About

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I’ve always been interested in math and physics but, unfortunately, few of us have the privilege of being able to study it on a full-time basis. About 15 years ago, I went into a bookshop in Old Delhi, and started selecting some text books. The owner of the bookshop asked me what I was looking for. An introductory textbook on physics, but it’s got to be comprehensive—including quantum math and all that, I told him. He gave me an original print edition of Feynman’s Lectures on Physics and told me that’s all I would ever need. So I started working on it but… Well… It’s kinda tough to grind through when you’ve got a day job. 🙂 So nothing much happened in those first years.

However, the so-called experimental confirmation of the reality of the Higgs field in CERN’s LHC accelerator in July 2012, and the award of the Nobel prize to the scientists who, back in the 1960s, thought that it might be there (including Peter Higgs and François Englert), then led me to buy Roger Penrose’s Road to Reality, A Complete Guide to the Laws of the Universe. So I started to try to read and understand it, and I also started writing this blog to externalize my frustration as I tried to cope with the difficulties involved. But then this blog got quite a few hits and, hence, I just continued it.

I consider myself to be of average intelligence only. However, I also consider myself to be a ‘citizen of the world’ and, hence, I think this is something we all should understand somehow. I don’t shy away from the math, however. So this is not a Guide to the Universe for Dummies. 🙂

Oh… And as for Penrose’s book, I put it aside and start re-reading Feynman’s Lectures again, which is why I have two site addresses for this blog: Reading Penrose and Reading Feynman. I have to admit most posts were basically about reading Feynman. His Lectures are the better deal,. 🙂 Maybe I’ll start reading Penrose again in some distant future, but… Well… Probably not: Penrose writes more about the math than about the physics, and I am more interested in the latter.

At this point, I should also acknowledge the incredible effort of two extraordinary people: Michael Gottlieb and Rudolf Pfeiffer, who have worked for decades to get those Lectures online. They also created a website for it which offers many more resources. That makes it accessible to all and everyone. However, there is no substitute for buying the Lectures yourself, and grinding through it yourself.

My adventure has let to a bit of an alternative explanation of it all—I call it a full-blown realist interpretation of quantum mechanics—but that shouldn’t deter you from reading one or more originals! Below you’ll find some notes I took over those many years. I should probably scrap them but I’ll leave them there to document the journey.

PS: I now think the Higgs field isn’t real. It’s just hype. Just like quantum field theory, renormalization and what have you. Classical quantum physics is OK, but theory since WWII is just Cargo Cult Science—that’s a term coined by Feynman, and he wouldn’t use it in this context, but I don’t shy away from it! Most modern physicists are mystery wallahs! I also would not want to study physics on a full-time basis. I took an MIT online course and all they do is try to brainwash you into accepting mainstream nonsense. Creativity is not encouraged—on the contrary! One of the professors I was in touch with, Prof. Dr. John P. Ralston says this about his own profession:

“Quantum mechanics is the only subject in physics where teachers traditionally present haywire axioms they don’t really believe, and regularly violate in research.”

We don’t think Prof. Ralston’s own interpretation of quantum mechanics is convincing – only ours is, of course 🙂 – but at least he’s honest about it—unlike others! We recommend you read Dr. Oliver Consa’s account of the rotten state of the subject-matter!

3 March 2016

I started this blog almost two and a half years ago. I am not where I had hoped to be. Not yet. But I do feel like I have a good grasp of quantum electrodynamics now. It feels good—like climbing Mont Blanc and seeing the summit ahead. 🙂 There is a lot more to learn before I’ll really get what it’s all about but—Hey! Feynman once wrote the following: “I think I can safely say that nobody understands quantum mechanics.” Well… I am not sure I fully understand it either—but I proved that the underlying math is structurally the same as that used in classical electrodynamical theory. So… Well… Perhaps we don’t ‘understand’ classical electrodynamics either.

19 March 2016

You probably heard about the discovery of gravitational waves by Caltech’s LIGO Lab. This makes our picture of the Universe pretty complete. As far as I am concerned, it confirms the wavefunction is, effectively, a propagation mechanism that is common to all forces. The fundamental question remains: what is the wavefunction? What are those real and imaginary parts of that ubiquitous complex-valued wavefunction?

I think I have an answer to that question now: the wavefunction does not only describe some oscillation in spacetime; it actually is an oscillation of spacetime.

