This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This paper develops a connection between the phenomenology of chemical bonding and the theory of relativity. Empirical correlations between electron numbers in atoms and chemical bond stabilities in molecules are first reviewed and extended. Quantitative chemical bond strengths are then related to ionization potentials in elements. Striking patterns in ionization potentials are revealed when the data are viewed in an element-independent way, where element-specific details are removed via an appropriate scaling law. The scale factor involved is not explained by quantum mechanics; it is revealed only when one goes back further, to the development of Einstein’s special relativity theory.

Can there exist any plausible connection between the phenomenology of chemical bonding and the theory of relativity? This paper argues in the affirmative. It stands as testament to the idea that the disciplines of Chemistry and Physics need to exist in intimate symbiosis with each other. Chemistry produces reams and reams of interesting data. Physicists should revel in that data: chemical experiments are far more feasible to conduct than cosmological ‘experiments’, and chemical data is far less costly to acquire than elementary-particle data. Chemistry needs Physics too, though perhaps not as much, to help infer simple laws from complex data.

The argument here begins with some comments on the Periodic Table. In Sect. 2, known empirical correlations between electron counts in elements and chemical bond stabilities in molecules are reviewed, and then extended beyond the familiar situations.

The argument then moves to a more quantitative domain. Clearly, the quantitative strengths of chemical bonds in molecules must reflect the same physics as do the quantitative magnitudes of ionization potentials of elements. The understanding of that physics is presently based on quantum mechanics (QM), and that understanding is very incomplete. Sect. 3 shows striking patterns in ionization potentials that are revealed only when the data are viewed in an element-independent way, where element-specific details are removed via an appropriate scaling law. The required scale factor is

The need for the

Sect. 4 introduces a variant version of QM, which includes known results about atoms, but also offers alternative interpretations and simpler calculation approaches, one of which accounts for the

Since the time of Mendeleev, the Periodic Table (PT) has been the fundamental organizing tool of Chemistry. Its history of development, and our present understanding of its significance, are documented Eric Scerri in [

Not being fully satisfied with understanding of the PT has driven many individuals to develop different display formats for the PT. The goal of organizing the elements according to chemical properties, like valence, has produced the wheels, spirals, helixes, three-dimensional pretzels, conics, trees, and more, collected and richly displayed by Spronsen [

The historically numerous revisits to the PT do express the strong tradition in science for looking at the same, known, information again and again, but arranged in a variety of different ways. This sort of exercise is important for scientists to do, and

I am no different from other authors: I too have been driven to understand better, and have developed a favored way of picturing the PT. The original conception had elements arranged in columns for chemical similarity. I like the idea of an architectural metaphor, but not that particular metaphor. As it has accommodated more and more newly discovered elements, the columns have come to include some very short ones to the center left, where the Lanthanide and Actinide series must go. Being unable to support any metaphorical ‘roof’ of all-encompassing understanding, those columns are generally stored away in the ‘basement’ (footnotes), to be remembered and retrieved as needed by the user. My preferred remedy for the situation is to change the architectural metaphor: instead of thinking ‘columns’, think ‘arch’.

Any architectural metaphor naturally attracts one’s attention to the idea of a ‘foundation’. The foundation of the PA is the red information along the bottom of the arch: the _{noble} :

Although actual element discovery is presently only up to ^{2} = 2(5)^{2} = 50, and so on, according to the pattern.

While the pattern, 2^{2} for

The arch metaphor further draws one’s attention to the idea of ‘keystone’. The keystones in the PA are the red elements up the middle of

The foundation algebra and the keystone elements of the PA turn out to be truly useful for making an initial qualitative comment on chemical bonds in this Section. Hydrogen turns out to be further useful for the subsequent quantitative analyses of ionization potentials in the next Section.

