Uncertainty, quantum math, and A(Y)MS

This morning, one of my readers wrote me to say I should refrain from criticizing mainstream theory or – if I do – in friendlier or more constructive terms. He is right, of course: my blog on Feynman’s Lectures proves I suffer from Angry Young Man Syndrome (AYMS), which does not befit a 50-year old. It is also true I will probably not be able to convince those whom I have not convinced yet.

What to do? I should probably find easier metaphors and bridge apparent contradictions—and write friendlier posts and articles, of course! 🙂

In my last paper, for example, I make a rather harsh distinction between discrete physical states and continuous logical states in mainstream theory. We may illustrate this using Schrödinger’s thought experiment with the cat: we know the cat is either dead or alive—depending on whether or not the poison was released. However, as long as we do not check, we may describe it by some logical state that mixes the ideas of a dead and a live cat. This logical state is defined in probabilistic terms: as time goes by, the likelihood of the cat being dead increases. The actual physical state does not have such ambiguity: the cat is either dead or alive.

The point that I want to make here is that the uncertainty is not physical. It is in our mind only: we have no knowledge of the physical state because we cannot (or do not want to) measure it, or because measurement is not possible because it would interfere (or possibly even destroy) the system: we are usually probing the smallest of stuff with the smallest of stuff in these experiments—which is why Heisenberg himself originally referred to uncertainty as Ungenauigkeit instead of Unbestimmtheit.

So, yes, as long as we do not look inside of the box – by opening or, preferably, through some window on the side (the cat could scratch you or jump out when opening it) – we may think of Schrödinger’s cat-in-the-box experiment as a simple quantum-mechanical two-state system. However, it is a rather special one: the poison is likely to be released after some time only (it depend on a probabilistic process itself) and we should, therefore, model this time as a random variable which will be distributed – usually more or less normally – around some mean. The (cumulative) probability distribution function for the cat being dead will, therefore, resemble something like the curves below, whose shapes depend not only on the mean but also on the standard deviation from the mean.

1920px-Normal_Distribution_CDF

Schrödinger’s cat-in-the-box experiment involves a transition from an alive to a dead state: it is sure and irreversible. Most real-life quantum-mechanical two-state systems will look very different: they will not involve some dead-or-alive situation but two very different states—position states, or energy states, for example—and the probability of the system being in this or that physical state will, therefore, slosh back and forth between the two, as illustrated below.

Probabilities desmos

I took this illustration from the mentioned paper, which deals with amplitude math, so I should refer you there for an explanation of the rather particular cycle time (π) and measurement units (ħ/A). The important thing here – in the context of this blog post, that is – is not the nitty-gritty but the basic idea of a quantum-mechanical two-state system. That basic idea is needed because the point that I want to make here is this: thinking that some system can be in two (discrete) physical states only may often be a bit of an idealization too. The system or whatever is that we are trying to describe might be in-between two states while oscillating between the two states, for example—or we may, perhaps, not be able to define the position of whatever it is that we are tracking—say, an atom or a nucleus in a molecule—because the idea of an atom or a nucleus might itself be quite fuzzy.

To explain what fuzziness might be in the context of physics, I often use the metaphor below: the propeller of the little plane is always somewhere, obviously—but the question is: where exactly? When the frequency of going from one place to another becomes quite high, the concept of an exact position becomes quite fuzzy. The metaphor of a rapidly rotating propeller may also illustrate the fuzziness of the concept of mass or even energy: if we think of the propeller being pretty much everywhere, then it is also more useful to think in terms of some dynamically defined mass or energy density concept in the space it is, somehow, filling.

propeller This, then, should take some of the perceived harshness of my analyses away: I should not say the mainstream interpretation of quantum physics is all wrong and that states are either physical or logical: our models may inevitably have to mix a bit of the two! So, yes, I should be much more polite and say the mainstream interpretation prefers to leave things vague or unsaid, and that physicists should, therefore, be more precise and avoid hyping up stuff that can easily be explained in terms of common-sense physical interpretations.

