Complete Unified Theory of Everything

The latest version of my C.U.T.E. paper has appeared today at arXiv:2109.06626v4. I hope you will agree with me that it is a big improvement on the previous version. I have taken out a lot of waffle, tidied up the mathematics, and re-organised everything into a more coherent and logical narrative. I beefed up the abstract a bit, but I didn’t dare try and change the title to what it should be (see above).

Those of you who have been following this blog regularly will have seen most of the physical ideas already. What you won’t have seen is the mathematical argument that drives inexorably from one simple assumption to a vast array of unexpected, surprising, beautiful and truly shocking conclusions, that destroy virtually the whole of 20th century theoretical physics in one majestic sweep.

What has become of Einstein’s castle in the air? Gone, vanished as if it had never been. What has become of quantum field theory? Gone, vanished as if it had never been. What has become of string theory? Well, actually there never was any string theory. Ground Zero. Welcome to the 21st century.

Why do batteries work?

I have never given much thought to this question until now, but I have thought long and hard about the essential differences between the four elements hydrogen, lithium, iron and lead. What is really important is the ratio of the number of neutrons to the number of protons, which is 0 for hydrogen, 1.33 for lithium, 1.15 for iron and 1.52 for lead. This is really important for all sorts of electromagnetic reasons, but what I have discovered over the past few years is that it is also important for gravitational reasons.

My model seems to imply that if you measure Newton’s “universal” constant of gravitation using iron you will get a slightly different answer from what you get if you use lead. Of course, Galileo denied this, but his experiments were not of the right kind. Cavendish did the right experiment in the 18th century, but his experiment was not accurate enough to detect the difference. In fact, it is only in the past two or three years that experiments have become accurate enough to detect the difference that my model predicts.

My model say that it is the different proton/neutron ratios that are responsible for this effect, which therefore implies a mixing between electromagnetism and gravity. This mixing is quite small, and I believe is parametrised by the fine-structure constant, approximately 1/137. But it seems to be true that the proton/neutron ratios have both electromagnetic and gravitational effects, so that this mixing is real.

Since one can easily make wet batteries with lead and hydrogen ions (from the acid), and dry batteries from lithium, it occurred to me to consider whether it makes sense to say that the battery in effect stores electrical energy in the form of (quantum) gravitational energy. And once I’d asked myself the question, the answer became obvious: yes, this is how batteries work. Both lithium and lead have more than the average proportion of neutrons, so they are more gravitationally active than they are electromagnetically active. They soak up electromagnetic energy and store it as gravitational energy, and release it again as electromagnetic energy when called upon to do so.

Quantum theory of everything

Maybe I exaggerate a bit from time to time. Not this time. Have a look at https://robwilson1.files.wordpress.com/2021/09/icosa6.pdf and tell me if you agree.

Works of art

I have read a lot of stuff about the pursuit of “beauty” or “elegance” in mathematics and in physics, both from people are “for” and “against”, but most of it seems to me to entirely miss the point. The people who are writing this stuff seem to understand nothing about art criticism, nothing about composition, or perspective, or colour, or texture, or narrative, nothing about the difference between form and content, or about communication, performance or presentation.

Both mathematics and theoretical physics must be treated in this context as art-forms, and judged as art-forms on criteria such as power, including explanatory power, and the power to provoke thought and reflection, surprise and shock, simplicity, iconoclasm, revelation, and bringing together elements that are normally kept separate. The utterly simplistic “criticism” of physical theories on the grounds that “beauty” is “irrelevant” is so shallow that I shan’t even bother to list any examples, of which there are many.

Einstein was a real artist. He understood narrative, he understood performance, he understood how to weave together different themes into a surprising, thought-provoking, iconoclastic, simple and elegant whole. This may be at least partly because he played the violin and liked to play string quartets. He famously said, everything should be made as simple as possible, but not simpler. It is the simplicity of Einstein’s ideas that are their hallmark, not their beauty. General relativity, for example, is horribly ugly. But the ideas are simple. His 1905 papers, on the other hand, are pure beauty.