We know that some molecules tend to be stable, whereas some tend to be highly reactive. For or example, some simple dimers, like H_{2} NaCl,

The present understanding for these simple cases is often phrased in terms of ‘complete’ and ‘incomplete’ electron ‘shells’, which are said to surround atoms. But what should be said about larger molecules, with many atoms in them? Evidently, molecules that are relatively stable must have strong chemical bonds throughout, and molecules that are strongly reactive must have some weak chemical bonds somewhere. In order to extend the somewhat limited ‘shell’ understanding to larger molecules, consider the following more general candidate statement:

The proposition implies redistribution of electron resources. The idea is that electrons are like cash money: totally fungible – even more so than cash money, since they have no serial numbers or other individually distinguishing characteristics.

The reader can readily verify that Proposition 1 is satisfied by the simple dimers like H_{2}, NaCl, _{2}O, CO_{2}, and many other simple trimers.

Observe in

The equidistant condition of Hydrogen perhaps explains something mysterious observed in deep space. Evidently, any Hydrogen atom would want either to form a Hydrogen molecule (2 electrons total), or if that were not possible, then to dissociate and form plasma (proton with no electron). Plasma is indeed frequently observed in deep space. The amazing possibilities for Carbon-Carbon bonds are well known (chains, rings, sheets, tubes, balls…life…), and seem likely to trace to its special equidistant condition. Silicon is known to be very similar to Carbon, and the other keystone elements may also turn out to be more similar than is presently recognized.

Sometimes, the condition specified in Proposition 1 cannot be achieved. For example, it cannot be achieved for any molecule that has an electron count that is an odd number. Also, it cannot be achieved for some atmospheric gasses, such as Oxygen O_{2}, Ozone O_{3}, or Nitrous Oxide NO. These molecules are often rather highly reactive. These situations prompt one to consider a second candidate statement that is the converse to Proposition 1:

The conclusion to be drawn from this preliminary qualitative analysis is that chemical bonding has less to do with pair-wise connection between atoms, and more to do with molecule-wide collective status of all atoms. Strong bonding is about assigning electrons in such a way as to promote every atom present, either to the status of ‘noble gas’ (possessing a comfortable number of electrons), or else to the status of ‘priestly class’ (needing no worldly electrons at all). If that goal is achieved, then the molecule has a population of well-satisfied atoms, constituting a relatively stable society.

It is desirable now to strive for more quantitative assessment of chemical bonds. But molecules are very complex, and it is rational to start with the constituent atoms. Atoms have ionization potentials (as scalar variables,

Even the

The points on

The lines on

The model-development approach is called ‘data mining’.

The work involved is a good example of continuing positive feedback between theory and experiment. Theory shows what to look for; experiment shows what to try to understand.

The first development step was fundamentally observational: for

First-order

Every ionization potential

For a given ionization order

Details follow.

For a given value of

where _{1,1} is the one and only ionization potential for atomic Hydrogen, and

The second element having an

Then inserting

_{IO}_{,}_{IO}_{+1}makes clear that for ^{2}, but also a contribution that scales with the linear

_{IO}_{,}_{IO}_{+1} presages the form of the

This _{IO}_{,}_{IO}_{+ 1}, but with the coefficient 1 / 2 replacing the coefficient _{1,3} replacing _{1,1}. Now we have two electrons remaining, instead of just one, as in _{IO}_{,}_{IO}_{+ 1}. The linear ‘resettling’ term is essentially the same in form, as if only the net positive charge of the ion actually matters, not the individual numbers of protons or electrons.

The fourth element having an

And in fact, _{next} = _{start} = 3 through _{next} = 9 in:

The 11’th element that has an _{next} = _{start} = 11 through _{next} = 17, we have

Every subsequent period is like that. We always have:

where _{start} = 3,11,19,37,55,87,...

