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, 18 January 2023

A Solution for the Hubble Tension.

The sound of an object moving away from you will shift to a lower frequency as the waves from your point of view are spread out. This is the Doppler effect and applies to light waves as well. Edwin Hubble noticed that the light from distant galaxies was red shifted, that is, the wavelength of the light we received from them was longer, implying in a similar way that the galaxies were moving away and that the further ones were moving away faster. This was taken to mean that all the galaxies were moving away from a common centre as if there had been a Big Bang 13.6 billion years in the past. There are other ways to view it as well in QI, but let's stick with this image for simplicity for now.

Looking at local galaxies, the Hubble expansion rate has been measured to be 73 km/s/Mpc. That is, galaxies one megaparsec (Mpc) away from us are apparently moving away from us at 73 km/s. Recently, a new method was devised to predict the Hubble constant from observations of the Cosmic Microwave Background, that represents the cosmos at a redshift of Z=1000, and then extrapolate forward using standard models assuming dark matter and dark energy. Perhaps not surprisingly they predicted a slower cosmos: 67.7 km/s/Mpc. The difference between these values is now beyond a plausible level of chance, so it is a real problem (See Ref).

Now let us calculate what part of this predicted Hubble constant they would miss given that they do not include the extra acceleration due to quantised inertia. It would be 2x10-10 m/s2 over the lifetime of the universe (4.4x1017s) at the cosmic edge (radius = 4.4x1026m). OK. So what would it be at only 1Mpc distance (1Mpc = 3x1022m)?

dH = 2x10^-10 x 3x10^22 x 4.4x10^17 / 4.4x10^26 = 6 km/s/Mpc

The observed discrepancy in the Hubble constant is 5.3 km/s/Mpc. Nice!

For headaches and Hubble tension, just take QI!


Riess, A. et al., 2019. Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM. The Astrophysical Journal, Volume 876, Issue 1, article id. 85, 13 pp.

Thursday, 24 November 2022

On the Cusp?

For the past five months my Chief Engineer (Richard Arundal) and myself have been busy in the lab attempting to prove that one can extract propellant-less thrust from a capacitor by using quantised inertia. QI thrust is implied theoretically (McCulloch, 2013, 2017), but a capacitor approach was first suggested and tested by Becker and Bhatt (2018) who had read my paper on thrust and dielectrics (2017) and did some lab tests in liaison with me. Their work has been seconded by Mansell/IVO Ltd.

Curious to test this approach I used the last remaining DARPA money to set up a lab at Plymouth University, hiring Richard. What we now have in the lab is shown above, with a few details withheld for IP reasons. The capacitor (blue plates with orange dielectric) is placed on an insulating tower on a digital balance on a heavy damping plate. The capacitor is charged up to 5 kV with a HiPot tester (on top) via wires that pass their current through Galinstan, a cool liquid metal that breaks the physical connection to the outside world and allows the capacitor to ‘float free’ on the balance.

For the past month we have been struggling with an unwanted electrostatic force, but we noticed an asymmetry as we flipped the capacitor. Recently I have looked at all the data and used maths (including matrix algebra, that I always wanted to use for something useful!) to separate out the EM force from the asymmetrical one. This extracted force is towards the anode and looks like QI. It is about 10 milligrams, only 1/3 of the force predicted (McCulloch, 2021) but there are good reasons why that might be, and we will now look at those.

In short, unless we can think of another effect that could cause a force towards the anode, then we have it and the transport & energy industry will never be the same.


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

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

McCulloch, M.E., 2017. Testing quantised inertia on emdrives with dielectrics. EPL, 118, 34003.  https://iopscience.iop.org/article/10.1209/0295-5075/118/34003

McCulloch., 2021. Thrust from symmetrical capacitors. Preprint: https://www.researchgate.net/publication/353481953_Thrust_from_Symmetric_Capacitors_using_Quantised_Inertia (submitted to Adv.Sp. Res.)

Thursday, 4 August 2022

Glimpses of QI in the Lab?

Starting in mid-June, Richard Arundal and I have completed 45 experiments, charging up capacitors 4x4 cm in area with either kapton or Polyethylene dielectrics between the plates. We have been carefully eliminating pesky artifacts, through trial and error, along with the appropriate amount of engineering, er, 'jargon', and taking readings with increasing accuracy. Here I summarise the cleanest data we have so far. The plot below shows the change in thrust up the y axis (a positive value is always a thrust towards the capacitor's anode) for eight runs. As we increase the voltage and move along the x axis, each point represents the weight change we saw (in grams) when we stepped the Voltage up by 100V. QI predicts that when we reach somewhere around the breakdown voltage for the capacitor, which is very uncertain but may be around 1 kV for the thin kapton and 1.5 kV for the thicker polyethylene, there should be a thrust towards the anode, ie: a shift up on the graph.

The first two cases shown: x27 and x28 (blue squares) used the polyethylene dielectric (30 micron). In plain English this means 'the plastic from plastic bags', and QI predicts (McCulloch, 2021) that the thrust should be

F = 0.00014IA/d^2

where I is the leakage current between the plates, A is the plate area and d is the plate separation. If we assume that the leakage current = 10^-9 x voltage (which fits what we have seen with our measurements of voltage & leakage current) then

F = 0.00014 x 10^-9 x VA/d^2


dF/dV = 0.00014 x 10^-9 x A/d^2

To convert force in Newtons to grams we multiply by 100 and then by another 100 to get from g/V to g/100V. For the 4x4, 30 micron dielectric then we have 0.002 grams/100V (100V was our increment). This fits the x27 and x28 data (blue squares) as the peak at 1.6-1.9 kV reaches just above 0.002 g/100V. The peak thrust from these two capacitors is at a likely breakdown point.

