*RB - the issue here was calculation of electron anomalous magnetic moment.*

Why is that more relevant? It is calculated from QED, a simpler and stunningly accurate theory that Mills dismisses as wrong. Mills has a closed form determination of it from alpha, and QED has closed form determination up to alpha^3, with monte carlo simulations for the higher order terms.

Although the correct (QED) determination does have electroweak (dependent on muon mass) and QCD (hadronic) components, which complicate the pure QED calculation, these are relatively small.

For this best of calculated, best of tested value, QED is consistent with experimental error, Mills theory is 200X SD wrong.

You might think Mills would want to propose some higher order correction, and refine his theory? But it seems he is not able to do this, and instead comments on the good fit using 1987 data.

It is not proper behaviour from a scientist. Although, of course, Mills has commercial interest in the matter, wants to promote investment in his company, and is not in any conventional sense a scientist (although he does have some experimental work published).

*QED 4 loop confabulation: https://arxiv.org/pdf/1704.06996*

This is a guy he is giving 100 digit accuracy for one component of the calculation (the QED 4 loop one). It is I guess good to have an exact numerical solution for this but at even 11 sig fig the QCD and electroweak components become significant, and practically I can't see the merits in this over other numerical techniques and in particular efficient monte carlo based techniques.

Still, it is a lot of effort...

*Mills vague accusations about QM*

I've read Box I.1 in Mills' 1000 page book. He makes major charges against conventional theories in one or two sentences with no (or almost no) references and no details. It is difficult to take this seriously. Each of these one liners would be (if real) the subject of 10s or even 100s of papers arguing and clarifying it, if real. In fact there are a lot of papers that do that on many topic within QM, arguing corners of it. Mills does not engage with this: and dismisses existing work without evidence.

RB - you say some of these one-liners seem interesting to you. Perhaps then you could do the literature survey that Mills avoids, show where the existing theory as described in research papers is wrong, and give full reasons? Or find somone else who has done that?

Otherwise this type of *sound bite scienc**e* is in my view contemptible, because it makes serious and weighty accusations without evidence or checking.

Let us do this for RB* interesting criticism 1.*

It appears based on https://link.springer.com/article/10.1023/A:1004605626054

Journal of Low Temperature Physics

August 2000, Volume 120, Issue 3–4, pp 173–204 | Cite as

On the Fission of Elementary Particles and the Evidence for Fractional Electrons in Liquid Helium

H.J.Maris

*We consider the possibility that as a result of interactions between an elementary particle and a suitably designed classical system, the particle may be divided into two or more pieces that act as though they are fractions of the original particle. We work out in detail the mechanics of this process for an electron interacting with liquid helium. It is known that when an electron is injected into liquid helium, the lowest energy configuration is with the electron localized in a 1s state inside a spherical cavity from which helium atoms are excluded. These electron bubbles have been studied in many experiments. We show that if the electron is optically excited from the 1s to the 1p state, the bubble wall will be set into motion, and that the inertia of the liquid surrounding the bubble can be sufficient to lead to the break-up of the bubble into two pieces. We call the electron fragments “electrinos.” We then show that there is a substantial amount of experimental data in the published literature that gives support to these theoretical ideas. The electrino bubble theory provides a natural explanation for the photoconductivity experiments of Northby, Zipfel, Sanders, Grimes and Adams, and possibly also the ionic mobility measurements of Ihas, Sanders, Eden and McClintock. Previously, these experimental results have not had a satisfactory explanation. In a final section, we describe some further experiments that could test our theory and consider the broader implications of these results on fractional particles.*

Let us do a citation check in google scholar:

2001 [Mills has a citation in which he critiques QM, but does not contribute to the "facrtional charge" mystery]

*The Schrödinger equation was originally postulated in 1926 as having a solution of the one electron atom. It gives the principal energy levels of the hydrogen atom as eigenvalues of eigenfunction solutions of the Laguerre differential equation. But, as the principal quantum number n⪢1, the eigenfunctions become nonsensical. Despite its wide acceptance, on deeper inspection, the Schrödinger solution is plagued with many failings as well as difficulties in terms of a physical interpretation that have caused it to remain controversial since its inception...*

2001 Jackiw, Rebbi, Schreiffer

*We argue that electrons in liquid helium bubbles are not fractional, they are in a superposed state.*

2001 Rae, Vinen

*It has recently been suggested that a bubble in liquid helium containing an electron could be excited into a state where the electron is divided between two smaller half bubbles, and that these “electrinos” would have increased mobility. This proposal is discussed critically, and it is concluded that, if such a state were to form, it would quickly collapse into an incoherent quantum superposition of two separated ground-state bubbles. All the measurable properties of this state are identical with those of a single bubble.*

2003 Maris

*We present calculations of a number of properties of electron bubbles in liquid helium. The size and shape of bubbles containing electrons in different quantum states is determined based on a simplified model. We then find how the geometry of these bubbles changes with the applied pressure. The radiative lifetime of bubbles with electrons in excited states is calculated. Finally, we use a quantum Monte Carlo method to determine the properties of a bubble containing two electrons. We show that this object is unstable against fission.*

2008 Moroshkin, Hofer, Weiss

*The studies of defects formed by impurity particles (atoms, molecules, exciplexes, clusters, free electrons, and positive ions) embedded in liquid and solid 4He are reviewed. The properties of free electrons and neutral particles in condensed helium are described by the electron (atomic) bubble model, whereas for the positive ions a snowball structure is considered. We compare the properties of the defects in condensed helium with those of metal atoms isolated in heavier rare gas matrices.*

