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

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

Saturday, 1 September 2018

Horizon drives / quantum rockets

Sorry for the gap in blog entries, but I have been traveling a lot, explaining to groups in Germany, exotic Hampshire, and the US, how quantised inertia predicts thrust. As you may know, I now have significant funding to do tests, and will report on these as openly as I can - this is important to me since I value feedback and comments and they help to progress the work.

So how does quantised inertia predict thrust? My explanation of this is becoming more streamlined as time goes on, so here is the latest (see, for background, McCulloch, 2016). QI says that all masses move because of the quantum 'jitter' that can be made anisotropic by horizons (barriers to information). The bold assumption in QI is that horizons are real and are able to reduce the 'dx' in the uncertainty principle, so that dp increases in that direction and the quantum jitter moves the object horizon-ward (see here). These horizons can be either relativistic, or solid conductors (as in the Casimir effect). If the quantum vacuum is more intense, you get more push. The quantum vacuum becomes more intense for accelerated objects because of the enhancement due to Unruh radiation. So the QI recipe for launch, so far, looks like this:

Step 1: Make something that accelerates very fast so that the quantum (Unruh) waves intensify and also shorten so much that they are short enough to interact with a metal structure. For example, to interact with a structure of size 1m, the acceleration of the core has to be about 10^18 m/s^2. This accelerating core could be a spinning object, resonating microwaves (as for the emdrive, which QI predicts) or a hyper-vibrating piezoelectric (as in the Woodward devices, which QI also predicts).

Step 2: Damp the Unruh waves on one side of the core more than the other. If the acceleration of the core (circle) is big enough, this can be done by putting a thicker conductor, say, above it (see the left schematic), or having an asymmetric cavity (see middle) or a patterned structure whose mesh size is bigger in one direction than another (see the figure on the right). All these structures would damp Unruh radiation (orange) more above the core (darker shade) moving them up.

Step 3: Watch the core accelerate towards the more shielded side. Be patient because at the present level of technical development (thrusts of about 1 microN) it would take 11.6 days for it to accelerate to 1 m/s (for a 10 kg setup), but now QI gives us hopefully an understanding of what is going on, it suggests ways to boost this force, and launch should one day be possible. It costs $62M to launch a SpaceX Falcon 9. At the moment, given the funding budget I've just had to submit, I'd estimate a potential factor of 100 reduction in cost for the kind of thruster QI should allow.


McCulloch, M.E., 2016. Quantised inertia from relativity and the uncertainty principle. EPL, 115, 69001, https://arxiv.org/abs/1610.06787

Monday, 25 June 2018

Does QI Predict The Woodward Effect?

James Woodward in the US has been boldly experimenting with capacitors which appear to show thrust since the 1990s. I was recently reading about one of them, and to me it looks very much like the emdrive. Also, as I will show tentatively below, the thrust from it can be predicted quite well by quantised inertia, in a far simpler way to Woodward's own explanation which mis-predicts the thrust by several orders of magnitude (ie: I admire his experiments, but I do not accept his theory).

Woodward's thrusters or Mach Effect Thrusters (see Mahood, 1999, Tajmar, 2017) typically look like the image below. An AC current is input into a capacitor (the vertical black lines) making an EM field. There is a dielectric in between (yellow) or sometimes to the side, which is a piezo-electric material (PZT) that vibrates when the EM field is applied. The setup is asymmetric because there is a heavy reaction mass (plate), here shown on the left.

Quantised inertia predicts that this contraption should move towards the end with the large brass plate (just as it is observed to do) just as the emdrive moves towards its narrow end, because in both cases Unruh waves are more damped at the end with the massive plate, so photons of the em field will always gain mass on going towards the wide end or the end with less metal, and so, to conserve momentum, the thruster itself must thrust left. The above also looks similar to the horizon drive.

So, let's get a bit more quantitative. A simplified version of the QI thrust formula is

F=(PQL/c) x ((1/w1)-(1/w2))

where F is the thrust towards the end with the massive plate, P is the power input, Q is the quality factor, L is the length and w1 and w2 are the 'widths' of the cavity at the two ends (which affects the amount of Unruh-damping). Now, how can we model exactly the damping of the Unruh waves by the two end caps' thickness? I cannot yet do it in detail, but one way to do it, to predict the maximum thrust obtainable would be to assume that the thin brass cap on the right does not damp the Unruh waves, so the photon can see the cosmos and w2 = the Hubble scale. The other end, being thicker, does damp the Unruh waves so the width (w1) there is roughly the distance between the centre of the dielectric and the middle of the brass end plate. The particular experiment I will look at is Mahood (1999) for which L=0.025m and P=145 W. To estimate Q, I have had to use the dissipation constant of 2% given for another thruster in a report by March and Palfreyman (2006). So Q=2pi x 100%/2% = 314. The thrust toward the large plate end is then predicted (in a very crude way) by QI to be