Having said that, I think that only sounds slightly less polite, and I also continue to think some Nobel Prize awards did exactly that: they rewarded the invention of hyped-up concepts rather than true science, and so now we are stuck with these things. To be precise, I think the award of the 1933 Nobel Prize to Werner Heisenberg is a very significant example of this, and it was followed by others. I am not shy or ashamed when writing this because I know I am in rather good company thinking that. Unfortunately, not enough people dare to say what they really think, and that is that the Emperor may have no clothes.

That is sad, because there are effectively a lot of enthusiastic and rather smart people who try to understand physics but become disillusioned when they enroll in online or real physics courses: when asking too many questions, they are effectively told to just shut up and calculate. I also think John Baez’ Crackpot Index is, all too often, abused to defend mainstream mediocrity and Ivory Tower theorizing. At the same time, I promise my friendly critic I will think some more about my Angry 50-Year-Old Syndrome.

Perhaps I should take a break from quantum mechanics and study, say, chaos theory, or fluid dynamics—something else, some new math. I should probably also train to go up Mont Blanc again this year: I gained a fair amount of physical weight while doing all this mental exercise over the past few years, and I do intend to climb again—50-year-old or not. Let’s just call it AMS. 🙂 And, yes, I should also focus on my day job, of course! 🙂

However, I probably won’t get rid of the quantum physics virus any time soon. In fact, I just started exploring the QCD sector, and I am documenting this new journey in a new blog: Reading Einstein. Go have a look. 🙂

Post scriptum: The probability distribution for the cat’s death sentence is, technically, speaking a Poisson distribution (the name is easy to remember because it does not differ too much from the poison that is used). However, because we are modeling probabilities here, its parameters k and λ should be thought of as being very large. It, therefore, approaches a normal distribution. Quantum-mechanical amplitude math implicitly assumes we can use normal distributions to model state transitions (see my paper on Feynman’s Time Machine).

The metaphysics of physics

So if we take all of the scaffolding away, what concepts are we left with? What is substance and what is form? Forget about quarks and bosons: the concepts of a charge and fields are core. A force acts on a charge, and matter-particles carry charge. The charge comes in units: the elementary charge. Anti-matter carries an opposite charge—opposite as defined with respect to the matter-particle of which the antimatter-particle is the counterpart.

Pair creation-annihilation is mysterious but not incomprehensible. It happens when the two particles have the same structure and opposite spacetime signature: ++++ versus +–––. Electrons and positrons annihilate each other, and protons and antiprotons—but not electrons and protons. A neutron disintegrates into a proton and an electron outside of the nucleus. That is why a proton and a antineutron – or a neutron and a antiproton – will also vanish in a flash of energy: a neutron is a composite particle—it consists of an electron and a proton. The exact pattern of the dance between the electron and proton inside of a neutron has not been modeled yet—as opposed to the dance between electrons and the positively charged nucleus in an atom (Rutherford’s contribution to the 1921 Solvay Conference comes to mind here).

The elementary charge itself is mysterious: the charge (and mass) density of an electron is very different from that of a proton. Both elementary particles can be modeled as ring currents, however. The Planck-Einstein relation applies to both but with a different form factor.

Mass is mass without mass: a measure of the inertia of the Zitterbewegung motion of the charge. Einstein’s mass-energy equivalence relations models an oscillation in two dimensions. Euler’s wavefunction represents the same. A proton is very different than an electron: massive and small. The force that keeps the charge inside of a proton together suggests the force may be different: this is the idea of a strong force—strong as compared to the electromagnetic force.

This strong force is not Yukawa’s force, however: inter-nucleon forces – what keeps protons and neutrons together inside of a nucleus – can be explained by the coupling of the magnetic moments of the ring currents.

The Zitterbewegung of the charge explains the magnetic moment of matter-particles. The anomaly in the magnetic moment tells us more about the structure of the charge inside of matter-particles: the charge is pointlike but not dimensionless.

What else can we say? Charge is conservedalways, but we must allow for pair creation-annihilation. Energy and momentum are conserved too. Physical systems are either stable or unstable. Atoms, for example, are stable. They too can be modeled as an oscillation respecting the Planck-Einstein relation. Planck’s quantum of action is like a sum of money: you can spend it very quickly, or you can spend over a longer period of time. Same bang for the buck, but you can bang it fast or slow. 🙂 That is what the E·T = h expression of the Planck-Einstein relation tells us: the same amount of physical action (6.626×1034 N·m·s) can be associated with very different energies and, therefore, very different cycle times.

