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

Monday, 23 April 2018

Conservation of EMI

I'm always looking for ways to simplify quantised inertia since it is not the easiest concept to get across, and also simplification usually leads to a deeper understanding. My usual argument using Unruh waves and horizons is equivalent to what follows below, but there is now a simpler way to frame quantised inertia, which I published in 2016. First of all, just as Einstein assumed that physics should not be frame-dependent, quantised inertia assumes that physics should not be scale-dependent. To explain: a huge entity the size of a galaxy (say) should agree with us on the physics it sees. Therefore, Heisenberg's uncertainty relation (below) should apply to stars too


This is illustrated by the diagram which shows a large object (black ball) and its uncertainty in position (solid envelope) and momentum (dashed envelope). Since hbar must be kept constant, then the more an object knows its position (dx smaller, the solid line is closer to the ball) the more it does not know its momentum (dp is bigger, the dashed line is further from the ball).
Now let us forget for a moment that quantum mechanics and relativity usually get on like two cats in a bag, and combine them. If the object accelerates to the left (red arrow) then information from far to its right can never catch up and a relativistic horizon (like a black hole event horizon) appears at a distance of


in the rightward direction (see the solid right-angle). So the uncertainty in position is reduced since the object's space has been curtailed from the cosmic scale to a scale 'd'. As a result, the uncertainty of momentum to the right is increased (the dashed line is far from the ball) and the ball will jiggle more rightwards: against its original acceleration. This predicts the inertial force (blue arrow) in the modified form needed for quantised inertia, and so it predicts galaxy rotation without dark matter and cosmic acceleration without dark energy. QI is, simply put, the quantum and relativistic equations shown above rammed together in the way shown in the diagram. To put it more physically: new mass-energy (dp) appears if information about space (dx) is curtailed. Put another way: what is conserved in nature is not mass-energy, but M-E plus information (conservation of EMI).

Now imagine putting a large mass next to an object. To some extent this mass will block information from that direction, reduce dx in the uncertainty principle and increase the momentum (or quantum jitter) that way. The two objects will then jitter-themselves together. This looks very much like gravity, and in the 2016 paper I show that you get Newtonian gravity from it. To get something like general relativity (in a QI form) the same derivation will have to be done fully relativised.

Now imagine that instead of putting a large mass next to the object, we put an information horizon there that reduces 'dx' in that direction and increases the quantum jitter (dp). The object should see a thrust. Since quantum waves are partly electro-magnetic, a conducting metamaterial should do. In my opinion this has already been seen in the emdrive, since QI predicts it well, and everything I have published over the last 11 years implies that this new thrust is possible. Can it be powerful enough to oppose gravity? I think so. Good news: solid lab tests are coming.


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

Monday, 5 March 2018

A paper on QI & cold fusion

I've just published a paper on cold fusion, in Progress in Physics which is a nice open access journal that has the laudable goal of encouraging research that challenges the standard paradigm.

As I described in more detail in a previous blog, the phenomena known as cold fusion or LENR (Low Energy Nuclear Reactions) is a process that appears to produce fusion by packing deuterium atoms (hydrogen atoms whose nucleii have an extra neutron) into palladium metal, which acts a bit like a sponge when it comes to deuterium. When this is done, in certain circumstances, unexpected heat is given off, more than can be explained by normal chemistry, so the argument goes (and as arguments go, this one has lasted decades!) it must be fusion, but how is this possible when these deuterons are both positively charged and so they repel very strongly? Normally you need temperatures of over 100 million Kelvin to get them to collide and fuse, and hence the 25 billions dollars spent so far on reproducing the centre of the Sun on Earth (eg: with huge fusion reactors like ITER). Cold fusion appears to do it in a test tube, at room temperature and without emitting harmful radiation and the phenomena has been repeated often (see Storms, 2006). It offers the possibility of cheap energy for all, but as so often, it doesn't agree with the standard model so very few dare to investigate it (see an interesting article by Huw Price, link).

Well, as many of those who read my blog know, nature doesn't agree very well with the standard model either, but quantised inertia (or MiHsC) does rather better and one prediction of it, is that in tiny, closed informational spaces the temperature should increase. So what about tiny cracks or defects in the palladium? They do exist as both Ed Storms (who prefers cracks, see his report below) and Russ George have told me (the latter told me about very effective Japanese 'Samurai' palladium, full of defects). If the defects are of a size 28 nm then quantised inertia predicts a temperature of 27,000K. 

