Energy from nuclear fusion

In these days of soaring energy prices, it is worth thinking about nuclear fusion as a possible source of energy. I know at least one person who has spent their entire career working on this project, during which time the goal seems not to have come any closer. The question we should now ask is, what is the reason for this? Is a nuclear fusion reactor (a) a technological challenge, (b) practically impossible, or (c) theoretically impossible? Looking at the project from the outside, it seems that in the past 40 years or so it has progressed from (a) to (b). In this post I want to suggest that it may soon progress to (c), at which point the attempt becomes futile.

For this purpose I want to distinguish four different types of energy: (1) gravitational energy, (2) nuclear energy, (3) kinetic energy and heat, and (4) electromagnetic energy. The point of a power station is to convert energy from (1), (2) or (3) into (4). Some, like wind farms, go directly from (3) to (4). Hydroelectric power converts (1) to (3) to (4). Nuclear (fission) reactors convert (2) to (3) to (4). Conventional fossil fuel power stations convert (4) into (3) and back into (4) again, but in a more useful form. A fusion reactor is also supposed to convert (2) to (3) to (4), so the question is, why doesn’t it work?

Now we need to understand that we do not have a complete theory of the transfer of energy between these four different forms. We have two inconsistent theories that describe parts of this energy transfer. The part that links (2) and (4) at a fundamental level is the standard model of particle physics. This model also describes (3), so is the one we need for understanding how a fusion reactor does or does not work. There are several crucial parameters that describe the interface between (2) and (4) in the standard model. One of these is the mass of the W boson.

You may have heard that there is an inconsistency in the measurement of the mass of the W boson, significant at the 99.999999% level. Even if this confidence level is exaggerated (as it usually is in particle physics experiments), it suggests there is something badly wrong in the standard theory of the interface between (2) and (4). If so, then the current theory, that predicts a transfer of energy from (2) to (4) in nuclear fusion, may need to be replaced by a new theory, in which there is no such transfer of energy, or at any rate, a smaller transfer of energy. A smaller transfer of energy could easily transform a promising project into a dead end (q.v.).

In practice, a nuclear fusion reactor uses a very strong magnetic field to hold the fuel in place so that the fusion reaction can occur. It therefore uses a lot of (4) as input to the process that converts (2) into (3), before (3) is converted to (4) in a conventional manner. If we don’t have a proper hold on the transfer of energy from (4) to (2), then we don’t have a proper hold on the cycle of energy from (4) to (2) to (3) to (4). In the normal run of things, entropy ensures that if we cycle energy between different forms, then we lose some of that energy on the way around. This is why it is not possible to build a perpetual motion machine without some way of topping up the energy that is lost. Is it possible that a nuclear fusion reactor is actually a perpetual motion machine, and therefore theoretically impossible?

Experiment certainly seems to support this conclusion, but theory does not. The theory is known to be incomplete, and possibly even wrong in places, but surely not that badly wrong? After all, nuclear fusion does take place in the core of the Sun, and does release a lot of energy that ultimately causes the Sun to shine, so we know it is possible to get a lot of energy out of nuclear fusion. The only question is, where does that energy ultimately come from? In experiments on Earth, it may come from the electromagnetic energy that provides an artificial gravity to keep the fuel in a confined space. This suggests that we need to consider the effects of gravity, that hold the Sun together, and keep the fuel in the Sun in a confined space at high temperature and pressure to enable the nuclear fusion reactions to take place.

At this point we have no plausible theory to unify gravity with the nuclear forces, so we are reduced to speculation. But the hypothesis that the energy for nuclear fusion actually comes ultimately from gravitational energy is not at all unreasonable. We know that nuclear fusion only occurs in nature in regions of very strong gravity. Inside the Sun, the gravitational energy (1) is first converted into electromagnetic energy in the form pressure x volume (4) as well as kinetic energy in the form of heat (3), which then get converted into nuclear energy (2) by the fusion reaction, with a byproduct of more heat (3) and electromagnetic energy in the form of sunshine (4).

