The fine-structure constant

Let me first admit that I don’t understand what the fine-structure constant really is. It is a subtle thing to do with splitting of spectral lines, and plays an essential role in calculating in quantum electrodynamics. The constant itself is measured at almost but not quite exactly 1/137, and calculations in QED expand things in power series in this small constant.

But what it means in spectral lines is that it is a red-shift: it splits a spectral line into two very slightly different frequencies. Now what I appear to have discovered is that it is a gravitational redshift caused by the Solar System. I tried to calculate it from the orbit of the Moon around the Earth and the orbit of the Earth around the Sun, and I got a figure of 1/137.92. I then tried to add in a correction for Jupiter, and I got a figure of 1/137.009. Bingo!

If you think I have finally taken leave of my senses, and become an astrologer instead of an astronomer, you may be right. But I would like to remind you of the correct meanings of these words: Astronomy means the law of the stars, and astrology means the study of the stars. Astronomers lay down the law, and tell the stars what to do, rather like King Canute. The stars refuse to do what they are told. They obstinately refuse to go where Einstein told them to go.

I study the stars, and ask them where they are going, instead of telling them. They tell me where they are going, and I listen to them. They tell me a strange and wonderful tale. I ask them *why* they are going where they are going, and they tell me. They tell me an absolutely incredible tale. I didn’t believe it at first. I still don’t believe it. It is literally unbelievable. No-one can possibly believe it, unless they study all the evidence very very carefully. And I mean *all* the evidence.

To do this you need to suspend a huge amount of disbelief. It is psychologically almost impossible to suspend this amount of disbelief. If you do, you run a very real risk of going completely mad. I have talked at length over the years to people who have in the eyes of society at large over-stepped this line. I have been called a lunatic myself. But I know, and many people know, that lunacy actually *is* dependent on the phase of the moon. This isn’t just a word, it is an experimental fact. That means I can look at the moon, and judge how mad I am likely to be at that moment. And bi-polar disorder actually *is* dependent on the time of year – not the weather, not the length of the days, but the *change* in the length of the days.

My best ideas come at the winter solstice, and develop fastest at the spring equinox. Which, by the way, is today. Then they settle down and mature in the summer. For ten years I have suspended my disbelief in what the stars and planets are telling us about life on Earth, and they have rewarded me with a tale of such beauty and simplicity that only Tolkien’s Elves could have told such a tale. They told it to me, Bilbo Baggins, and I am trying to write it down for you. But nobody believes in hobbits any more, so you think it is fiction.

But it isn’t. If you want to understand the fine-structure constant, don’t just read the textbooks – look at the Star of Earendil. And destroy the 9+7+5+3+1 rings: epicycles, all of them. But most of all, you have got to destroy the one ring, the one ring to rule them all and in the darkness bind them – otherwise known as the Higgs boson. That is the biggest epicycle of them all, and without it the work of Sauron will be destroyed. We can go back to the Shire and rebuild science on the basis of reality and not fantasy.

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The particle zoo

There’s electrons and muons, tau particles too,
Each with neutrinos to match, it is true.
There are quarks up and down, top and bottom, charmed or strange,
All in three colours, called red, green and blue.
These are the fermions, the basic range,
From which matter is made, and me and you.

There’s pions and kaons, D-mesons and B-,
In varieties with plus charge, or minus, or free.
There are photons and gluons, the Ws and Z,
Etas and other such things, as you see.
These are the bosons, that stick fermions together,
Or blow them apart, depending on whether.

There’s leptons and mesons and baryons (or hadrons),
Including the protons, the lambdas and neutrons,
The sigmas, the deltas, the xis and omega,
And so they go on getting bigger and bigger.
This is only the start of the particle zoo –
I wouldn’t bother if I were you.

Brewing

Previously on this blog I have talked about the process of “cooking up” theories of physics, and developed the metaphor probably much further than you wanted me to. It is true that theories cooked up in this way do not last long, and get “eaten up” very quickly. Recipes for cooking are typically measured in minutes, with extremes of the order of one second and 24 hours. Brewing is an altogether more sedate process, with typical measurements in days, and extremes of the order of one hour or 24 weeks. Perhaps, therefore, I should consider the possibility that theories of physics are not so much cooked up, as brewed.

The trick then is to create a brew that can be laid down for decades, or even centuries (if you’re really ambitious). My brews don’t last that long. A beer that is still drinkable after 6 months is a good achievement, and a wine that is still drinkable after 5 years is a goal I have so far failed to achieve. The same applies to my theories of physics. But recently I have been less insistent on doing everything from scratch, and decided to allow myself to make wine from grapes grown by somebody else, and to follow their recipe instead of my own. The result was a revelation. The same applies to my theories of physics.

But my ambition is not for a wine that lasts a couple of years. I want one that lasts 20 or 30 years. The same applies to my theories of physics. The process should be measured not in minutes (as in cooking) or days (as in brewing) but in years. Which it is, of course. My theories of physics have been brewing now for about ten years. They are still fermenting strongly, not ready for bottling yet. That is as it should be. Einstein fermented his general theory of relativity for ten years. It lasted 50 years or so before it started to go off a little bit. Most people are still drinking it, and insisting that that is how it is supposed to taste. Some people started to notice the off-taste 40 years ago, and have been insisting ever since that the bottle is corked!

Vintage port is a very fine drink, and I have tasted some at 40+ years old that tasted as good as new. But even that doesn’t last for ever. I have tasted some at 30 years old that had faded to little more than sugar water. There is no point in trying to pretend that this stuff is still worth keeping. String theory started to go off 20 years ago, and is now completely undrinkable.

