Archive for the ‘Uncategorized’ Category

Peer review

November 17, 2022

It is no secret that the system of peer review that is supposed to keep the progress of science on the straight and narrow is badly broken. This isn’t a new problem, although it certainly appears to be worse now than it was a few decades ago, but it is almost as old as the history of science itself. It is in essence one of those “unconscious bias” problems. Unconscious biases against the non-male or the non-white are not the only ways in which peer review exerts a malign influence on the progress of science. Unconscious bias against the innovative is equally culpable.

Ask any individual peer-reviewer, and they will deny any such bias. But it is an established fact that is proved in the aggregate. Research Councils in the UK woke up to the fact many years ago, when they realised that they were funding only safe, predictable and boring research, and the exciting and innovative stuff was no longer happening. They reacted by forcing their reviewers to evaluate innovation and speculation as positive rather than negative. But it hasn’t had enough of an effect, and it hasn’t had any effect on universities, which stifle creative innovation coming from below, and impose stultifying “innovation” from above.

Another demonstrable unconscious bias of peer review is a bias against interdisciplinary research of all kinds. This is effectively a bias of peer reviewers against all disciplines other than their own. Research Councils and other research funders have to react by specifically diverting funds into interdisciplinary research. But these funds are often not taken up, because interdisciplinary scientists are squeezed out of their jobs by the insidious effects of peer review within universities. I know this from personal experience – by 2014 I had moved whole-heartedly into an interdisciplinary area between mathematics and physics – and within three years, my academic career was at an end. I am not alone – this is a generic problem for interdisciplinary research, caused by the mechanisms of peer review, and needs to be addressed at a fundamental level.

Truly innovative thinkers are always discriminated against in academia, which is heavily biased in favour of the status quo, and likes a comfortable existence. Anyone who threatens to rock the boat in any way is punished, often by being thrown out of the boat and left to drown. New ideas are only allowed to come from the top, never from the bottom.

The worst part of peer review, however, happens not in research funding bodies or universities, but in journals. Journals have ceased to be a vehicle for dissemination of ideas, as they once were, and have become a vehicle for profit and status. They still use what they call “peer review”, which is a form of slave labour in which academics provide their work for free to keep the journals making profits. Peer reviewers often take their revenge by writing shoddy, ill-informed reports in which their unconscious (or conscious) biases have free reign to do their worst, under cover of anonymity.

I know this, because I have just received such a report. The reviewer bases their recommendation on the assumption that the paragraphs labelled “Speculative remark” in my paper form the “main point”. Now the universal convention in the scientific literature is that paragraphs labelled “Remark” are peripheral to the main text, and can be omitted without damage to the main arguments. They never form the “main point” of anything. The journal was the Journal of Mathematical Physics, the editors of which ignored these grounds on which I submitted an appeal, and simply repeated the insulting and untrue comments of the reviewer.

Unfortunately, taking time to read a scientific paper properly, to understand what it says and critique it fairly, is something that no academic these days can afford to do – there simply isn’t time, and there is no credit to be gained from it. So academics have largely given up doing it, and resort to quick short-cuts that make the unconscious bias problem much worse than it used to be. As a result, peer review no longer works. It is a system that is no longer fit for purpose, and must be abandoned if scientific progress is to resume.

Peer review creates large herds of scientists who are unwilling or unable to think for themselves. Real progress in science relies on the lone wolf who thinks outside the box. The wolf is extinct in the UK, and progress in science is going the same way.



November 13, 2022

I don’t claim to be an expert on cooking, but it seems to me that there are essentially two schools of thought: there are those who look at the recipe first, and then get the ingredients; and there are those who look at the available ingredients, and then find the recipe. I belong firmly to the second school of thought. If I have to invent a new recipe that no-one has thought of before (unlikely, but still) then that is what I will do. Some culinary disasters undoubtedly arise from this strategy, but some remarkable successes can also arise.

Much the same applies to theories of physics. There is the theoretical school of thought, that looks at the textbooks, and tries to find the ingredients (e.g. curved spacetime, dark matter, spin 2 gravitons, supersymmetry, etc etc), with conspicuous lack of success. There is the practical school of thought, that looks at the evidence provided by experiment, and tries to find a way to cook up a theory that looks and tastes like the universe we observe.