In other words, inside the Sun the energy lost in the fusion cycle (4) to (2) to (3) to (4) is topped up by gravitational energy. We do not have that option on Earth. Therefore a nuclear fusion reactor on Earth is a form of perpetual motion machine, which is theoretically impossible.

C, P and T symmetries

The C, P and T symmetries of classical electromagnetism are quite clear: C negates the charge, P negates one or all three directions in space, and T reverses the direction of time. It is also clear that none of these symmetries can be realised in practice: C converts electrons, of which there are zillions everywhere, into positrons, which scarcely ever exist in the real world; P converts the real world into the looking-glass world, which as Lewis Carroll reminds us, is a figment of our imagination; and T causes time to go backwards, which, as we know, does not happen.

On the other hand, the combinations of any two of C, P and T are symmetries of classical physics, including electromagnetism: CP means that if you reverse a current, you reverse the poles of the electromagnet that the current creates. CT and PT both mean essentially the same thing, from a slightly different philosophical point of view, but with the same mathematical result. Therefore the combination of all three, CPT, is *not* a symmetry of classical physics. Please take careful note of this, I will test you on it later: CPT is NOT a symmetry of classical physics.

Now let us turn our attention to quantum mechanics. In quantum mechanics, there is a theorem called the CPT theorem, which says that CPT *is* a symmetry of quantum mechanics. Ergo, quantum physics is inconsistent with classical physics. Ergo, it is not possible to derive classical physics as a limiting case of quantum physics. Ergo, the measurement problem has no solution. Ergo, the search for a theory of everything is a pointless waste of time. Ergo, why are we wasting so much money on this problem?

I prefer to argue from a realist position, not from a mathematicist position, and take as an axiom the obvious fact that quantum mechanics *is* consistent with classical physics. If this axiom is false, then the universe could not exist. The universe does exist, ergo this axiom is correct. Ergo, the CPT theorem is false. Ergo, at least one of its assumptions is false. Now let us ask, which one of the CPT theorem’s hidden assumptions is false?

Well, I don’t want to get too technical, but the proof of the CPT theorem involves an “analytic continuation” from a Lorentzian spacetime (required for classical electromagnetism) to a Euclidean spacetime (required for quantum theory). It therefore requires spacetime to be a *complex* 4-space, not a real 4-space. But spacetime, in actual hard physical reality, is real, not complex. This is a clear, and obviously false, hidden assumption.

So, if any physicist cares to argue this with me, I will prove that if the CPT theorem holds, then the universe does not exist. Or, in contrapositive form, I will prove that if the universe exists, then the CPT theorem is false. It then depends whether the physicist is a theorist or an experimentalist: if the former, they will dogmatically assert that the CPT theorem is a correct statement about the universe, and will therefore be forced to deny their own existence and that of the entire universe; if the latter, they will (dogmatically?!) assert that they and the universe do exist, and will then set about designing an experiment to test the CPT theorem to destruction.

As complicated as necessary, but not more so

You are no doubt familiar with Einstein’s famous dictum that a theory should be “as simple as possible, but not more so”. When I taught elementary mathematic logic, I set exercises to translate such sentences into the contrapositive. A theory should be “as complicated as necessary, but not more so”. That, I feel, is where physicists have gone wrong in the past half century. The Standard Model of Particle Physics was, in the 1970s, pretty clearly as complicated as necessary, but not more so. All attempts to go beyond the Standard Model, almost without exception, have been, equally clearly, more complicated than necessary, since they all, almost without exception, predict physical phenomena which have not been observed in the real world, despite extensive and very expensive searches.

My own attempts in this direction have been guided especially by the principle that the theory should be as complicated as necessary, but not more so. Some of my models are not complicated enough. Some of them are too complicated. But my guiding principle for many years has been to steer a middle ground. Of particular importance is to estimate how many free parameters there are. If there are more than 24 free parameters, the theory is too complicated. If there are fewer than 24 free parameters, the theory is probably not complicated enough.

