Blogging out

May 5, 2022

I have explained at length how to solve the big problems of fundamental physics, and if people still refuse to listen it is their problem not mine. All of them come down to one simple phrase: “rest mass”. In physics there are several mutually contradictory definitions of rest, and several mutually contradictory definitions of mass. Sort those out, and you’re laughing.

Classical Newtonian mass is defined on a Solar System scale, in order to make Newton’s laws of motion and gravity work. The Solar System is considered to be at rest, and we move within the Solar System. This classical mass was good enough to work on the laboratory scale as well, as long as accuracies better than 1/10000 were not required. But when particle physics sought greater accuracy in the 1960s and 1970s, they were forced to switch to a new definition of mass that works when the laboratory is considered to be at rest, rather than the Solar System. These two definitions of mass are inconsistent with each other, as particle physicists are now starting to find out, when they discover that certain particle masses are not what they are supposed to be.

Astronomers want to extend the laws of gravity in the other direction, to the galaxy scale. And they have found that the definition of mass that works on a Solar System scale does not work on a galaxy scale. The reason is clear: the Solar System is not at rest within the galaxy. Our definitions of rest and mass have failed to take into account the fact that the Solar System rotates around the centre of the galaxy. The local Solar System definition of mass, if extrapolated to the whole galaxy, fails to provide enough mass to keep the Solar System in this orbit. Is it the galaxy that is wrong, or is it us? It is quite unbelievable how many people insist that it is the galaxy that is wrong. No, it is our definition of mass that is inadequate to explain the gravitational pull of the galaxy on us.

The inconsistency of laboratory mass (Dirac mass, defined in 1928) with classical mass (Newton or Einstein mass) is a mathematical theorem, due to the fact that their symmetry groups are inconsistent with each other. It is quite unbelievable how many physicists think that physics is somehow immune to the laws of logic. It is quite unbelievable how many physicists ignore both mathematics and experiment, and insist that their theory is correct when it contradicts both.

It is necessary to devise a mathematical model that explains how to transform between different definitions of “rest” when rotations are involved. That I have done. It is necessary to match this model up with experiment. That I have done. It is not necessary to quantise this model, but I have done it anyway. What more do you want?

The big problems are all solved. You can work on filling in the details. I’m blogging out.

“You can’t do physics like that!”

April 23, 2022

This is something I was told many years ago, that I have struggled ever since to understand. I still do not understand it, and I suspect I never will. It all hinges, I suppose, on what “like that” means. As far as I was concerned, I spent a long time thinking about what the real problem was, and then I spent a long time looking for the experimental evidence that I felt was relevant to the problem, and then I spent a long time sorting through this evidence to find what I felt were the vital clues to why the problem had not been solved yet, despite the efforts of thousands of physicists over several decades.

When I found these clues, of course, I had no answers to any questions, no solutions to any problems, no deep insights into the nature of the universe, no mathematical models to explain anything, no physical insight into anything, and no reason for anyone to listen to anything I said. But I had some good questions. I had spent years thinking about the questions, so I knew they were really good questions. The thing that was really difficult to deal with was not that physicists rejected my answers, because I didn’t even have any answers, but that they rejected my questions.

It is absolutely fundamental in all aspects of life, not just in science and mathematics, but in law, journalism, the humanities, politics and life in general, to ask the right questions. One does not have to be an expert in a particular subject to recognise the symptoms of failing to ask the right questions. If you don’t ask the right questions, you don’t solve the problems, and a failure to solve the problems is something that does not require a huge amount of specialist knowledge to recognise.

Fundamental physics in the last 50 years is a particularly egregious example of an area in which the interested layman can easily detect a failure to solve the big problems about the universe we live in. The problems actually go back at least 90 to 100 years, at which time serious contradictions in the theory of fundamental physics began to reveal themselves. Einstein analysed these problems very carefully, but by that stage he was regarded almost as a crackpot, and the mainstream tried to demolish his arguments, rather than engaging with the real problems that he drew attention to. This is, unfortunately, still the case. But Einstein asked the right questions. No-one today is asking the right questions.

To me, there is only one question: “What is mass?” No physicists can answer that question convincingly, and until they can, I do not accept their right to reject my answers, however tentative or partial, to this question.