This is not enough to initiate fusion, but now imagine two ships in a choppy sea. Waves hit them from all around, but there will be a sheltered region between them and therefore fewer waves will push them outwards from between them, than are pushing them inwards. The result is that the ships will move together in a way not dependent on the usual physics (at sea this phenomenon is called the Maritime Casimir effect, you can guess what it is called in dry physics).

If you now think similarly about two deuterons in a palladium defect or crack then they will be pushed together in the same way by the thermal waves in the crack, as I described here. I showed in the paper (see here, or the link below) that if the crack/defect is less than 28 nm in width then this new force is strong enough to push the deuterons together through their Coulomb repulsion and they will fuse.

So, does this explain cold fusion? It is maybe a start but there are some problems. First of all, when predicting things it is best to have a observed number to test the theory on. For testing quantised inertia on galaxy rotation the test data is the observed speed of the stars. For the emdrive it is the measured thrust. With cold fusion all I have done so far is predict that defects of 28 nm width are needed. What size are the cracks in palladium where the fusion occurs? I don't know!

The other problem is that, whereas this process might possibly explain the lack of neutron emissions in cold fusion experiments (they may also be subject to the mutual sheltering effect) it does not obviously explain the lack of gamma emission observed. This radiation may be absorbed by the lattice as suggested by others, but there is certainly a lot of work to do yet.

All the same, this explanation is a simple and visualisable process, it needs no adjustment, and links cold fusion with lab scale (emdrive) and astrophysical (galactic) anomalies, so it is at least a good addition to the debate, and should help to broaden it and embed it in wider new physics.


McCulloch, M.E., 2018. Can cold fusion be explained by quantised inertia? Progress in Physics, 14, 2, 63-65. Open access pdf.

Storms, E., 2012. A students' guide to cold fusion. http://lenr-canr.org/acrobat/StormsEastudentsg.pdf

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

Saturday, 20 January 2018

Cold Fusion and Hot Soup?

Since I have just submitted a short paper on this, I'd like to explain how I think cold fusion might be happening. The following makes a nice story, but still could be wrong. We'll see. It is also dangerous ground, but it is necessary to keep pushing into such territory, because that is where the new physics is (partly because very few people have dared to go there yet).

I've been thinking about LENR (ie: cold fusion) since before Christmas, ever since Bob McIntyre on twitter noted that my earlier paper on quantised inertia and the proton radius anomaly [ref 1 below] might apply to it. It is also pretty clear that QI predicts that an earlier, much smaller, universe would have been hotter [ref 2] and you can see this without QI, simply from the uncertainty principle: dp.dx>hbar, where hbar is the reduced Planck's constant. If you shrink the 'known space' of an object (dx), then its uncertainty in momentum must increase, and therefore its temperature.

I've been reading a lot of Ed Storms' papers and the comment he made that impressed me was that the common factor in all the successful LENR experiments are nanoscale cracks or gaps in the palladium or other metals. In my space- and horizon-obsessed mind these are just mini-universes. See the schematic below of a crack (the white area) inside an area of red-hot palladium metal.

Coming back to the uncertainty principle: in cracks, the uncertainty in position (dx) is small, so dp and hence the temperature of the walls must be high (the red area). For the nanoscale cracks in palladium, the predicted temperature is still not hot enough for fusion, which needs temperatures of 100 MK, but recently I was cooking soup and noticed that the walls of the pan were hot and the soup was moving towards the centre. This is a different convective process, but it gave me the idea that the crack walls might be radiatively pushing the deuterons together (see the red arrows in the schematic). I've scribbled through the maths and it turns out that if the cracks are smaller than 86 nm, then the crack's walls are hot enough, and the radiation pressure, is strong enough to push the positively-charged deuterons together over their mutual repulsion and cause fusion. It might also account for sonoluminescence: light emission from small bubbles. So what do you think? Physics from the kitchen?

(Note: Argh! I have found an error in my derivation :( Thank goodness for dimensional analysis, so I will leave this blog entry here to record my blunder, and get back to the drawing board. Apologies. Correction No.2: I've decided now it was right all along, so have resubmitted it.).