Now in my cupboard I have a lot of ingredients that many people consider inedible. You do have to be careful with them, because they can be poisonous if not cooked properly. Acorns, beech nuts, mahonia berries, laurel berries, fuschia berries – all grow in my garden, and can be eaten if you know how to treat them. But why would I need to, when we’ve had the best apple season for years?

Theoretical physics uses a number of ingredients that many people consider inedible. You do have to be careful with them, because they can lead you astray. Differential geometry, spin connections, chiral spinors, Clifford algebras, gauge groups – they all grow in my garden, and can be useful if you know how to treat them. But why would I need to, when my group algebras provide the tastiest apple pie theories you could ever hope for?

Of course, those physicists who are looking for ever more exotic ingredients that grow only in some as yet undiscovered (and probably mythical) spice islands are not interested in something as simple, straightforward and wholesome as apple pie. But, trust me, if you understand apples as well as I do, and as well as Newton did, then you have no need to look any further.


August 24, 2022

My joint paper with Corinne Manogue and Tevian Dray, entitled “Octions: An E_8 description of the Standard Model,” was published online today, 08-24-2022, in Journal of Mathematical Physics (Vol.63, Issue 8). It may be accessed via the link below:
DOI: 10.1063/5.0095484

It represents one view of how E8 can contain the Standard Model of Particle Physics, and incorporate three generations of fundamental fermions. It does not contain any of the more radical proposals that I have made to alter the Standard Model rather than extend it.

What is wrong with General Relativity?

August 14, 2022

It has been obvious for the best part of half a century that there is something wrong with General Relativity, Einstein’s theory of gravity that is supposed to explain how the universe fits together. I won’t rehearse the evidence here – you can find lots of it on tritonstation or darkmattercrisis (see blogroll). But the difficult question is what is wrong with it? And how do we put it right? Well, I’m glad you asked…

There are many things wrong with GR, but the most basic and most important is that it is based on the principle of conservation of mass: the principle that the total mass of an object stays the same (though if it falls apart, burns or explodes, you might have some trouble accounting for all the little bits of it). But we now know that mass is not conserved, for example in radioactive decay on Earth or nuclear fusion in the Sun. We can hardly blame Einstein for this, because these experiments were decades in the future at the time he devised the theory.

You might also say, does it matter? These changes in mass are small details, and if you account for all the energy lost in the process, surely everything will be all right? Unfortunately, it is not a small detail, it is a fundamental principle, and it is wrong. It means that the symmetry group of the theory is wrong, because it does not take account of the fact that mass can change. Einstein used the Lorentz group SO(3,1) under which mass is both conserved and invariant. He extended to “general covariance”, which means you can use any coordinates you like for spacetime, and still get the same answer. That means you can use any coordinates you like for momentum and energy, but you are not allowed to change your mass coordinates.

That is why it doesn’t work properly: in the real universe, you have to be able to change your mass coordinates. Your theory has to be covariant under SO(4,1), not generally covariant, which means covariant under GL(4,R).

Which brings me to another problem. Despite the advertisements, GR is not a theory of gravity. Let me explain. Newton’s theory of gravity was a theory of matter: how matter moves relative to other matter. It was not a theory of how matter moves relative to space. This is important, because it means you do not need a physical “space” in which matter moves. In any case, the existence of such a “space” (called “aether”) was already long discredited by the time of Einstein’s GR. But strange to tell, Einstein’s theory is a theory of spacetime. It is a theory of how spacetime moves relative to matter. But there is no such thing as spacetime, so how can it move?

Well, you may say it’s just a mathematical abstraction that is useful in the equations, and that doesn’t mean it has a physical reality. That is the same way physicists try to explain away the wave-functions in quantum mechanics, and it fails for the same reason: reality itself disappears, and we all just become figments of the physicists’ fevered imaginations. A theory of gravity must be a theory of how matter moves relative to other matter. For that we need the concepts of mass, momentum and energy. Nothing else. Einstein’s mass equation tells us the symmetry group here is SO(4,1).