Maxwell, after jotting down his equations for the electromagnetic wavefunction, wrote the following back in 1862: “The velocity of transverse undulations in our hypothetical medium, calculated from the electromagnetic experiments of MM. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”

We now know there is no medium – no aether (we do have the Higgs field, however!) – but we still haven’t answered the most fundamental question: what is it that is oscillating? We haven’t gone beyond the abstract math. I dare to say now that it must be spacetime itself. I guess that, in order to prove this, I’ll have to study Einstein’s general theory of relativity.

PS: Feynman’s developed his series of famous Lectures at Caltech. For some reason I don’t quite understand, it gives me immense satisfaction that the LIGO Lab is a Caltech initiative… Or… Well… I should add that Caltech arch-rival (MIT) is also involved. While it’s one of these things the scientific community had to find, I am so happy they did! 🙂 We live in exciting times!

6 June 2016

About three weeks ago, I brought my most substantial posts together in one document. This crowns many years of self-study, and many nights of short and bad sleep – as I was mulling over yet another paradox haunting me in my dreams. It’s been an extraordinary climb but, frankly, the view from the top is magnificent.

What a journey ! But I think I am slowly starting to find those words – the words that the Buddhist psychoanalyst, Robert Langan, refers to:

“We are in the words, and at the same time, apart from them. The words spin out, spin us out, over a void. There, somewhere between us, some words form some answer for some time, allowing us to live more fully in the forgetting face of nonexistence, in the dissolving away of each other.” (Robert Langan, in Jeremy Safran (2003), Psychoanalysis and Buddhism: an Unfolding Dialogue)

As all of physics is expressed in the language of math, I should substitute the “words” in that quote for “the math”: it’s the math that spins me out now, not the words—over some void. And the math forms some answer, for some time at least. 🙂 I also do think it allows me to live more fully – in the face of existence, or nonexistence. I am not sure which, but then existence and nonexistence are just dual mathematical spaces, so they must describe the same reality. 🙂

Post scriptum added on 6 April 2020): the mentioned document evolved into my manuscript on a realist interpretation of quantum mechanics.

3 October 2017

As expected, the LIGO team got the Nobel Prize for Physics this year. It happened just now! They should have gotten it last year but… Then… Well… I guess the professors on the Committee needed more time to understand what it’s all about. 🙂

I wrote them a congratulatory message, and sent them my paper. I can’t believe I actually did that, but I did. In the best case, I just made a fool of myself. In the worst case… Well… I just made a fool of myself.

This might be the end of my journey. I’ve reached the summit. I’ve got the answers I was looking for. This is the e-mail I sent:

Subject: Congrats from Einstein 🙂

Dear Professors – Congratulations with the well-deserved Nobel Prize.

I am sure Einstein is very pleased. So… Well… Perhaps it is time to look at Einstein’s ideas about the quantum-mechanical wavefunction again – so as to try to connect the cosmos with the nano-world again.

If we look at Planck’s constant as a scaling constant only, then the argument of the wavefunction re-acquires a physical dimension (action) and, therefore, we then just need to find a suitable physical dimension for its components. As electromagnetic fields are associated with the N/C dimension (force per unit charge), it is quite natural to associate the N/kg = m/s2 dimension (force per unit mass) with the components of the matter-wave (i.e. the real and imaginary part). To make a long story short, the wavefunction can be interpreted as a tiny traveling gravitational wave itself. The results can be derived easily, and are elegant and intuitive:

  • Probabilities are proportional to energy densities (and, of course, we get a physical normalization condition, complementing the mathematical normalization condition);
  • Schrodinger’s equation becomes a diffusion equation for energy (interpreted as a two-dimensional oscillation of mass);
  • The boson-fermion dichotomy is explained intuitively (the physical dimension of the components of the electromagnetic wave are expressed in force per unit charge (N/C), while we use the mentioned N/kg unit for matter-particles).
  • Spin angular momentum is explained by the left- or right-handedness of the matter-wave and – as an added bonus – we get the electron radius (scattering radius) from a geometric argument.
  • Also, the interpretation of amplitudes as traveling fields should also make it possible to derive the rotation matrices for amplitudes in an equally intuitive way.

I pre-published the key ideas on viXra.org (http://vixra.org/abs/1709.0390) – and also enclose them here. If not serious, then at least it’s fun as a didactic approach. I’ll probably try to publish this – in due time – in one of the more philosophical (read: less serious) journals. 🙂

Kind regards and congratulations once again.