The other runs show the 7 micron kapton dielectric runs (blue-red circles). Those that do show a positive peak: x38, x43 and maybe x45 show it at 1-1.3 kV which fits because these capacitors are thinner and should break down at lower voltage. From the equation above, the kapton should produce 0.046 grams/100V and that is close to what we saw. The faint box represents the area I expect for the QI thrust. It is uncertain in the x direction as the quoted breakdown voltages of dielectrics have a large range.

One problem remaining is that we do not yet have a perfect example of turning the capacitor over and getting a reverse thrust. We can maybe see that in x37, x45 and especially x48 which were reversed but the peaks are small and these runs were not very clean (x45 was drifting well before 0.1kV was reached). x48 gave us a sustained peak at the right time, but there was a brief glitch while powering up.

In summary, we have a few positive peaks which are encouraging. So is the fact that the kapton runs show both a lower break down voltage and a higher thrust than the polyethylene. Are these peaks due to QI? If so, the world has changed, but time will tell. We need a good clean reversal of force. Richard Arundal has been excellent - he is a skilled engineer who does not give up. Please go and see his youtube channel linked below. The last six weeks have been a roller coaster, but with a slow geological scale uplift.


McCulloch, M.E., 2021. Thrust from symmetric capacitors using quantised inertia: https://www.researchgate.net/publication/353481953_Thrust_from_Symmetric_Capacitors_using_Quantised_Inertia

Arundal, R., 2022. https://www.youtube.com/channel/UCO00nPk5WkpV0ggLGLnHHiQ

Saturday, 9 July 2022

How to (Maybe) See QI in Your Lab.

NOTE: Only act upon this if you have experience with high voltages.

Here is a practical way to (maybe) see QI thrust at home. I've been musing about using Unruh radiation and QI for thrust for 17 years in my theoretical papers (McCulloch, 2008, 2013) but the capacitor method was proposed by Frank Becker and Ankur Bhatt (2018) and has since been improved by several people, many of whom wish to remain anonymous, but they especially include my post-doc & my research assistant Richard Arundal. Here I describe the thruster we are testing at Plymouth University.

1. The QI Sail / Horizon Drive. A capacitor should be built consisting of a dielectric layer 10-20 micron thick made of kapton (or Krapton as Richard calls it - very fiddly to handle) or polyethylene, and 6x6 cm in area. This is sandwiched between two 4x4 cm aluminium foil plates, finely sanded in their inward facing sides to make sharp 'peaks' to encourage the field emission of electrons. Copper plates, of about 2x2cm are added outside these plates in electrical contact, and power wires are soldered to these copper plates.

2. The power supply can be a 12V battery, but converted up to, 1kV, by a DC to DC converter. There are many other methods. The power is applied to the capacitor. Take care. In our case we slowly ramp up the voltage over 20 minutes, and then slowly discharge the capacitor at the end. The important thing is to have a potential difference between the plates of about 1-2kV, and make sure the dielectric reduces the current across itself to a so-called leakage current on the order of a microAmp. This ensures that the electrons are 'jumping' across at a very high acceleration and therefore see Unruh waves short enough to interact with and be damped asymmetrically by the metal plates. The plates damp the Unruh waves causing a gradient in the field that causes a push (McCulloch, 2021).

3. Place the setup on a balance capable of measuring to 0.01g. Ideally the setup should be self-contained, but this is hard to do. We hope to see forces too large to be explained by interactions between the current & the Earth's magnetic field, for example. These other effects can be calculated anyway.

4. You may want to use a vacuum bag, evacuated of air, around the capacitor to reduce the chance of air pockets in the gaps, which can cause tiny explosions (you see little <1mm punctures in the foil and hear a popping). Also, try to make sure the desk you use is stable (leaning on it can cause a reading) and there are a minimum of conductors nearby. Place a shield around the setup to reduce air flow.

5. Switch on, ramp up the power, watch the balance. If the capacitor anode is facing up, you may see a force down, an increase in weight, since the copper plate below the capacitor is damping the Unruh field below and the drive will move down towards the damped part of the vacuum, or the horizon (which is the copper plate). In our 22 tests so far 14% of them have shown a thrust. See plot below. The rest showed no thrust, suggesting that electrostatics is not a problem). For a theoretical explanation of what is happening, see McCulloch (2021). The QI force you should expect is given by F = 0.00014IA/d^2 where I is the leakage current, A is the plate area and d is the plate separation. For videos of the setup see Arundal (2022) and other videos on his youtube channel.

6. Since I am sharing this information openly, please do the same and tell me about your results. Also, take great care, and it is best if you try this only if you have experience of high voltage. 1kV is not trivial.

7. Enjoy being cutting edge! You are now a Horizoneer.

Plot: Our three positive thrusts so far. The thrust (y axis, in grams) increased with voltage (x axis, kV), until in the first two cases (grey and blue) it reduced & there was a fizzling as the dielectric burned out.


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

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

Arundal, R., 2022. Podcast on recent build: https://www.youtube.com/watch?v=sB3pqlHvA_s

McCulloch, M.E., 2021. Thrust from symmetric capacitors. Preprint: https://www.researchgate.net/publication/353481953_Thrust_from_Symmetric_Capacitors_using_Quantised_Inertia

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).