April 13, 2021

Brains have evolved over billions of years, mainly for the purpose of endowing the owner of the brain with a superior power to outwit, evade and overpower their enemies, in order to survive in a hostile environment and pass on an inheritance to their children. The main purpose of a brain, therefore, is to negotiate the difficulties of everyday life. The brains of theoretical physicists, like the brains of most other people, are largely devoted to this task. Anyone who wants to employ clever people, whether they be physicists or anyone else, to think about problems other than the problems of day-to-day life, needs to ensure that they do not need to spend too much of their brainpower on dealing with the problems of everyday life.

In earlier times, such people were either from wealthy backgrounds and did not need to worry too much about everyday problems, or simply didn’t care about having enough to eat or a warm place to live. Such people could often be found quite cheaply, by providing them with a warm enough place to live and enough to eat, and allowing them to spend their brainpower on thinking about other things. Hence the success of the mediaeval universities. Nowadays, we have largely reverted to the older style, that if you want to think for yourself you have to be either wealthy, or prepared to live in a tent.

It is hard to understand how we came to this pass. The premise is irrefutable. In my time in academia, over the best part of half a century, the fiscal powers have done their utmost to ensure that many of the cleverest brains waste most of their time in pointless tasks aimed at ensuring their own survival. The whole point of these powers employing these brains is precisely to avoid this problem. After a while I refused to play the game any more, because life is finite and I wanted to spend what remaining time I might have thinking about the real problems, not about the problems of how to write a grant proposal to pay a meagre salary to someone I would then have to spend a lot of time working with on problems I was no longer interested in. The result was predictable: I took early retirement by mutual agreement with my employer.

Too many theoretical physicists are having to spend too much of their valuable brainpower on ensuring their own survival, instead of thinking about the fundamental problems. No-one these days can afford to spend ten years thinking about a problem in the way that Einstein did. That is why there is no new Einstein. And never will be, while this crazy situation continues in universities the world over.

Failure of unification?

April 10, 2021

I think I am going to have to give up reading Peter Woit’s blog. The relentless negativity of it is just so depressing. In today’s discussion he again goes over the top to over-hype the undoubted failure of one or two attempts at unification as a failure of the whole idea of unification. If that is your attitude, you might as well just give up and go home, and stop infecting everybody else with your negativity.

My PhD supervisor taught me that it was important to work on four problems at the same time: one easy, one hard, one trivial, and one impossible. That is what I have always tried to do, and continue to do – except that, now I have retired, I’ve more or less abandoned the easy and hard problems, and restrict myself to the trivial and the impossible. But it is essential to understand the word impossible in the sense that the US Armed Forces use: “the difficult we do immediately; the impossible takes a little longer”.

This is the sense in which we need to understand the “impossibility” of unification. You have to believe in the possibility of unification, or you should not be in the business at all. The current situation is that two or three promising ideas for unification have failed. How many ideas are there for unification? Hundreds and hundreds. How many ideas do people like Peter Woit listen to? None.

The problem is obvious. It is not the lack of ideas. It is the lack of listening.

Muon g-2

April 9, 2021

There has been a lot of excitement about the latest measurement of the gyromagnetic ratio of the muon, and the confirmation that the measured value of g-2 differs significantly from the value calculated using the standard model. Both experiments that measured this value, 20 years apart, were conducted in the same 15-meter diameter storage ring, so that there is no control for the size of the ring, and therefore no control for the variation in the direction of the gravitational field from one side of the ring to the other.

It is completely clear that experiments of this kind *must* control for effects of this kind, and if they don’t, then the conclusions cannot be considered robust in any way. The rush to predict new forces and new particles is premature, when the experiment has not ruled out the possibility that the “new force” is nothing more nor less than our old friend gravity. If you have a candidate quantum theory of gravity, now is the time to use it.

