# Lasers, masers, two-state systems and Feynman’s Lectures

The past few days I re-visited Feynman’s lectures on quantum math—the ones in which he introduces the concept of probability amplitudes (I will provide no specific reference or link to them because that is apparently unfair use of copyrighted material). The Great Richard Feynman introduces the concept of probability amplitudes as part of a larger discussion of two-state systems—and lasers and masers are a great example of such two-state systems. I have done a few posts on that while building up this blog over the past few years but because these have been mutilated by DMCA take-downs of diagrams and illustrations as a result of such ‘unfair use’, I won’t refer to them either. The point is this:

I have come to the conclusion we actually do not need the machinery of state vectors and probability amplitudes to explain how a maser (and, therefore, a laser) actually works.

The functioning of masers and lasers crucially depends on a dipole moment (of an ammonia molecule for a maser and of light-emitting atoms for a laser) which will flip up and down in sync with an external oscillating electromagnetic field. It all revolves around the resonant frequency (ω0), which depends on the tiny difference between the energies of the ‘up’ and ‘down’ states. This tiny energy difference (the A in the Hamiltonian matrix) is given by the product of the dipole moment (μ) and the external electromagnetic field that gets the thing going (Ɛ0). [Don’t confuse the symbols with the magnetic and electric constants here!] And so… Well… I have come to the conclusion that we can analyze this as just any other classical electromagnetic oscillation. We can effectively directly use the Planck-Einstein relation to determine the frequency instead of having to invoke all of the machinery that comes with probability amplitudes, base states, Hamiltonian matrices and differential equations:

ω0 = E/ħ = A/ħ = μƐ0/ħ

All the rest follows logically.

You may say: so what? Well… I find this very startling. 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: here is the link to the paper.

What’s the implication? 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!

I actually find this more than startling: it is shocking! I started studying Feynman’s Lectures – and everything that comes with it – back in 2012, only to find out that my idol had no intention whatsoever to make things easy. That is OK. In his preface, he writes he wanted to make sure that even the most intelligent student would be unable to completely encompass everything that was in the lectures—so that’s why we were attracted to them, of course! But that is, of course, something else than doing what he did, and that is to promote a Bright Shining Lie

[…]

Long time ago, I took the side of Bill Gates in the debate on Feynman’s qualities as a teacher. For Bill Gates, Feynman was, effectively, “the best teacher he never had.” One of those very bright people who actually had him as a teacher (John F. McGowan, PhD and math genius) paints a very different picture, however. I would take the side of McGowan in this discussion now—especially when it turns out that Mr. Feynman’s legacy can apparently no longer be freely used as a reference anyway.

Philip Anderson and Freeman Dyson died this year—both at the age of 96. They were the last of what is generally thought of as a brilliant generation of quantum physicists—the third generation, we might say. May they all rest in peace.

Post scriptum: In case you wonder why I refer to them as the third rather than the second generation: I actually consider Heisenberg’s generation to be the second generation of quantum physicists—first was the generation of the likes of Einstein!

As for the (intended) irony in my last remarks, let me quote from an interesting book on the state of physics that was written by Doris Teplitz back in 1982: “The state of the classical electromagnetic theory reminds one of a house under construction that was abandoned by its working workmen upon receiving news of an approaching plague. The plague was in this case, of course, quantum theory.” I now very much agree with this bold statement. So… Well… I think I’ve had it with studying Feynman’s Lectures. Fortunately, I spent only ten years on them or so. Academics have to spend their whole life on what Paul Ehrenfest referred to as the ‘unendlicher Heisenberg-Born-Dirac-Schrödinger Wurstmachinen-Physik-Betrieb.

# The mystery of the elementary charge

As part of my ‘debunking quantum-mechanical myths’ drive, I re-wrote Feynman’s introductory lecture on quantum mechanics. Of course, it has got nothing to do with Feynman’s original lecture—titled: on Quantum Behavior: I just made some fun of Feynman’s preface and that’s basically it in terms of this iconic reference. Hence, Mr. Gottlieb should not make too much of a fuss—although I hope he will, of course, because it would draw more attention to the paper. It was a fun exercise because it encouraged me to join an interesting discussion on ResearchGate (I copied the topic and some up and down below) which, in turn, made me think some more about what I wrote about the form factor in the explanation of the electron, muon and proton. Let me copy the relevant paragraph:

When we talked about the radius of a proton, we promised you we would talk some more about the form factor. The idea is very simple: an angular momentum (L) can always be written as the product of a moment of inertia (I) and an angular frequency (ω). We also know that the moment of inertia for a rotating mass or a hoop is equal to I = mr2, while it is equal to I = mr2/4 for a solid disk. So you might think this explains the 1/4 factor: a proton is just an anti-muon but in disk version, right? It is like a muon because of the strong force inside, but it is even smaller because it packs its charge differently, right?

Maybe. Maybe not. We think probably not. Maybe you will have more luck when playing with the formulas but we could not demonstrate this. First, we must note, once again, that the radius of a muon (about 1.87 fm) and a proton (0.83-0.84 fm) are both smaller than the radius of the pointlike charge inside of an electron (α·ħ/mec ≈ 2.818 fm). Hence, we should start by suggesting how we would pack the elementary charge into a muon first!

Second, we noted that the proton mass is 8.88 times that of the muon, while the radius is only 2.22 times smaller – so, yes, that 1/4 ratio once more – but these numbers are still weird: even if we would manage to, somehow, make abstraction of this form factor by accounting for the different angular momentum of a muon and a proton, we would probably still be left with a mass difference we cannot explain in terms of a unique force geometry.

Perhaps we should introduce other hypotheses: a muon is, after all, unstable, and so there may be another factor there: excited states of electrons are unstable too and involve an n = 2 or some other number in Planck’s E = n·h·f equation, so perhaps we can play with that too.

