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

## 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.

References

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:
https://www.paypal.me/MikeMcCulloch

## 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..

References

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.

References

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

## Monday, 30 October 2017

### Dark Matter Does Not Exist

I was inspired to write this blog post when I saw an advert online for "Dark Matter Day", which mainstream physics is trying to set for 31st October. I think it should actually be celebrated on the 32nd October, since dark matter doesn't exist. How do I know it doesn't exist? This blog entry is intended to present some of the evidence against it.

1. Renzo's rule. When we look at galaxy rotation curves (how the orbital speed of the stars varies as you go out from the centre) the variations in the orbital speed are always coincident with variations in the light intensity (ie: the visible mass). The rotation curve follows the light curve. This means that the speed is determined totally by the visible mass, and not by anything invisible. Renzo's rule has been generalised and broadened by Lelli et al. (2016) (see the references below).

2. Milgrom's acceleration cutoff. As pointed out by Milgrom a long time ago, galaxies only start to misbehave when the acceleration of the stars as you go out from the centre drops below about 2x10^-10 m/s^2. This dynamical relation is very difficult to explain with any sort of matter distribution. This cutoff is also suspiciously close to the cosmic acceleration, a clue that should not be ignored.

3. Globular clusters. In order to fudge general relativity to predict galaxy rotations right, astrophysicists have to add dark matter in a particular smooth halo in and around the galaxies, and so they have to invent physics for it to stay smoothly spread out. This is why the result of Scarpa et al. (2006) is so crucial. They showed that tiny globular clusters (little conglomerations of stars within galaxies) also showed a galaxy rotation problem writ small and this cannot be explained by dark matter, which must be smooth and not congregate, without messing up the full scale galaxies.

4. Even more revealing than globular clusters, binary star systems definitely should not contain lumps of diffuse dark matter, and yet when two binaries are orbiting very far apart (so-called wide binaries) they too show a galaxy rotation problem writ even smaller (Hernandez et al., 2012).

5. The cusp-core problem. The lambda-CDM (cold dark matter) model dominates astrophysics since it predicts the CMB spectrum (if you set its arbitrary numbers right), but when it is used to predict the distribution of dark matter in galactic centres, it produces a distribution that causes GR to predict the wrong rotation speeds, and so this disribution is 'adjusted' (de Blok, 2009). A fudge of a fudge!

6. Lack of evidence. Dark matter has not been found after 40 years or so of expensive looking, something not mentioned by most cosmology books, just as the aether was not found..

7. Philosophical objections. dark matter was invented because general relativity did not predict the rotation of any real galaxies. It had failed, but instead of changing the theory astrophysicists worked out with computers what complex distribution of invisible matter was needed to make GR work and went to look for it. This has worked in the past, look at Neptune which was needed to explain the odd orbit of Uranus, but Neptune was a small amount of mass in the plausible shape of a planet, whereas dark matter is the invention of 10 times as much mass as is seen (sometimes up to 1000 times), in a completely arbitrary distribution, and requiring new dark-physics to go with it. You can explain almost anything with a hypothesis like that, and yet predict nothing..

8. Quantised inertia predicts the rotation of disc galaxies of all scales very simply, non-arbitrarily and without dark matter (see my latest paper).

As said above, I shall celebrate Dark Matter day on the 32nd October and I invite you to join me :)

References

Lelli, McGaugh, Schombert & Pawlovski, 2016. One Law To Rule Them All: The Radial Acceleration Relation of Galaxies https://arxiv.org/abs/1610.08981

Scarpa et al., 2006. Globular Clusters as a Test for Gravity in the Weak Acceleration Regime https://arxiv.org/abs/astro-ph/0601581

Hernandez et al., 2012. Wide binaries as a critical test for Gravity theories https://arxiv.org/abs/1205.5767

de Blok, W.J.G., 2009. The core-cusp problem. https://arxiv.org/abs/0910.3538

## Friday, 20 October 2017

### The Joy of Anomalies

It is the fashion in mainstream physics today to always start from the existing theory. For example, general relativity is always assumed to be right. If you don't believe that, try questioning it and see what happens! As a result the mainstream need to work out what data they need to find to make it right. Hence the search for dark matter, dark energy, dark flows, which brings in lots of funding too. This is the process everywhere, but it is the opposite of the scientific method which puts data first and reigned between say 1660 (founding of the Royal Society, who said 'disregard theory and look at data') and 1988 (when data-driven Feynman died). If you want to be cheeky, you could call the post-1988 way the 'religious' method, but without the attached morality.