F = (145 x 314 x 0.025 / 3x10^8) x (1/0.025 - 1/huge)

F = 15x10^-5 N

The observed thrust was 5x10^-5 N (Mahood, 1999) so the prediction by QI is not bad, and far better than Woodward's model which was several orders of magnitude out (according to Mahood, 1999). As expected from the assumptions, the QI prediction overestimates the thrust. This is obviously a very crude calculation, which is why I'm spouting it here, and not in a journal yet, but it is interesting that QI predicts this Mach Effect Thruster, and also of course the emdrive, galaxy rotation, cosmic acceleration...etc. The thruster may allow a new way to test QI, and could be an example of the horizon drive. I do need to look at the other thrusters because I believe some of them were not asymmetric, and build up a more statistically-significant results list for comparison with the predictions of QI.


Mahood, Thomas L. (February 1999). "Propellantless propulsion: Recent experimental results exploiting transient mass modification". AIP Conference Proceedings. Space Technology and Applications International Forum-STAIF 2000, Albuquerque, New Mexico. 458. American Institute of Physics. pp. 1014–1020. Link

Tajmar,M., 2017. Mach-effect thruster model. Acta Astronautica, 141, 8-16.

March, P. and A. Palfreyman, 2006. The Woodward effect: math modelling & continued experimental verifications at 2 to 4 MHz. CP813, STAIF-2006.

Friday, 15 June 2018

Visit to Julich Supercomputing Centre

I was recently invited by Prof. Dr. Dr. Lippert to give a talk about quantised inertia at his Computing Centre in Julich, Germany, and it has proved to be very stimulating. Most of mainstream physics is still in 'shunning' mode, so this was a great chance to talk to some highly-qualified physicists.

After my talk, I chatted with Prof Lippert and an astrophysicist. Their first comment was on precision. In my talk I showed three ways to derive QI. One using Unruh radiation, the second using the uncertainty principle and the third using information and Landauer's principle. There is a fourth thermodynamical way, but I skipped that. The point I was trying to make was that if there are four closely-related ways to derive QI it is a good thing - if all roads lead to the same place, then it is probably somewhere important, like Rome, and this indicates that there is a deeper, unifying, derivation. Prof Lippert made the good point that it would be better to present the best derivation only.

He also said that I should make the point more often that QI provides an explanation for MoND. MoND (Modified Newtonian Dynamics, devised by Moti Milgrom) is an empirical theory (an effective theory) that predicts galaxy rotations but has to use an adjustable constant (a0) to do it. QI predicts MoND behaviour without the adjustable constant, so QI provides a basis and a physical underlying reason for MoND. Instead of the free parameter a0, QI has the unadjustable '2c^2/cosmic_scale', where c is the speed of light, so QI predicts things that MoND cannot, for example: changes of galaxy rotation in the distant past when the 'cosmic scale' was smaller. Also QI can predict MoND but MoND cannot predict QI. Prof Lippert's point was that emphasising the connection to MoND means I can claim all the successes that MoND has had, and also gain allies among the MoNDians who might welcome a physical basis for it (but they may also get annoyed). The bridge here may be Prof McGaugh who has shown interest in QI but is doubtful that Unruh radiation is strong enough (I have shown it is here).

Another useful comment related to my simplified approach. For example, the spin of a solid object would produce a whole range of accelerations since the solid-body acceleration a=v^2/r changes with radius. So to properly model it I need to consider a whole family of Unruh spectra. That sounds like a job for a simulation, and Julich is the place for that. I was shown the supercomputer they have, an impressive setup capable of several Petaflops of processing power. Useful for galaxy modelling or modelling the interaction between Unruh waves and matter (QI) at a more detailed level.

The Julich, JSC is an impressive place. Situated in a beautiful forest, populated by about 6000 staff, several supercomputers, and with a physicists' cafe whose pizzas are all quantised. I wasn't allowed a slice, it was all or nothing. Planck would have loved it.

Vielen dank Prof. Dr. Dr. Lippert. I look forward to many collaborations with you in the future.


The abstract for my talk: Link

Website of the Julich Supercomputing Centre: https://www.fz-juelich.de/ias/jsc/EN/Home/home_node.html

If you wish to support my work a little, you can do so here: