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 & some observed lab thrusts 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, 4 May 2022

The Black Hole Information Paradox

The cosmos, empty space, is known to be full of virtual particles. They appear in pairs to conserve momentum and then recombine after a short while. In 1976 Hawking showed that black hole event horizons can separate these pairs by trapping the one on the wrong side of the horizon. The star-crossed lovers are unable to recombine, so one of them becomes real and is emitted as Hawking radiation. This means that whereas black holes can hoover up information-full objects such as flowers and manuscripts (see below left), they can only emit thermal, random, Hawking radiation (see below right). This means the information in the flower and the manuscripts has been lost.

Hawking, Kip Thorne and Roger Penrose were perfectly happy to have information destroyed, but Leonard Susskind and Gerard t’Hooft published a manuscript called The Black Hole War saying that Hawking was violating one of the laws of the universe: the conservation of information. Since when has that been a law? They argued that in quantum mechanics the wavefunction at any one time is supposed to be predictable from the wavefunction at any other time and if you lose information then you can't do that. You lose what they call the unitarity of the wavefunction. They suggested that the information that goes into the black hole survives and proposed the holographic principle which says that information is stored in horizons (a nice idea). Hawking conceded he had lost but Penrose and Thorne did not concede. In my opinion, there may be some merit to both approaches, if combined right.

The debate is at the heart of physics, which has still not come to grips with the new concept of information, but let us see what empiricism and a little logic can offer. Landauer’s principle (reference 1) argues that when computer memory is erased say from the complex 11010 to the uniform 00000, then this is a loss of information, and a reduction of disorder or entropy, which cannot be allowed, so heat must be released. This heat has now been observed (ref 2) whereas the 'unitarity of the wavefunction' has not. One point for information loss. Another point is that quantised inertia (QI) and therefore the observed galaxy rotation without dark matter can be derived beautifully by assuming information loss (ref 3).

The picture is not complete though. In QI, if you accelerate, a horizon obscures your backwards view of the world, erasing information and providing, via Landauer, exactly the right amount of energy to fuel the inertial back-push (ref 3). However, if you stop accelerating, then that information comes back again. Where was it hiding in the meantime? The QI approach may offer a compromise here since accelerating objects see Unruh radiation that inertial (unaccelerating) observers do not. In QI information is in the eye of the beholder. Each object has its own informational universe, and what has been deleted in one may be retrieved by negotiation from another.


Landauer, R., 1961. Irreversibility and heat generation in the computing process. IBM J. Research and Development. 5, 3, 183-191.

Hong et al., 2016. Experimental test of Landauer's principle in single-bit operations on nanomagnetic memory bits. Science Advances, 2, 3, e1501492 Link

McCulloch, M.E., 2020. Quantised inertia, and galaxy rotation, from information theory. Adv. in Astrophysics, 5, 4, 92-94. Link

Sunday, 23 January 2022

Learning from Experiments

It's a tricky thing taking a cosmological theory (QI) and applying it to the lab, applied cosmology, because although I am sure of QI from a theoretical and astrophysical point of view because it predicts galaxies and wide binaries in a simple and specific way, its behaviour in the lab is more subject to detail.

That was the reason I received my funds, to see if it could be done. The data from the project has partly changed my mind about solid state details, but I have not changed the fundamental QI theory.

I had originally thought that the best way to get thrust from QI was to use light or microwaves. Light is clean. The photons will see Unruh waves which will be damped by metal structures asymmetrically and the structures will move toward the damped regions. It turned out that QI thrusters based on light alone did not perform well (Tajmar, 2021) and yet QI thrusters that are based on electrons did (the capacitor approach of Becker and Bhatt, 2019). I have thought a lot about this over Christmas, and going back to the QI equations there is an explanation for this in that light, is well, light (it has very little mass), and it does not stick around in cavities for long so the mass-energy you can focus is low, whereas electrons have much lower speed and more mass, but still high accelerations and so the mass-energy you can focus is much higher. Thus thrusters based on electrons are 1000 times more effective and QI predicts them perfectly (see McCulloch 2021). Look at Eq. 2 in this paper. The problem was caused by me earlier assuming that v=c, not so for electrons! When you use the correct speed, you get this plot:

The graph shows a comparison between QI predictions (x axis) and the various experimental thrusts (y axis) from Shawyer, Tajmar, Madrid and Moddel. QI still predicts the emdrive  (top right), which may now not be due to the Unruh waves from the microwaves but from the Unruh waves seen by electrons accelerated by the microwaves in the metal walls, if you make a resonance. This makes no difference to QI mathematically, but it is a different physical interpretation. It accounts for the effectively zero thrusts seen by Tajmar's team for the laser cavities (bottom left) and the tiny but confirmed force seen in Moddel's photoinjector. It implies that the positive Spanish result was an artefact (middle-left) (unless the electrons in glass were the accelerand) and QI predicts the capacitor results perfectly (top right): results now seen in two labs.

It would have been nice if I could have said this years ago, of course, but QI has been since 2005 a learning experience and I am doing the best I can. For example, my first attempt at galaxy rotation in 2006 did not work because I assumed the only accelerations were rotational. I later learned there are other accelerations, and with more detail - better prediction. Over all this time I have not needed to change the QI theory or the maths, but I have changed the detailed understanding of what is going on. I am not adding arbitrary factors either because the behaviour of stars or electrons are known quantities.

QI has not been falsified. In systems where it is the only factor present, such as galaxies or wide binaries, it performs perfectly. In lab applications, my lack of awareness of physical or engineering details has been a problem, but I am willing to be wrong and therefore to learn.


Bhatt, A.S and F.M. Becker, 2019. Electrostatic accelerated electrons within symmetric capacitors during field emission condition events exert bidirectional propellant-less thrust. https://arxiv.org/abs/1810.04368

Neunzig, O., M. Weikert and M. Tajmar, 2021. Thrust measurements of microwave-, superconducting and laser type emdrives. Link 72nd IAC, Dubai.

McCulloch, M.E., 2021. Thrust from Symmetric Capacitors using Quantised Inertia. https://www.researchgate.net/publication/353481953_Thrust_from_Symmetric_Capacitors_using_Quantised_Inertia

Tuesday, 2 November 2021

A Thrust from 'Nothing'.

In a small lab in Plymouth, a new quantum thruster is taking shape. I have been theorising about getting thrust from quantised inertia and trying to work out how best to do it for DARPA (see ref 1). With Prof Perez-Diaz we managed to get a few microNewtons out, and I had considered asymmetric plates, but engineer Frank Becker read my papers, remembered a capacitor-based Biefeld-Brown-type experiment he had done, and with a few discussion with me, he and Ankur Bhatt tried it and produced milliNewtons of thrust (see ref 2). This test made my year. Even DARPA emailed me saying something like "What the heck is this!?". One problem was that they had used a high voltage with a digital balance so there was a potential for glitches. Then Richard Mansell of IVO Ltd tried it with an analogue method and agreed with them. This new Mansell group has also blazed the path in innovation as well.

In its simplest form, anyone, with a little care for safety, can try this experiment. If you have a humble desk and a power socket then the cost is £800. I know because I've just spent that much on it! Not bad for a technology that promises to revolutionise just about every industry we have: satellites, rockets, cars, energy...etc. The trick is to ensure no artefacts, and that we hope to do at Plymouth.

The method is to setup a potential difference of 5kV between the plates of a capacitor, and separate them by about 10 micron with a dielectric. You then allow electrons to quantum tunnel across the gap at a very low current (1 microAmp) but at a massive acceleration. The theory of quantised inertia says that they will see a field of nice hot Unruh radiation everywhere, except between the capacitor plates, as for the old Casimir effect. There will be then a quantum void between the plates that will pull the electrons out of the cathode faster than expected and this will add momentum to the system which will thrust towards the anode. A thrust from 'nothing'. As you can see in the theory paper below (ref 3), QI predicts the results of Becker and Bhatt and Mansell exactly, even the changes as you vary the plate separation.

I'm glad that my openness about QI theory and its possible applications, partly in this blog, encouraged talented engineers to contribute because in my opinion they have shaved years off the path to QI application. This includes the above-mentioned folk, but also many on twitter and many who made comments here. My question is, what is my role now? Of course, I will continue to develop the QI theory, and I have two novels describing it written, and a second text book in the works, but my DARPA funding ends at the end of 2022. I hope to give DARPA a quantum thrust of 10 mN by then. What then?

What I'd like to do is to maintain freedom to continue to develop QI, to write about it, to not starve (!) and not have to be too distracted with business! One possibility would be to setup a Horizon Institute (HÎ)? Perhaps more like a Federation of Labs. The idea would be to use crowd funding or Venture Capital funding to provide support to labs developing QI thrusters, space & interstellar tests and new energy sources based on it, provide advice based on QI, and also a testing facility. In the present era it might be best outside academia? There are already two university labs (In California and Texas) crying out at me for money to start their experiments. As usual, I can see the horizon but not the detailed path to get there! Please make comments below - you might get us to Proxima Centauri quicker!


McCulloch, M.E., 2018. Propellant-less propulsion from quantised inertia. J Space Explo, Volume: 7(3). https://www.tsijournals.com/articles/propellantless-propulsion-from-quantized-inertia-13923.html

Becker, F. and A., Bhatt, 2018. Electrostatic accelerated electrons within symmetric capacitors during field emission condition events exert bidirectional propellant-less thrust. https://arxiv.org/abs/1810.04368

McCulloch, M.E., 2020. Thrust from symmetric capacitors using quantised inertia. https://www.researchgate.net/publication/353481953_Thrust_from_Symmetric_Capacitors_using_Quantised_Inertia (Submitted to JPC).

Tuesday, 12 October 2021

The Mayflower Institute?

The big change since I last wrote is that I have a new post-doc (Dmitri) who is tasked with testing for QI thrust right here at Plymouth. I'm pleased with him. He has suggested that, since we are dealing with radical new physics, our testing methods should be as conventional as possible. I like to call it the Caesar approach - Julius Caesar was seen to be too flashy by his stolid Roman peers so he made his memoires deliberately dull. Anyway, Dmitri has comprehensively studied the field of small thrust measurement, looking at techniques from the UK's NPL and the US's NIST and other esteemed places and has suggested a torsion balance method, in a soft vacuum, with an electrostatic or electromagnetic force source and capacitor transducers. He has produced a beautiful design which will take five months to build. In the meantime, I have many other labs to keep me occupied and the goal now is to enhance the thrust so it is above the noise. One of my funders said something like:

"We'd like to see it floating over the desk, rather than just over the noise". That goes for everyone I guess.

Dmitri and I have also discussed setting up an more permanent thrust-test program here. I'd like to go further and set up an institute, not just for studying QI thrust, but to go all the way from lurch to launch. An Institute for Horizon Science and Engineering? (IfHSE) pronounced "Ifs". A good word for a testing centre? Or perhaps, alluding to Interstellar Possibilities, the Mayflower Institute as I have been discussing with my friend Bill Smith who visited me last week. Exactly how to do this is not clear yet.

Tuesday, 27 July 2021

How to Predict (Almost) Everything

Well, my title is a little cheeky but I think it's fair to say that if physicists and engineers actually knew what quantised inertia predicts, that they just can't, then they'd start work on it tomorrow. So here is a sort of abridged summary:

QI predicts the recently-observed cosmic acceleration perfectly without needing any infusions of invented dark energy. QI explains why the universe is flat (PE=KE) and always has been, so gets rid of the need to imagine our particular era is 'special'. QI predicts the value of the gravity constant G from the cosmic mass and scale and speed of light. This means that physics has lost a free parameter and has become simpler for the first time since 1905. QI predicts galaxy rotation, and specifically why the oddities always begin at a particular acceleration. MoND has to input this acceleration, QI does not - it predicts it itself. QI further predicts the observed variation of this critical acceleration with cosmic time. QI predicts the low-l CMB anomaly in which it looks like the longest waves in the cosmos are smoothed out, and the CMB peaks as well, but not their heights. It predicts a relation between the area of something and its mass. QI predicts the first, and a few others of the quantised redshifts seen by Halton Arp - the others may appear when we look at other electron transitions. It shows why the Magellanic clouds appear to have broken free of the Milky Way but have left a 'stream' behind them that curves around the galaxy implying they are still bound. QI predicts the motion of wide binary stars which show identical anomalies to galaxies when they are far apart, and orbit below the critical acceleration. Dark matter can't explain them because it can't be packed into the small scales of binaries and still predict large galaxies. You can't have it both ways, so dark matter can now hit the road. QI predicts the very beautiful shape of Hoag's object which is almost like a poster child for the theory. It predicts the orbit of our neighbour Proxima Centauri, which is orbiting far too fast, just like those wide binaries and the larger galaxies. QI predicts the bending of light by the Sun, just as general relativity does, but it is successful with galaxies too, which GR is not. QI predicts relativistic jets in galaxies and so gets rid of the contrived & complex, and conveniently invisible, black hole explanation. QI predicts the Casimir effect, the emdrive, Mach effect thrusters and the asymmetric and symmetric capacitor thrusters that half the planet thinks are hoaxes and half think are the saviours of mankind. It predicts some aspects of the Podkletnov gravity shielding effects, which are much maligned but were published in good journals and have not yet been falsified. QI predicts the test results from my lab in Spain who observed thrust from a laser loop, shielded on one side. If this is confirmed then we become an interstellar species, which would be timely! QI predicts the photons seen coming out of the Dynamical Casimir Effect. It provides an explanation for cold fusion, or LENR if you prefer, and for the excess light seen coming out of nanocavities. A new source of energy from the vacuum? Similarly it predicts sonoluminescence. QI provides a new way to understand pair production and it predicts the ratio between the proton and electron mass, and the Planck mass. QI provides the first ever intuitive explanation for inertia which has always been brushed under the carpet in physics.

To finish, QI is conceptually challenging but technically very simple & can be used to predict a massive range of phenomena. I am writing a book to detail all this which might be called 'The Empiricist Strikes Back' or 'How to Predict (Almost) Everything'. Now I should say that of course I do not necessarily believe every anomaly listed here, but I think this list, which has taken me 15 years to present, implies something!

Sunday, 6 June 2021

Whose Hand on the Tiller?

Here is a Letter I just emailed to New Scientist. I doubt they will publish it so I am putting it here to avoid having wasted my time:

In 2007, I started to publish peer reviewed papers suggesting a new theory called quantised inertia which predicts disc galaxy rotations without dark matter, simply and without adjustment. I've published 25 peer-reviewed papers on it and I am now funded to test its predictions of propellantless thrust, but I have had difficulty getting the message out. The arXiv publishes preprints of papers before they appear in journals, but its anonymous editors have refused to publish some of my papers even after they were published in good journals. Those it did accept, it hid away in a section called 'general physics' which is a sort of naughty boys' room that few people look at. Anonymous people also wreak havoc on wikipedia & google. When you search for quantised inertia, you find excoriation, whereas in reality there is far more evidence for quantised inertia than for dark matter - though admittedly that is not difficult since dark matter has no evidence at all. Scientists use these public sources for their convenience and make decisions based on them so it is not right that anonymous people, who could be unqualified, or with a conflict or interest, are having such an impact on research that has been through rigorous peer review. We have to reinstate the scientific method or we may be manipulated into making the wrong decisions.