The model given here is the simplest and best presently available. Its weakest area is its fit to second-order and third-order

The algebraic model seems to have a simple message to convey. Evidently, the typical

Removal of ^{2}. So it has to be the term

But before that must come removal of _{next}. So it has to be the term _{1,Nnext+1}

There must also be reconstruction/reinstallation of the smaller population of

The first two _{Z,Z}_{IO,IO}_{1,1} × ^{2} [_{Z−1,Z} = _{IO}_{,}_{IO}_{+1}_{1,1} × ^{2}+ ½ × _{1,2}× _{1,1} is deficient in information as a period-start reference for other more normal elements. Observe that the general sum of the absolute coefficients in ^{2} terms for the first two

These comments complete the demonstration that first-order

The consistency of the rises of 7 / 2 can be appreciated, if not fully understood, as a manifestation of periodicity: all periods in the PT/PA are fundamentally similar. The numerical value 7 / 2 can be understood in relation to the already noted connections between

can be written

or

with

The factor of 2 instead of the factor 1 / 2, which any reference to Hydrogen requires;

The factor (^{2} factor, which is appropriate because Helium has nuclear charge

The zero in place of to use. _{1,}_{N}_{1,2}to use.

All of this suggests that the connections between first

However, there exist many more details to specify. Within the periods beyond the first one, the rise is nowhere steady; there is a lot of detailed structure in the

A total rise over the run, and

An intercept with the ‘main-highway’ straight line through the period.

The rise appears to be a function of the parameter

The rise for

where

The first factor in square brackets is just the ratio of the multiplicity of ^{2}. The second factor, (

The intercepts for

The main conclusion to be drawn from this Section is that a great body of data about

But we do not

Consider first the Hydrogen atom. The electron orbits at radius _{e}_{p}

This situation implies that the forces within the Hydrogen atom are not central, and not even balanced. This situation has two major implications:

The unbalanced forces mean that the system as a whole experiences a net force. That means the system center of mass (C of M) can move.

The non-central individual forces, and the resulting torque, means the system energy can change.

These sorts of bizarre effects never occur in Newtonian mechanics. But electromagnetism is not Newtonian mechanics. In electromagnetic problems, the concepts of momentum and energy ‘conservation’ have to include the momentum and energy of fields, as well as those of matter. Momentum and energy can both be exchanged between matter and fields. ‘Conservation’ applies only to the system overall, not to matter alone (nor to fields alone either).

Looking in more detail, the unbalanced forces in the Hydrogen atom must cause the C of M of the whole atom to traverse its own circular orbit, on top of the orbits of the electron and proton individually. This is an additional source of accelerations, and hence of radiation. It evidently makes even worse the original problem of putative energy loss by radiation that prompted the development of QM. But on the other hand, the torque on the system implies a rate of energy gain to the system. This is a candidate mechanism to compensate the rate of energy loss due to radiation. That is why the concept of ‘balance’ emerges: there can be a balance between radiation loss of energy and torquing gain of energy.

The details are worked out quantitatively as follows. First, ask what the circulation can do to the radiation. A relevant kinematic truth about systems traversing circular paths was uncovered by L.H. Thomas back in 1927, in connection with explaining the then-anomalous magnetic moment of the electron: just half its expected value [

Applied to the old scenario of the electron orbiting stationary proton, the gradually rotating _{e} relative to the C of M will be judged by an external observer to be orbiting twice as fast, at frequency Ω′ = 2Ω_{e} relative to inertial space. This perhaps surprising result can be established in at least three ways:

By analogy to the original problem of the electron magnetic moment;

By construction of Ω′ in the lab frame from Ω_{e}in the C of M frame as the power series

By observation that in inertial space Ω′ must satisfy the algebraic relation Ω′ = Ω + ′/2, which implies Ω′ =2Ω_{e}.