Probably because I was educated in a more grounded form of physics (BSc in physics, PhD in ocean physics) and loved reading Feynman, I am pre-1988. What I like to do, and have ever since my physics degree, is look for interesting anomalies (data that defies the theory). Actually, before my physics degree I was fond of theories and philosophy and did not bother much about data. I spent hours in the library reading about Spinoza, and trying to devise theories from beautiful thoughts alone, but something changed when I did my third year research project at York University: An analysis of a chaotic Duffing oscillator. I built such an oscillator in the university's metalworking lab. It was a beautiful thing and I wish I still had it! (see my schematic below). A metal pendulum with a magnet at its base, repelled from its equilibrium point by a magnet underneath. It had two side-arms with magnets attached pointing down. One arm was driven sinusoidally with a electromagnetic coil around the magnet, the motion of the magnet on the other side was sensed with another electromagnetic coil. The signal was fed to a BBC computer, that also by integration could work out from the measured speed, the position of the pendulum. I collected and plotted strange attractors of the chaotic motion - the pendulum oscillates between two stable positions chaotically.

When I started my PhD shortly after, I began reading Feynman's books. Also, I eventually focussed on a beautiful anomaly. Cruise data has shown that every summer, a thin cold, fresh surface layer spreads over the north Atlantic. Why? I built a simple layered computer model of it, showed the spreading was due to wind-driven (Ekman) flow blowing polar water south and showed that the air-sea interaction heated the cold surface as it went, but did not erase the freshness, so it becomes unexpectedly buoyant (being now warm and fresh, both properties reduce water density). It forms an insulating cap on the ocean that has implications for climate (paper).

Later when I worked at the Met Office I was tasked with looking at the output of the ocean model and I decided, being fond of data by now, to look at the output without the smooth interpolation that was being done. I pixelated the raw sea surface salinity data instead, and what immediately appeared were nice bands of fresh surface water underneath rainbands. So I developed a simple model of those as well, and that predicted consequences for weather too.

I've always been keen on fundamental physics & astronomy and so I couldn't help but notice anomalies like the galaxy rotation problem, the Pioneer anomaly and that they both involve the same odd acceleration 10^-10 m/s^2. I developed a simple model to explain those, called MiHsC or quantised inertia and it turns out it predicts a lot of other anomalies, such as the emdrive, and cosmic acceleration which I did not know existed till it heard about it on the car radio and thought "MiHsC predicts that!"

I do love looking for anomalies or mysteries. That is why mainstream physics now seems so dry because they are so confident that they know it all and anomalies are brushed under the carpet with arbitrary fudges like dark matter. In my latest attempt to fight back, I have started writing #AnomalyoftheDay on twitter, documenting all the well-observed anomalies that prove that physics is very incomplete (eg: it only predicts 4% of the cosmos). There are many anomalies now, from the proton radius being different depending on how you measure it, the gravitational constant not being constant (blog), tapered microwave ovens which thrust slightly without expelling propellent (emdrives), odd lights flying around in Hesdallen, Norway (link), galaxies rotating in violation of Einstein, and the Cosmic Microwave Background being aligned with the Solar system in a way that would make Copernicus weep! (paper, see Figs. 1 and 2). I have a list of 40 or so anomalies and it is growing.

The tendency I and some others are fighting in mainstream physics is a huge one, a combination of hero-worship, intellectual laziness, group-think and a bias in physics towards mega-expensive solutions like dark matter detectors since bringing in the most funding gets academics promotion. My hope is to get physicists to look up from old books and funding applications and look at real anomalies again (an act which requires little or no funding and repays you with fun), or at least get taxpayers to demand they do. Only then will the mainstream see the utility of quantised inertia.