Well, my quantum theory of gravity already explains the CP-violation of neutral kaon decay as an effect due to the change in direction of the gravitational field. The actual value of the effect in that case seemed to be about 3/4 of the sine of the angle between the directions of the gravitational field at the two ends of the experiment, but the apparent factor of 3/4 is not statistically significant, and a factor of 1 is completely consistent with the experimental results.

So let us attempt the same thing in this case. The angle between the two directions of the gravitational field is approximately .015/6000 radians, so that the sine of this angle is around 2.5 parts per million. The reported discrepancies between theory and experiment are around 2.4ppm for the original Brookhaven experiment, and 2.0ppm for the new Fermilab experiment, with a weighted average of 2.15ppm, described as 4.2 sigma.

The discrepancies between experiment and my conjecture are therefore .1ppm for Brookhaven, .5ppm for Fermilab, and .35ppm for the weighted average – in all cases less than 1/4 of the discrepancies from the standard model. Time for people to start listening to me?

There is no evidence at all for any new physics here. Instead there is clear evidence for a mixing of gravity with the standard model.


April 1, 2021

There are two important fundamental forces for life: electromagnetism and gravity. The former, in its quantum form, is the basis of chemistry, therefore of biochemistry, therefore of life as we know it. But what of quantum gravity? Does that not also have an effect on life? By ignoring bio-gravity, are we ignoring half of the facts of life? Of course we are! By only studying what we can see (with photons), and not what we can feel (with neutrinos), we fail miserably to understand what life is, where it came from, what is consciousness, what sleep is for, and what is death.

So here is my manifesto for the new subject of biogravity, that is the application of quantum gravity to biological problems. At the basic quantum level we need to distinguish between atomic number (or lepton number), that is the number of electrons, that determines electromagnetic and chemical properties, and atomic mass (or baryon number), that is the number of protons and neutrons, that determines gravitational properties. The ratio of baryon number to lepton number is equal to 1 for hydrogen (H), and 2 for carbon (C), nitrogen (N) and oxygen (O), the basic elements of organic chemistry.

In particular, there is a huge bio-gravitational difference between the structural elements (C,N,O) and the hydrogen coat. Most other biologically important elements lie in the range 2.0 to 2.1. This includes sodium (2.09), magnesium (2.02), phosphorus (2.07), sulphur (2.00), chlorine (2.09), potassium (2.06), calcium (2.00) and iron (2.15). Elements with higher ratios are generally avoided, including lithium (2.31), beryllium (2.25), boron (2.16), fluorine (2.11). Heavy metals, with ratios between 2.4 and 2.5, are mostly highly toxic.

So the basic question now becomes, to what extent is this choice of elements down to chemistry, and to what extent is it down to gravity? Clearly chemistry is important: gold is not toxic, because it has almost no chemistry. But equally, for the same reason, it is of no use to most life-forms that we know of. What about lithium? Is it its chemical reactiveness that makes it a potent drug, or is it its biogravitational effects that are important?

The important applications of biogravity are in the 3-dimensional structures of life, such as the DNA/RNA helix, and the folding of proteins to make complicated 3-dimensional shapes. The helix has a chirality, which in life is always the same. In particle physics, likewise, neutrinos are always left-handed. Gravity also has a chirality, which is not often recognised: we are significantly affected not only by the Earth’s gravity, but also the gravity of the Sun and the Moon, and the three associated rotations, of the Earth on its axis, of the Moon around the Earth, and of the Earth around the Sun, create a massively chiral environment for life.

In other words, tidal forces acting on the primordial soup at a molecular level create a tendency for molecules to twist around each other in one particular direction. Thus biogravity is an essential ingredient in the origin of life: without the Moon, there would be no DNA or RNA. Once life got going, however, the external gravitational effects of the Moon could be replaced by internal biogravitational control mechanisms. So that although the Moon is necessary for the origin of life, it is not so essential for its continuation. Whatever biogravitational process evolution has come up with as a replacement for the Moon, can be adapted for all sorts of molecular origami. Once the basic mechanism is in place, you just need a book of instructions that you can read to make any particular shape that you might need. And you need a printing press to print multiple copies of the book.