The relation Ω′ = 2Ω_{e} means the far field radiation power, if it really ever manifested itself in the far field, would be even stronger than classically predicted. The classical Larmor formula for radiation power from a charge _{e}^{2}^{2} / 3^{3}, where _{e}_{e}= 2Ω_{e}, the effective total acceleration is _{e}× 2^{2}. With electron-proton total separation nominally _{e}_{p}_{e} = ^{2}/ (_{e} + _{p})^{2}, _{e} = _{e} / _{e}, and the total radiation power is approximately

However, that outflow of energy due to radiation is never manifested in the far field because it is compensated by an inflow of energy due to the torque on the system. This is what overcomes the main problem about Hydrogen that was a main driver in the development of QM; namely, that the Hydrogen atom ought to run down due to radiative energy loss.

Generally, the inflow power _{T} = _{e}, where _{e} × _{e} + _{p} × _{p}|, and _{e} × _{e} ≡ _{p} × _{p}, so _{e} × _{e} |. With two-step light, the angle between _{e} and _{e} is _{p}Ω_{e}/2_{e}/ _{p})(_{e}Ω_{e} / 2_{e}/_{p})(_{e}Ω_{e} / ^{2}/ (_{e} + _{p})] and the power

Now posit a balance between the energy gain rate due to the torque and the energy loss rate due to the radiation. The balance requires _{T} = _{R}, or

This equation can be solved for _{e}_{p}

Compare this value to the accepted value _{e}_{p}^{−9}cm The match is fairly close, running just about 4% high. That means the concept of torque versus radiation does a fairly decent job of modeling the ground state of Hydrogen.

The result concerning the Hydrogen atom invites a comment on Planck’s constant _{e} +_{p} is expressed in terms of

Here μ is the so-called ‘reduced mass’, defined by μ^{−1} = _{e}^{−1} + _{p}^{−1}. Using μ ≈ _{e} in (13b) and equating (13b) to (13a) gives

This expression comes to a value of 6.77 × 10^{−34} Joule-sec, about 2% high compared to the accepted value of 6.626176 × 10^{−34} Joule-sec. Is this result meaningful? To test it, a more detailed analysis accounts more accurately for ‘sin’ and ‘cos’ functions of the small angle _{p}Ω_{e}/2

The analysis so far is for the ground state of Hydrogen. To contribute to a covering theory for QM, that analysis has to be extended, first to cover trans-Hydrogenic atoms, and then to cover the so-called ‘excited states’ of Hydrogen, and the trans-Hydrogenic atoms, and even molecules.

The first concept for creating extensions is to replace the proton in Hydrogen with other nuclei. This replacement immediately gives the reason for the ^{2}, and (12b) is additionally scaled by 1/ _{e} + _{Z}_{e}_{p}_{H} = e^{2}/ (_{e} +_{p}); for the element ^{2} changes to ^{2}, so overall, the single-electron energy changes to

If it weren’t for neutrons, the scale factor

The second concept for creating extensions is to replace the single electron and single proton in Hydrogen with multiple electrons and multiple protons (with neutrons too), charges of each sign bound in coherent subsystems called ‘charge clusters’. In the journal Galilean Electrodynamics, we have occasionally had reports and commentary about the apparently incomprehensible phenomenon of electrons clustering together [

The idea of charge clusters suggests a new interpretation of ‘excited’ states for Hydrogen. The conventional idea involves an electron teetering in an upper ‘shell’, ready to fall back to a lower ‘shell’. But the present simple two-body analysis of Hydrogen does not allow anything so complicated. The simple torque

Support for an excitation model based on multiple atoms comes from the known fact that light emission is always a little bit laser-like, in that photons are emitted, not as singletons, but rather in bursts [_{H} Hydrogen atoms all working together in a coherent way. In particular, suppose that the _{H} electrons make a negative cluster, and the _{H} protons make a positive cluster, and the two clusters together make a scaled-up Hydrogen super-atom.