Our answer to such musings is: yes, you can. But please do let us know if you have more luck then us when playing with these formulas: it is the key to the mystery of the strong force, and we did not find it—so we hope you do!

So… Well… This is really as far as a realist interpretation of quantum mechanics will take you. One can solve most so-called mysteries in quantum mechanics (interference of electrons, tunneling and what have you) with plain old classical equations (applying Planck’s relation to electromagnetic theory, basically) but here we are stuck: the elementary charge itself is a most mysterious thing. When packing it into an electron, a muon or a proton, Nature gives it a very different shape and size.

The shape or form factor is related to the angular momentum, while the size has got to do with scale: the scale of a muon and proton is very different than that of an electron—smaller even than the pointlike Zitterbewegung charge which we used to explain the electron. So that’s where we are. It’s like we’ve got two quanta—rather than one only: Planck’s quantum of action, and the elementary charge. Indeed, Planck’s quantum of action may also be said to express itself itself very differently in space or in time (h = E·T versus h = p·λ). Perhaps there is room for additional simplification, but I doubt it. Something inside of me says that, when everything is said and done, I will just have to accept that electrons are electrons, and protons are protons, and a muon is a weird unstable thing in-between—and all other weird unstable things in-between are non-equilibrium states which one cannot explain with easy math.

Would that be good enough? For you? I cannot speak for you. Is it a good enough explanation for me? I am not sure. I have not made my mind up yet. I am taking a bit of a break from physics for the time being, but the question will surely continue to linger in the back of my mind. We’ll keep you updated on progress ! Thanks for staying tuned ! JL

PS: I realize the above might sound a bit like crackpot theory but that is just because it is very dense and very light writing at the same time. If you read the paper in full, you should be able to make sense of it. 🙂 You should also check the formulas for the moments of inertia: the I = mr2/4 formula for a solid disk depends on your choice of the axis of symmetry.

Dear Peter – Thanks so much for checking the paper and your frank comments. That is very much appreciated. I know I have gone totally overboard in dismissing much of post-WW II developments in quantum physics – most notably the idea of force-carrying particles (bosons – including Higgs, W/Z bosons and gluons). My fundamental intuition here is that field theories should be fine for modeling interactions (I’ll quote Dirac’s 1958 comments on that at the very end of my reply here) and, yes, we should not be limiting the idea of a field to EM fields only. So I surely do not want to give the impression I think classical 19th/early 20th century physics – Planck’s relation, electromagnetic theory and relativity – can explain everything.

Having said that, the current state of physics does resemble the state of scholastic philosophy before it was swept away by rationalism: I feel there has been a multiplication of ill-defined concepts that did not add much additional explanation of what might be the case (the latter expression is Wittgenstein’s definition of reality). So, yes, I feel we need some reincarnation of William of Occam to apply his Razor and kick ass. Fortunately, it looks like there are many people trying to do exactly that now – a return to basics – so that’s good: I feel like I can almost hear the tectonic plates moving. 🙂

My last paper is a half-serious rewrite of Feynman’s first Lecture on Quantum Mechanics. Its intention is merely provocative: I want to highlight what of the ‘mystery’ in quantum physics is truly mysterious and what is humbug or – as Feynman would call it – Cargo Cult Science. The section on the ‘form factor’ (what is the ‘geometry’ of the strong force?) in that paper is the shortest and most naive paragraph in that text but it actually does highlight the one and only question that keeps me awake: what is that form factor, what different geometry do we need to explain a proton (or a muon) as opposed to, say, an electron? I know I have to dig into the kind of stuff that you are highlighting – and Alex Burinskii’s Dirac-Kerr-Newman models (also integrating gravity) to find elements that – one day – may explain why a muon is not an electron, and why a proton is not a positron.

Indeed, I think the electron and photon model are just fine: classical EM and Planck’s relation are all that’s needed and so I actually don’t waste to more time on the QED sector. But a decent muon and proton model will, obviously, require ”something else’ than Planck’s relation, the electric charge and electromagnetic theory. The question here is: what is that ‘something else’, exactly?

Even if we find another charge or another field theory to explain the proton, then we’re just at the beginning of explaining the QCD sector. Indeed, the proton and muon are stable (fairly stable – I should say – in case of the muon – which I want to investigate because of the question of matter generations). In contrast, transient particles and resonances do not respect Planck’s relation – that’s why they are unstable – and so we are talking non-equilibrium states and so that’s an entirely different ballgame. In short, I think Dirac’s final words in the very last (fourth) edition of his ‘Principles of Quantum Mechanics’ still ring very true today. They were written in 1958 so Dirac was aware of the work of Gell-Man and Nishijima (the contours of quark-gluon theory) and, clearly, did not think much of it (I understand he also had conversations with Feynman on this):

“Quantum mechanics may be defined as the application of equations of motion to particles. […] The domain of applicability of the theory is mainly the treatment of electrons and other charged particles interacting with the electromagnetic field⎯a domain which includes most of low-energy physics and chemistry.

Now there are other kinds of interactions, which are revealed in high-energy physics and are important for the description of atomic nuclei. These interactions are not at present sufficiently well understood to be incorporated into a system of equations of motion. Theories of them have been set up and much developed and useful results obtained from them. But in the absence of equations of motion these theories cannot be presented as a logical development of the principles set up in this book. We are effectively in the pre-Bohr era with regard to these other interactions. It is to be hoped that with increasing knowledge a way will eventually be found for adapting the high-energy theories into a scheme based on equations of motion, and so unifying them with those of low-energy physics.”

Again, many thanks for reacting and, yes, I will study the references you gave – even if I am a bit skeptical of Wolfram’s new project. Cheers – JL