Jean Louis Van Belle, Drs, MAEc, BAEc, BPhil

[Post-scriptum dated 23 February 2020: I would not dare to write that e-mail again—not because I lost my boldness (I didn’t) but because I don’t think the wavefunction models some gravitational wave. The idea did lead to better ideas, though.]

9 December 2017

I just published my second paper on the electronic e-print archive of the Los Alamos National Laboratories site (viXra.org). The article itself is pretty dense, but readable, and one of the reviewers e-mailed me personally—saying he loved my writing style (“very clear and readable”). He also gave me some references to recent literature on “four-cylinder” metaphors for the wavefunction.

That’s nice because… Well… He’s an eminent physicist who does not look down upon me. It was quite a struggle. The few who initially bothered to react to my attempts to make sense of Einstein’s basic intuition in regard to the nature of the wavefunction all said pretty much the same thing: “Whatever your geometric (or physical) interpretation of the wavefunction might be, it won’t be compatible with the isotropy of space. You cannot imagine an object with a 720° symmetry. That’s geometrically impossible.”

Well… Almost three years ago, I wrote the following on this blog: As strange as it sounds, a spin-1/2 particle needs two full rotations (2×360°=720°) until it is again in the same state. Now, in regard to that particularity, you’ll often read something like: “There is nothing in our macroscopic world which has a symmetry like that.” Or, worse, “Common sense tells us that something like that cannot exist, that it simply is impossible.” [I won’t quote the site from which I took this quotes, because it is, in fact, the site of a very respectable  research center!] Bollocks! The Wikipedia article on spin has this wonderful animation: look at how the spirals flip between clockwise and counterclockwise orientations, and note that it’s only after spinning a full 720 degrees that this ‘point’ returns to its original configuration after spinning a full 720 degrees.

720 degree symmetry

So… Well… I am still pursuing my original dream which is… Well… Let me re-phrase what I wrote back in January 2015: Yes, we can actually imagine spin-1/2 particles, and we actually do not need all that much imagination!

In fact, I am tempted to think that I’ve found a pretty good representation or… Well… A pretty good image, I should say, because… Well… Read my latest post. 🙂

23 December 2018

My explorations have resulted in a coherent set of papers on the viXra.org site and, hence, I would strongly suggest interested readers go there and check it all out. Frankly, I have come to the conclusion that a lot of so-called quantum-mechanical models can be explained in terms of classical physics. I therefore launched a sort of call to arms: the (quantum-mechanical) Emperor may not have any clothes. This is what I posted a few days ago.

Sent: Thursday, December 20, 2018 12:59 PM
To: All Rebels
Subject: A Manifesto for the Revolution?

Dear All – Thanks for the bilateral exchanges. Perhaps it is time to bring all spacetime rebels together here. 😊

I think we are all agreed on the fact that the Big Ship is not moving anymore. It feels like there has been a sort of academic brain freeze ever since Heisenberg imposed his Diktatur on how we should think about quantum mechanics. Orthodox quantum mechanics is broken beyond repair. Hence, we need to build our own spaceship to venture out to the New Universe. It should be small and nimble. The Seeds of the Revolution are the following:

1. The + or – sign in front of the argument of the wavefunction has a meaning. It’s a degree of freedom in the mathematical description that has not been exploited by physicists. If we want to give it a meaning, then it’s probably the spin direction. It is plain weird that we need the concept of spin in all of our discussions and models on quantum physics but that the Founding Fathers of QM chose to limit the power of Euler’s function to describe a spin-zero particle only.

Once we acknowledge that, all these weird symmetries (720-degree symmetry for spin-1/2) disappear, so there is no ‘excuse’ anymore to not think about a geometric/physical interpretation of the wavefunction. That should trigger a new burst of creative thinking. For starters, we’ll have a different interpretation of Schrödinger’s wave equation. In fact, I would dare to say that, for the first time, we will actually have a (geometric) interpretation of Schrödinger’s wave equation (and its solutions – the orbitals – of course).

2. The difference between the g-factor for spin versus orbital momentum (2 versus 1) can easily be explained by a form factor. If we think of the (free) electron as some disk-like structure (a two-dimensional oscillation, that is), then we’ll have a ½ factor in the formula for its angular momentum and the ‘mystery’ is solved. The anomalous magnetic moment is then not anomalous anymore: it’s just a coupling between the spin and orbital angular momentum that occurs because of the Larmor precession.