A toy model of the W/Z mass ratio

April 19, 2022

A miracle has occurred. The arXiv has actually posted one of my physics papers without putting it on hold on suspicion of heresy. Not only that, but they posted it on hep-ph, despite the fact that they would only allow me to submit it to math-ph. You can find it at

Newsflash: quantum gravity found at last!

April 13, 2022

Five days ago, the results of a 10-year experiment at Fermilab were published. The results were shocking, showing a 7 sigma discrepancy with the standard theory. No-one can believe this, because the theory is so good, it can’t be this badly wrong! Well, in a sense it is not. What the experiment actually found, although nobody appears to have realised it yet, is a quantum gravity signal from the Moon. So all we need to do is add a good quantum theory of gravity to the standard model, and everything will be fine.

The only problem is, no-one seems to have a quantum theory of gravity that makes any testable predictions at all. Well, I do, so they can have mine if they want. It comes with a whole load of testable predictions already built in. Last week’s announcement confirms my first prediction, but there are plenty more where that came from. There are also a large number of “postdictions” – i.e. explanations of experimental anomalies that have already been discovered. I’ve written about several of them before – the muon g-2 anomaly, kaon oscillations, neutrino oscillations, parity violation in beta decay, and so on.

My second prediction is that a more careful analysis of the data from this experiment will reveal a correlation between the experimental measurements and the oscillation in the inclination of the Moon’s orbit. My third prediction is that a similar anomaly, correlated with the same oscillation, can be found in the mass ratio of charged to neutral kaons, with a slightly smaller amplitude of .05%. To find this subtle anomaly, of course, one has to design the experiment carefully to look for it, so it is not surprising that it hasn’t been found before. My fourth prediction is that if the kaon oscillation experiments are conducted with vertical kaon beams instead of horizontal kaon beams, the results will be different.

I’m sure you get the idea. If you want any more predictions, you only have to ask. Evidence for quantum gravity has been piling up steadily since the mid 1950s. But particle physicists have simply been unable to see the wood for the trees. Now they have found a huge tree, much bigger than they can believe, and it has stopped them dead in their tracks. My prediction is that they will now drill a hole through the tree, build a road through it, and pretend it isn’t there. In other words, they will continue to ignore gravity.

The basis for all my predictions is really very simple. Changes in the gravitational field correlate with changes in neutrino energy (and flavour). This is true even in the standard model, though it is ignored, because the changes in average energy are too small to have any (macroscopic) effect. But the changes in individual neutrino energies are not necessarily too small to have a noticeable effect on individual elementary particles. The particular experiment whose results have just been reported relies on the precision measurement of the energies of a very large number of neutrinos. It is assumed, therefore, that the gravitational effect can be ignored, because one just averages over large numbers of neutrinos, so the effects cancel out. This might be true if they were random neutrinos, but they are not. They are very special neutrinos produced by a very specific process, so that the gravitational effect on all of them is the same, and does not cancel out.

It follows that quantum gravitational effects can in principle be detected in any experiment involving neutrinos, that is to say in any experiment involving weak force processes. Not only in principle, but also, we now see, in practice. We have discovered quantum gravity. Let’s celebrate!


April 12, 2022

There is a special magic about the number 8. Whole books have been written about the magic of the number 8. I have spent a large part of my career studying the ramifications of the number 8 in the higher reaches of mathematics. On the arXiv today I have posted some of this work, at This work was mostly done in 2014, but has not been published before because my co-authors are of the opinion that it contains the vital secrets to the ultimate theory of everything. I am of a different opinion: it is simply an interesting piece of mathematics, that has nothing whatever to do with physics in any form whatsoever.

There is a companion paper, which is aimed at embedding the standard model of particle physics into this piece of mathematics. It is on hold at the arxiv, for the usual reason that it espouses a heretical version of the official mathematicist religion. This particular heresy is well-known, and is called the E8 heresy. I was a member of this heretical sect for about eight years, from 2007 to 2015, after which I became a hermit and founded my own sect, living in a solitary cave in the desert. My heresy is not well-known, and does not have a name, other than the generic label “crackpot” – which is equivalent to saying “hermit”.