A new brew needs to ensure two things: (a) pure ingredients, and (b) sterilised utensils. Every tool that is used must be scrupulously cleaned to ensure no contamination from the previous brews that have gone off. That means our new theories of physics must ruthlessly eliminate all rotten ingredients such as quantum field theory and curvature of spacetime, especially excrescences of supersymmetry, dark matter, dark energy and other contamination that will ruin the brew before it has even started. And, above all, avoid any contact with the sour old guard who will turn your new brew into vinegar in days.

The kilogram

In 2019 the official definition of the kilogram changed from the mass of a particular “standard” lump of platinum/iridium alloy, to a defined value of Planck’s constant in kilogram-metres-squared-per-second. This marked the end of a long process of transformation from a gravitational definition of mass to an inertial definition. It is the same process that happened earlier to the metre – once defined as the distance between two marks on a particular bar of platinum-iridium alloy, it long ago acquired a more accurate definition via a defined value of the speed of light in metres-per-second.

What is wrong with that, you might ask? If we need more precise definitions as time goes on, surely we are allowed to change the definition from time to time? Yes, up to a point. But you have to be sure that you haven’t at the same time changed the concept that you are measuring. This is a subtle but very important point, that is never satisfactorily addressed by physicists. Philosophers sometimes concern themselves with this issue, but physicists don’t listen to philosophers.

Let us first consider the metre. The original definition allowed the Michelson-Morley experiment to determine that the speed of light in a vacuum was independent of the velocity of the observer, at least in the limited circumstances of the experiment itself. The new definition requires the speed of light in a vacuum to be independent of the observer under all circumstances. What if this isn’t actually true in the real universe? Well, in a sense this is a meaningless question. The question really is, could a more general version of the Michelson-Morley experiment detect subtle differences in the speed of light as measured by different observers, if these observers are accelerating with respect to each other?

The new definition of the metre pre-judges this issue, and assumes that this could not happen in principle. This is a very dangerous attitude to take. This is the King Canute syndrome – physicists presuming to tell the universe how to behave. For practical purposes, it doesn’t matter, because the speed of light is sufficiently constant on and around the Earth that the metre so defined is sufficiently accurate for all practical purposes. But what happens if you send a spacecraft to the outer edges of the Solar System? Can you be sure that the metre stays the same length on that scale? Can you be sure that your spacecraft remains the same size? The honest answer is no, you cannot be sure. But don’t expect a physicist to give you this answer.

If you insist on defining the speed of light to be constant in this way, then you may be forced to measure a changing metre as you travel through the universe – this leads to the “curvature of spacetime” that is the modern interpretation of General Relativity. Not Einstein’s interpretation, by the way. If, however, you regard this definition as unsafe, because it is based on hidden assumptions that are not adequately supported by experiment, then you are labelled a crackpot. In this sense, I am a crackpot – although I prefer the term “sceptic”.

Now let us consider the kilogram. Originally, masses of objects were compared to the standard mass(es) with weighing scales, which determine which of two masses is the greater. If the masses are sufficiently finely balanced that you cannot tell which is heavier, you say the masses are equal. So if you have two masses which balance each other, and which added together balance a kilogram, you can say they are half a kilogram each. And so on. But each time you halve the mass, you introduce extra uncertainty. So very small masses are very difficult to measure accurately. That is the main reason why the “standard kilogram” eventually became inadequate for modern purposes.

Weighing scales of this general type, with cast iron “standard” weights, were in universal use in shops, markets and kitchens when I was a child. Such scales compare the (local) gravitational effects on the masses directly, and therefore measure the (local) gravitational mass. There was another type of weighing machine, based on a spring of some kind, which worked by balancing a gravitational force against a mechanical force. The mechanical force is ultimately an electromagnetic force between the atoms of the mechanism being employed, so that these weighing machines measure a “compromise” gravitational/electromagnetic mass.

Experiments, of course, support the idea that gravitational and electromagnetic masses are the same, to within certain tolerances, on or near the Earth. But that is not the same as saying that they are the same, exactly, universally throughout the cosmos. Modern physics assumes they are the same, universally. I say this is an unsafe assumption. It is not adequately supported by experiment.

If you define gravitational and electromagnetic mass to be equal in this way, then you may be forced to measure mass differently for different observers. If you refuse to do so, you may be forced to conclude that the universe if full of invisible “dark matter”, to account for the discrepancy between the mass that we measure locally on Earth, and the mass that is measured locally in a distant galaxy. If, however, you regard this definition of mass as unsafe, you are regarded as a crackpot. In this sense, I am a crackpot, because I don’t believe in “dark matter”, and I do believe that different types of weighing machines are measuring different types of mass. I prefer to say I am a sceptic, because I listen more to the experimental evidence than I do to my initial hunches and inherited assumptions and prejudices. To me, a belief in “dark matter”, without experimental evidence, is the mark of a crackpot.

Now to get back to the kilogram. In the century or so that the International Prototype Kilogram in Paris was used as the definition, and many copies have been kept around the world, and calibrated and re-calibrated from time to time, some curious changes in the relative masses have been observed. While many of these changes can be explained by differences in cleaning or lack of cleaning, it is not clear that all the changes can be explained in this way. Perhaps they can, but for the moment I remain, shall we say, sceptical. It is important to note that the calibrations are not done purely gravitationally, because such calibration is not sufficiently accurate. It is done, therefore, with a mixed gravitational/electromagnetic experiment. Perhaps the ratio of gravitational to electromagnetic mass actually does differ very slightly in different parts of the world? Perhaps it actually does change very slightly over time in any given place on Earth? Either of these effects might be enough to explain any observed discrepancies that cannot be attributed to more mundane causes.

Peer review

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.

Cooking

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.

Octions

My joint paper with Corinne Manogue and Tevian Dray, entitled “Octions: An 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:

https://doi.org/10.1063/5.0095484
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?

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

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

“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.