I believe I am in a small minority who think that the ugliness of general relativity is a sign that it may be wrong. But this opinion is irrelevant. What is relevant is that astronomical evidence has proved beyond a shadow of doubt that general relativity is wrong. Einstein seemed to think the general relativity was very beautiful, and many people seem to agree with this assessment. I don’t. But beauty is in the eye of the beholder, so this is irrelevant.

Physics is in the eye of the beholder also. This is a truth to which lip-service is often paid, but which is almost never taken seriously. Einstein’s general principle of relativity says exactly this, but is widely misunderstood. Einstein himself abandoned it quite early on, and replaced it by the equivalence principle, which says that everybody sees physics the way we see it. This patently absurd assumption remains at the heart of theoretical physics today. But we cannot communicate with anyone who sees physics differently, so that the assumption remains unfalsifiable.

Many theoretical physicists today misunderstand Popper, and think that “unfalsifiable” means “irrefutable”. Etymologically these words may appear to be equivalent, but semantically they are almost exact opposites. Nevertheless, neither concept belongs in science. There is nothing in science that is irrefutable, and nothing that is unfalsifiable belongs in science.

Well now, I have outstayed my welcome. Six paragraphs is enough for a blog post. Any more than that and the symmetry is lost, the composition becomes untidy, the narrative falls apart, the perspective becomes confused, the texture and the colour become messy, the form and the content become divorced, the performance drags on and communication ceases, and the presentation comes to an end.

Coffee and beer

It is well-known that research, and many other types of work, consists of two phases, often dubbed “inspiration” and “perspiration”. Estimates vary about the proportions of the two, but somewhere between 1% inspiration to 99% perspiration, and 10% inspiration to 90% perspiration seems to be typical. In theoretical physics, the “shut-up-and-calculate” school has probably shifted this to somewhere in the region of 99.99% perspiration, and virtually no inspiration at all. Certainly the evidence is that there has been essentially no inspiration at all for half a century.

It is completely clear to anyone who understands the process of theoretical research on a sociological level, that perspiration work is driven by coffee, and inspiration work is driven by beer. It is therefore completely clear that theoretical physicists drink far too much coffee, and not nearly enough beer. My work since I retired has largely consisted of perspiration work in the morning, followed by inspiration work in the afternoon, followed by an early night and an opportunity for my brain to synthesise the two, ready to repeat the process the next day.

This does mean that I often drink beer (or other alcohol) earlier in the day than is perhaps good for my health, but it does wonders for my inspiration. It is possible to vary the drugs a bit, and it is not necessary to have one upper and one downer: it is only necessary to have one concentrator and one de-concentrator. Erdos for example was well-known for using two uppers, including a non-alcoholic deconcentrator. The oft-quoted maxim, due I believe to Renyi, about a mathematician (especially Erdos) being a “machine for turning coffee into theorems” only tells half the story. Both drugs are needed, and coffee alone is ineffectual.

My current rate is about 20% perspiration to 80% inspiration. That may not be good for my liver, but it is very good for my brain.

The real deal

My new preprint is posted today at arXiv:2109.06626. The previous six preprints were just warming-up exercises. This one is the real deal. Well, it will be once I’ve revised it and extended it a few times. This one really does contain the foundations for a theory of everything. It explains what is wrong with the Georgi-Glashow SU(5) theory, and what is wrong with the Pati-Salam SU(2) x SU(2) x SU(4) theory, and why they do not fit together into an SO(10) theory. It explains how SU(5) symmetry is broken to SO(5), and SU(4)=Spin(6) to Spin(5), so that the map from Spin(5) to SO(5) is the correct way to combine the two theories. It explains why strong SU(3) sometimes looks like SU(2,1) and sometimes like SL(3,R), but never like compact SU(3). It explains all the symmetry-breaking, and how the 24 parameters can be arranged in a real 5×5 trace 0 matrix, so that the 14 symmetric matrices are mass parameters, and the 10 anti-symmetric matrices are mixing angles. It explains why gluons don’t exist, and why neutrinos are the key to understanding both the strong force and gravity. It explains why there are three neutral kaons, as experiment demonstrates, rather than two, as the standard model defiantly and counterfactually insists. It explains why and how kaon oscillation is determined by the gravitational field, and correctly postdicts the magnitude of the effect. And so on.