Of course, this is only half the story. If there are 24 free parameters, then these parameters cannot be explained. This means that we need to assess the Standard Model as being more complicated than necessary, if we want to explain these unexplained parameters. That is where I get into trouble, when everybody else is looking for models that are more complicated than the Standard Model, and I insist that we should be looking for models that are less complicated than the Standard Model.

But I insist that Einstein was right: a model should be as complicated as necessary, but not more so.

Dead ends

I apologise to my readers for not writing anything here for a month – somehow I feel I’ve said everything there is to say on this subject, but yet again I have been proved wrong. An article in the Guardian yesterday by Sabine Hossenfelder is as clear a message to the general public saying “The Emperor has no clothes” as I have ever seen in such a high profile outlet. You can hear the outrage, but she is 100% correct. I could tell you what she says, but why don’t you read it for yourself?

https://theguardian.com/commentisfree/2022/sep/26/physics-particles-physicists

The argument is, in a nutshell, should you spend trillions on testing modified versions of one mainstream theory that has already been robustly falsified, or should you spend a few million here and there testing thousands of crazy ideas, one of which just might work? To me, the answer is obvious. I was brought up on the proverb about not throwing good money after bad. When things don’t work out, move on. Try something else. Try everything else. But the more bad money you have spent, the harder this becomes. Psychologically, the longer you carry on throwing money at a problem, the harder it becomes to stop.

Peter Woit, as usual, comments on Sabine’s article, disagrees with it, and censors other people’s comments. So I don’t recommend you go there. A bit ironic, really, when no-one takes his ideas seriously either. Except me. I think he has some really good ideas. But he is missing something that I think is important. He won’t listen to me, of course (I know, I’ve tried), so there’s another dead end.

Sabine doesn’t listen to me either, although I think her idea about virtual kaons mediating quantum gravity is a really important idea. You see, neutral kaons are observed in two different forms (or “eigenstates”, to use the technical term), which are easy to distinguish, because one of them has a lifetime nearly 1000 times longer than the other, and their decay modes are completely different. It was observed in 1964 that as the kaons travel through a gravitational field, they change from one eigenstate to another. The standard model has no physical explanation for this, but Hossenfelder’s virtual kaon version of Verlinde’s “emergent” quantum gravity possibly does. She is missing something important, however, and although I have tried to interest her in what I think this something is, so far I have failed.

My models are full of dead ends as well. I fully admit it. But when I hit a dead end, I turn round, look at my mistakes, correct them if I can, or try something else. The strange thing is, though, that every time I throw an idea away, it comes back like a boomerang. It hasn’t hit its mark yet, but it has come back to me ready to be used again. That is how I know my ideas are fundamentally right, even if wrong here and there in the details.

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 colour?

No doubt you have thought about this deep philosophical question at some stage(s) in your life. Why is the sky blue, why is grass green, why is blood red? What does ‘blue’ even mean? Do we see the same colours as other people? Do animals see the same colours we do? Why are there three primary colours? Are there three primary colours? Do we see three dimensions of colour because we sample three different frequencies of light? Could we see more dimensions of colour if we sampled more frequencies? Is colour real, or just a sensation in our brains?

In modern physics, colour is treated as an infinite-dimensional Hilbert space of frequencies, and the 3-dimensional colour that we see with our eyes is treated as a figment of our imagination, and not as physical reality. But how can an infinite-dimensional Hilbert space be physically real? Obviously it is useful as a mathematical tool for understanding the world, but it can’t be physically real. But a 3-dimensional world of “colour” could, just possibly, be physically real.

That at any rate is what my G2 model of physics proposes. Or, to be more precise, if space and time are real, then 3-dimensional colour is real. So if colour is not real, then space and time are not real either. You are free to choose whichever of these philosophical positions you want, but you are not allowed to mix and match. The reasons are two: first, physicists use time/distance (frequency/wavelength) to measure colour; second astronomers use colour to measure time/distance.

