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

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

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

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

April 13, 2021 at 6:14 pm |

It is all too true that in academia there is the need for survival. “Publish or perish” is a mantra in academia where the number of papers and citations matters more than the content and ideas in a given paper. And things like gender and race are used against many who are just trying to survive. And with the limited resources and the government putting most of its funds elsewhere (politicians never see much of a need for truth and knowledge), it looks to me a lot like the Hunger Games. And one certainly relies on one’s brain in that setting.

April 13, 2021 at 6:31 pm |

It is not so much a question of how much funding there is, it is more a case of how it is allocated. Governments are hugely culpable for allocating funding accordingly to the law of the jungle.

April 13, 2021 at 10:47 pm |

Yeah, i can very much relate to that. Due to financial reasons ultimately made me end up working for an insurance company. Having a very comfortable, secure and well paid work made me abandon the idea of an acadamic career, considering how well i did compared to others that stayed at the university. So I sadly have to agree in every way with you.

ironically now however i have maneuvered into a very comfortable situation of entirely flexible working hours, 4 workdays, working from home if i want and i can mostly pick my work as see fit.

but without the stress and too much free time the restless nights came back haunting me again with horrors of quantum theory and its unsolved mysteries 😀 – so ironically i have now more time trying to make sense of it by asking my own questions than i could when i was at the university. well, it’s not all good, since when i talk to my friends that ask me what i did last weekend i can’t tell them i spend all my time reading about conformal geometry or they declare me nuts 😛

April 14, 2021 at 6:59 am |

I rather enjoy the sleepless nights now that I realise they are an evolutionary response to solving problems. One of the purposes of sleep is for the brain to get on with thinking, without being constantly interrupted by the conscious self. And the purpose of waking up is for the unconscious brain to communicate the results to the conscious self. So a sleepless night is caused by the unconscious brain wanting to communicate a lot of results. I therefore regard it as a good thing. Last night, for example, my unconscious brain sorted out how to link the Dirac equation to the gauge group of quantum gravity, and hence determine the masses of the elementary particles. It woke me up at 3am to communicate the first part of the result, before starting work on the second. My job now is to write it all down, filling in the details as I go, so that I can communicate it to other consciousnesses.

But, as you say, most friends do not want to hear about group algebras or quantum gravity. The fact that I do not want to talk about anything else can put a strain on friendships!

April 15, 2021 at 9:59 pm

I don’t bother much the sleepness nights either… i mean having an great idea will cause your brain to be flooded with serotonin which renders it a positive experience by definition… and that serotonin light bulb will keep me sleepless until i think it through which is always satifsfying if it leads to a result. it’s only the day after that may become a negative experience if the sleep deprivation got too extensive.

What bothers me though is that because i work far off from physics i lost most connection with the people i could talk with about these topics. so without those with a deep enough knowledge to critically challenge every idea and argument i come up with is most upsetting – so i don’t know whether i’m just an idiot basing my understanding on mistakes and wrong leads, or if its even worse and some of my thoughts might actually be on point validating David Hilberts postulate that “physics is becoming too difficult for the physicists”.

I’ve tried to gain some insight on the physicsforums.com but it turns out most people there have a very hard time with any mathematical argument that goes beyound the core calculus. most physicist there seem to only know/understand the part of mathematics which they need directly for their calculations – i.e. they seem to lack critial understanding of the mathematics theories used to model physics beyound the calculus – at least this is what i observed for those most quick to answer my questions. ultimately, that makes communicating with them really hard.

…and every time i stumble upon people that i can talk to… they turn out to be mathematitians…

April 16, 2021 at 7:30 am |

I too suffer from a lack of colleagues to talk to. It means that the process of correcting my mistakes takes place more slowly than it otherwise might. And it does lead to existential doubts that have led me sometimes to abandon the project for months, if not years, at a time. By now, however, too much of the model is working out correctly for it be fundamentally wrong. I still make mistakes, of course, but it is all starting to take shape as a consistent picture of reality in all its glory.

My experience of physicsforums.com is similar to yours. Plus when I ask what I believe to be a deep question, it is interpreted instead as a stupid question, and treated accordingly.