Euclidean spinors and twistor unification

This is the title of a paper by Peter Woit, available at arXiv:2104.05099.  I didn’t read it properly at the time it came out, but I should have done. It has some genuinely new ideas in it, some of them closely related to ideas I have put forward in arXiv:2102.02817, arXiv:2104.10165 and arXiv:2106.00550. But he works entirely in the conventional setting of real and complex geometry, without any finite symmetries. 

He has a quantum gravity with an SU(2) gauge group, as I do. He treats spacetime as a spinor, as I do. He breaks the symmetry by choosing a time coordinate, as I do. He uses much the same tensor products of representations that I use, for much the same purposes, except that his representations are of the gauge groups, rather than the finite group. But he doesn’t have 3 generations of fermions, and he doesn’t have any way to put in the masses, because he doesn’t have any finite symmetries.

In fact, the paper of mine that is most closely related to Woit’s paper is the one I have just submitted, that ought to appear tomorrow, but won’t, because the inquisitors first have to check it for heresy. For example, he classifies the fermions of one generation with a tensor product (2+2)x(1+3), which corresponds in my paper to (2a+2b)x(1+3b) = 2a+2b+2b+4b+6. But for some reason he splits 2b as 1+1 in order to separate the right-handed neutrino from the right-handed electron. Conversely, he does not have the splitting 2b+4b of the right-handed quarks, which gives colour confinement.

Moreover, he interprets 6 = 2a x 3b as 3 colours of left-handed up and down quarks, where I interpret this as three generations, since in both his version and mine 3b is the adjoint representation of the SU(2) gravity gauge group. This is where the extra subtlety of the finite group is important, since 2a x 3b = 2b x 3a in my version but not in his. That is why I can have three generations, and he cannot.

On the importance of being Wrong

The importance of being wrong was drummed into me from an early age: “Them as never made a mistake, never made anything”. Mistakes are inevitable, and trying to avoid making mistakes altogether is a mistake. The most effective strategy is to accept that there will be mistakes, and to have a good method for finding mistakes and correcting them. Peter Woit makes a good point on his blog recently, that the leading lights in theoretical physics (as in many fields) do not have much experience of being wrong, and do not know how to deal with it when it happens.

Being wrong is, first and foremost, a learning experience. Those who have lost the ability to be wrong, have lost the ability to learn. By that, of course, I really mean those who have lost the ability to see that they are wrong. No-one ever really loses the ability to be wrong – but this is observer-dependent, so I prefer to use the observer-independent property of being able to see they are wrong. It is certainly the case that many of the leading lights of theoretical physics these days have lost the ability to see that they are wrong. This has been observed by many different observers independently, and can therefore be taken as an experimental fact.

If you have been following this blog, you will have noticed that I am frequently wrong. What I don’t understand is, why some people use this as an excuse to ignore me. Ideas can be, and often are, useful even when they are wrong. More or less the whole of theoretical physics relies on this incontrovertible fact. So it really is pretty silly for anyone to criticise my ideas for being wrong. They should be asking instead, are they useful?

Newton’s third law

Newton’s third law is, in my view, the single most profound observation in the whole of physics. Which is why I really do not understand why Einstein felt it necessary in his general theory of relativity to go against this law, and therefore to conclude that gravity is not a force. Don’t get me wrong, I certainly accept that this is, at least up to a point, a valid point of view. But it goes against the most basic principles of physics, and if it isn’t necessary, why do it?

Newton’s third law implies that, if a force is described by a tensor, then it is an anti-symmetric tensor. Einstein sets up his general theory of relativity on the basis of a symmetric tensor, the Ricci tensor. At this point alarm bells should already be starting to ring. When you then ask, what is it a symmetric tensor of?, and you see that it is a Minkowski spacetime, or equivalently its dual, 4-momentum, then the alarm bells should turn into an instruction to evacuate the premises immediately. Because 4-momentum as a concept denies the very existence of the fifth dimension of the Einstein equation . How can you build a theory of gravity that denies the existence of mass as a dynamic variable?