Anyway, to get back to the number 8. We are all familiar with ordinary arithmetic with whole numbers (integers), and most of us are familiar with the standard extensions to negative numbers, zero, and fractions. We think therefore that we are familiar with all the “real” numbers, forming a continuous line of numbers stretching to infinity in both directions. In fact, we are not at all familiar with “real” numbers, which are a very difficult concept to understand, and raise all sorts of mathematical, philosophical and physical problems. However, let’s leave that discussion for another day, and take it that we understand the real number line to a reasonable degree. This line is one-dimensional, so we can associate it to the number 1.

The extension from the number 1 to the number 2, or from the 1-dimensional real line to the 2-dimensional complex plane, is necessary for solving quadratic equations. This problem is several thousand years old, but the complex numbers didn’t make an appearance until a few hundred years ago. Usually only the continuous version is taught, but the discrete versions are more fundamental. Any child who has ever played with arranging pennies into patterns knows that you can fit exactly 6 pennies around the edge of another penny, with no gaps. And then you can extend this pattern as far as you like, limited only by how many pennies you’ve got. This pattern of pennies is a pictorial representation of a discrete form of the complex numbers, known as the Eisenstein integers, which is of great importance.

The extension from the number 2 to the number 3 occupied Hamilton for many years. For physical reasons, he wanted to describe a multiplication on 3-dimensional space, but he couldn’t do it. Then, in 1843, he suddenly realised he needed four dimensions, and the Hamiltonians (now called quaternions) were born. The extension to 8 dimensions was then accomplished by Graves in 1845, re-discovered by Cayley in 1847, and the Cayley numbers (now called octonions) were born. And there the line ends.

Let’s go back to the pennies, and ask how many 3-dimensional pennies (balls) you can fit round another one. It was known to the ancient Greeks that you can fit 12, but there are gaps. It is not obvious that you can’t fit 13, although if you try it you’ll be wasting your time – it was proved only a few years ago that it can’t be done. A standard football (soccer ball to some of you) has 12 black pentagons that tell you where to put the 12 surrounding footballs, and you can see for yourself how big the gaps are. It is this sphere-packing that provides the basic mathematical model for my version of physics. The gaps are the important thing, because they allow for physical concepts of dynamics and uncertainty, for example.

With 4-dimensional pennies, there are no gaps. You can fit 24 around each one. This gives you an integer version of quaternions, known as the Hurwitz quaternions. It was Hurwitz who proved you can’t do sensible arithmetic in more than 8 dimensions. In 8 dimensions, you can fit 240, without gaps. It is this 8-dimensional sphere-packing that defines what is known to mathematicians as E8. The four cases are known as A1, A2, D4 and E8, in 1, 2, 4 and 8 dimensions respectively.

Now to understand what this means to physicists, let’s go back to the pennies again. Suppose we have a large 2-dimensional expanse of pennies, and we want to describe some physics. First we need to know where we are: that takes two numbers to tell us how far along and how far up to go. Then we need to know what is around us: that takes six numbers, one for each of the adjacent pennies. Altogether we have 8 numbers, which we now put into an 8-dimensional space, wave a magic wand, and out comes what physicists (and mathematicians) call the Lie algebra of type A2, otherwise known as su(3), which is a fundamental part of the standard model of particle physics: it describes the strong force.

Let’s do the same thing in one dimension: you need one number to say where you are, and two more to describe what you see on your left and what you see on your right, making three numbers altogether. The magic wand gives you su(2), which in the standard model describes the weak force. Now comes the mathematicist’s divine revelation: if A1 and A2 describe the standard model, then D4 must give us a better model, and E8 must give us the ultimate model, the ne plus ultra theory of everything. It’s a seductive vision, but unfortunately it turns what was already a corrupt orthodox religion into pure mysticism. As I said, I was under the spell of this mystic vision for 8 years, before the hard light of day revealed it for what it was.

So let us return to the mathematics. The Lie algebra of type D4 consists of 4 dimensions to tell you where you are, and 24 to tell you what is around you, making 28 altogether. If you add in your next-nearest neighbours as well, you get another 24, making 52, giving the Lie algebra of type F4, which is also worshipped by this mystical sect. Finally, E8 itself consists of 8 dimensions for where you are, and 240 for your surroundings, making 248. There are also various intermediate algebras coming from sphere packings in 3, 5, 6 or 7 dimensions.