April 16, 2021 at 6:15 am |

In your paper, “Subgroups of Clifford Algebras”, you mention near the end that going up to Cl(4,4) could help to fit in SU(3). But earlier you suggested a lot of other, smaller, also viable algebras. One that stuck out to me was Cl(1,5). There are papers by Claude Daviau on that one, and his work builds on Besprosvany’s, which starts with Dixon’s. Besprosvany uses Cl(1,5) instead of the Division Algebras, and Daviau goes further and gains a full unification with SU(3)c. The Dirac equation is in there too I’m sure. Me looking around at Clifford Algebras with a focus on both the Dirac equation and the Gell-Mann matrices keeps leading me back to this one paper of yours. I’m not entirely sure what Daviau does, but the SU(3) part caught my eye in his ideas. But I have little idea if they are leading somewhere further, as you pointed out many algebras that could build a model. Your paper is very insightful. I can’t imagine that the arxiv had something against posting it.

April 16, 2021 at 7:16 am |

One of the reasons I have abandoned this line of attack (for the moment, at least) is that there are too many possibilities, and I cannot see a clear way forward. The finite group approach seems more promising, because I can actually identify individual coordinates and parameters, such as the Weinberg angle, the Cabibbo angle, and the CP-violating phase. In the Clifford algebra approach, everything is too vague.

April 17, 2021 at 4:57 am |

According to Claude Daviau, the Dirac equation is not invariant under the Lorentz group, but SL(2, C). So the group he uses to model the Dirac equation is GL(2, C). Which is equal to his algebra of choice, CL(3). His CL(3) model then takes in the spacetime algebra, CL(1,3), and the unification happens in the enlarged algebra of CL(1,5). And he has created a full unification regarding SU(3). The model predicts a Weinberg angle of 30◦. However, he does not look at the three generations in detail, leaving work to be done on them and if his model is viable with them. And mentions an extension of the SM with complex space-time vectors that are physically interpreted as magnetic monopoles. He also claims, to incorporate gravitation, he can put in a mass term in the wave equation for the first generation of fermions, but just that first generation is all he says anything about and then says that the calculations are too long for the current paper. The work is not a complete theory and has many gray areas. I agree with your conclusion to look around at all the CL(n,m) algebras and then also that they do not provide any straightforward framework in fully unifying QM and GR, despite their insights and intricate mathematical nature (of which is very vague in the context of physical theory, as you’ve said). Tony Smith also made some models of this very same nature, only more vague because he chooses larger algebras. One was CL(1,7), which he speculated on a connection with the XLA to its 256 dimensions. That’s a good example of the vagueness, I’ll say that much. The XLA is an alphabet made by Shea Zellweger to provide a geometrical picture of the 16 binary logic operations, where one can make connections to symmetry, algebra, geometry, etc. Somehow I feel like I’ve learned more from Tony than my education has insofar provided me with! To be clear, also, I am very doubtful of the ideas that I’ve described above, but very much respect them because they inspire new insights!

April 17, 2021 at 5:14 am

For the record, I misspoke about the XLA stuff. Tony Smith was looking at the Logical Garnet, not the XLA itself. This structure takes 14 of the binary connectives (all the non-trivial ones, 16 – 2), and embeds them in a rhombic dodecahedron as to model them and help explain the propositional calculus.

April 17, 2021 at 7:40 am

Certainly many people have had many interesting ideas that seem to have something to say about various parts of the standard model. The real problem is that it seems to be necessary to deal with everything at once. The GL(2,C) part of my model also predicts a Weinberg angle of exactly 30 degrees, but this is modified by other parts of the algebra which split the complex numbers into two independent real numbers. This splitting introduces a large number of small parameters, which I am trying to identify with things like the fine-structure constant, the electron/proton mass ratio, the up/down quark/proton ratios, the two small angles in the CKM matrix, and the deviation of the Weinberg angle from 30 degrees.