But I must point out that quantum electrodynamics on its own is not sufficient for a theory of molecular origami, because it is not chiral. Without the neutrinos to tell you which is left and which is right, you have only dead 2-dimensional sheets of paper, not living proteins.

What is sleep for? It must be for turning off as much biochemistry as possible, to allow the biogravity room for manoeuvre. Shutting out the photons, and allowing the neutrinos to do their work. Where do dreams come from? Are they brought to us by neutrinos travelling from other parts of the world? How do our brains continue working on problems while we are asleep? Are they picking up neutrino signals that we are blissfully unaware of? Too many questions, too few answers – as you’d expect in a new subject with huge potential.

If we can pick up neutrino signals while we are asleep, could this explain alleged paranormal effects, such as telepathy, predictive dreams, astrology, psychics and so on? Could such a mechanism drive the appearance of ghosts, or even poltergeists or psychokinesis? What about levitation? Could we control local biogravity to such an extent?

What about consciousness? Does it arise from an interplay between biochemistry and biogravity? What about the soul? Do we have souls made out of neutrinos? When we die, is it because we have lost our neutrinos? Do our souls literally “go to heaven”, or become one with the cosmos? Is mental illness not so much an imbalance in brain chemistry, as an imbalance in brain gravity, that is an imbalance in brain neutrinos? What effect do neutrino oscillations have on brain biogravity?

Maybe you feel that my neutrinos are in need of some re-balancing. There certainly seem to be a lot of them buzzing around in my brain.

Beauty and the Beast

March 27, 2021

Maybe you have seen this latest announcement:

which reports on some new ways in which the universe stubbornly refuses to obey the rules that theoretical physicists have laid down for it. But what conclusion do they draw from this? That the model is wrong? Heaven forbid! No, it must be the universe that is wrong!

So, do you side with the beauty quark, doing what it always does and always has done in the universe, or do you side with the beast (aka the Frankenstein’s monster of a standard model) that is trying to force the poor quark into doing its will? Is the universe wrong, or is the model wrong?

It is some six years now since it first became clear to me, from examining the experimental evidence, that the weak and strong nuclear forces (especially the weak) cannot be understood independently of gravity. My latest attempt at founding a model that combines the weak force with a quantum gravity was submitted to the arXiv nearly three weeks ago, but is still “on hold” – which I take as code, meaning that they want to reject it, but they can’t think of a good excuse for doing so.

This paper is instalment 4 of a series that starts with

  1. arXiv:2009.14613: A group-theorist’s perspective on symmetry groups in physics.
  2. arXiv:2011.05171: Subgroups of Clifford algebras.
  3. arXiv:2102.02817: Finite symmetry groups in physics.

The first is a general introduction to the symmetry groups in fundamental physics, why they don’t fit together, and what might be done about it. I examined three scenarios: (a) transplant the groups from particle physics to relativity, (b) transplant the groups from relativity to particle physics and (c) start again with some finite groups to build a genuine quantum theory. I rejected the first (perhaps prematurely), on the grounds that it is incompatible with special relativity. The other two are then investigated in detail in the next two papers.

The second paper attempts therefore to build a model of particle physics that is generally covariant, in the sense of having a symmetry group SL(4,R) or GL(4,R). Despite some semblance of progress, this attempt seems to fail for much the same reason that the Pati-Salam model, built on SU(4), fails, and for much the same reason that a direct quantisation of general relativity using GL(4,R) fails: in all cases, there are symmetries in the model that do not seem to correspond to symmetries in the real physical universe.

The third paper attempts to build a quantum theory from scratch, using nothing more than the existence of three generations of spin 1/2 electrons as its inspiration. This, I believe, succeeds remarkably well, since it produces all of the gauge groups of the standard model out of essentially nothing. But what it tells us about gravity is that the symmetry group is not GL(4,R) as Einstein told us, but only GL(3,R).

