Monday, 22 October 2018

Quantised Inertia Needs You!

It was not long ago that I myself was trying to get a full time post, now, not only do I have one but I am offering a post-doctoral position. So, if you are good at the numerical modelling of the interaction between em radiation and physical systems, preferably using COMSOL/Java, you fully understand what is behind the terms Unruh radiation and Rindler horizons, and you are keen to help with the conquest of space by helping to develop an 'electric rocket' for much safer, cheaper launch and propellant-less thrust in space (ie: saving both the planet and the human race) then this job advert is for you:

-- x --

Research Fellow in Modelling Propellantless Thrust, University of Plymouth, UK.

We are seeking an enthusiastic postdoctoral researcher with excellent skills in physics & numerical modelling, to develop a predictive model based on a ground-breaking theory called quantised inertia. The numerical model will be used to design a new kind of thruster.

The new theory suggests that inertia is caused by an interaction between Unruh radiation and matter. It explains, for example, galaxy rotation without dark matter, but in order to enable accurate experimental tests of the theory, it must be fully coded into a numerical model that can predict exactly how Unruh radiation will push on any given configuration of matter. Your role will be to do this coding.

You must have a PhD in physics, experience in translating physics into numerical models, an understanding of the interaction between radiation and matter, quantum mechanics and relativity. Experience of COMSOL and java will be an advantage.

You will work with Dr Mike McCulloch. The post includes short trips to Dresden (Germany) and Madrid (Spain) to liaise with groups who are setting up experiments.

-- x --

It's not every day you get a well-paid chance to make history.
In order to apply please go to:  Link

Monday, 24 September 2018

Wide Binaries 2.0

As I have repeated many times on this blog, galaxies spin far too fast to be bound by their visible matter. This anomaly disagrees with standard physics and yet it has not only been brushed under the carpet, but it has been forbidden in many places to even admit that there is a carpet. A serious flaw (floor) in the mainstream attitude :) The carpet is the dark matter that has been invented to cover this up and save general relativity (which may be fine for high acceleration, but does not work for low).

There are two cases though, in which the dark matter fudge cannot be applied 1) globular clusters (see Scarpa et al., 2008 below) and 2) wide binaries which are even better (discussed earlier here). Wide binaries are twin star systems that orbit with a separation of more than 7000 AU and they show the same impossibly fast orbits that larger galaxies do. Dark matter cannot be used to fudge them because in order for dark matter to predict galaxy rotation it must stay spread out and therefore it cannot be squeezed into little wide binary systems. So wide binaries are the astrophysics equivalent of testing the emdrive in a vacuum which rules out air currents - wide binaries rule out dark matter.

I have started looking a wide binaries again, going back to a paper of Hernandez et al. (2014) who processed a lot of data on them. The data is shown in the Figure by the blue and red crosses. The x axis shows the separation of each pair in parsecs and the y axis is their orbital speed (km/s). I've shown the uncertainty in the data crudely by the blue and red coloured areas around the crosses, so you can see that the SDSS data (blue) is far less accurate then the Hipparcos data (red). To be deemed successful a theory has to predict within the blue and red areas.

I have added to the plot the predictions of general relativity (the dotted curve) which lies outside the coloured areas for all separations greater than about 0.03 parsecs. Therefore, because dark matter cannot be applied in these cases (unless they add more bells and whistles to it) we can say that general relativity has been falsified. This is a strong indication that it is wrong in galaxies as well, since the anomalies are very similar.

The other curves show Modified Newtonian dynamics (MoND, the dashed curve)  and quantised inertia (the solid curve). Both theories predict the data, but MoND has been tuned to work by arbitrary adjustment of its free parameter. Quantised inertia predicts the data all by itself, without any tuning, an advantage which shows it is deeper, more predictive (it can predict the change in the systems' rotation with cosmic time too) and also simpler. Occam's razor cannot be repealed. Note that the acceleration used for QI here includes that due to their mutual spin and their movement around the galaxy.

The next steps are to submit this to MNRAS, and try to shrink the blue and red areas of uncertainty in the data using the new GAIA dataset. This is an elegant way to debunk general relativity at these low accelerations, dark matter too, and demonstrate the advantages of QI - better data is needed though.


GAIA dataset: http://cdn.gea.esac.esa.int/Gaia/ (Thanks to F.Zagami for the link).

Hernandez X., A. Jimenez, C. Allen,2014. Gravitational anomalies signaling the breakdown of classical gravity. Astrophysics and Space Science Proceedings 38, 43. https://arxiv.org/abs/1401.7063

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophys. Space Sci., 342, 575-578. http://arxiv.org/abs/1207.7007

McCulloch, M.E., 2017. Galaxy rotations from quantised inertia and visible matter only. Astrophys. & Space Sci. 362, 149. Link to open access paper

Scarpa et al, 2006. Globular clusters as a test for gravity in the weak acceleration regime. Proceedings of the 1st crisis in cosmology conference. http://arxiv.org/abs/astro-ph/0601581