What my model has, that no other model has, as far as I am aware, is a gauge group for mass: there are four masses that at present must be `gauged’ experimentally, and then all other masses are in principle determined. I am going to try and write up this bit today. It is becoming clear that one reason why I have not found enough mass equations is that there are factors of the square root of 3 all over them, and I was previously only looking for rational equations.

April 18, 2021 at 4:28 am |

Is the Lorentz group still facing reconception? Your earlier post that regards questioning Lorentz group is something that no other model has also, I believe. Penrose did identify the Mobius transformations with the Lorentz group SO(3,1), though it’s not remotely close to asking if the Lorentz group even holds genuine in all of nature. And has the binary tetrahedral group stayed around, or no longer part of any current approach?

April 18, 2021 at 7:09 am |

The one thing that has remained constant while other things have changed, is that identifying the Lorentz group SO(3,1) with the Moebius transformations, i.e. with SL(2,C), is definitely wrong. In Dirac’s original conception, this “identification” was only an analogy. Analogy is correct, identification is not. The model I am working on at the moment is an extension of the binary tetrahedral group by an automorphism of order 2, so that this group is still around, but some of the proposed interpretations have changed. The new model does have a copy of the Lorentz group SO(3,1) in it, but this group does not play an important role. More important is the group GL(4,R) of general covariance, so that by embedding spacetime in the model in a suitable place, I get a model that is generally covariant, in a way that the standard model is not.

April 19, 2021 at 5:38 pm

Quaternions seem to play a fundamental role in nature with some of the assumptions that I am making. The Quaternion group Q8 is a subgroup of the Binary Tetrahedral group 2T. And 2T is a subgroup of SU(2). And SU(2) is intricately tied to the Quaternion’s unit sphere, S3. Might an extension of 2T have a generalized version of Q8 present in its construction? And still be a subgroup inside of SU(2)?

And then SU(2) ties back to the En lie algebras (at least through Dynkin diagrams as far as I know), which could be the coincidence behind the relative success of other models that use them…

April 19, 2021 at 6:19 pm |

There is no doubt, I think, that the quaternion group is absolutely fundamental in physics. But it is also fundamental in so many things, that the difficulty is really knowing which way to go beyond the quaternion group. So many things look promising, as so many people have discovered. But which way is the right way? Currently I am looking at embedding Q8 in the semidihedral group of order 16. This looks like a good way to extend from non-relativistic quantum mechanics to relativistic quantum mechanics. I hope to post a first draft of a paper shortly.

April 20, 2021 at 2:16 am

That paper already sounds very interesting to me. Very closely related to the dihedral groups are the dicyclic groups, and with the dicyclic groups one can generalize Q8 very plainly. And with this arises some other models I’ve looked at, but they have yet to even consider looking at a ToE… or relativistic QM, which is a very exciting aspect of your model!

April 20, 2021 at 6:20 am |

The dicyclic groups are indeed an obvious generalisation of the quaternion group. They all lie inside SU(2), which makes them appealing from a physics point of view. What seems to be special about the semidihedral group is that it lies in U(2) but *not* in SU(2). That is what allows it to do the job of electro-weak unification.

April 20, 2021 at 6:30 pm

Electro-weak unification via U(2) is an interesting idea. The Weinberg-Salam model has rather dominated the field as the experimental results matched its predictions well. U(2) could have some unintended predictions, a possibility that steers many away from it, if not the giant successes awarded on the Weinberg-Salam theory already. Tony Smith, writing on the whole SM group structure in the instance I am citing, shows that there are several equivalent ways of dealing with the SM, but points out that not all of the global group structures are equivalent. He points out that John Baez said the “true” SM gauge group is smaller than SU(3) x SU(2) x U(1). Tony gives these structures for one to contemplate the SM with:

SU(3) x SU(2) x U(1)

SU(3) x U(2)

U(3) x SU(2)

S(U(3) x U(2)) [also written as U(2 x 3)]

Although the mathematics is used by advocates of the SU(5) model, at least the SM in itself has been simplified so that the trivial actions of the unnecessary Z6 symmetry is taken out effectively. The semidihedral group of order 16 is something I have yet to see in the physics literature but I think it will be so much more suitable for nature than SU(5), and if U(2) has a role in nature than sooner or later it will be the end of the era of the Weinberg-Salam electroweak interpretation!