Two clumps of matter are each described by 5 coordinates: one for mass, one for energy and three for momentum. The force between them (if we assume it is instantaneous, and Newton’s third law applies) is an antisymmetric tensor in these coordinates, so is 10-dimensional in total. That is equal to the 10 dimensions in the Einstein field equations, but they are not the same. I’m going to have to spell this out in detail, I’m afraid. Hang on to your hat.

Newton had one of these 10 terms, namely m1.m2 (the mass of the first object times the mass of the second object). Einstein generalised this by adding three mass x momentum terms, three momentum x momentum in the same direction, and three momentum x momentum in perpendicular directions. All for the sake of changing m1.m2 to E1.E2, in other words using total energy instead of rest mass. The result of this is simply to change the Lorentz group SO(3,1) to SO(4), which was a lot of effort to go to in order to make no progress at all.

Now if we use the correct group SO(4,1), and the anti-symmetric tensor instead of Einstein’s symmetric tensor, then we don’t get any m1.m2 terms or E1.E2 terms, what we get instead is m1.E2 – E1.m2. Interesting, wouldn’t you say? If there are no momentum terms, then this is all there is. In Special Relativity, this collapses to zero, because the masses are constant and equal to the energies. But the reality is more complicated. The masses are not constant, and because the force propagates at the speed of light, the masses of the two objects are measured at different times, and this difference in mass is what causes the force of gravity. In Newtonian terms, m1 and m2 are the inertial masses, and E1 and E2 are the (active) gravitational masses. But it is the time delay due to the finite speed of light that causes the gravitational constant G to be non-zero.

Now consider the gravity of the Sun. It takes 8 minutes for this gravity to reach us. During those 8 minutes the Sun has burnt a lot of hydrogen to make helium, and has lost a significant amount of mass. So we think the Sun is more massive than it “really” is. Where has that mass gone? It has gone into neutrinos. Lots of them. Where have those neutrinos gone? Through the Earth. Did the Earth notice? Yes, it did. Not much, but a little. What did the Earth do when it noticed? It fell a little bit further towards the Sun. In other words, the Earth is measuring the rate of decrease in the mass of the Sun. Isn’t that clever? That is how gravity works. You heard it here first.

Symmetry and physics

August 10, 2022

A new post with this title has appeared on Peter Woit’s blog, with his typically inane content that has very little to do with either symmetry or physics. He doesn’t allow comments from anyone who actually knows anything about symmetry, because they will show up the fact that he doesn’t know much about symmetry. So he has deleted three of my comments so far, and will no doubt continue deleting as many as I submit.

My main objection to what he has written is that he thinks all (interesting) representations of all (interesting) groups are unitary. The classification of representations into orthogonal, unitary and symplectic goes back to the last decade of the 19th century, and the underlying linear algebra is older still. Of these, the unitary ones are the least interesting. If you want to understand classical physics, you need orthogonal representations and groups, and if you want to understand quantum physics you need symplectic representations and groups.

It is the stupid belief of Woit and others that unitary representations and groups describe quantum physics that is the single most important reason why they have not made any progress in 50 years. It is no good Woit pontificating about the ills of string theory, when he is just as much a part of the problem as everyone else.

Almost there

August 9, 2022

“Are we nearly there yet?”

The physicists’ answer: “Yes, we’re nearly there, any minute now.”

The mathematicians’ answer: “How do we know, until we get there?”

Physicists believe that the Standard Model of Particle Physics is “nearly there”. And has been for fifty years. Er, excuse me? What exactly does that mean? You’ve missed 49 holidays in a row sitting in a traffic jam on the motorway?

Time to wake up, find a service station, buy some coffee, SMELL THE COFFEE, and get a reality check.

Take a deep breath. Doesn’t that coffee smell GOOD? Just imagine what it will do to you when you drink it! At my service station, I have prepared some amazing coffees. You should just try them, they will blow your mind. I have got one or two decaffeinated versions, suitable for the arXiv and other sensitive people. But why bother? Why not drink the real thing?

Get rid of that hangover. See the universe in all its amazing colourful glory. Don’t listen to the physicists who tell you that the colours of Quantum ChromoDynamics are not observable. They are! That doesn’t mean you need hallucinatory drugs, but it does mean you need some good coffee.