But none of these Lie algebra constructions use the multiplicative structure of the original number system. We are therefore missing something important. The paper posted today puts the multiplicative structure of the octonions back into the construction of the Lie algebra of type E8. We make heavy use of the well-known use of the multiplicative structure of the octonions in the construction of D4 and F4. When it comes to putative physical applications, we actually restrict from E8 to D8 in order to separate spinors from vectors, so that what E8 does for us is really to replace the usual Clifford algebra structure in the construction of spinors. This reduces the dimensions from 248 to 120.

It is really this 120 that is the magic number. But as I have explained, the continuous algebras cannot be used to describe fundamental physics accurately, because continuity implies the ultraviolet and infrared catastrophes, regardless of how clever and sophisticated you are. So we need a discrete structure of 120 things. That is what my model provides. My hope is that the E8 model provides enough motivation to switch eventually to my discrete model.

The mass of the W bosons

April 8, 2022

Apparently there is a report today that the recent Fermilab measurement of the W boson mass came up with a figure of 80.434 GeV/c^2, compared to the expected 80.379 (+/- .012, according to wikipedia). This is a significant discrepancy, and demands explanation. My explanation was ready and waiting seven years ago, but no-one took any notice then, and I don’t suppose they will now.

In several of my papers, I explain how the W/Z mass ratio is essentially the cosine of a sum of two angles. In my model, one has to take the two angles separately, but because the standard model only uses complex numbers, not quaternions, it has to map both angles into the same circle, which has the effect of simply adding them together. Indeed, my model really has three angles, but the third one is small (about half a degree), and its effects on the mass ratio are similarly small, so in the interests of simplicity I shall omit it from this discussion.

Because we are measuring mass, these angles are angles that have a significant effect on the geometry of the gravitational field. They are the angle of tilt of the Earth’s axis, and the angle of inclination of the Moon’s orbit. The current axial tilt is about 23.4364 degrees, while the Moon’s orbital inclination varies from 4.99 to 5.30 degrees on a 347 day cycle. Ignoring the effects of the other planets, therefore, the formula for the W/Z mass ratio is just the cosine of the sum of these angles, varying from about 28.43 to 28.74 degrees (spurious accuracy removed) with an average of 28.58 degrees. So the cosines vary between .87940 and .87681.

Now normalise this to a predicted average value of 80.379 GeV/c^2, which requires subtracting an angle of .40 degrees, to get a conjectured variation with amplitude .119, so between 80.260 and 80.498. In this model, a measured value of 80.434 does not look at all unreasonable. The precise value of course depends on the timing of the experiment, and the statistics of the averaging process used to produce the result. But a discrepancy of around half the predicted maximum is just about what you’d expect from an experiment conducted at a random time in the lunar cycle.

You may call me a crackpot and a madman if you like, but I predicted this discrepancy seven years ago, well in advance of the experiment, and with the correct order of magnitude for the error. The standard model did not predict it, and cannot explain it.


March 26, 2022

Over at you can read a lot about mathematicism and its alleged failings as a philosophical standpoint from which to judge physical theories. I have a lot of sympathy for these arguments, which in a nutshell blame the problems of modern theoretical physics on an over-reliance on mathematics. The only criticism I have is that “mathematics” is here considered in a unitary sense, and one mathematic is not distinguished from another. I would argue that “mathematics” is not a “universe” but a “cosmos” – to borrow the terminology from that blog.

I would argue, in other words, that the problem is not an over-reliance on mathematics, per se, but an over-reliance on the wrong mathematic. By the late 19th century it had become clear that the physical phenomena of light and electricity were not continuous, but discrete. Yet, in the 21st century, continuous mathematics are still used to describe these phenomena, despite being inappropriate and inadequate for the task. The result of this misuse of mathematics is that physicists are still unable to explain the properties of polarised light at the level of individual photons. But please do not blame mathematics for this problem. It is entirely the fault of physicists for choosing the wrong mathematic.

A good discrete mathematic can easily explain the observed physical properties of polarisation of entangled photons, as I have explained repeatedly both here and elsewhere. No continuous mathematics can possibly do this – almost by definition. All the supposed paradoxes of entangled particles arise from the same cause – a vain attempt to use continuous mathematics to describe discrete physical processes.

