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

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

Saturday, 13 March 2021

Bend Light, Not Space

I feel like I am now entering the end game, which probably just means my troubles are just beginning. For a while now I've had a theoretical goal that can be boiled down to two things:

1) Reproduce the bending of light by the Sun, just like general relativity.

2) Retain the ability of quantised inertia to predict MoND-like behaviour in galaxies.

It was Alex Unzicker's books (especially "Einstein's Lost Key") that convinced me that the best way to do this would be to focus on a curious path followed by Einstein in 1911-1912 just before he was persuaded away into untestable geometry by Marcel Grossman. While in Prague Einstein devised a version of GR that treated space as if it had a refractive index. The idea was that the speed of light c=fL reduces close to masses because relativity reduces both f (frequency) and L (wavelength) there, and so light beams bend around the Sun twice as much as Newton would have predicted. Unfortunately, at the time he forgot the reduction in L and predicted only half the correct bending of light. This error was corrected by Dicke in 1957 but by then it was too late and the later geometrical-tensor GR had taken over because it was not stymied by the factor of two error.

To agree with the data on light bending by the Sun (data: the only important consideration), the correct theory must predict this equation for the speed of light c a distance r away from a mass M:

For a lot of last year, on and off, and for several weeks this year I have been trying to get this relation from QI. I did it last year and rejected it for various intuitive reasons. Last week I did it again and realised that it was the right way! The solution is obvious and beautiful in a way that cannot be explained until you actually see it, but it's not published yet so I can't tell you the whole story.

What quantised inertia says is that the zero point field (and its energised version: Unruh radiation) close to matter is damped (reduced) so light bends towards the matter, sliding down the zpf gradient. This gives Newtonian gravity (see my 2013 paper), but in QI we also have to consider the cosmic horizon of the light which reduces the inertial mass of the photons even more than expected so they bend towards the Sun twice as much as expected. It all works out nicely and gives the equation above. The great advantages of the new QI dynamics are that it gets rid of dark matter, it predicts cosmic acceleration and practical thrust and, unlike bent space which cannot be directly tested, it could be directly tested by measuring the zpf in different places with, say, a Casimir probe.

Given the lab results that are starting to come in (see my blog last month) and this latest theoretical result I expect breathless requests for zoom presentations will come flooding in from physics departments all over the globe! (I always like to end on a humorous note).


McCulloch, M.E., 2013. Gravity from the uncertainty principle. Astrophys & Space Science, 349, 957-959. Link to Pdf

Unzicker, A., 2015. Einstein's Lost Key.

Saturday, 6 February 2021

Horizon Engineers

In 2017, an electrical engineer called Frank Becker contacted me, saying that he'd read my papers on quantised inertia and the emdrive and he particularly noted my discussion that dielectrics placed inside an emdrive might enhance thrust. It reminded him, he said, of an experiment that he'd done years ago trying to replicate the Biefeld-Brown effect with tin foil capacitors and dielectrics. Indeed he had seen thrust towards the anode just as Biefeld & Brown did.

After he emailed me, we liaised on occasion via skype, and the following year or so he teamed up with an actor called Ankur Bhatt who also has an MSc in engineering and they did some Frank-ly (forgive the pun) brilliant experiments. I advised them as much as I could on QI. A schematic of the experiment is shown in the Figure and you can find the details in the paper below. The capacitor plates are on the right hand side (the grey lines). You can see the electrons accelerating to the right from the cathode to the anode (red arrows).

The electrons accelerate to the right over an inter-plate distance of 10 microns and a potential difference of 5000V, so their acceleration is huge (10^19 m/s^2) so they see a Rindler horizon only about 2 cm to their left (the black line). Normally in QI, when an object accelerates rightwards the Rindler horizon on its left damps the quantum vacuum on that side pulling it back against the acceleration. But, here, this is reversed since the two plates damp the vacuum to the right (a Casimir effect) more than the horizon does. The yellow shading here denotes less vacuum energy than the orange shading. So, here there is an extra push to the right and the electrons accelerate more than you'd expect, pushing the anode more when they get there.

