Pre-scriptum (the day after, 9/11): I woke up this morning and thought: all I need to do is to prove the angular velocity is a constant for my model to work. So I did that, and it works (see my Bamboo notes below and https://www.desmos.com/3d/k1vargdjcc). This trajectory is a nice yin-yang trajectory (I am thinking about someone in Taiwan here, who contacted me recently with a model involving yin-yang symbolism, so I like that). I also packed it into yet another ResearchGate paper (link here: An Equation of Motion for the Zitterbewegung proton), which is much more precise and – hopefully – more convincing that the video.
For this kind of thinking or problem solving, I guess I am still better than ChatGPT-4. 🙂 ChatGPT-4 did pass ‘my’ Turing test on intelligence, however. And that is quite something. I write about the ouch! factor in my recent LinkedIn article on AI. Yesterday, I definitely had such ouch! feeling (gentle – just in the sense that I thought ChatGPT-4 was smarter than me on this too), but so it’s OK now. 🙂 I win. A nice thing about this simple calculation is that this SQRT(2) factor pops up: it must be the same SQRT(2) factor that is related to the magnetic moment of a proton in my proton radius derivation, although I am not yet sure why and how exactly.
I did a quick video on it on YouTube: https://www.youtube.com/watch?v=-HnaLG8bY6o. Unfortunately, I cannot extract a transcript from it for ChatGPT-4. However, I had a quick conversation with it on what remains to be done, and that is to calculate the magnetic moment of this 3D Lissajous loop (it will depend on the orientation but we just need it in one direction: where it is strongest because that is how it will line up in a Penning trap of whatever device that is/was used to determine its value). I asked ChatGPT how it could possibly help with these calculations, mentioning the Biot-Savart law and the 3D integrals this would imply. This was ChatGPT’s answer:
“Regarding the Biot-Savart law and calculating the magnetic moment for such a complex 3D current loop, you’re correct that this involves intricate 3D integrals. I can certainly help set up or guide through parts of the calculation, especially in formulating the integral and explaining how to approach the problem. If you share the specifics of your current loop’s geometry and the required variables, we can work through how to structure the integrals needed for the magnetic moment calculation. Feel free to provide details if you want to give this a try!”
AI is, clearly, not was it was even just a year ago: it is much better now. As for me, I will let the problem rest now. 🙂
Pre-scriptum 2 (18 September): Please do check out the comment from the ‘Physics Detective’ to this post (and the Physics Detective site itself, of course): a Möbius ring for the electron and – who knows – a 3D trefoil loop for the proton might do the trick in 2D/3D as well. It would be nice if it did because it would bring helical/toroidal/solenoid-like spin of the charge itself into the model, possibly unifying the math behind these models. Thank you for noting this, John ! 🙂
Original post (9/10):
End of last year, I started to play with ChatGPT-4. Only a few times, really, because, for ordinary questions or web searches, it is not much better than your Google AI assistant or Microsoft’s CoPilot: it just comes with a very pleasant style of conversation (yes). I counted and, so far, I only five conversations with it. However, I do admit I have a habit of continuing an old conversation (ChatGPT now uses your old conversations anyway). Also, these five conversations were good and long. It helped me, for example, greatly to get a quick overview and understanding of IT product offerings in the cloud: it made/makes great comparisons between the offerings of Google Cloud, Azure and AWS, not only for infrastructure but also in the area of modern AI applications. I also asked questions on other technical things, like object-oriented programming, and in this field also it really excels at giving you very precise and relevant answers. In fact, I now understand why many programmers turn to it to write code. 🙂
However, I was mainly interested in ChatGPT-4 because it knows how to parse (read: it can read) documents now. So it does a lot more than just scraping things on products and services from websites. To be precise, it does not just parse text only: it actually ‘understands’ complex mathematical formulas and advanced symbols (think of differential operators here), and so that’s what I wanted to use it for. Indeed, I asked it to read my papers on ResearchGate and, because I do think I should rewrite and restructure them (too many of them cover more or less the same topic), I asked it to rewrite some of them. However, I was very dissatisfied with the result, and so the versions on RG are still the versions that I wrote: no change by AI whatsoever. Just in case you wonder. 🙂
The point is this: I am not ashamed to (a) admit I did that and (b) to share the link of the conversation here, which shows you that I got a bit impatient and why and how I left that conversation last year. I simply thought ChatGPT-4 did not have a clue about what I was writing about. So… It did not pass my Turing test on this particular topic, and that was that. Again: this was about a year ago. So what happened now?