Tuesday, 27 April 2021

Response to Tajmar's New Cavity Results

First of all, there is no criticism of Tajmar's team here. Their work ethic & professionalism have always been impressive and their results are useful, as you will see. The problems that have arisen are my fault, and probably caused by not demanding detailed schematics before the experiments.

I employed the Tajmar group, to test quantised inertia as part of my DARPA project. They manufactured several very attractive copper and silver cavities. All of them had asymmetric distributions of metal to asymmetrically damp Unruh waves and hopefully cause thrust. A laser was fired into each and a sensitive double pendulum balance was used to detect very small (nanoNewton) forces.

Unfortunately, and I did not know this until I read their paper last month (mea culpa). On page 7 they say “every copper [and silver] cavity was encapsulated in an aluminium case, similar to the beam trap mentioned earlier to reduce heat radiation to balance components”. The problem is that the addition of a symmetric metal box will cancel the thrust from quantised inertia. Here is a schematic to explain.

Figure (a) shows an incomplete understanding of quantised inertia. The Unruh waves seen by a highly-accelerated object (photon, black circle) in an asymmetric cavity are more energetic (hotter) at the wide end (red), and cooler at the narrow end (blue), so an internal object is pushed left, but the cavity is not: any forces are only internal. A better picture is (b): the Unruh waves seen by the accelerated object also exist outside the cavity which is partially transparent to them and therefore the cavity ‘falls down’ the Unruh gradient. This is how quantised inertia predicts thrust. In case (c), representing Tajmar’s copper or silver cavity tests, the cavity is inside a metal box so there will be a push (see colours) between the cavity & box but friction stops movement. QI predicts that the combined cavity+box must show no or much less thrust: there’s no background gradient.

Tajmar's thrust results indeed show no thrust. It is important to point out that none of the results I'm going to discuss now are significant since the error bars are about the same size as the values, but please look at this graph which I made to summarise Tajmar's thrust data. The x axis shows the expected photon thrust from the laser (F=P/c). The y axis shows the observed thrust minus the expected photon thrust. So dots above the x axis show the thrust we hope to see.

Firstly, most of the points are above the x axis, so there is slightly more than the photon thrust (but not significantly). This might be expected since all of the cavities, no matter what their geometrical shape had a thicker wall in the positive thrust direction, and quantised inertia predicts more Unruh damping in that direction which predicts a positive thrust. This 'wall thickness' effect should be more robust to the addition of the metal box than the variations in the geometry of the cavities which are thin walled, like the metal box.

Second, the silver cavities (labelled Ag) show more ‘thrust’ then the copper (Cu) ones. This is interesting & makes sense because the Q value for Cu was 9 and for the Ag it was 39 (silver is more reflective) so we would expect 4.3 times the energy to be present in the silver cavities and 4.3 times the thrust from them. The average thrust is shown on the plot as the narrow dashed line for copper at .05 nN and 0.16 nN for silver. The factor is 3.2.

Again, these results are all smaller than the errors, so we cannot say anything solid from them. Yes, I know, excruciatingly frustrating, blame me, but given that the cavities were inside a metal box, it's the best we can hope for from this data and on this blog I will give you the real deal, not just the slam-dunk stuff. The next step will be to do the same tests without a metal box while also trying out the capacitor method of Becker & Bhatt which is perhaps 1000 times more powerful.

The true path never did run smooth!

I thank the Tajmar team because these results are very useful.


Neunzig, O., M. Weikert and M. Tajmar, 2021. Thrust measurements and evaluation of asymmetric infrared laser resonators for space propulsion. SP2020+1, March 2021. Link https://www.researchgate.net/publication/350108417_Thrust_Measurements_and_Evaluation_of_Asymmetric_Infrared_Laser_Resonators_for_Space_Propulsion