Now, under normal circumstances, as a mathematician, I would carry on and explain what you should see when you’ve had some good coffee. But this is not mathematics, this is physics. So I have to insist that you go and get yourself a cup of coffee. I’ll wait.

Chci pivo

August 8, 2022

When you travel to a foreign country, I imagine you learn a few words of the language before you go. Some people take this very seriously, and spend months or years preparing, others may learn one or two words. The latter are more interesting, because the interesting question is, what do you learn in order to maximise your enjoyment and minimise your effort? It didn’t take me long to discover that the most important word to learn in any language is the word for beer. And the next most important word to learn is two. If you know those words, the locals will teach you everything else you need to know.

The first time I stayed in Prague (not my first stay in Czechoslovakia), on a hot summer’s day in Hradcany, I went to go into a pub, to find my way barred by a large man who asked me “Co chces?” Since I had by that time learnt a few more words of Czech, I immediately replied “chci pivo”, which seemed to be an acceptable answer, so he let me in. I flatter myself that my musical ear had given me a reasonably good pronunciation of the word “chci”, which to an English speaker is almost unpronounceable. So he probably assumed I was Czech. He soon learnt his mistake, but did not seem to regret it. In any case, it would probably have been enough if I had just said “pivo”. The word “pivo” is, as you undoubtedly know, the word for beer in most (but not all) Slavonic languages, but literally it simply means “a drink”. I suppose that goes back to the time that, in much of the world, it was not safe to drink water, and only beer was safe to drink. Thus water is for washing, and beer is for drinking.

In Finland, “olut” is, surprising as it may seem, cognate to the English word “ale”, borrowed from Swedish, and still useful in North-Western parts of Russia such as Karelia (historically Finnish) and St Petersburg, where I found it more useful to be able to count in Finnish than in Russian. In Korea, I learnt the word for beer is mekju, and the word for rice wine is soju, and then I discovered that if you want an alcoholic drink, they all end in -ju. Now that is what I call a well-designed language!

Written Korean is no less amazing. It looks like Chinese, and you imagine it is equally difficult to read. Not a bit of it. It was designed by King Sejong the Great to be a democratic writing system to destroy the power of the Chinese elite, since you can learn to read it in one day instead of ten years. And I can testify that it works: you can learn it in one day. That is because it is an alphabet, as used by all peoples west of China for thousands of years.

Written Chinese, on the other hand, is more like physics. You have to spend many years learning all the epicycles for every different word, after which you find there is a deliberate ambiguity in everything that is written, which is great for literature (especially poetry), but not so great for science. King Sejong would cut through all this nonsense, and insist on complete clarity and simplicity. So would anyone else with any sense. Why does mathematical physics still get away with writing in Chinese characters that are (a) illegible, (b) ambiguous, (c) incomprehensible, and (d) meaningless?

A lot of learning is a dangerous thing

August 4, 2022

The well-known proverb “a little learning is a dangerous thing” is a typical elitist attitude to education, no less so today than it was in the 18th century. It expresses the arrogance of the learned towards “hoi polloi”, and conveys the intended meaning that education is wasted on ordinary people. My career in education has taught me that this proverb is as jejune, negative and false as it is possible to be. The real dangers of learning lie in doing too much of it.

An example: I had a PhD student once, who was obsessed with learning, and could never do enough of it. Despite my best efforts, he never understood that a PhD was about learning by doing, not about learning by reading. He never got his PhD. A lot of learning is a dangerous thing.

Another example: when I talk to physicists about new ideas, they always know so much that it is easy for them to find a reason why my ideas are wrong. They know so much that it is easy for them to prove that *all* new ideas are wrong. They know so much, therefore, that it is literally impossible for them to accept new ideas, and therefore it is literally impossible for them to make progress. A lot of learning is a dangerous thing.

The same has always been true. The use of epicycles to describe astronomical motions was a very difficult and erudite theory, requiring vast amounts of calculation and learning. Too much learning. A new idea comes along: have you tried using ellipses instead of circles? WHAT?!! ARE YOU MAD?!! You’ll be burnt at the stake! Well, history reveals that the simple idea of using ellipses instead of circles renders all of that learning about epicycles completely redundant. A lot of learning is a dangerous thing.