The replacement of single charges with charge clusters must affect both the radiation energy loss rate and the torquing energy gain rate, and the balance between them. Every factor of _{e} or _{p} scales by _{H}. Starting from (12a) for the radiation, one finds that the energy loss rate scales by _{H}^{4}. Starting from (12b) for the torquing, one finds that the energy gain rate scales by _{H}^{3}. The solution radius for system balance therefore scales as _{e} + _{p} → _{nH} = _{H} (_{e} + _{p}). [Note: if this multi-atom model captures the real behavior behind atomic excitation, and if one attempts to model that behavior in terms of a single atom with discrete radial states identified with a principal quantum number _{1} → _{n}^{2}_{1}, as is seen in standard QM.].

The overall system orbital energy then scales as _{1} → _{nH} = _{H}^{2}_{1} / _{H} = _{H}_{1}. This energy result is exactly the same as the orbital energy of _{H}

Spectroscopic data indicates that the energy required to bring the _{H}^{th} Hydrogen atom from complete separation to complete integration into an existing super atom of _{H} − 1 atoms, thus forming a super atom of _{H} atoms, is |_{1}| [(_{H}−1)^{−2}−_{H}^{−2}]. The inverse squares can be understood as follows. The radial scaling _{nH} = _{H} (_{e} + _{p}) suggests that all linear dimensions scale linearly with _{H}. If so, the volume of the clusters scales as _{H}^{3}. The number density of charges in clusters therefore scales as _{H}/_{H}^{3} = _{H}^{−2} The positive energy locked in the pair of clusters therefore depends on the number density in the clusters. This is something like having energy proportional to pressure, as is seen in classical thermodynamics.

The charge-cluster model for excitation suggests that there ought to be some similarity between Hydrogen in its first excited state (_{H} = 2) and a Hydrogen dimer molecule. Both have two electrons; both are favored, just like a Helium atom is favored. The preference for a two-atom excited state would explain why the spectrum of Hydrogen so strongly features transitions that terminate, not with the ground state, but rather with the first excited state.

The idea of charge clusters suggests that if ‘shells’ of any kind exist in trans-Hydrogenic atoms, then they are probably not centered on the nucleus, but instead nested in an electron charge cluster. The innermost shell must have two electrons. The number of electrons in remaining shells has to increase with the radius of shells, keyed to

One general conclusion to be drawn from this Section is that charge clusters are important, and possibly ubiquitous in atoms. But explaining how charge clusters can even exist requires the same sort of information as does explaining the ‘half-retarded’ directionality notion at the beginning of this Section; namely, an expanded SRT. This comes next.

Einstein [_{0} and magnetic permeability μ_{0}, which together imply a light speed

Inasmuch as SRT is founded on Maxwell’s theory, and Maxwell’s theory cannot handle the Hydrogen atom, SRT is unlikely ever to be fully compatible with QM. Einstein was involved in the development of QM, through his Nobel-Prize winning work on the photoelectric effect, but he was not fond of QM, and in later years did not work so much on it. Instead, he mainly went back to SRT, embraced the Minkowski tensor formulation for it, and exploited the metric tensor therein to develop General Relativity Theory (GRT).

GRT has the same fundamental character as Maxwell’s theory: it is a field theory, and as such, it is not designed for something so complicated as a two-body problem. It is the extreme opposite to Newton’s point-particle theory, which excels on the two-body problem. Late in life, Einstein wrote to his friend M.A. Besso about his misgivings concerning field theories:

I consider it quite possible that physics cannot be based on the field concept,

Acknowledging such doubts is, I believe, the mark of a truly great scientist. Einstein’s present-day followers usually do not harbor such doubts.

But SRT has produced an extensive literature about ‘paradoxes’, especially featuring twins, clocks, trains, meter sticks, or barns, or spinning disks,

The key Moon-Spencer-Moon

In any event, continuing control by the source implies that ‘light’, whatever it is, has a longitudinal extent (Of course! Light possesses wavelength, does it not?), and the longitudinal extent is expanding in time. That expansion naturally raises the question: exactly what

My own work [

This variation on the Moon-Spencer-Moon

The revised light postulate is what I have called ‘Two-Step Light’. It is illustrated in _{0} at the beginning of the scenario, _{1} at the mid point, and _{2} at the end. Particle _{1}).