April 20, 2021 at 7:22 pm |

I think maybe you misunderstood me: there is nothing new about using U(2) for electroweak unification. What is (probably) new is using a finite group instead. The whole point is to make the finite groups fundamental, and derive the Lie groups from them, rather than the other way round. What is fundamental is that there are three generations of electrons, not that the tau particle has approximately 3477 times the mass of the electron.

April 21, 2021 at 12:25 am

Because of my ignorance, I thought U(2) would be a new model… Is saying U(N) = SU(N) x U(1) the correct way of looking at the math, where U(2) = SU(2) x U(1), and the theory is the exact same? And they are the same gauge model? I was going to question why I have never before seen the SM as SU(3) x U(2), but it looks to be just a matter of notation… So if I took a group U(3,3), could I use the expression U(3,3) = SU(3,3) x U(1) = SU(6) x U(1) = SU(2) x SU(2) x SU(2) x U(1) = SO(3,1) x U(2)? Or U(9) = SU(9) x U(1) = SU(3) x SU(3) x SU(3) x U(1) = SU(3) x SU(6) x U(1) = SU(3) x SU(2) x SU(2) x SU(2) x U(1) = SU(3) x SO(3,1) x U(2) = SU(3) x U(2) x SO(3,1)? I am certain that with my limited scope on mathematics that I have made many mistakes, and I am not proud of showcasing my ignorance to the world, but I choose to do so anyway because knowing how wrong I am is the first step for me to make any self-progress… Please forgive me for my uneducated comments, although I do rather enjoy gaining insight that is invaluable now and for the future…

April 21, 2021 at 7:23 am |

It is not exactly true that U(N) = SU(N) x U(1): what actually happens is the U(N) is a quotient of SU(N) x U(1) by the scalar group of order N. Physicists tend not to make the distinction very clearly, or at all, and for many purposes it really doesn’t matter. But, technically, the electroweak gauge group that is often written as SU(2) x U(1) is considered by many physicists to be more accurately described as U(2). In my models, I don’t pay much attention to this issue, as it is a relatively minor (though still important) detail and there are much bigger problems to deal with.

April 21, 2021 at 11:25 pm

Beginning with SU(2) x SU(2) = SU(4), would the spheres S^3 x S^3 = S^6? I would think so because of the relation SU(4) = SO(6), but I feel like I’m doing something wrong… And also with spheres does it make sense to say that S^1 x S^3 x S^7 = S^11? The 12D sphere would relate to Dixon’s model and it’s ties to Spin(12,1), with the timelike dimension from the division algebra R = S^0 (1D sphere)… It’s likely that this is all wrong but these are even more structures I have yet to fully grasp not unlike my conception of U(N)…

April 22, 2021 at 2:26 pm |

I am not sure where you are trying to go here. SU(2) x SU(2) is not SU(4), it is Spin(4). And SU(2) acts on S^2, not S^3. And the product of spheres is not a sphere. I cannot see how a 12D sphere is relevant to physics. Yes, I can put a 47D sphere into my model, but it has no physical meaning whatsoever. I think we need 3D spheres to understand spacetime, but I can’t see the need for anything bigger.

April 22, 2021 at 2:45 pm

I wasn’t focused on physics at all, just the mathematics with a mathematical standpoint. I have no idea how to find the product of two spheres so I’ll begin reading into it, as well as some things on the basics of lie groups… I didn’t imply anything for physics with it. The whole Dixon algebra itself, in my view, is a mathematical idea of mathematical interest…

April 23, 2021 at 12:53 am

Might it be, as SU(2) = SO(3), it is tied to H because H naturally describes rotations in three dimensional space, so SU(2) acts on S^2, the three dimensional sphere… I think one mistake of mine was to take H as the four dimensional algebra that it is, and jump from there to its four dimensional unit sphere S^3. However, S^3 is parallelizable and equivalent to the lie group SU(2). Hence SU(2) being connected to the algebra H. I should’ve written S^2 x S^2 for that one question, and now I’m still looking into how to correctly solve it out…