New horizons

Looking back and forward

I want to revive this blog. I have not written anything substantially new since a very long time (OK, all is relative: since one year only), except short posts pointing to a new paper when I put one online on my ResearchGate site. However, I have started to think my blog is still worthwhile. I effectively keep getting a few likes here and there (if only from a handful of some of the followers (only 186 people in total, which is not a whole lot), and the sheer size and history of this blog suggests it can be revived rather easily: when I worked rather intensively on it (second half of 2022 and first half of 2021, basically), the stats did see a significant surge according to the site’s statistical dashboard (below).

Of course, a lot (if not most) of this traffic is semi-automatic because it is driven by hash tags out there on rather arcane topics such as Maxwell-Boltzmann and Bose-Einstein versus Fermi-Dirac statistics (I cannot imagine the top posts that WordPress automatically lists on this site are really top posts), but I will think positively of this and, yes, try to present both simpler as well as more relevant material in the coming years. In short: I feel like going at it again.

The problem with writing blog posts is that the process is rather tedious when it comes to quickly inserting some mathematical formula or argument to make a point (which is what, inevitably, one has to do when writing about physics), but I guess that is also why the readers of this blog turn to a blog rather than to my ResearchGate papers: they do not necessarily want to dig into all of the formulas. Hence, I need to separate out the two. Not to separate the two audiences, because I do believe the two audiences are similar: both are searching for some kind of truth or explanation (as opposed to a calculation), right? I just need to work harder on using the blog to highlight essential points, and then point to the papers for the math behind it.

Before I try my hand at that, let me say a few things about the papers. These papers are and remain working papers: I have academic credentials, but not in this field (quantum physics), which is why I will probably never really break through mainstream academic thought on all of the topics I write about. I gave up on trying to publish in journals or get a book published by a publisher. I tried several scientific publishers but, despite of all the hard work involved in making sure you get copyright on illustrations, and inserting more bibliographic detail, it did not work out. I stick to Einstein’s style: few references, because I believe the logic should speak for itself and, hence, one should only use what is strictly necessary and relevant in this regard, so as to improve readability (I feel that I use too many footnotes in my papers already, so more bibliographic detail would further downgrade the flow of my papers).

Nevertheless, papers like the one on my interpretation on the de Broglie frequencies as orbital rather than linear frequencies get high RI (research interest) scores on that RG site: the score of that particular paper, for example, is higher than 96% of all research items published in 2020). The RI scores of my rather critical papers on the formalism of quantum math and on the boundaries between Maxwell’s equations and the world of the smallest of small field oscillations (both of which I revised recently) are equally impressive in my, yes, not-so-humble (not anymore) view (the RI scores of these two papers are higher than 90% of all research items published in 2020). More relevant, of course, is the CV of the people who download them, most of which have that one PhD (in physics) which I am lacking (I got on ResearchGate because I could demonstrate I had published scientific papers in other fields in a far-gone past – mainly economics, as I once was an assistant professor working on a PhD in econometrics, which I did not finish, as a result of which I only have an old Doctor in Science (Drs) title, which is a rather particular title that is no longer valid).

In fact, I sometimes think I might get censured on RG for that one day, but I do not think so: my overall RI score in the field of quantum physics is now higher than 70% of researchers in the same field, despite me publishing these working papers on RG only since 2020. The quick rise and interest is evidenced by the fact that my overall RG score remains stubbornly higher than 99% of ResearchGate members who first published in 2020. Again, this does not prove much, perhaps, but it should convince both you as well as myself that I am not some kind of Cosmic Stan, although I did have my bad moments while pushing myself very hard on the very questions that drove geniuses like Ehrenfest into depression or, in his particular case, suicide.

Sure, I did have my bad moments too, as evidenced in this 2020 blog post at the occasion of Freeman Dyson’s demise. However, I will keep it there, if only because it mentions Oliver Consa, whose instinct (something is rotten in the state of modern physics) I share, but he was (and probably still is not) in a mood to collaborate on anything. If you read this blog, I recommend you read his article, which suggests the mysteries of quantum physics are there and are being perpetuated because of a weird mix of post-war secrecy around atomic physics and, much more probable now (the second world war is only a distant memory now), manipulation by a select group of academics aimed at keeping research money flowing.

Ten or twenty years ago, I would have dismissed such thinking out of hand, but I have myself been subject to rather weird attempts to take down this very blog of mine. I was surprised because I am quite vocal on social media, such as LinkedIn or Twitter, and I also have other blogs, on other topics that are often quite controversial (on current tensions between the US, Europe, Russia and China, or other questions of war and peace, for example), and I did not experience anything like that there. It may be Sayre’s Law: “Academic politics is much more vicious than real politics, because the stakes are so small.”

In any case, let us get back to the matter at hand: this blog and its future. What do I want to do with it? What can I usefully do with it? One experiment I want to try out is to distill the essence out of my papers as I have started a process of revising them one by one. Yes, unlike what I wrote about in the overall Post Scriptum to all of my 29 papers (that it was too much work to do that, basically), I think I should do that. I am getting older and, hence, I now think of that as a rather nice pastime.