Photons do no carry charge but they carry energy. They carry energy as electromagnetic fields traveling in space. This begs the question: what is oscillating, exactly? We do not know: the concept of an aether has no use beyond the idea of mediating this oscillation—which is why we can forget about it.

Particle interactions involving the strong force also involve the emission and/or absorption of neutrinos. Neutrinos may, therefore, be thought of as the photons of the strong force: they ensure energy and momentum is being conserved for strong interactions too.

There is no weak force: unstable particles disintegrate because they are in a disequilibrium state: the Planck-Einstein relation does not apply and, hence, the unstable state is a transient oscillation only—or a very short-lived resonance.

The idea of virtual particles going back and forth between non-virtual particles to mediate the electromagnetic or strong force is like the 19th-century aether idea or, worse, a remnant of medieval scholastic thinking: all forces must be contact forces, right? No. Of course not. No force is a contact force: forces work through fields. That’s mysterious too, but it is much simpler than accounting for messenger particles: they must have momentum and energy too, right? It becomes hugely complicated. Just forget about it! No gluons, no W/Z bosons, and no Higgs particle either.

[…]

Is that it? Yes. That’s it! I could write some more but then I would exceed the self-allotted one-page for my summary of all of physics. 🙂 Is all of this important? Maybe. If you are reading this, then it is probably important to you. You want to know, right? The most remarkable thing of all of it is the order that emerges from it. Two electrons in the same atomic orbital will align their magnetic moments so as to lower their joint energy: single electrons are valence electrons, and explain why atoms will share them in molecules. Molecules themselves come together in larger and stabler structure. Now it is Darwin’s “survival of the fittest” that comes into play: weaker structures do not survive their environment. At some point in time – very long or not so long ago (depends on your time scale) – some macro-structures became organisms that interacted, in a extremely primitive but real way, with their environment to reproduce themselves. Darwin’s principle tells us that being strong and stable is good, but being able to multiply is even better. So these structures started consuming other structures to multiply. Complexity increased: order and entropy go hand in hand. And so here we are: thinking about where we came from – some raw and uncomplicated state – just before we go back to it. Soon enough. Too soon. As an individual, at least. :-/

That is the true Mystery: your mind—our Mind. Our understanding of things using a very limited number of concepts, equations and elementary constants: the electric charge, Planck’s quantum of action, and the speed of light. Nothing more, nothing less. At larger scales, it is systems interacting with each other and their environment. That’s it. You should think about it. Don’t get lost in math. And surely don’t get lost in amplitude math. It’s not worth it. 🙂

[…] One more thing, perhaps: please do enjoy thinking about this Mystery! A friend of mine once remarked this: “It is good you are studying physics only as a pastime. Professional physicists are often troubled people.” I found the observation strange and sad, but mostly true (think of what Paul Ehrenfest did, for example). There are exceptions, though (H.A. Lorentz and Richard Feynman were happier characters). In any case, if you study physics but you are troubled by it, then study something else: chemistry, biology, or evolutionary psychology, perhaps. Don’t worry about physics: unlike what some are trying to tell you, it all makes sense. 🙂

Where is the Paul Krugman of physics?

We were so busy deconstructing myths in the QED sector of physics that we hardly had time for the QCD sector—high-energy physics. In any case, we do not think quantum field theory or the quark hypothesis have much explanatory power, so it is not like I feel I missed anything. What Paul Dirac wrote about the sorry state of physics back in 1958 still rings very true today:

“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.” (Paul A.M. Dirac, The Principles of Quantum Mechanics, 4th edition (1958), p. 312)

Dirac did not find it necessary to change these words in his lifetime. Moreover, as he got older – he left Earth in 1984 – he became increasingly vocal about the New Nonsense which came out of various Departments of Theoretical Physics after WW II. His skepticism was grounded both in logic as well as in what has become increasingly rare among academics: a deep understanding of the physicality of whatever it is that physicists are studying. He must have felt pretty lonely, for example, when stating this at the occasion of one of his retirement talks:

“Most physicists are very satisfied with the situation. They say: “Quantum electrodynamics is a good theory, and we do not have to worry about it anymore.” I must say that I am very dissatisfied with the situation because this so-called ‘good theory’ [Dirac refers to perturbation and renormalization theory here] involves neglecting infinities. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small—not neglecting it just because it is infinitely great and you do not want it!”