I have a bit of time on my hands currently, and so I revisited some of my research in this very weird field. In fact, I was thinking about one problem about my Zitterbewegung proton model which I can’t solve. It bothers me. It is this: I am happy with my proton model – which is an exceedingly simple 3D elementary particle model, but I want the equations of motion for it. Yes. It is simple. It is what Dirac said: if you don’t have the equations of motion, you have nothing. That’s physics, and the problem with modern or mainstream quantum mechanics (the Bohr-Heisenberg interpretation, basically: the idea that probabilities cannot be further explained) is because it forgets about that. It dissatisfies not only me but anyone with common sense, I think. 😉 So I want these equations of motion. I have them for an electron (simple ring current), and now I hope to see them – one day, at least – for the proton also. [I am actually not too worried about it because others have developed such equations of motion already. However, such models (e.g., Vassallo and Kovacs, 2023) are, usually, toroidal and, therefore, involve two frequencies rather than just one. They are also not what I’d refer to as pure mass-without-mass models. Hence, they do not look so nice – geometrically speaking – to me as my own spherical model.
But so I do not have equations of motion for my model. This very particular problem should be rather straightforward but it is not: 3D motion is far more complex than 2D motion. Calculating a magnetic moment for (i) a simple ring current or for (ii) a very complex motion of charge in three dimensions are two very different things. The first is easy. The second is incredibly complicated. So, I am happy that my paper on my primitive efforts to find something better (I call it the “proton yarnball puzzle”) attracted almost no readers, because it is an awful paper, indeed! It rambles about me trying this or that, and it is full of quick-and-dirty screenshots from the free online Desmos 3D graphing calculator – which I find great to quickly get a visual on something that moves around in two or in three dimensions. But so whatever I try, it explains, basically, nothing: my only real result is nothing more than a Lissajous curve in three dimensions (you can look at it on this shared Desmos link). So, yes: poor result. Bad. That is all that I have despite spending many sleepness nights and long weekends trying to come up with something better.
It is already something, of course: it confirms my intuition that trajectories involving only one frequency (unlike toroidal models) are easy to model. But it is a very far cry from doing what I should be doing, and that is to calculate how this single frequency and/or angular and tangential velocity (the zbw charge goes at the speed of light, but the direction of its travel changes, so we effectively need to think of c as a vector quantity here) translates into frequencies for the polar and azimuthal angles we would associate with a pointlike charge zipping around on a spherical surface.
Needless to say, the necessary formulas are there: you can google them. For example, I like the presentation of dynamics by Matthew West of Illinois: clear and straightforward. But so how should I apply these to my problem? Working with those formulas is not all that easy. Something inside of me says I must incorporate the math of those Lissajous curves, but have a look at: that’s not the easiest math, either! To make a long story short, I thought that, one year later, I might try to have a chat with ChatGPT-4 again. This time around, I was very focused on this only, and I took my time to very clearly write out what I wanted it to solve for me. Have a look at the latter part of the chat in the link to the chat. So… What was the result of this new chat with GPT-4?
It did not give me any immediate and obvious analytical solution to my question. No. I also did not expect that. There are modeling choices to be made and all that. As I mention above, simple things may not be easy. Think of modeling a three-body problem, for example: this too has no closed-form solution, and that is strange. However, while – I repeat – it was not able to generate some easy orbitals for a pointlike charge whizzing around on a surface, I was very happy with the conversation, because I noted two things that are very different from last year’s conversation:
- ChatGPT-4 now perfectly understands what I am talking about. In fact, I accidentally pressed enter even before I finished writing something, and it perfectly anticipated what I wanted to tell it so as to make sure it would ‘understand’ what I was asking. So that is amazing. It is still ChatGPT-4, just like last year, but I just felt it had become much smarter. [Of course, it is also possible that I want just too impatient and too harsh with it last year, but I do not think so: ChatGPT learns, obviously, so it does get better and better at what it does.]