So, I will stop rambling and make a first attempt at elucidating some aspects of my world vision, so to speak, for the intermediate-level hobbyist. To be clear on what I mean with that: I still consider myself to be an intermediate-level hobbyist as well but, looking at those RG stats, I think I might have it easier with some of the mathematical formalism than others, so that is why I am going to try to avoid it.

Let us go for it. In the next section(s) of this blog post, I am going to condense and distill the key conclusions in regard to the essential nature of mass, because that is still the question that intrigues most of us: what is it – not approximately, but exactly? If we know what matter is all about, then we know, pretty much, what reality is all about, right? Maybe. Maybe not. We miss a great deal about the mystery of fields and radiation but, yes, it is an important piece of the whole intellectual puzzle, so let us start here.

The nature of mass

We explained the nature of mass in our papers on elementary physics.[1] However, we did use rather advanced mathematical concepts (if you are not familiar with imaginary units or vector algebra, that is), so let us summarize the very basics here.

At the macro-level, mass appears as inertia to a change in the state of linear motion of an object or particle. That is how it appears in Newton’s first law of motion which – in its relativistically correct form – is written as F = dp/dt = d(m·v)/dt.[2] Now, the idea of a particle is a philosophical or ontological concept and we will, therefore, avoid it – to some extent, at least – and prefer to speak of things we can measure, such as charge and, yes, mass. We will also speak of physical laws because these are based on measurements too.

Now I do have to insert one formula. It is simple (just a formula that says a rather particular ratio is equal to some number). Try to think through it. From the Planck-Einstein and mass-energy equivalence relations (E = h·f and E = m·c2, so h·f = m·c2), we get the following fundamental equation for a frequency per unit mass (f/m or, expressing frequency in radians per second rather than cycles per second, ω/m):

f/m = c2/h = 1.35639248965213×1050

This humongous value[3] is an exact value since the 2019 redefinition of SI units, which fixed the value of ħ, and just like c and ħ, you may think of it as some God-given number but you should not do that: just like the fine-structure constant[4], this is just a number which we derived from a more limited number of fundamental constants of Nature. [Of course, you will note that the number depends on the units, and that both the second and the kg are very large units when talking about small things, but you can recalculate the number using other units, just like you can do that for other constants.]

The point is this: this simple formula, and that enormous number, reflect the true nature of mass at the micro-level. You must appreciate that is quite different from mass being, at the macro-level, a measure of inertia. At the most fundamental level, matter is nothing but charge in motion. Such interpretation may not be mainstream (although it should be, judging from how physicists actually treat matter) but it is consistent with Wheeler’s ‘mass without mass’ ideas and – more importantly, probably – with the 2019 revision of the system of SI units, in which mass also appears as a derived unit from more fundamental constants now, most notably Planck’s constant.

This f/m ratio is, of course, valid for all matter or – let us be precise – for all (stable) elementary particles.[5] However, it is important to note that, while the f/m ratio is the same for both the electron as well as the proton mass, the q/me and q/mp ratios are, obviously, very different. We, therefore, do associate two very different charge oscillations with them: we think of the electron and proton as a two- and three-dimensional ring current, respectively. Hence, while these specific oscillator equations are, theoretically and mathematically, compatible with any mass number, we do not think of the electron and proton energies as variables but as constants of Nature themselves.

In short, we must think of the electron and the proton mass as fundamental constants too because, as far as we know, these are the only two stable constituents of matter, and they also incorporate the negative and positive elementary charge, respectively.[6] The f/m = c2/h formula above holds for both and, combined with Newton’s force law (m = F/a: mass as inertia to change of (a state of) motion), we conclude that the mass idea is one single concept but that we should, at the very minimum, distinguish between electron and proton mass. Of course, Einstein’s mass-energy relation tells us it might be better to just talk about two fundamental energy levels (Ee and Ep), and to re-write the f/m = c2/h expression above as the Planck-Einstein relation applied to two (different) oscillations. We insert the mathematical representation of that idea below too, but do not worry too much about it:

As mentioned above, in the realist interpretation we have been pursuing, we effective think of the two oscillations as a planar and a spherical oscillation, respectively, which is reflected in the wavefunction which we use to represent the electron and proton, respectively. Indeed, the effective radius of a free electron follows directly from the orbital velocity formula v = c = ω´r = ω´a and the Planck-Einstein relation[7]:

The point here is not to burden you with formulas (we said we would not, but we cannot help it here), but to show you how easy it is to get the measurable properties of the electron from the basic equations. Now that we are doing that, we will also quickly introduce the wavefunction of both the electron and the proton, although you can skip through the next paragraphs if you would not like that (we are just doing it for the more academic or advanced reader, to show that we are not afraid of the math and formalism). We write the wavefunction of an electron as:

This notation introduces the imaginary unit, which serves as a rotation operator and, therefore, denotes the plane of oscillation. The sign of the imaginary unit (±) indicates the direction of spin and, interpreting 1 and 1 as complex numbers (cf. the boldface notation), we do not treat ± p as a common phase factor.[8]