My G2 model says that the fundamental concept of physics is 7-dimensional, and consists of three dimensions of “space”, one of “time” and three of “colour”. These are the concepts we abstract from the dual concepts (measurements) of momentum, mass/energy and angular momentum, respectively. Mainstream physics does not distinguish adequately between momentum and angular momentum, and therefore sees the world in black and white. Einstein introduced 50 shades of grey into gravity, and Dirac introduced one colour (let us call it blue, after the sky) into quantum mechanics. After that, physics got the blues, as it persistently failed to reconcile Einstein with Dirac. (I won’t even mention how they tied themselves up in knots after they invented string.) So what makes me see red?

The short answer is that it is impossible to have just one colour. Colours only exist by contrast with other colours. Therefore you need at least two of them. But it is mathematically impossible to have two colours without having three, because each colour converts Einstein’s shades of grey (real numbers) into complex numbers, and there is no 3-dimensional number system, as Hamilton discovered in 1843, when he discovered quaternions. Quaternions, then, allow for a consistent world of three primary colours. In the version of Hamilton’s notation that I use, the primary colours are called I, J and K.

Let’s say I is green, J is blue and K is red. Or perhaps I should say I am green, I feel blue and I see red. In the second person you, J, are blue, feel red and see green. In the third person, K is red, feels green and sees blue. This is how the theory of relativity works in the G2 model. It is necessary to distinguish between what you see (with electromagnetism), what you feel (with gravity) and what you are (an insignificant dot on an insignificant dot orbiting an insignificant star on the outer edge of the Milky Way).

So, to relate this to ordinary physics, which tries to measure 3-dimensional colour with 1-dimensional time (i.e. frequency). Time is dual to energy, which is equivalent to mass, so that mass (which is very difficult to measure directly) is always measured as an equivalent frequency (which is much easier to measure accurately). The problem with this is that frequency depends on gravity, at least according to Einstein, so that measurements of mass that are actually made on Earth cannot be separated from the gravity that we feel. It is usually considered that this effect is too small to worry about, but I have demonstrated in many different ways that it is not.

Unification of the fundamental forces depends on unifying time with colour into a 4-dimensional concept. I am certainly not the first person to suggest that time should be more than 1-dimensional, and there is plenty of literature on the subject. Three is a popular choice, but I have been vacillating for many years between three and four. It seems I have now definitely decided that four is correct. (Until the next time I change my mind, of course.) You see, the question of how many dimensions of time there are is the same question as how many independent fundamental masses there are, and I have identified exactly four fundamental masses, of the proton and three generations of electron. The only thing that still worries me is whether the Koide formula might actually be correct – if it is, then it reduces the dimension of time down to three. But I am pretty sure the Koide formula is only approximate, not exact.

Now if you just take the Lorentz group SO(3,1) with one-dimensional time, and extend to four-dimensional time, you get the group SO(3,4). But of course this is not really the symmetry group of physics, because there really is a physical difference between time and colour, even if they do get mixed together in practice. The only group that is available to mix time and colour and space together in this way is G2. There is no other symmetry group available. Therefore G2 (the split version) is the symmetry group of the unified concept of space-time-colour.

If you fix the time coordinate, so that you fix mass and energy, what is left is the strong force (in particle physics) or gravity (in classical physics), with a symmetry group SL(3,R) acting on space-colour. In other words the “colour” of quantum chromodynamics is not just a metaphor, it is mathematically equivalent to the classical concept of colours of light. Therefore it is observable in practice, contrary to the assumptions of the Standard Model. And “gauge-gravity duality” is no longer just a vague feeling that the mathematics looks similar in gauge theories and in gravity, it becomes a genuine isomorphism between the symmetry groups in the two cases.

That is how to unify spacetime with colour to create a consistent theory of everything.

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.

Chci pivo

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?