Schwinger’s α/2π factor says it all here: if the fine-structure constant is just a dimensional scaling factor explaining the disk-like shape of the (free) electron, then we would expect to see it pop up in some form in the final equations for the motion of real-life electron, which combines orbital motion, Larmor precession (just the effect of magnetism) and spin. I’ve re-written my paper on the anomalous magnetic moment in this sense (it’s on the Los Alamos site for rebels – yes, sorry, I don’t bother to even try to get stuff published in a proper journal) – but I need to do so more work on it. These motions are complicated and to get the coupling factor, we can – unfortunately – not just superpose motions: there is only one value for the magnetic field vector, and the magnetic moment/angular momentum of the whole thing (i.e. the real-life (disk-like) electron moving in this complicated orbital).

3. Interference and diffraction – stuff like the Mach-Zehner experiment – should be explained the way one would usually explain diffraction and interference: if we are going to force a wave through a slit or an aperture, the wave shape is going to change. We need to distinguish between linear and circular polarization ‘states’ – which become real states here! And we should think about how plane waves become spherical waves when they go through an aperture. I think a photon is a circularly polarized wave, but when it goes through the beam splitter, it might be broken up in two linearly polarized waves – each going in a different direction (to the top or, alternatively, to the bottom mirror). If one of them finds its way blocked, it will – somehow – rejoin the other direction (it might just bounce back, right?). Weak measurement shows there is something there. Weak measurement shows the idea of an amplitude is real. It’s not just a mathematical thing. We just need to do some hard thinking on wave shapes and form factors.

We’re not challenging any basic results of quantum mechanics here. We’re just challenging the standard Copenhagen interpretation, which is – basically – that we should not even try to understand what’s going on.

So… Well… On-on ! Check my papers and then think for yourself now. Let’s honor the Spirit of Ludwig Boltzmann: “Bring forth what is true. Write it so it’s clear. Defend it to your last breath.”

I would add: Please enjoy while doing so! 😊

Dōgen

24 May 2019

Weird. I had a contract with the Institute of Physics, and an endorsement by the owner of World Science Publishing, to get a proper book published. It is all ready. It’s here – on Phil Gibbs’ site. But some jealous reviewers – followers of Hestenes, or Hestenes himself – blocked the publication. They think it isn’t ‘scientific enough’. In other words: I didn’t echo what they were writing and I didn’t cite their work enough. So I am back on my day job – which is working on development projects in weird places. I’ll find time to work on this stuff again. And then I’ll just self-publish it. One shouldn’t waste time with academics.

13 June 2019

I am where I wanted to be: I think I have a comprehensive common-sense explanation for the so-called mysteries in quantum mechanics. In the QED sector, at least. I started to write small papers instead of blog posts, which I published on viXra.org and academia.edu.

This has been a long journey. Five years. It’s been a nice experience. This blog did not bomb the Internet but I was quite happy with the traffic and the encouragements. I got 150,000+ visitors over the years – and many of you left encouraging questions and comments. So it’s been a gentle and understanding community. Thanks for that !

On-on ! 🙂

Jean Louis Van Belle

PS: I am currently reviewing this website because Mr. Gottlieb complained I am using the online edition of Feynman’s Lectures a bit too liberally (see my 20/02/2020 post). We’ll do our best to make him happy. 🙂 I was planning to review the site anyway to add some references here and there to my more recent models of the photon, the electron and the proton.

9 March 2020

This weekend was a good one. I managed to compress all of my ideas into 10 pages (you can find it on either Phil Gibbs’ site or on academia.edu). In addition, while I feel I’ve been good at debunk much of the mystery of quantum mechanics (see, for example, my paper on boson-fermion theory), I got this email (below) from Oliver Consa. It’s absolutely brilliant. He does more than just debunking some faulty argument. He unequivocally proves what we’ve been suspecting all along: mainstream quantum mechanics is a bright shining lie ! It sure made my day, and I hope it makes you happy too ! 🙂

I’ve been vaguely thinking to set up a new website with all of this ‘new knowledge’ because this one as become quite unwieldy. Don’t get me wrong: I will keep this one—if only to document the historical evolution of my thoughts on all of this—but the new one would be organized around the new theory, rather than around arguing with the old one. I have an unused domain name (https://ideez.org/) which I could use for it. I’ll keep you updated on progress !