As mentioned several times already, we think of the proton oscillation as an orbital oscillation in three rather than just two dimensions. We, therefore, have two (perpendicular) orbital oscillations, with the frequency of each of the oscillators given by ω = E/2ħ = mc2/2ħ (energy equipartition theorem), and with each of the two perpendicular oscillations packing one half-unit of ħ only.[9] Such  spherical view of a proton fits with packing models for nucleons and yields the experimentally measured radius of a proton:

The 4 factor here is the one distinguishing the formula for the surface of a sphere (A = 4πr2) from the surface of a disc (A = πr2).[10] So do we consider the (in)famous proton radius puzzle solved? Yes. We do. Let us – for the more advanced reader again – write the proton wavefunction. We think of it as a combination of two elementary wavefunctions:

While the electron and proton oscillation are very different, the calculations of their magnetic moment based on a ring current model (with a square root correction to take the spherical nature of the proton into account) strongly suggest the nature of both oscillations and, therefore, the nature of all mass, is electromagnetic. However, we may refer to the electron and proton mass as electromagnetic and nuclear mass respectively because protons (and neutrons) make up most of the mass of atomic nuclei[11], while electrons explain the electromagnetic interaction(s) between atoms and, therefore, explain molecular shapes and other physical phenomena.

Finally, the two oscillations may be associated with the two lightlike particles we find in Nature: photons and neutrinos. These lightlike particles carry energy (but no charge) but are traditionally associated with electromagnetic and nuclear reactions respectively (emission and/or absorption of photons/neutrinos, respectively), which also explains why referring to the three-dimensional proton oscillation as a nuclear oscillation makes sense.[12]

Is that it, then? You may have a few immediate reactions and one of them would be this: we reduce mass to charge in motion here. So what is charge, then? And can we reduce charge to something else. It would take me quite a bit of text to reply to that, so I will only be short here.

First, getting rid of one concept in physics is already a great simplification, and we cannot get rid of the concept of charge by reducing it to mass. In contrast, we do have this nice ‘mass without mass’ model here, and so that is great. Second, never forget that mass (and energy) are relative: you will measure them differently in different reference frames. In contrast, charge is absolute: the proton and electron charge are a unit of charge that does not change depending on your frame of reference. It is just like the speed of light, or Planck’s constant: these constants are c and h, respectively. They are absolute. So that is why we can get rid of the mass concept, so to speak. We cannot get rid of (electric) charge.

So, this is it. See you next time (for my next post, that is)?


[1] See our papers in our K-12 level physics series.

[2] The formula is relativistically correct because both m and v are not constant: they are functions varying in time as well and that is why we cannot easily take them out of the d()/dt brackets.

[3] A number with 50 zeros would be referred to as one hundred quindecillion (using the Anglo-Saxon short scale) or one hundred octillions (using the non-English long scale of naming such astronomic numbers).

[4] The fine-structure constant pops up in electromagnetic theory, and is co-defined with the electric and magnetic constants. Their CODATA values are related as follows:

[5] Note that the electron and proton (and their anti-matter counterparts) are stable, but the neutron (as a free particle, i.e., outside of a nucleus) is not, even if its average lifetime (almost 15 minutes) is very large as compared to other non-stable particles.

[6] As mentioned above, the neutron is only stable inside of the nucleus, and we think of it as a combination of a positive and negative charge. It is, therefore, reducible and, as such, not truly elementary. However, such view is, obviously, part of another speculative model of ours and, hence, should not be a concern to the reader here.

[7] We write this as a vector cross-product, and assume an idealized circular orbital when writing the position vector r as a wavefunction r = ψ = a·e±iθ = a·[cos(±θ) + i · sin(±θ)]. The magnitude ½r½is, obviously, equal to ½a·e±iθ ½ = a. This is a variant of Wheeler’s mass-without-mass model because the model assumes a pointlike (but not necessarily infinitesimally small or zero-dimensional) charge, whose rest mass is zero and, therefore, moves at lightspeed and acquires relativistic mass only. As such, it is photon-like, but photons (light-particles) carry no charge. The a = r notation may be somewhat confusing because a is also used to denote acceleration¾an entirely different concept, of course!

[8] See our paper on Euler’s wavefunction and the double life of -1, October 2018. This paper is one of our very early papers – a time during which we developed early intuitions – and we were not publishing on RG then. We basically take Feynman’s argument on base transformations apart. The logic is valid, but we should probably review and rewrite the paper in light of the more precise intuitions and arguments we developed since then, even if – as mentioned – I have no doubt as to the validity of the argument.

[9] Such half-units of ħ for linearly polarized waves also explains the results of Mach-Zehnder one-photon interference experiments. There is no mystery here.

[10] We also have the same 1/4p factor in the formula for the electric constant, and for exactly the same reason (Gauss’ law).

[11] Binding energy – also electromagnetic in nature – makes up for the rest.

[12] See our paper on the nuclear force hypothesis, April 2021.

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