2008 Maris

*An electron injected into liquid helium forces open a small cavity that is free of helium atoms. This object is referred to as an electron bubble, and has been studied experimentally and theoretically for many years. At first sight, it would appear that because helium atoms have such a simple electronic structure and are so chemically inert, it should be very easy to understand the properties of these electron bubbles. However, it turns out that while for some properties theory and experiment are in excellent quantitative agreement, there are other experiments for which there is currently no understanding at all.*

**Maris 2003 looks like a good one to dig in: Maris posed the initial anomaly and goes on working on it. **

*When an electron is injected into liquid helium, it forces open a cavityfree of helium atoms, referred to as an electron bubble. In a recent paper1(referred to as I), we considered what happens when an electron bubble isilluminated by light. If the electron is excited from the lowest energy 1Sstate of the initially spherical bubble to the 1P state,2 the bubble shape willchange. At high temperatures, the liquid contains many thermal excitations(phonons and rotons) and the damping of the motion of the bubble wall islarge. One can therefore expect that the bubble will slowly relax to a newequilibrium shape. It was shown that this equilibrium shape resembles apeanut. However, at lower temperatures, the liquid contains few excitationsand so the damping of the bubble wall becomes small. As a result, thebubble will change shape rapidly and after the equilibrium shape has beenreached, the liquid surrounding the bubble will still be in rapid motion. Theinertia associated with the liquid may then be sufficiently large to cause thewaist of the peanut to shrink to zero, thus dividing the bubble into twoparts. What happens after this point was not definitely established, and isunder experimental investigation. Elser3 has argued that before the divisionof the bubbles takes place the wave function of the electron will cease todeform adiabatically as the bubble shape develops and that, as a result, allof the wave function will end up in one of the parts. This part would thenexpand and become a conventional 1S electron bubble and the other part,containing no wave function, would collapse. A different argument hasbeen presented by Rae and Vinen.4 They claim that if the bubble dividesinto two baby bubbles each containing half of the wave function, this statewould quickly collapse into an incoherent quantum superposition of twoseparated ground-state bubbles which would have properties no differentfrom ordinary 1S bubbles.*

*When electron bubbles are introduced into helium, a space charge fieldis set up which drives the bubbles out of the liquid. This limits the numberdensity of the bubbles. As a result, conventional optical studies of thebubbles are extremely difficult.5, 6 Several experiments have shown thatthe absorption of light results in a change in the mobility of the bubbles;7–9the origin of this change in mobility is not clearly established. Veryrecently, a new experimental method for the study of the bubbles has beendeveloped.10 In this experiment, a negative pressure is applied to the liquid.If the pressure is negative with respect to a critical pressure Pc , an electronbubble in the liquid will become unstable and explode. The explosion pressure Pc is different for each quantum state. Thus, a measurement of thepressure required to make a bubble explode provides a means to identifythe quantum state. This provides the basis for a new method to study theproperties of electron bubbles in excited states.*

So, basically, no fractional charge particles. Maris proposed (speculatively) that when a one-electron bubble splits it is

possible that the wave function would be stable in a coherent split between the two halves (possible) leading to two bubbles

sharing an electron!

It is an interesting idea, and Maris explored it (he is the expert on He electron bubbles). However others pointed out that such a coherent structure would have a very short lifetime, even in liquid helium. Maris has one on to explore lots more stuff about these electron bubbles without finding evidence for fractional charge. One of the issues is that bubble mobility varies with electron excited state, and after teh first paper he found a neat way to explore the energy state of the bubble's electron by varying pressure and looking at when the bubble exploded. With this more powerful tool he has a lot more stuff on bubbles, but no more speculation about fractional charged bubbles because of no evidence for them after better experimental work.

Maris 2008 (more He bubbles)

*An electron injected into liquid helium forces open a small cavity that is free of helium atoms. This object is referred to as an electron bubble, and has been studied experimentally and theoretically for many years. At first sight, it would appear that because helium atoms have such a simple electronic structure and are so chemically inert, it should be very easy to understand the properties of these electron bubbles. However, it turns out that while for some properties theory and experiment are in excellent quantitative agreement, there are other experiments for which there is currently no understanding at all.*

Mauracher et al 2014

*Helium droplets provide the possibility to study phenomena at the very low temperatures at which quantum mechanical effects are more pronounced and fewer quantum states have significant occupation probabilities. Understanding the migration of either positive or negative charges in liquid helium is essential to comprehend charge-induced processes in molecular systems embedded in helium droplets. Here, we report the resonant formation of excited metastable atomic and molecular helium anions in superfluid helium droplets upon electron impact. Although the molecular anion is heliophobic and migrates toward the surface of the helium droplet, the excited metastable atomic helium anion is bound within the helium droplet and exhibits high mobility. The atomic anion is shown to be responsible for the formation of molecular dopant anions upon charge transfer and thus, we clarify the nature of the previously unidentified fast exotic negative charge carrier found in bulk liquid helium.*

It looks like more recent work has identified anomalies previously noted in these systems.

**Summary of Mills/RB interesting criticism 1.**

This is certainly interesting work on He3 superfluidic systems which can expose all sorts of weird effects. Jumping from this to fractional charged electrons is only done by Mills. Fractionally charged bubbles after fission due to coherence, as was was tentatively proposed by Maris but not supported by better later experiements - does not seem likely. Maris has continued doing this work.

Related (a bit more google search) finds this fascinating work on splitting wave packets (very fast time resolution - since as noted above such coherent splits cannot last for long).

https://phys.org/news/2015-05-electron.html

There is a pattern here. Science is complex, and all sorts of anomalies have multiple possible solutions. If you are Mills you leap to the solution that requires reformulating the whole of physics in a way that requires new particles, and no longer correctly predicts fundamental constants, or the non-local results of QM.

If you are anyone else you do real experimental work to understand the phenomena, come up with a whole load of other explanations, and eventually work out which one if right based on better empirical evidence!