It is still not generally accepted that gravity is also a discrete phenomenon. Perhaps it isn’t – but the astronomical observations that have led physicists to invent dark matter and dark energy have all the hallmarks of a quantum effect taking over once the gravitational field falls below a certain well-defined strength. As “thisislanduniverse” points out, there are four fundamental particles of matter, the electron, muon, tau lepton and proton. To understand gravity as a discrete phenomenon it is obviously necessary to consider all four. Conventional theories only consider two of them – the electron and proton. Therefore they cannot explain what actually happens in the cosmos.

This isn’t the fault of the mathematics, it is the fault of those physicists who insist on using complex numbers to describe a 2-dimensional concept of matter, when the physics requires quaternions in order to describe a 4-dimensional concept of matter. The fact that quaternions are required was known to Hamilton in the 19th century, and was emphatically confirmed by the necessity for using non-commuting operators in quantum mechanics in the early 20th century. Yet even today, physicists refuse to use quaternions.

Putting these two arguments together, we see that the only possible mathematic for use in fundamental physics is a mathematic of discrete quaternions. What I have shown over the past year or so is that this mathematic actually works.

The definition of time

March 13, 2022

Finally I am ready to tackle the question of how to define time. I have looked at the definition of mass, which is linked to the definition of energy via Einstein’s famous equation E = mc^2, and energy is linked to time via Hamiltonian duality, or, in quantum mechanics, the Heisenberg uncertainty principle. So, if there are two different definitions of mass, that I have called Einstein and Dirac mass, then there should be two different definitions of time, that I might call Einstein and Dirac time. But it is actually rather more complicated than this, as there are two different concepts of Dirac time.

For the sake of giving them labels, I will call Einstein time, neutron time, since the Einstein mass is not directly associated with charge, and I will call the two sorts of Dirac time, electron time and proton time, since they are associated with charge. Practical time is a compromise between these three types of time, and the Heisenberg uncertainty principle is nothing more than an uncertainty as to which type of time is intrinsic to the particle being measured.

The fact that the neutron and proton masses are almost exactly equal, and the electron mass is very small, implies that practical time is more or less exactly the average of neutron time and proton time. This is reflected in the fact that the proton is completely stable, as is the electron, and the neutron is almost stable, having a lifetime nine orders of magnitude greater than the next most stable particle (the muon). Dirac time, or what I would like to call “real time”, on the other hand, is defined by the stable particles, so is a suitable average of electron time and proton time.

Atomic clocks are based on the behaviour of electrons in atoms, and scientific time is defined by these clocks. Atoms consist of electrons, protons and neutrons, so atomic clocks measure a practical time, not a real time. The time that atomic clocks measure is not the always the same: this is the reason why GPS systems need to be corrected for general relativity. In other words, practical time varies, where real time does not.

The assumption that is made in the whole of physics is that practical time and real time are the same thing. Or, in mathematical terms, that Einstein time and Dirac time are the same thing. This would imply that Einstein mass and Dirac mass are the same thing. But, as I have shown, this is, unfortunately, simply not true.

Maxwell’s equations for electromagnetism use practical time, which in Einstein’s theory of special relativity is assumed (incorrectly) to be Einstein time. Re-writing Maxwell’s equations using real (i.e. Dirac) time has the rather remarkable effect that the equations of classical electrodynamics then become identical to the equations of quantum electrodynamics. This is quite an extraordinary thing, because physicists have spent 100 years trying, unsuccessfully, to understand how classical electrodynamics arises out of quantum electrodynamics. The reason for this lack of success is now clear: it is a simple failure to distinguish correctly between Einstein time and Dirac time.

Einstein’s equations for gravity also use practical time, again assumed (incorrectly) to be Einstein time. If we want to quantise gravity, we should therefore expect to have to convert Einstein time to Dirac time in the Einstein equations. I tried this, and differentiated the gravitational field with respect to 5-dimensional Dirac spacetime, to see what happened. First of all, the theory reduced from 4×4=16 dimensions to 3×5=15, thereby removing the cosmological constant and the Ricci scalar (and therefore also the spacetime metric) from the equations. Second of all, the equations of general relativity became equal to the equations of the standard model of particle physics, but without a Higgs field.