I have always lived by the maxim that a lot of learning is a dangerous thing. If a project requires a lot of learning, I generally eschew it. That is why I became a mathematician, which requires very little learning, especially if you are good at it. Mathematics is about learning as little as possible, as efficiently as possible.

That is why mathematics is properly regarded as an art, and not as a science. It is not about doing calculations (of epicycles, for example), it is about avoiding calculations. Most people don’t seem to understand that.

The universe is cheating

July 31, 2022

There are some famous stories of people caught cheating, in which the primary evidence is statistical – no-one could have got that many answers right if they weren’t cheating. Secondary evidence is then found which detects how exactly they were cheating, and the rest is history. A thousand to one chance is usually considered the benchmark at which cheating is suspected, and further investigation is required. This is just as true in particle physics as it is in ordinary life. A million to one chance is usually considered the benchmark at which cheating is definitely proved, even without any evidence of how the cheating was done. This is just as true in particle physics as it is in ordinary life.

A billion to one chance is just no contest. One of my brothers told me today of just such an example he was involved in investigating. A billion billion to one chance is about as close to certainty as you could possibly get, wouldn’t you say? Why is it, then, that when the universe has been caught cheating the accepted rules of physics, at the billion billion to one level, no-one takes a blind bit of notice? No-one is going to say the universe is wrong, of course (actually, people do, sad to say) – the universe is what it is. It is the accepted rules of physics that are wrong, not the universe.

Particle physics produces answers to questions about masses of elementary particles, that are very suspiciously close to answers to questions about gravitational properties of the Solar System. How does the universe know that these apparently completely different questions have the same answers? At one level, it doesn’t matter how the universe knows. What matters is the statistical evidence that the universe does know. That means the universe knows something we don’t know. That is the biggest clue to what is wrong with our physical theories that we could ever hope to find. Why don’t we act on it?

Probably for the same reason we don’t act on global warming. We just don’t care.

A new mass equation

July 31, 2022

One of the remarkable things about the series of models I have been building is that each one suggests a new mass equation that is extraordinarily close to experiment, but not always in exact agreement. The latest model has thrown up a copy of the strong force, in which the 8 massless gluons are replaced by four fermions (up and down quarks and anti-quarks) and four bosons (pions, including two separate neutral pion states: up-anti-up and down-anti-down). In particular, the sum of these four pion masses should have a sensible meaning. Previously, of course, I have taken for granted the standard model assumption that there are three pions, not four, and never found any meaning at all for the sum of three pion masses.

Two charged pions at 139.570 and two neutral pions at 134.977 makes 549.094 +/- .001, which is quite close to the eta meson (closely related to pions) at 547.862 +/- .018, with a discrepancy of only 1.232 +/- .018. What do you think this discrepancy can be? The difference between an up quark and a down quark? The difference between a proton and a neutron? The latter weighs in at 1.293, or 3.4 standard deviations away from 1.232. So, this explanation is unlikely, but not very unlikely. A textbook I have to hand (2008 revision) gives the eta mass as 547.51, or 20 standard deviations from the current value, so it is very likely that the experimental uncertainty in this mass has been underestimated (as often happens in particle physics).

Still, there are serious objections to such a formula, not least the fact that the charges don’t match. This suggests we need both the proton/neutron difference and the up/down quark difference, at which point the uncertainties in the quark masses completely swamp the discrepancy we are trying to account for, so all bets are off.

There is another possibility, that the two neutral pion states actually have slightly different masses. If so, then the value measured by experiment is a (weighted) average value. In what proportion do you think the two states occur in typical experiments? I would hazard a guess that there are more of the up-anti-up state in proton-proton interactions, and more of the down-anti-down state in neutron-neutron interactions. Experiments, I believe, are biased towards proton-proton interactions, so one would expect a bias in this direction. On the other hand, neutrons are more common than protons in matter, so perhaps the bias goes the other way? In any case, a bias probably exists.

All this discussion is somewhat inconclusive, and all we can really say at the moment is that m(\eta) \approx m(\pi^+)+2m(\pi^0)+m(\pi^-) with a discrepancy of about .2% that is somewhat less than the neutron-proton mass difference and may have a related cause.