From: Oliver Consa
Sent: Saturday, March 7, 2020 10:07 PM
Subject: New paper: Something is Rotten in the State of QED

Dear fellow scientist,

I send you this mail because you have been skeptical about Foundations of Physics. I think that this new paper will be of your interest. Feel free to share it with your colleagues or publish it on the web. I consider it important that this paper serves to open a public debate on this subject.

Something is Rotten in the State of QED
https://vixra.org/pdf/2002.0011v1.pdf

Abstract
“Quantum electrodynamics (QED) is considered the most accurate theory in the history of science. However, this precision is based on a single experimental value: the anomalous magnetic moment of the electron (g-factor). An examination of QED history reveals that this value was obtained using illegitimate mathematical traps, manipulations and tricks. These traps included the fraud of Kroll & Karplus, who acknowledged that they lied in their presentation of the most relevant calculation in QED history. As we will demonstrate in this paper, the Kroll & Karplus scandal was not a unique event. Instead, the scandal represented the fraudulent manner in which physics has been conducted from the creation of QED through today.”  (12 pag.)

Best Regards,
Oliver Consa

4 April 2020

The ideez.org site – with a highly compressed realist interpretation of quantum mechanics – is ready. In any case, I’ve also incorporated the material in the other pages of this site—just in case the other site wouldn’t pick up.

Enjoy ! 🙂

5 May 2020

I combined my three last blog posts into a small paper. While doing so, it occurred to me that my search for the meaning of the wavefunction, and the quantum-mechanical wave equation (Dirac’s equation for an electron in free space, or Schrödinger’s equation for the bound electron in a (hydrogen) atom) might have come to end.

The (elementary) wavefunction models the ring current in a particle—the spin that causes the magnetic moment. As for the wave equation, there is no need for it. If it models anything, then it’s the properties of the vacuum—and Maxwell’s equations do so perfectly well. Much better, in fact, because there are no annoying aberrations such as ‘run-away electrons’ (Dirac’s problem) or other mathematical issues that need to be fixed through perturbation or renormalization theories or the assumption of quantized fields.

There was, in fact, no need to invent matter-waves. There is, therefore, also no need for pilot waves (the pilot wave theory was de Broglie’s solution to the problems he had created). When everything is said and done, it is now clear to me that the fan club of Bohr and Heisenberg did not pay enough attention to the magnetic force—inside of charged particles or in-between them. The assumptions of a ring current and a charge with a non-zero physical dimension are all that’s needed to make sense of things quantum-mechanical.

So, yes, the quantum-mechanical wave equation is a fairly meaningless construct which exists only in the mind of physicists. In contrast, the wavefunction – the solution to wave equations – exists only in our mind too, but at least it represents something real.

That’s it, then? I guess so. It took me about 15 years to arrive at this conclusion. Fortunately, it did not take me a lifetime.

27 May 2020

My articles – which I also posted on ResearchGate now (besides the usual viXra.org and academiu.edu sites) – seem to be getting some downloads. I know I should transform them into an article for a proper scientific journal, but I think some kind of popular endorsement (by readers like you) is far more important.

19 June 2020

I feel it is time to move on. In my last paper, I show that we actually don’t need the machinery of state vectors and probability amplitudes to explain how a maser (and, therefore, a laser) actually works. That’s huge!

Indeed, when looking back, I realize I’ve been systematically dismantling a lot of ‘quantum-mechanical myths’, and so this seemed to be the last myth standing. It has fallen now.

The implication is that we can analyze all of the QED sector now in terms of classical mechanics: oscillator math, Maxwell’s equations, relativity theory and the Planck-Einstein relation will do. All that was published before the first World War broke out, in other words—with the added discoveries made by the likes of Holly Compton (photon-electron interactions), Carl Anderson (the discovery of anti-matter), James Chadwick (experimental confirmation of the existence of the neutron) and a few others after the war, of course! But that’s it, basically: nothing more, nothing less. So all of the intellectual machinery that was invented after World War I (the Bohr-Heisenberg theory of quantum mechanics) and after World War II (quantum field theory, the quark hypothesis and what have you) may be useful in the QCD sector of physics but − IMNSHO − even that remains to be seen!

So I want to look at that QCD sector now. The math is going to be hellish – and I am sure I’ll find a lot of it is nonsense too – but it should be an interesting journey !