This might seem innocuous to you or me, but it is apparently so shocking and so outrageous that no mainstream theoretical physicist is prepared to listen to a word of it. Because GL(3,R) does not contain the Lorentz group SO(3,1). So any theory of gravity built on SO(3,1), such as general relativity, is inconsistent with the basic principles of quantum mechanics. Well, we knew that in the 1930s, so it shouldn’t be too shocking. What seems to be so shocking and outrageous is that I am proposing we should do something about this problem, instead of ignoring it.

So that is what my latest paper attempts to do.


It shows, in fact, that the same conclusions can be obtained completely independently of quantum mechanics, by re-examining the Lorentz transformations and the Lorentz group. Relativity, both special and general, is based on the reality of spacetime. Of course, we regard it as self-evident that space and time exist. But experiment casts some doubt on this assumption. Consider for example the twin clocks experiment: two identical very accurate clocks are synchronised, and one is sent on a long journey. When it comes back, it is found to have lost time relative to the clock that stayed at home. Now ask yourself, which clock is telling the correct time? If you think about this question clearly enough, you will realise that there is no such thing as the “correct” time.

In other words, there are serious dangers involved in allowing the Lorentz group to act on spacetime. There are hidden assumptions that might lead us astray. It is much safer to allow the Lorentz group to act on the electromagnetic field, which we know is quantised by photons that actually have a real physical existence. Well, yes and no. Certainly we can allow individual Lorentz transformations to act on the electromagnetic field. But if there is no 4-dimensional spacetime for them to act on, we cannot use such a non-existent action to deduce how they act on the 6-dimensional field. We might have got this wrong.

That would be even more shocking. That is the subject of paper number 5 in the series.

Amateur group theory

March 15, 2021

Group theory is an extremely powerful tool, in the right hands. When used by amateurs, without adequate training, it can be very dangerous. It is my professional opinion, based on deep study over many years, that the groups that are used in the various parts of fundamental physics have been cobbled together by amateurs, and are not fit for purpose. I therefore see it as my mission to find some better groups, that do a better job of describing the actual symmetries of physical reality.

I have tried many options, and often found some bit of group theory or representation theory that seems to describe some part of physics better than the current standard models. Some have turned out to be red herrings (that is to say, wrong), others have led in different (and therefore contradictory) directions. Some have posed problems of interpretation as bad as, if not worse than, Einstein’s problems of interpretation of spacetime. But eventually, a confluence of the ideas has started to appear. They all seem to be leading to the same place.

There is only one problem, and that is that this confluence does not contain the Lorentz group. Thus I have been forced to consider the possibility that the Lorentz group is only an approximation. My somewhat bruising encounter with was in part designed to test this idea. And it was successful. Those who engaged in the discussion unwittingly revealed the weak spots in the standard arguments, as indeed I hoped they would. So I am no longer worried that my proposals are inconsistent with Lorentz symmetries of spacetime. Because I can see where the Lorentz symmetries are only approximate, and I can see how my group repairs these approximations, and makes the symmetries exact.


March 13, 2021

Back in August last year, I wrote about reification of various concepts of mathematical physics. I didn’t seriously address the problem of reification of spacetime, which is an issue that has been of central importance to physics for at least 150 years. In the 19th century, it was phrased in terms of the existence of a “luminiferous aether” that is, a substrate that “carries” light. The Michelson-Morley experiment is generally regarded as proof that such an aether does not exist. But since the aether was nothing more nor less than a reification of spacetime, the logical conclusion is that spacetime itself is an illusion. Accepting this logical conclusion, however, was apparently a step too far.

Maxwell’s theory of electromagnetism did not seriously question whether space and time were real physical “things”. Nor did Einstein’s special or general theory of relativity. But the failure of general relativity to provide a description of the large-scale universe that is consistent with what astronomers observe requires us to revisit this question.