McCulloch, M.E., 2017. The proton radius anomaly from the sheltering of Unruh radiation. Progress in Physics, 13, 2, 100-101. Link

McCulloch, M.E., 2014. A toy cosmology using a Hubble-scale Casimir effect. Galaxies, 2, 81-88. Link

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

Sunday, 14 January 2018

How QI gets rid of dark matter

Many people have asked me for a simple, graphical explanation of how quantised inertia (QI) gets rid of the awful dark matter, so here it is, for them. We start off with a schematic of a galaxy (see below, in yellow). Outer stars have been observed to have a rotational speed (the red arrow) so big that the inertial (centrifugal) forces (white arrow) should be much greater than the gravitational forces from all the matter we can see (the black arrow) and so, if it had any decency, the galaxy ought to fly apart. The problem is that galaxies are showing no decency at all, and do not fly apart. Why? Mainstream astrophysicists add arbitrary dark matter to boost the gravity arrow and achieve balance that way. Quantised inertia shrinks the inertial arrow instead.

To explain quantised inertia I will start with an oceanographic analogy (see below). A ship is parked at a dock. Lots of ocean waves can exist and hit it from the seaward side (the wavy line), but no waves can fit within the gap between the ship and the dock, they don't resonate in that space, so on average the ship is pushed by the waves towards the dock. If the crew of the ship were unaware of the waves they would say "It is a magic force moving us towards the dock!".

There is another sea. One predicted by quantum mechanics. It is a sea of quantum particles, and we have only recently detected it because Hendrik Casimir showed that if you put two plates very close together, like the ship and the dock, the plates will move together. That has now been confirmed (in 1996) so this invisible sea really does exist. Now consider an object accelerating to the right (black circle, white arrow below). It will see the quantum sea, actually an enhanced version of it (Unruh radiation). Relativity now says that in the opposite direction to the acceleration, information will not be able to catch up with the object. So there will be a horizon, like a black hole event horizon (see the black crescent). In quantised inertia this horizon is treated just like the dock wall in the analogy. it damps the waves between the object and itself. As in the analogy the object sees more waves from the right and is pushed back, always against its acceleration. This 'asymmetric Casimir effect' predicts what we always assumed before to be a 'magical' inertial mass, because we couldn't see these quantum waves (which only exist in the object's reference frame).

Information also cannot get to us from beyond the Hubble horizon, since stars there are moving away from us at the speed of light. So this horizon damps the Unruh waves equally all around the object, and so it damps the waves on the right side (there already aren't any on the left) - see the change from the dashed waves to the solid waves, below. This reduces the effect of the aCe process detailed above, and the resistance to acceleration, the inertial mass. This reduction is more serious for the longer Unruh waves that occur for low accelerations,since these 'feel' the cosmic boundary more.

The prediction then is that inertial mass is lowered for stars at the edge of galaxies, since they orbit in a slow curve and have a very low acceleration. This reduces the centrifugal (inertial) force outwards (see the change from the dashed to the solid white arrow, below) and the inertial force now balances the gravitational force - quantised inertia predicts the balance exactly for these edge stars, using only the visible matter, the speed of light and the Hubble scale, so that no arbitrariness or dark matter is needed.

I hope you can appreciate the beauty and simplicity of this theory. It has not yet been tested on the insides of galaxies, I'll need a galaxy model for that, but it does predict a lot of other observations as well such as the cosmic acceleration and the emdrive.


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

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

Tuesday, 19 December 2017

Low Energy Nuclear Reactions & QI: 1

Fusion is a process by which two atoms/nucleii of hydrogen (a proton, possibly with neutrons attached) fuse to form an atom/nucleus of Helium (two protons, perhaps with neutrons). Since the two nucleii to be fused are positively-charged they repel each other, and to get them to fuse they have to be at a very high temperature. One hundred million degrees Kelvin or so is needed to give them enough kinetic energy to randomly collide. The sun's centre is hot enough, and it is a huge fusion reaction turning hydrogen into helium, and only avoids exploding and destroying the Solar system because of its own self-gravity, which holds it in.

Fusion releases a lot of energy, so for 70 years people have been trying to make it happen on Earth, in close confinement. So far 25 billion dollars have been spent on this (Storms, 2012) and the focus has been on huge machines that use magnetic fields to confine plasma: magnetic versions of the Sun (The so-called ITER project). Imagine the surprise then, when in 1989 Martin Fleischmann (then one of the world's experts in electro-chemistry) and Stanley Pons, claimed they had produced fusion in a little test tube! Their experiment is shown below.