## Monday, 16 October 2017

### The Allais Effect

I'm getting slightly respectable in my old age, being invited to talk at St Andrews University, but I always found that un-respectable anomalies (no real anomaly is respectable) are the essential signposts to new physics and to show that I have lost none of my radicalism I'm going to talk about the Allais effect and a possible way that quantised inertia might apply. Please note that this proposal is not yet solid and is just an exploration at this stage.

The Allais effect was discovered by Maurice Allais, a Frenchman who won the Nobel prize for economics. He was using a Foucault pendulum during a Solar eclipse in 1954. Usually these pendulums swing to and fro in the same plane of space because of their inertia, so that, to us on the spinning Earth, their plane of oscillation appears to turn with a period of a day (at the poles, see comments).

The first component of the Allais effect is that during a Solar eclipse the plane of rotation of the pendulum rotates more rapidly than expected during the eclipse moving through about 10 degrees and at the end of it, it rotates back into the expected orientation.

The second effect was found in 1961 by Gheorghe Jeverdan who noticed that during the eclipse the period of the pendulum also decreases by one part in 2000 or dT/T=0.0005, where T is period.

The third effect was seen by Mishra and Rao (1995) and involves a reduction of apparent gravity, and then an increase, both of about 0.5 microgals or 0.5x10^-8 m/s^2.

If confirmed, then these observations would be a useful clue in the development from quantised inertia into horizon mechanics (a new complete dynamical model). I noticed a few months ago that quantised inertia agrees with the second effect but in a manner that I hesitate to mention, because it sounds a little wacky, even to me, but here's to bold suggestions and freedom of speech.

Consider Allais' pendulum. It sees huge accelerations within the hot Sun. As you'll see, the actual acceleration doesn't matter, which is lucky since I don't know it. Lets just assume it is a big number. So according to quantised inertia the acceleration is big, the Unruh waves seen are short and a large proportion of them are 'allowed' since they fit inside the Hubble volume. Suddenly, the Sun gets covered up by the Moon, and the main acceleration the pendulum sees now is the acceleration of the Moon around the Earth which is 0.0024 m/s^2. The Unruh waves it sees are now longer, fewer fit inside the Hubble volume, and a greater proportion are disallowed so the inertial mass of the pendulum drops. The change of inertial mass predicted by QI is

dm/m = (2c^2/Theta)((1/a1-1/a2)

where c is the speed of light, Theta is the co-moving distance to the cosmic horizon and a1 and a2 are the accelerations in the Sun, and of the Moon around the Earth respectively. So putting in values

dm/m = 2x10^-10 x ((1/0.0024)-(1/bignumber))
dm/m = 2x10^-10 x ((1/0.0024)-0)
dm/m = 8.3x10^-8

The period of a pendulum (T) is given by

T = 2pi.sqrt(lm/gM)

where l is its length, m is the inertial mass of the pendulum bob, g is the gravitational acceleration and M is the gravitational mass of the bob (M .ne. m in QI). So the variation of the period will be the square root of the variation of the inertial mass, in other words

dT/T = sqrt(dm/m) = sqrt(8.3x10^-8)

dT/T = 0.0003

The observed variation in the pendulum's period (Duif, 2004, data from Saxl and Allen) was

dT/T = 0.0005

So quantised inertia (summarised here) predicts in the right ballpark. I have to say that, even to me, the process of Moon-shielding of Unruh radiation sounds quite wild at this stage, and it predicts that there should also be a diurnal effect as the Sun sets and goes behind the Earth (see second reference, far from conclusive), but I think it is important to get these edgy ideas out there, just in case someone else can add a little to it, and to avoid the descent into safe irrelevance.

References

Duif, C., 2004. A review of conventional explanations of anomalous observations during Solar eclipses. https://arxiv.org/abs/gr-qc/0408023

Saxl E.J., M. Allen, J. Burns, 1980. Torsion pendulum: peculiar diurnal variations in period. Letter submitted to Nature. https://www.researchgate.net/publication/284186911_AllaisBook_SAB1980