The most crucial component of this experiment is that Becker and Bhatt also played around with  putting metal plates in various positions around the setup (Edmund Blackadder - "It's not what you've got, but where you stick it!") and found that when they placed a metal plate to the right of the horizon it reduced the force (it's like a closer horizon) but when they put the plate behind the horizon (to the left) the effect of it vanished. This may be the first direct observation of a Rindler horizon and backs quantised inertia very strongly. I've just written a paper, soon to be submitted, that shows that QI predicts the thrusts they saw.

Becker & Bhatt deserve a lot of thanks for this experiment. If the thrust can be confirmed, it is one thousand times what I was hoping for from my photon-based experiments. I am now funded to reproduce their experiment at my university, starting in May.


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

Sunday, 11 October 2020

Patreon Site

I'm trying an experiment on Patreon. I'm publishing two chapters per week of my sci-fi comedy novel, based on quantised inertia, and I'm also trying to write entries on the other days on whatever physics I happen to be thinking about at that time. A sort of online science diary. As my position in academia is becoming a little tenuous I thought this might be a good plan B, or a way to transition to more independence. The first chapter of the story is at: https://www.patreon.com/posts/38133557 I hope you enjoy it!

Wednesday, 30 September 2020

Consider an Owl

I've just published what is possibly the most elegant paper I have ever written. I sent it to various journals who all turned their noses up at it (one sympathetic editor told me that reviewers were refusing to review it en masse) so thank you to Advances in Astrophysics for giving it a home. In it, I derive quantised inertia in eight lines from information theory, just by assuming that information is stored in Planck-length spaces.

Consider the diagram below. This represents, in one-dimension, an object (say, an owl) by the thicker vertical dashed line on the left. Initially the owl is just sitting there so it sees the cosmic horizon on its right, the right-most vertical dashed line. The owl has a lot of information about space. The Planck length is the smallest region of space in which information can be stored and in the diagram (not to scale!) Mr Owl can see 26 bits of space. Then imagine someone rudely moves him abruptly to the left. Suddenly information cannot catch up to him from far to the right and the horizon he sees moves closer - see the middle vertical line. Now the owl can only see nine bits of space.

This is a loss of information, and according to Landauer's principle, it also counts as a loss of entropy, just as deleting a computer memory would. This is a huge no-no from the point of view of thermodynamics - entropy must always go up. In the paper I show that if you calculate how much energy is released to Mr Owl in this case, it is exactly the amount of energy needed to produce, not just inertia, but specifically the form of inertia of quantised inertia, which models galaxy rotation without dark matter and predicts cosmic acceleration.

Now, of course, this example is only one-dimensional but I think it offers a new, simpler and deeper way to understand quantised inertia, and derive it. I hope that information theorists will pay attention. It is a sign that their subject is just about to conquer the rest of physics. Welcome to a new branch of physics. And the owl? Understandably, he's chosen a new branch to sit on. Higher up in the tree.


McCulloch, M.E., 2020. Quantised inertia and galaxy rotation from information theory. Adv. Astrophy., 5, 4. http://www.isaacpub.org/4/2050/5/4/11/2020/AdAp.html

Tuesday, 8 September 2020

The Ball and the Teapot

Imagine a ball in space. Strictly speaking in physics and especially in quantised inertia you can't start talking about it being stationary or not because it has to be moving relative to some other object, so let's say it's static relative to a nearby teapot, but far enough away that the attraction from the teapot is small.

Now put a horizon on one side of it. According to quantised inertia this will damp the Unruh waves from the direction of the horizon and so the ball will be pushed by the imbalance in the Unruh radiation field towards the horizon. Another way to think about the same thing, the informational way (see reference) is that the horizon deletes the knowledge the ball has about the cosmos beyond it. Landauer's principle says that every time you delete information, say, you erase 101011 to 000000, then entropy decreases. That cannot be allowed, so the second law of thermodynamics says that high-entropy heat energy must appear to compensate. So computers get warm when you erase data. I've calculated this energy for the deletion of space, and it turns out to be just enough to power the movement of the ball predicted by quantised inertia (see ref).