They put an electrolyte containing heavy water in a test tube (heavy water is just like water H2O, but the hydrogen H is replaced by deuterium D, which has an extra neutron, so D2O). They put two electrodes in, the cathode (negative charge) made of palladium and the anode (positive) of platinum, and passed a current between them (electrolysis). The D2O separated into oxygen, which being negative headed for the anode and bubbled off, and deuterium which, being positive, packed itself into the palladium cathode, since palladium has this odd property of soaking up deuterium like a sponge. Several scientists over the past 50 years had predicted that the deuterium could fuse in palladium being in such a packed state. Apparently it did, releasing a lot of heat, see the orange-red 'star'. The announcement of that thrilled the world with the possibility of having such a FusionCell in every home. Virtually limitless cheap energy.

But revolutions are never pretty and this was the usual hysterical mess, because very soon it was noticed that if the deuterium was actually fusing, it should be emitting neutrons and gamma rays and whatever was happening wasn't doing that. A bonus for safety, but because the observations did not fit standard theory, cold fusion was classified as fringe. A few brave souls continued to investigate, and instead of cold fusion, they now call the field LENR (Low Energy Nuclear Reactions). So far there have been about 200 independent replications of the excess heating effect so something odd and potentially very useful, is certainly happening, but why?

I was persuaded to look at LENR recently by twitterer B.McIntyre who pointed out that my 2017 paper on the proton radius anomaly (link to blog entry) might have implications for LENR. His tweet exploded in my head during a tutorial the following day. A few days later I calculated the size of the effect on the train to St Andrews and it was too small, but then on the train back from St Andrews I read Ed Storms' summary (see below) and found out that LENR happens whenever there are tiny cracks in the palladium. See the gray mottled pattern on the palladium in the schematic - cracks in the palladium where the fusion happens. I have applied QI to confined cavities/horizons before (the early cosmos, emdrives, sonoluminescence..) and it changes the physics in intriguing ways..


Fleischmann, M., S. Pons, M. Hawkins, 1989. Electrochemically induced nuclear fusion of deuterium. J. Electroanal. Chem., 261, 301-308.

Storms, E., 2012. A students' guide to cold fusion. http://lenr-canr.org/acrobat/StormsEastudentsg.pdf

Friday, 8 December 2017

Visit to St Andrews University

The University of St Andrews is one of the best in the UK, and its Physics and Astronomy department, according to the Guardian, is the best physics department in the UK, so, of course, they wanted to hear about quantised inertia (QI) :)

I went up there by train on Monday and stayed with them for a couple of nights and gave a seminar on quantised inertia on Tuesday. The talk seemed to go well since there were quite a few questions at the end, and no-one stood up and threw general relativity textbooks at me.

The most useful and enjoyable activity was discussing things informally, and often with a beer :) and Indian food, with the Professor who invited me, and two keen young cosmology PhD students who made some very good points. In the first meeting they made a toast to quantised inertia, and then they started, as they should, to try to pull apart the theory. That is a extremely fruitful approach.

Their first criticism went something like this. It seems inconsistent that I model a star orbiting round a galaxy by using the very low acceleration of its galactic orbit (v^2/r) and saying that the inertial mass has dropped because of QI (and thereby explaining anomalous galactic rotation without dark matter), but the actual components of the stellar system, say the Sun and Jupiter show a much higher mutual acceleration, and the atoms in the Sun for example are zooming around at very high acceleration, so shouldn't the inertia of the system be normal in QI?

I gave an answer to that in this blog post. That is still valid and I explained it to them (they had some questions about whether Rindler horizons mask the cosmic ones), but a simpler way to say this is that in quantised inertia, inertia is not a property of an object, but is a property of an interaction between objects. This makes philosophical sense, since an object alone in an empty universe would not be able to have any meaningful inertia because it would have no way to know if it was accelerating or not. I agree with Mach and the early Einstein so I do not see space-time as something that one can determine one's motion relative to. This means that for Jupiter, when you work out its response, in QI, to the gravity from the galactic centre, the inertia needs to be reduced in line with its low acceleration relative to the galactic centre (the inertia of that interaction), but when you work out Jupiter's response to the gravity from the Sun, the acceleration is large so the inertial mass in QI is not reduced. This means that the theory predicts the behaviour of the atoms in the Sun, the Sun and Jupiter, and the whole galaxy in a self-consistent way. It also means that each object has more than one inertia. The challenge remains how to encode this in the maths, and that was their other criticism: that the maths for QI is not yet fully formed, and does not use the same symbols or metrics as the maths they use, and this is advisable if I want cosmologists to start modelling with it.