He was over 70 then, but still very active: the Wikipedia article on him notes that, at that age, he was still walking about a mile each day, and swimming in nearby lakes! However, the same article also notes that “his refusal to accept renormalization resulted in his work on the subject moving increasingly out of the mainstream”, so nobody cares about his later writings. Too bad. I think Dirac died rather unhappily because of that, but at least he did not go crazy or, worse, commit suicide—like Paul Ehrenfest.

What Dirac refers to as the ‘pre-Bohr era’ in physics – so that is now – resembles the alchemical period in chemistry, which is usually defined as an era which preceded the era of fundamental understanding of chemical processes. Indeed, alchemy’s Elixir Vitae, the Grand Magisterium, and the Red Tincture have been substituted by the modern-day equivalents of quarks and gluons, W/Z bosons and various other condensates, including the Higgs field. All utter nonsense! We have found only one fundamental ‘condensate’ in Nature so far, and that is the electric charge. Indeed, the elementary charge presents itself in very different shapes and densities depending on whether we look at it as being the essence of an electron, a muon, a proton or as a constituent of a neutron. This remarkable malleability of the elementary charge, both as a physical quantity as well as a logical concept, is the one and only true mystery in quantum physics for me.

Can we analyze it any further going forward? Maybe. Maybe not. The dynamics of pair creation and annihilation for electron and positrons suggest our interpretation of antimatter having an opposite spacetime signature makes sense, but proton-antiproton annihilation and – perhaps the most interesting process in high-energy physics – antiproton-neutron annihilation shows the idea of a strong force is and remains very relevant. Mainstream physics just went into a blind alley with the quark hypothesis to try to understand it. We should reverse gear and get out of that. Anti-proton neutron annihilation proves a neutron consists of a proton and an electron because, while we do observe proton-antineutron annihilation, we do not observe proton-neutron annihilation—and then there are a zillion other arguments in favor of explaining a neutron as a composite particle consisting of a proton and a neutron: think of their mass, magnetic moment, the way a neutron disintegrates outside of a nucleus, proton-neutron interactions, etcetera. We have analyzed this elsewhere so we cannot dwell on this here. So where are we?

I cannot answer that question on  your behalf. I can only say where might be. I spent about ten years on what I think of as a sensible theory of quantum electrodynamics, so I am happy about that. So that’s done and now I should move to something new. However, I am not so motivated to go beyond electrodynamics and dig into the math one needs to analyze a force whose structure is totally unknown. Why not? Because it is like moving from linear to non-linear models in math and statistics, or like moving from analyzing the dynamics of equilibrium states to non-equilibrium processes. If you have ever done one of the two (I did as an econometrist long time ago), you will know that is a huge effort. But, of course, it is never about the effort: it is about the potential rewards. The investment might be worthwhile if the reward would be great.

Unfortunately, that is not the case: what do we gain by being able to explain what might or might not be going at the femtometer scale? The ring current model explains the Compton radius, mass, spin and the magnetic moment of electrons, protons and neutrons – and everything above that scale (call it the picometer scale) – perfectly well. Do we need to go beyond? We are, effectively, entering what Gerard ‘t Hooft referred to as the Great Desert. Indeed, I have always said we should not be discouraged by physicists who say we cannot possibly imagine the smallest of smallest scales and, therefore, meekly accept concepts like hidden or rolled-up dimensions without protest. However, I do have to admit that trying to imagine how one can possibly pack like 400,000 TeV into some femtometer-scale space may effectively be beyond my intellectual capabilities.

The proposition is outright unattractive because the complexity here is inversely proportional to the number of clues that we have got here. So I do not think we will get out of this alchemical period of high-energy physics any time soon. Mankind has constructed colliders whose powers we can double or triple over the next decades, perhaps, but those experiments still amount to studying the mechanics of a Swiss precision watch by repeatedly smashing it and studying the fragments. I think there are serious limitations to what we can learn from that. Oliver Consa is right in saying that more ‘US$ 600m budgets to continue the game’ will not solve the problem: “Maybe it is time to consider alternative proposals. Winter is coming.”