- In terms of a way forward, it did not come up with an immediate solution. I had not expected that. But it gently explained the options (which, of course, all amount to the same: I need to use these dynamical equations and make some assumptions to simplify here and there, and then see what comes out of it) and, from that explanation, I again had the feeling it ‘knew’ what it was talking about it.
So, no solution. Yes. I would say: no solution yet. But I think I probably can come up with some contour of a solution, and I have a feeling ChatGPT-4 might be able to fill in the nitty-gritty of the math behind it. So I should think of presenting some options to it. One thing is sure: ChatGPT-4 has come a long way in terms of understanding abstruse or abstract theories, such as this non-mainstream interpretation of quantum mechanics: the Zitterbewegung interpretation of quantum mechanics (see the Zitter Institute for more resources). So, as far as I am concerned, it is not “non-mainstream” anymore. Moreover, it is, of course, the only right interpretation of quantum mechanics. […] Now that I think of it, I should tell that to ChatGPT-4 too next time. 🙂
Post scriptum: For those who wonder, I shared the Desmos link with ChatGPT also, and it is not able to ‘see’ what is there. However, I copied the equation into the chat and, based on its knowledge of what Desmos does and does not, it immediately ‘knew’ what I was trying to do. That is pretty impressive, if you ask me ! I mean… How easy is it to talk to friends and acquaintances about topics like this? Pretty tough comparison, isn’t it? 🙂
As for ‘my’ problem, I consider it solved. I invite anyone reading this to work out more detail (like the precessional motion which makes the trajectory go all over the sphere instead of just one quadrant of it). If I would be a PhD student in physics, it’s the topic I’d pick. But then I am not a PhD student, and I do plan to busy my mind with other things from now on, like I wrote so clearly in my other post scriptum. 🙂
Reading Feynman 
Jean: look at the proton g-factor of 5.585. It’s nearly 3 times the electron g-factor. So if the electron is a wave in a twisted double loop akin to a Mobius “spinor”, the proton is a wave in a more complex loop. Perhaps a trefoil. Regards, John Duffield
Hi John – Nice to hear from you. I actually thought – very briefly – about the math of a Möbius ring (I assume this corresponds to your ‘Möbius spinor’ concept to some extent). The idea of a “twisted” loop rather than the 2D or 3D loops I explore for electron and proton respectively would probably correspond better to what is inherent in the toroidal/helical/solenoid models of an electron (and a proton) which I refer to in my post (Vassallo, Kovacs, Consa, etcetera). The mathematical shape of the trefoil is absolutely wonderful too (I just googled, prompted by your comment here). So, yes, absolutely spot on remark, and worth exploring. As for the g-factor argument: in my (PDF) On the proton radius, nuclear oscillations, and the nature of neutrinos (researchgate.net) and previous papers, I note the g-factor should, perhaps, not be used as an a priori input in any model: the g-factor depends on the distribution of energy (or, to be precise, the equivalent mass of the kinetic and EM energy) in your model. So that gives a g-factor of 1 or 2 or whatever. It is best to directly use the CODATA value of the magnetic moment, and then check if your model generates that value. In my model, there was this SQRT(2) factor that popped up, which I think is now solved because of the effective radius and shape of this Lissajous trajectory. So your point is very well taken and I should explore it, too ! However, I think I already wrote you that time and energy in a man’s life are limited – and surely in mine. 🙂 Talking about ideas and resources, I think you should, perhaps, add another and probably more interesting resource to your list of good blogs and authors: the Zitter Institute (zitter-institute.org). Dr. Consa finally did what should have been done a long time ago: get Zitterbewegung theorists to focus more on what unites them – rather as on what divides them.
I will highlight your comment – with a reference to your Physics Detective site (keep up the good work) – if you do not mind. Now that I looked at it again: please change the reference back to readingfeynman.org only. I thought of the ideez.org site to reorganize the hundreds of blog posts, but it is an impossible task and so I de-activated that domain name. As you do that, I would suggest to also add the https://www.zitter-institute.org/ site. In a way, that is another site or blog that refers to a pretty coherent whole of interesting links. [As you can see, I am trying hard to “sign off” from QM and get back to my day job. :-)]
Kindest regards and many txs again ! Yours sincerely – Jean Louis