The only way to build a consistent theory is on the basis of a 5-momentum, not a 4-momentum. Instead of a symmetric tensor on 4 variables, we need an anti-symmetric tensor on 5 variables. It looks the same, if you’re not looking carefully enough – both are 10-dimensional, and 6 of the components are the same in both cases. But the other four are not. And the interpretations that are given to the 10 components in general relativity do not make sense in the context of a Newtonian force (i.e. a force that satisfies Newton’s third law).

I am tired of being told that my ideas are wrong because they contradict Einstein. My ideas are based on those of a far greater genius than Einstein, namely Sir Isaac Newton. Where Einstein contradicts Newton, instead of improving on Newton, Einstein is wrong.

The Hatter’s Mad Tea Party

Before you start to complain that the title of this post should be “The Mad Hatter’s Tea Party”, I refer you to the original source (Lewis Carroll, Alice’s adventures in wonderland, Chapter 7 (1865)), which makes it perfectly clear that it was the tea party that was mad, not the hatter. It is this carelessness with the placing of adjectives that is the cause of many of the problems with the standard model of particle physics. Specifically, I refer to the adjective “left-handed”, which is bandied about with such carelessness that its original meaning has been completely lost in the confusion.

But the reason I want to talk about the Mad Tea Party has less to do with adjectives, than with nouns. I use the Mad Tea Party as an allegory for the standard models of fundamental physics, the guests representing the various theories of special and general relativity, quantum mechanics, and weak and strong nuclear forces. In particular, quantum mechanics and general relativity both want to sit in the same seat, as a result of which everybody has to move on one place.

As I see it, in 1928 Dirac said to Einstein, “move on one place, I want a clean cup”, and parked his group SL(2,C) where Einstein’s SO(3,1) used to be. This immediately creates a contradiction between general relativity and quantum mechanics, because they cannot both occupy the same seat. So now everyone else has to move on one place as well. The result is what we call the standard model of particle physics. I used to think it was a dog’s breakfast, but now I understand it is the Hatter’s Mad Tea Party.

As long as everybody moves, everybody still has a seat. But general relativity refused to move. Well, you can have a tea-party either in the original seats or in the moved on seats, but you have to choose. For the Hatter, as you remember, Time stands still. This converts the Lorentz group SO(3,1) to the compact form SO(4) inside the symmetry group SO(4,1) of (the dual of) mass-momentum-energy. But this doesn’t happen by complexifying spacetime, as in the standard model, it happens by taking energy conservation as an axiom.

The Hatter, therefore, has left-handed and right-handed copies of SU(2) in SO(4). These are gauge groups, not spinors, and they have chiralities. The spinors are mass-momentum vectors, and do not have chiralities. So how do you get left-handed and right-handed spinors? Well, first you take two copies of the mass-momentum vector, so you can get the left-handed and right-handed groups to act on one each. Then, because the left-handed and right-handed groups are both copies of SU(2), you pretend they are the same. So now you have transferred the adjectives from the gauge groups, where they belong, to the spinors, where they do not belong. Then you need some mathematics to distinguish left from right, because you’ve thrown away the original mathematics that did that. So you extend SU(2) to SL(2,C) so you’ve got a complex structure to make the distinction. Finally you pretend that this SL(2,C) is the same as the group SO(3,1) that you started with, when it is not.

Do you see why I liken the standard model to the Hatter’s Mad Tea Party? All the work that general relativity should have been doing at the quantum level to mix up left-handed and right-handed gauge groups has been translated into some meaningless nonsense about left-handed and right-handed spinors, that cannot be interpreted in relativistic terms at all, because it has no meaning in that context. So all the work that general relativity should have been doing has had to be taken over by somebody else.

No wonder Alice (that’s me) is bemused and confused.

Anyway, I’ve been busy trying to put things back where they belong, and build a model that makes sense. The absolutely essential thing is to get rid of the spinors. They have no physical meaning, no possible physical interpretation, and are both mathematically and physically nonsensical. After that, I think it’s pretty much plain sailing.