I am not so skeptical. I think summer is coming: after 100 years, this Bohr-Heisenberg revolution (or Diktatur, we should say, perhaps) is finally running out of steam. Why? Not because it failed to convince academics: that, it did all too well—some Nobel Prizes have obviously been awarded a bit prematurely. It is running out of steam because it failed to convince the masses: they are smarter and think for themselves now. It is e-democracy now, and does not stand for elite. Summer may not come with a lot of answers—but summers usually do come with a lot of fun. 🙂

Economics was once being described as the dismal science because it defended the wrong things. I am an economist myself, and I credit Paul Krugman by turning that perception around, almost single-handedly. Paul Krugman is extremely smart. More importantly, he had the guts. Who is going to be the Paul Krugman of physics? If they do not find him or her soon, the science of physics may evolve from a rotten state – hopelessly Lost in Math, as Hossenfelder writes – to something that is far worse: the obsolete state. The good thing about that is that the academics are leaving the space wide open for people like me: spacetime rebels and philosophers. 🙂

Post scriptum: In case you wonder where the 400,000 TeV and femto-meter reference would come from, I am effectively referring to a delightful popular book which was written by Gerard ‘t Hooft—a few years before he and his PhD thesis advisor (Martinus Veltman) got the 1999 Nobel Prize in Physics “for elucidating the quantum structure of the electroweak force”: In Search of the Ultimate Building Blocks (1996). Based on the quantum field theories he contributed so much to, he finds things start to go crazy when trying to imagine frequencies of 1032 Hz or higher.

We think things get crazy much sooner. The Planck-Einstein relation tells us that a frequency of 1032 Hz corresponds to an energy of E = h·f ≈ (4×10−15 eV·s)·(1032 Hz) = 4×1017 eV = 400,000 tera-electronvolt (1 TeV = 1012 eV). A photon with such energy would actually be much smaller than a femtometer (10−15 m): λ = c/f = 10−24 m. This, of course, assumes a one-cycle photon model—but such model is quite straightforward and logical. In-between the femtometer scale (10−15) and that 10−24 m scale, we are missing a 1,000,000,000 factor, so the question is actually this: how can one pack 400,000 TeV (think of the energy of 400,000,000 protons here) into something that is 1,000,0000 times smaller than a proton?

Of course, you might say that we should probably not use a photon-like model of a particle here: why would we assume all of the energy should be in some (linear) electromagnetic oscillation? If there is another force – another force than electromagnetic – then it will have a very different structure, right? Right. And so that should solve the problem, right? No. Not right. That makes things even worse: some non-linear multi-dimensional force or potential allows one to pack even more energy in much smaller spaces! So then things start looking crazy at much larger scales than that 10−24 m scale. When calculating the (strong) force inside of a proton using a two-dimensional oscillator model, for example, you get a number that is equal to 850,000 newton (N), more or less. For an electron, we get a much more modest value (0.115 N, to be precise) but it is still enormous at these small scales.

We should wrap up here—this is just a blog post and so we cannot be too long here. Just note it is already quite something to explain how a proton, whose radius is about 0.83-0.84 fm, can pack its energy—which is less than one GeV. We can do it, but calculations for smaller but more massive stuff (particles that would be smaller than protons, in other words) quickly give very weird results: mass or energy densities quickly approach those of black holes, in fact! Now, your imagination may be more flexible than mine, but I am not ready yet to think we all consist of black holes separated by nothingness.

Now you will ask: “So what is your theory then? And what is its comparative advantage to other theories?” It is rather simple: I think we consist of protons, neutrons and electrons separated by electromagnetic fields, and the main advantage of my theory is that I can explain what protons, neutrons and electrons actually are. One cannot say the same of quarks, gluons, W/Z bosons, Higgs particles and other New Nonsense concepts. Someone with more credentials than me wrote this a while ago:

“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.” (Doris Teplitz, Electromagnetism: Paths to Research, 1982)

I’d rather help finish the house than entertain New Nonsense.

