Ah, what the hell – How about we give the article a look. I’ll admit I ran out of steam part way through. I just couldn’t take it anymore. But this post will be long enough in any case.
First, one more journal note having read (most of) this text. There really is zero publication service (manuscript formatting, copyediting, etc.) being provided by ScienceDomain. They really did just post his unedited Word document directly on the web site after sending it through a PDF filter to add stock headers, footers, and frontmatter.
Anyway, to the article. The first 35% of the document (through page 8) has zero content. However, it’s like watching a lonngggg stage magician act. You know that you just witnessed 10 minutes of misdirection and that at some point the rabbit was put into the hat before it was pulled out again, so nothing really happened, but there it all is anyway.
His big conclusion is that he derives a “quantized expression” for the Schwarzschild radius using a novel holographic approach. Except he doesn’t do anything of the kind. There’s nothing being quantized and there’s no holography. In fact, there’s nothing at all because across these eight long, tediously numerical, eye-numbing pages, he manages to multiply in a bunch of physical constants then divide them all back out again to claim that he’s constructed the expression for the Schwarzschild radius, r = 2Gm/c. There are no explained physical principles behind his manipulations, and there is no mathematical ground covered during them. If one insists that I address the physics of this section, I cannot, because there is none. To be sure, there are passages with physics jargon strung together but there isn’t a definition or underlying principle in sight.
If this assessment is unsatisfying, the a more direct way to look at this section is that, regardless of the manipulations involved, it is literally impossible to get an expression for the radius that involves G that isn’t exactly in the form r=<number>Gm/c given that h-bar is the only other quantity in the problem. So, he couldn’t not get the right form. For the leading coefficient (in this case, the number 2), he introduced apparently arbitrary ratios of geometric quantities (suitably obfuscated first) along the way. Need a factor of 4? Divide the area of a sphere by the area of a circle. Why? Why not.
In the next couple of sections of the article, he switches topics to the mass and radius of a proton. He says he chooses a proton “due to the fundamental nature of protons in the hadronic picture.” I could spend the whole post quoting such doublespeak, but this example will suffice. This phrase read to a layman as meaningful, but it’s entirely empty. The hadronic picture? Protons as fundamental? Fundamental to what? Protons are about the least fundamental thing you could pick even if “the hadronic picture” meant something specific.
Okay, so we’ll go with the proton. His conclusion through this section is that he can get a relationship between the proton radius and its mass using Planck quantities based on the “holographic” derivation down in the first section. A couple of things. First, it’s been known for ages that the proton mass is smaller than the Plank mass by about the same factor that the proton radius is larger than the Planck length. If you give yourself the freedom to spin in some coefficients, you can make this relationship rather close. He does this (with a admittedly simple coefficient) to about 1% or 4% depending on which values of proton radius and mass he uses. But this is just numerology.
Second, and more curious, is that he appears to deviate from the relations derived ages early. As mentioned, dimensional analysis guarantees that you will get the right form for the Schwartzchild radius if you put the right quantities into the math. However, nothing guarantees that that will give you anything useful for the proton radius / proton mass numerology. And it doesn’t. So, he swaps numerator and denominator and then multiplies by 2 with no mention of why.
(It’s painful to follow the discussion in detail, though, because he introduces variable after variable, each just a ratios of others and all with unconventional symbols chosen. This might sound like a slight at the author and not the content, but on the contrary: a cogent idea should be presentable in a cogent way. In the enterprise of scientific research, sharing an idea clearly is as central as having the idea in the first place.)
With the numerology complete, he claims he has demonstrated both that the muon-based proton charge radius measurement is sound and that the holographic approach is sound. The issue at hand with the proton radius, though, is that you get different answers when you use muonic hydrogen versus electronic hydrogen. Since there are no usable physical principles described in his derivation, there is no explanation why the procedure should work for one and not the other. He just ignores the disagreement from the electron case. Further, you can’t in the same logical breath conclude that the mathematical approach is sound because it aligns with the muonic measurement and conclude that the muonic measurements are sound because they are supported by the mathematical approach.
Some of the language implies that this is all fundamental (despite the form of the expressions changing mid-stream), so you might expect some discussion of why this doesn’t work for electrons or quarks or whatnot. If he wants a bound state like the proton (Why? I thought we wanted fundamental?), what about the pion or a purely leptonic system like positronium? Of course, you could make it work for any system, but only one system at a time since the coefficient will need to be different. I calculate that for positronium you need a factor of around 280, depending on what you want to take as the characteristic radius. If you allow a dozen pages to throw around geometric arguments (you could even bring the term “multidimensional” into it by invoking the volumes and surface areas of various n-spheres), you could introduce that factor to within a few percent pretty easily. 9pi[sup]3[/sup] gets to within 0.4%. But this closeness cannot logically justify itself. It’s needs something behind it.
And, indeed, if there were physical principles in this article, you could have a discussion about how you might test it in other systems or what broader implications the principles might have. This isn’t done.
And this is where I lost interest. The final third or so of the paper appears to claim a holographically derived connection between the timescale of strong-force decays and the above numerology. Without even looking at the math I’m going to go ahead and wager that it’ll be equivalent to a straightforward order-of-magnitude statement that the energy scale of strong decays is about 1 GeV and the timescale for strong decays is about h-bar/(1 GeV), with the energy “1 GeV” motivated as the scale of the strong force by the proton mass itself, as its mass is almost entirely from its (strong force) binding energy.