The mid points of the light arrows may be said to resemble the Moon-Spencer-Moon

Consider the problem of processing data consisting of successive light signals from a moving source in order to estimate the speed

The estimate

One is obviously invited to look also at a related construct

The superscript ↑ is used to call attention to the fact that ^{↑} has a singularity, which is located at ^{↑} has the property of the so-called ‘proper’ or ‘covariant’ speed. Interestingly, past the singularity, ^{↑} changes sign. This behavior mimics the behavior that SRT practitioners attribute to ‘tachyons’, or ‘super-luminal particles’: they are said to ‘travel backwards in time’. The sign change is a mathematical description, while the ‘travel backwards in time’ is a mystical description.

The relationships expressed by (16) and (17) can be inverted, to express ^{↑}. The definition ^{2} / 4^{2}) rearranges to a quadratic equation (^{2})^{2} −

Multiplying numerator and denominator by

which makes clear that for small

Similarly, the definition ^{↑} = ^{2} / 4^{2}) rearranges to a quadratic equation (− ^{↑} / 4^{2})^{2} − ^{↑} = 0, which has solutions

Multiplying numerator and denominator by

which makes clear that for small ^{↑}, ^{↑} (which is negative there), and another value essentially equal to ^{↑}.

To see that ^{↑} are not only qualitatively

which is the definition of covariant speed familiar from SRT, made slightly more precise by inclusion of the minus sign for situations beyond the singularity.

Similarly, substitute (19b) into (16) and simplify to find

which is again a relationship familiar from SRT, made slightly more precise by inclusion of the minus sign for situations beyond the singularity.

The information contained in ^{↑} goes negative, it is the absolute value of ^{↑} that is plotted.

Speed can be seen as a proxy for many other interesting things in SRT, like momentum, relativistic mass,

The word ‘interesting’ is sometimes a euphemism for the word ‘paradoxical’. The fact that Galilean speed

Expressed in Gaussian units [

where κ = 1 − ngβ, with β being source velocity normalized by _{observer}(_{source}(

The 1/_{retarded}:

But the 1/^{2} fields are Coulomb-Ampère fields, and the Coulomb field does not lie along _{retarded} as one might naively expect; instead, it lies along (_{retarded}.

Consider the following scenario, designed specifically for an instructive exercise in _{retarded} and a not-so-small acceleration _{retarded}. Observe that the radiation and the Coulomb attraction/repulsion come from different directions. The radiation comes along n_{c}from the retarded source position, but the Coulomb attraction/repulsion lies along (_{retarded}, which is basically (_{retarded})_{projected}, and lies nearly along _{present}. This behavior seems peculiar. retarded, Particularly from the perspective of modern Quantum Electrodynamics (QED), all electromagnetic effects are mediated by photons – real ones for radiation and virtual ones for Coulomb-Ampere forces. How can these so-similar photons come from different directions?

Two-Step Light theory resolves the directionality paradox inherent in the Liènard-Wiechert fields. Because of the various 2_{retarded} changes to _{half retarded}, and the Coulomb attraction/repulsion direction (_{retarded})_{projected} changes to (_{retarded})_{half projected}. These two directions are now physically the same; namely the source-to-receiver direction at the mid point of the scenario, _{mid point}. The potentials and fields become:

and

Observe that the Coulomb attraction or repulsion is now aligned with the direction of the radiation propagation.

Applied in the Hydrogen atom,

The main conclusion to be drawn from the present Section of the present paper is that the extended SRT gives two key ingredients for the variant QM:

The main conclusions to be drawn from this paper overall are:

An important factor presently limiting the development of both physics and chemistry is Einstein’s Second Postulate concerning light speed. We do not have to retain that Postulate. We can consider other postulates instead, and adopt another one if it works better. For example, we can adopt Two Step Light. In that case, what comes out is a covering theory for Einstein’s SRT. Since it contains SRT, researchers who are happy with SRT need not sacrifice anything. But researchers who need something more can perhaps find something they need in Two Step Light.