So the ball accelerates towards the horizon. Now, as pointed out by several people online or in emails, what happens if suddenly the horizon disappears so the ball gets back all its knowledge about the cosmos behind it? The problem is, it still has the kinetic energy it picked up from the loss of information. Does it lose the energy when it gets the information back? The answer is not necessarily "Yes", because although the second law of thermodynamics says that 101011->000000 must release energy, there is no such imperative for 000000->101011, since there is no drop in entropy.

Can we use this asymmetry, and repeat the process to generate energy? I think that is what is happening with the cycling photons (near and horizon, then far..etc) in the emdrive. However, this brings up many fascinating new questions to ponder. Where is the information 'stored' while the horizon is close, so the system can get it back when the horizon is gone? Can information or heat be swapped between reference frames? How does this relate to the black hole information paradox?

Getting philosophical for a moment it makes sense that our new ability to model worlds ourselves (simulations, games) is inspiring new models of the one we are in, including my recent attempt to express quantised inertia using information theory. Is it just the latest useful analogy? (Probably). Is the cosmos a self-evolved bit-system? Or are we in a deliberate simulation? I'm sure the theologists will spend many a happy hour discussing that!


McCulloch, M.E., 2020. Quantised inertia, and galaxy rotation, from information theory. AdAp (accepted). Summarised in my ANPA talk here (the relevant bit starts at 16:24)

Thursday, 3 September 2020

What I said to Wired

An article has just appeared in WIRED about Woodward's theory. The author Daniel Oberhaus emailed me a couple of weeks ago asking my opinion of Woodward's work and he quotes me in the article as saying "In my opinion there is no merit to Woodward's theory". See this link for the article. This quote is a 'slight' truncation of what I said :) See his questions in bold, and my answers below:

Wired: How would you sum up your feelings about Jim's theory in a sentence or two? Is he crazy or is there merit to his ideas?

In my opinion there is no merit to Woodward's theory. It shares the problem of most of modern physics that it is constrained to work within the framework of general relativity so the derivation is complex and contrived and contains many unlikely assumptions and even some arbitrarily added factors, and yet it is still orders of magnitude away from predicting the Mach effect thrust it was intended to predict! The Mach Effect experiments are interesting but we have to consider the possibility that they are vibrational artefacts.

Wired: There's clearly a lot of skepticism around Jim's Mach effect theories. If you count yourself a skeptic, what don't you buy about this theory?

There are many theoretical problems with it, see eg Rodal 2019 and in going through the derivations you see that a lot of arbitrary factors are added in. However, my main reason for disregarding it is that it does not work. It fails to predict even the lab observations it was designed to explain - its predictions of observed thrust have been shown to be a factor of one thousand times out (eg: Mahood, 1999). I note that in the papers written about it the data is rarely compared with the observations directly.

Wired: What would it take to convince you that it was correct, if anything?

To convince me it would need a simply-derived non-arbitrary formula that predicts all the Mach Effect thrust experiments and a demonstration that the thrust varies as expected given the parameters in the theory, to rule out artefacts. So pretty much the opposite of what has happened so far.

Wired: Jim's been claiming to have produced propellantless propulsion for years. Do you think these results are real, or just noise / measurement error?

I think the experimental results are more interesting than the theory, but there is a significant possibility with vibrating solid objects that artefacts can occur (as seen with the Dean drive).

Wired: If not Mach effects, what do you think is a better explanation for what could be producing this apparent thrust? Why do you feel its a better explanation?

Vibrating objects have artefacts that can appear to be thrust. If the thrust is real then it does not seem to agree with the Woodward theory anyway. I have suggested the theory of quantised inertia (McCulloch, 2007) which predicts galaxy rotation without dark matter and predicts some, not all, of the Mach effect tests (McCulloch, 2018). 


Rodal, J.A., 2019. A Machian wave effect in conformal, scalar–tensor gravitational theory. General Relativity and Gravitation, Volume 51, Article number: 64.

Mahood, T., 1999. Propellant-less propulsion: recent experimentla results exploiting transient mass modification. AIP Conf proc. STAIF-2000. AIP, 1014-20.

McCulloch, M.E., 2007. Modelling the Pioneer anomaly as modified inertia. MNRAS, 376(1), 338-342. 
McCulloch, M.E., 2018. Propellant-less propulsion from quantised inertia. J Space Exploration, Volume: 7(3).