Experiment demonstrates conclusively that photons exist, and that they are capable of reifying the electromagnetic field in a way that is consistent both with Maxwell’s equations and with experiment. So the electromagnetic field has been successfully reified. Not so spacetime. So we need a symmetry group of the electromagnetic field. But we do not necessarily need a symmetry group of spacetime. If spacetime is an illusion, peculiar to each individual observer, then it does not need a symmetry group, or rather, it does not have a symmetry group.

So the question is, what is the symmetry group of the electromagnetic field? Special relativity says it is the group SO(3,C) of orthogonal transformations of a complex 3-space. This is weird. This is the only place in the whole of theoretical physics where a non-compact symmetry group is used. Why? There must be a reason. Probably a very good reason. But I can’t see it. And when I went on and asked, I was treated like an imbecile. They were quite happy to explain how Lorentz transformations worked in 1+1 spacetime dimensions, but when I asked about 2+1 spacetime dimensions, they were unable to answer, and resorted to insults to get rid of me.

Everywhere else in physics where there is a complex vector space, it is always assumed to be unitary. Not here. Why not? Is this a mistake? It is clear to me that the physicists who replied to me on don’t understand the problem, and simply accept the dogma that has been handed down through the generations, without actually understanding what it means. Mathematically, it is a question of whether a certain complex number needs to be replaced by its complex conjugate at a particular point in the theory.

It’s only a theory, so why not try both and see which one works better? No, apparently, that is a waste of time, because they know what the correct answer is. Well, excuse me, but knowing the correct answer in advance of the investigation is the surest way I know of screwing things up. I’m doing the investigation, and the more I work through it, the clearer it becomes that it was indeed a mistake. The symmetry group of the electromagnetic field appears in fact to be SU(3), or rather U(3), and not SO(3,C), that is SO(3,1). The latter is only used because it is supposed to be a symmetry group of spacetime, and SU(3) does not act on 4-dimensional spacetime.

But if you think clearly enough about it, experiment proves that spacetime is an illusion. The most conclusive proof is the experiments with clocks, that send two identical clocks on different journeys, such that when they come back to the same place in space, they disagree about the time. I’m sorry, but if you can’t see that that disproves the existence of spacetime as a meaningful concept, let alone a physically real thing, then I have no sympathy with your failure to construct a consistent physical model of reality.

Nullius in verba

March 13, 2021

After 360 years the motto of the Royal Society (of London) is wearing a little thin. As a motto for how science should be done, it is second to none. As for how science is done, these days, it is completely and utterly ignored. I don’t even have to argue the case. It is self-evident.

The trouble with physics

March 9, 2021

In 2006, Lee Smolin published a book with this title. If you haven’t read it, I recommend you do. It is a good book. He identifies quite a number of “Troubles with physics”, but I wouldn’t say that he identifies “the” trouble with physics.

More recently, I have identified a number of troubles with the mathematics that underlies theoretical physics. Each time I have thought that I’d identified “the” trouble, it turns out that there is an even deeper trouble. Most of this blog is concerned with a trouble that I discovered at the beginning of 2019, which is essentially that although there is a mathematical equivalence between the rotation group SO(3) of space and the quotient of the spin group SU(2) by scalars, the assumption that this equivalence has a physical meaning leads inevitably to a contradiction. At the time, I thought I had discovered “the” trouble with physics. And in a sense I still do think that. But the problem is broader and deeper.

The problem is to understand the difference between two (as in SU(2)) and three (as in SO(3)). You may have noticed a number of posts in which I meditate on this difference at some length. Mathematically, these numbers 2 and 3 are dimensions. The 3 is the dimension of physical space. And after a while it dawned on me that the 2 is also the dimension of physical space. So that the trouble with quantum mechanics is that it is a 2-dimensional theory in a 3-dimensional world. The third dimension therefore hides all the unexplained bits of quantum mechanics, from Heisenberg uncertainty to the Born rule, from Schroedinger’s cat to neutrino oscillations, from entanglement to decoherence, from the origin of mass to the arrow of time.

Of course, no-one believes me, because they learnt in school that the spin group is a double cover of the rotation group, and since they don’t really understand this, they just repeat it like a mantra. What they don’t realise is, that they don’t need to understand it, because although it is true, it is irrelevant to physics.