Even more remarkably, the Riemann Curvature Tensor turned out to be the derivative of Einstein spacetime with respect to Dirac spacetime (or vice versa). Or to be more precise, the 20 components of this derivative almost match up with the 20 components of the tensor, but there is a subtle difference in 6 of the components, that have to be tweaked to take account of the fact that the electron comes in three generations. The three generations arise from differentiating Einstein 3-space with respect to Dirac 3-space, rather than with respect to another copy of Einstein 3-space.

But most remarkable of all, this derivative is quantised, so that where the curvature tensor is quantised by 5 neutrons and a neutrino, the replacement is quantised by 3 electrons (one from each generation) and 3 protons. I haven’t quite understood what this means physically, but I think it provides a physical mechanism by which Einstein and Dirac spacetimes can drift apart, one atom at a time.

New preprints and old

March 9, 2022

Today the arxiv posted a new version of my paper “Integer versions of Yang-Mills theory” at, in which you can find more details of some of the things I have been writing about recently. In particular, I have added a detailed discussion of the equivalence or otherwise of the Einstein and Dirac definitions of mass, and a precise mathematical explanation for why the hypothetical “spin 2 graviton” is a myth. The latter is because the “spin 2” part of the model is non-compact (in a precise technical sense), and Yang-Mills theories are always compact.

For historical interest only, the first time I proposed the current model in writing was in July 2019, in the paper, that was a revision of the 2015 paper The latter was simply drawing attention to the remarkable formula I had found for the masses of the three generations of electron, and proposing it as more plausible than the Koide Formula. The revision was an attempt to relate the formula to a discrete model of quantum mechanics, but there wasn’t enough rigorous mathematics for this to be really successful.

The mathematical proof of inequivalence of Einstein mass and Dirac mass was included in in April 2019, revised in in May 2019. If you look at these papers you will see that at that time I had a somewhat different interpretation of the result, and only gradually came to the interpretation I now prefer.

All of these papers contain a lot of speculation about physical interpretations, not all of which has stood up to scrutiny, so they need to be taken with a big pinch of salt. Nevertheless, I claim that they contain important and fundamental ideas that should be taken seriously and discussed, rather than rejected out of hand.

Lieutenant Kije

March 8, 2022

I wonder if Lt. Kije is still fighting in the Russian Army, his legendary, but entirely fictitious, exploits reported daily to the Commander-in-Chief? This is one of many hypotheses I have examined in recent days in an attempt to comprehend the incomprehensible. While many commentators have looked to history for parallels, and there is much written about Putin harking back to the days of Khrushchev or Brezhnev, this “standard model” of Russian/Soviet history does not seem to me to get to the heart of the matter. Putin is not interested in Khrushchev or Brezhnev, or Stalin or Lenin, he wants to be Peter the Great.

You may think this is nonsense, but in order to understand Putin, you have to get inside his mind. To understand his mind, you have to get inside your own mind. I got inside my own mind, and I realised that I am not interested in Feynman, or Dirac, or Einstein, or Maxwell or Hamilton, I want to be Isaac the Great (or Sir Isaac Newton, as he is sometimes known). So, if you want to deal with Putin, study the history of Peter the Great, to find out where the weak points are. Peter the Great was not satisfied with the title Tsar, used for the rulers of Russia from 1547, and proclaimed himself Emperor in 1721. Newton was older than Peter the Great, but they both died in the 1720s. At the time of the publication of Newton’s Principia, Peter had been Tsar for five years.

So, if you want to deal with attacks from the standard models of physics, study the work of Sir Isaac Newton, to find out where the weak points are. I did. I know where the weak points are. And I have attacked them relentlessly for several years. And I make jokes out of them. Comedy and satire are the most powerful weapons against the humourless rulers of orthodoxy, of whatever form. Those who take themselves too seriously are always doomed to fail in the long run. Real comedians, like Zelensky, know how to see life from both sides and balance the two. They know, in other words, where to draw the line between a joke and seriousness. Those who know only seriousness are liable to go down in history as a (sick) joke.

String theory is one of those sick jokes. It should have succumbed to the waves of glasnost and perestroika in the 1980s and 1990s, but it did not. The KGB deployed its thought police to ensure that string theory maintained its one-party rule over theoretical physics. Still we hear the same mantra “the only game in town” – that is simply because it has deliberately, cynically and obstructively destroyed all other games in town, and continues to do so.