Dismantling myths

I just published a paper in which I show we do not need the machinery of state vectors and probability amplitudes to describe quantum-mechanical systems (think of a laser here, for example). We can describe these systems just as well in terms of a classical oscillation: the Planck-Einstein relation determines frequencies, which can then be used to determine the probabilities of the system being in this or that state.

The paper was quite an effort. The subject-matter is very abstract and the ruse and deceit in the quantum-mechanical argument (that basically assumes we do need all that humbug) is very subtle. It is, therefore, difficult to pinpoint exactly where the argument goes wrong. We managed to find and highlight the main deus ex machina moment, however, which is the substitution of real-valued coefficients by complex-valued functions.

That substitution is not innocent: it smuggles the Planck-Einstein relation in – through the backdoor, so to speak – and makes sure the amplitudes come out alright! The whole argument is, therefore, typical of other mainstream arguments in modern quantum mechanics: one only gets out what was already implicit or explicit in the assumptions, and those are rather random. In other contexts, this would be referred to as garbage in, garbage out.

The paper complements earlier logical deconstructions of some of these arguments, most notably those on the anomalous magnetic moment, the Lamb shift, 720-degree symmetries, the boson-fermion dichotomy and others (for an overview, see the full list of my papers). In fact, we have done so many now that we think we should stop: this last paper should conclude our classical or realist interpretation of quantum mechanics!

It has all been rather exhausting because we feel we had to cover pretty much everything from scratch. We did—and convincingly so, I think. Still, critics – I am quoting from one of the messages I got on ResearchGate here – still tell me that I should continue to “strengthen my arguments/proofs” so to “convince readers.” To those, I usually reply that I will never be able to convince them: if 60+ papers (with thousands of downloads) and a blog on physics (which also gets thousands of hits every month) is not sufficient, then what is? I should probably also refer them to a public comment on one of my papers—written by someone with (a lot) more credentials than me:

“The paper presents sound and solid reasoning. It is sobering and refreshing. The author is not only providing insight into central conceptual problems of modern physics but also recognizing the troubles that indoctrination causes in digesting this insight.”

Let us see how it all goes. I know I am an outsider and, therefore, totally insignificant. I should just stop writing and wait a bit now. This mysterious hyped-up Copenhagen interpretation should become irrelevant by itself: people will realize it is just hocus-pocus or, worse, A Bright Shining Lie.

That may take a long time, however, and I may not last long enough to see it happen. Mainstream physicists will soon be celebrating 100 years of what Paul Ehrenfest referred to as the ‘unendlicher Heisenberg-Born-Dirac-Schrödinger Wurstmachinen-Physik-Betrieb.

On the other hand, it is not because the indoctrination has, obviously, been very successful, that we should give up. An engineer, alumnus of the University of California, also encouraged me by sending me this quote:

“Few people are capable of expressing with equanimity opinions
which differ from the prejudices of their social environment. Most
people are even incapable of forming such opinions.” (Einstein: A Portrait, Pomegranate Artbooks, Petaluma, CA, 1984, p. 102).

That is as good as it gets, I guess. And if you read these words, it probably means you are part of that group of few people. We will not celebrate 100 years of metaphysical nonsense. We will keep thinking things through for ourselves and, thereby, find truth—even if only for ourselves.

That is enough as a reward for me. 🙂

Planck’s quantum of action

I find it most amazing that – with few physical laws and geometry formulas – we are able to understand reality.

These laws – Maxwell’s equations, Einstein’s mass-energy equivalence relation, and the Planck-Einstein relation – are not easy. The geometry formulas – Euler’s formula, basically – are not easy either. But once you get them, all falls into place—like Enlightenment (or kensho, satorinirvana, etc. if you’d happen to like Buddhist philosophy). 🙂

All has a resonant frequency: photons, electrons, protons, neutrons, atoms, molecules, complex systems—all that is stable. Unstable particles and systems do not obey the Planck-Einstein relation: ω = E/ħ. They die out: they are short-lived transients or even shorter-lived resonances. We should not refer to them as particles or particle-systems, and we need non-equilibrium math to analyze them.

It is all most beautiful. I will, therefore, not say anything more about it here. I’ve written about the nitty-gritty elsewhere.