There is a second, related, problem, that SU(2) requires complex numbers (or, worse, quaternions), which also has the effect of removing it from the real world. Hence complex numbers infect almost all parts of theoretical physics, and one has to go to enormous trouble to get them back out again, so that the result can be interpreted in the real world. What physicists don’t realise is, that they don’t need these complex numbers, because they can use SL(2,R) instead, by the simple expedient of taking the factor of i out of the second of the three Pauli matrices.

Hence all of the theories that use SU(2), SL(2,C), SL(2,R) and so on are inherently 2-dimensional theories. This includes electromagnetism, and therefore special relativity, and general relativity, and the theory of the weak force. General relativity, for example, is a small perturbation of a 2-dimensional theory of gravity that applies in the 2-dimensional Solar System. They can all be upgraded to 3-dimensional theories by simply extending the 2-dimensional group SL(2,R) to SL(3,R), and adding in a real scalar to measure energy and time.

There are only two genuinely 3-dimensional theories in fundamental physics, namely Newtonian gravity and quantum chromodynamics. Unfortunately, they are both wrong. But they can be quite easily corrected. All one needs to add to Newtonian gravity to make it a correct and universal theory of gravitation is to add the assumption that the force of gravity, like electromagnetism, propagates at the speed of light. All one needs to do to correct QCD is to take out the irrelevant complex numbers, and thereby replace SU(3) by SL(3,R). And add in a scalar for measuring mass. And quantise, to get GL(3,Z).

Doing this unites all the four fundamental forces of nature in the symmetry group GL(3,R) of all invertible 3×3 matrices. This is the group generated by the Lorentz transformations, written with respect to the observer-independent basis (x-ct,y-ct,z-ct,ct) instead of the observer-dependent basis (x,y,z,t). The Lorentz group, on the other hand, is not a universal symmetry group for spacetime, since it relies on a distinguished set of observers, called inertial observers. It cannot therefore be used as a symmetry group for a universal force such as electromagnetism.

This removes another difficulty from the conceptual foundations of physics, that is Minkowski spacetime, and the mixing of space and time implied by the Lorentz group. The correct group is GL(3,R), which reveals that time is universal, and space is emergent. The whole difficulty arises from the illusion that space is real, and the resulting attempt to use coordinates for space in the theory. This attempt succeeds to a certain degree, but unfortunately hard-wires the observer into the theory. In particular, it hard-wires the motion of the Earth into every theory that assumes the laboratory frame is an inertial frame.

One ring to rule them all

March 7, 2021
Three rings for the Newtonian field of gravity,
Seven for the quantum theory of electricity,
Nine for the Einstein tensor doomed to die,
One for the dark matter and the dark energy,
In the depths of spacetime where the shadows lie.
One ring to rule them all, one ring to find them,
One ring to bring them all, and in the darkness bind them,
In the depths of spacetime where the shadows lie.


Now those of you who know the plot of the Lord of the Rings will instantly grasp the moral of this story. (Spoiler alert!) The quest is to destroy the dark matter (Sauron), after which physicists will live happily ever after, except that they will get home to find their beautiful little (standard model) Shire devastated and unrecognisable. And the Newtonian Elves will depart across the Western Sea, their work done once the new unified theory starts to rule Middle-Earth. And the electromagnetic Dwarves (Maxwell’s demon, Schroedinger’s cat, Bell’s theorem, the EPR paradox and all the other hidden variables) will be heard of no more. And the nine mortals will understand their mortality, and accept it as a mathematical fact that cannot be altered. No longer string-wraiths, without detectable bodies, and with purely theoretical mass, only detectable when they hitch a ride on some matter, they dissolve into primordial massless neutrinos. Photons to photons, neutrinos to neutrinos, that is simply a fact of the universe. But they can be recycled, and new matter will arise out of the discarded neutrinos, and the universe will continue for ever and ever, world without end. And without beginning.