As for Feynman’s Lectures, I guess they’ve become what, perhaps, they’ve always been: old-fashioned and irrelevant, It may, therefore, be good that Mr. Gottlieb has embarked on a mission to prevent its use as reference material. 🙂 I think I’ll re-visit the posts and insert small preliminary notes to all of the mutilated posts but that will be it: I would probably re-write large sections of these posts anyway, so it is good Mr. Gottlieb has marked them as irrelevant already. 🙂

So… Well… I am signing off here. If you want to follow me, follow my new blog: ideez.org.

20 thoughts on “About

  1. I totally disagree, I thought Penrose’s book was eminently readable, definitely the clearest popular physics book I’ve read. Sure, it took work to get through some things, but to me that’s preferable to finishing [the other pop-physics books] and feeling like I knew nothing.

  2. Sirs: I tried ,unsuccesfuly, to print out the January 2015 “Strange theory of light and matter”. I recognize that it would be of enormous help in understanding Feynman’s QED. Please send copy to my email or some option to pay for hard copy to N H Gaffin 704 Endicott Ave Cinnaminson NJ 08077. Thanks Norman Gaffin

  3. I came across your blog when I bought The Road to Reality and like you, I decided to buy Feynman’s lectures because I really want to getter a better grasp of the Physics. I’ve really enjoyed reading parts of your blog even though I’m still in the very nascent stage of my reading. I guess I will go back and read all of it as I progress through climbing my own Mont Blanc. Thanks for taking the time out to write this for those of us who really enjoy reading it.

    1. Thanks for writing. It took me a long time to get through it – but it’s worth the effort. There are still many things I want to have another look at now, and maybe I’ll try to get a formal degree in physics now. I’d say the key thing is to understand Euler’s formula (complex numbers) and then, unfortunately, you do need to study the vector analysis in Volume II as well (concepts like curl and circulation). Finally, there is all the stuff related to waves (harmonics) and the principle of superposition. Good luck !

  4. Hi Jean, and first of all thank you for your book Quantum Mechanics The Other Introduction. It is the best book on Kindle! Other books are nothing compared to yours.

    I just want to let you know that the colour of the font in the book appears very pale grey on kindle paperwhite (the kindle you can read in full sunlight, the screen is black and white or grey) and hard to read because of it. I would love if you update the font to more readable black one. Please, please, please 🙂

    Thank you for your genius

    1. Dear Sergey, thanks so much for your compliment. If you like the book, please write a recommendation on the Amazon site, so its popularity increases ! I changed the font to black and uploaded it again. I also added a chapter with the dimensions of the real and imaginary component of the wavefunction – taken from my http://www.probe.live site – which is a bit of a summary of the book with a more philosophical introduction to it. Please let me know if this works better ! Cheers, JL

      1. Hi, thanks for your work!
        What about the site probe.live? Is he abandoned or am I not working correctly with him?

      2. Ok, thank you. Your site very helpful for me with my reestablishing physics after undegrad engineering 🙂 Whats next for you? doing formal degree(or already did)? or leave physics? The upcoming book is a finale?

        I think i am found the miswriting symbol (english not my native)
        deep blue -> God, Newton, Lorentz and the absolute speed of light -> Mathematical note
        * so you may think we could us that formula* use?
        this is premoderation comment, and delete this part or whole 😊

  5. For 720 degree challenge you described well above, my work is re-working Dirac’s monopole as a duopole (2 repulsive poles for the electron-nucleon interaction). At Dirac’s 1931 (9) hc/(e_mu) = 2 becomes * Pauli’s 1/2hc/(e*mu) = 1. That is, Pauli’s 1/2 becomes a hemisphere, and Bose’s wonderful proof of QM “seems to be a magnetic so I multiple one side by 2” all follow a physical model, and the ‘1’ gets rid of a set of discontinuities.
    Love your approach.

  6. Excuse me, i have a simple question, but its make me confused. this is the question:

    An engineer claims that because all objects in the world contain electrical charges within the constituent atoms, we can always generate electromagnetic waves by grasping any object around us and moving these objects in a circle above our heads. Do you agree or disagree with the claim above

    1. Hi Marco. The claim is not correct because most composite objects – such as atoms – are electrically neutral: they combine positive and negative charges. Even a very simple composite object such as a neutron does that: one positive charge and one negative charge. Hence, Maxwell’s equations tell us this will not generate an electromagnetic wave. Cheers – JL

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