I thoroughly enjoyed my visit to St Andrews University. The town itself is very pleasant: they have a city wall, huge golf links (though I don't play) and a beach, but I did not see it this time. I was told, and I thought it was very Scottish, that as a mild 'test of courage' the University gets students to walk along the pier in their gowns. My impression of the people in the Physics and Astronomy department was good because the audience I had seemed curious and open-minded (they did not look at me as if I was a bug, as sometimes happens!) yet they were keen to try to identify any problem. I noticed that someone in the department was also bothering to leave interesting articles lying open on tables for students to read, and the academics pin up their papers outside their doors. There was a general attitude, not of looking efficient, but of genuine interest in what they were doing.

Tuesday, 14 November 2017

QI: Physics Reunited

Someone recently asked me to explain quantised inertia in a series of four drawings. I am probably overfond of brevity, so here it is in one drawing, but also with an explanation of how quantised inertia really does reunify physics in a new, beautifully simple and useful way.

Quantised inertia (Qi) deals with the property of inertial mass, for a long time, in my opinion, the blind spot of physics. The figure below shows a ball (black circle) accelerated to the left (red arrow) and also shows Heisenberg's uncertainty principle which states that for an quantum object, its uncertainty of position (dx) times its uncertainty in momentum (dp) must be equal to or greater than a constant (hbar, a very small number). Now we introduce relativity which says that information is limited to the speed of light and so information from a certain distance behind the ball in its acceleration can't catch up, so there is a unknowable zone to the right from the point of view of the ball. There is also an unknown zone very far away since stars far off are moving away faster than light thanks to cosmic expansion. The result is the solid black line in the Figure, a horizon around the ball. If we now apply the uncertainty principle at each angle around the ball, then you get a value for the momentum uncertainty at each angle that is a mirror image of the position uncertainty. The uncertainty in momentum around the ball is shown by the dashed shape. This schematic is only two dimensional, the actual shapes will be twin-lobed and will looked more like an egg-timer.
The dashed shape means that in the opposite direction to the acceleration, the ball's uncertainty of momentum is higher and therefore there is more of a chance that quantum fluctuations will push the ball backwards against its acceleration, in this case to the right, and this predicts the inertial force we know and love (the blue arrow) which keeps our balls traveling in straight lines on pool tables (see the 1st paper below for details). Any deviation is cancelled by this combination of relativity and quantum mechanics (called quantised inertia).

Quantised inertia also predicts something new: that if the acceleration is very low, then the solid-lined shape starts to expand to the right, becoming more circular and at very low accelerations it is just a circle (sphere). So the momentum (dashed) shape is also a circle and symmetrical on both sides, and so it is equally likely that quantum fluctuations will push the ball in any direction and so the inertial mass disappears in a new way at low accelerations in this model. Qi happens to predict galaxy rotation precisely, and without dark matter, since the inertia mass and centrifugal force on slowly-accelerating galactic edge stars is lower than expected (see the 2nd reference below).

Quantised inertia also predicts that if we could shrink the dx envelope (solid-lined shape) in one direction by making our own horizon there, then because of the uncertainty principle the momentum envelope (dashed-lined shape) would expand in the opposite direction. What does this mean? It means things would move in a new manner in that direction. This is what I think is happening in the emdrive. In fact the emdrive looks very much like the solid-lined shape, so Qi predicts it should move towards its narrow end, and it does! It does so by the amount, well, in most cases, predicted by a crude application of quantised inertia.

There you go: physics reunified in at least one way, simply, dark matter gone and a new reaction-mass-less propulsion method. What's the catch? Well, more direct experimental evidence is needed, and a full mathematical structure needs to be worked on: there's lots of scope for people to join in.


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

McCulloch, M.E., 2017. Galaxy rotations from quantised inertia and visible matter only. ApSS, 362, 149. Paper