For example, expanding SRT allows one to adopt an approach for understanding atoms that is completely different from traditional QM. We need not postulate the value of Planck’s constant, or the nature of its involvement in the mathematics of ‘probability’ waves,

The algebraic QM supports an algebraic model for ionization potentials,

Beyond that, it is to be hoped that detailed knowledge about

Some surprises emerge from the ^{2}/ (1 +_{e}_{nucleus}). The algebraic model has no ^{2}, and its nuclear mass dependence is much stronger − 1/^{2}/ (1 + _{e}/_{nucleus}) scale factor was just an early guess, offered before spectroscopy was so well developed, or so many

For another example, the algebraic model gives a prominent role to terms in squared ionization order, ^{2}. This raises a subtle point. When one speaks of ionization at order ^{2} scaling, I now believe the latter vision.

Some loose ends remain for future resolution. For example, there is not yet a satisfactory explanation for the parameter

Charge clusters will probably play a role in explaining ^{2} for ^{2} can be understood as a reference to a cluster of electrons that is spherical in shape, with constant electron density over radius. The mystery that remains is the repetition indicated by

I have not detailed how

The concept concerning chemical bonds that this paper offers is holistic: Propositions 1 and 2 speak about molecules overall, and not about individual atom-to-atom bonds. Those Propositions are here offered for future testing and possible refinement or replacement.

In response to Propositions 1 and 2, a reviewer pointed out that oxygen, ozone, and nitrous oxide do possess ‘all-neon’ configurations. This is indeed true, when ‘bonds’ are imagined as electrons ‘shared’ between two atoms, and those shared electrons are ‘double counted’, so that O + O = 8 + 8 = 16 becomes 20 = 10 + 10, or O + O +O = 8 +8 + 8 = 24 becomes 30 = 10 + 10 + 10, or N + N + O = 7 + 7+ 8 = 22 becomes 30 = 10 + 10 + 10. Propositions 1 and 2 do not allow double counting, and for that reason, they identify oxygen, ozone, and nitrous oxide as being quite different from the many other molecules that they identify as ‘stable’. My thanks go to the reviewer for raising this issue.

Guest Editor Prof. Dr. Mihai V. Putz called my attention to his related works [^{+}) and ‘soft acid’ (HO^{+}) with ‘hard base’ (OH^{−}) and ‘soft bases’ (many kinds exist) are studied in [

Dr. Putz also recalled for the author the efforts of Lois de Broglie and his intellectual descendants David Bohm and Jean-Pierre Vigier to rewrite quantum mechanics in a less mysterious way, by introducing the concept of ‘pilot waves’, within which a point particle would travel, a bit like a surfer. There does exist symmetry between that work and the effort described here to rewrite special relativity theory in a less mysterious way; in this case, by introducing an elastic boundary condition for light, a sort of expanding/contracting ‘water balloon’, within which light waves would be confined. By releasing energy, the source would set in motion the first phase front - call it the ‘primary’ one. That primary wave front would then induce other wave fronts, ahead of and behind itself, filling the ‘balloon’ end to end. Individual phase fronts would travel at speed

This author is a little old lady – a sort of Grandma Moses figure. I have now been out in the desert working on aspects of this story for nearly the requisite forty years. From time to time, manna arrives. The invitation from Dr. Putz conveyed by Dr. Angelika Kren was indeed such manna. I thank them most heartily for the opportunity to tell this story to this audience. I also thank Ms. Rawan Halawi, who came along later, for her help in bringing the publication to completion.

The Periodic Arch (PA).

Ionization potentials, scaled appropriately and modeled algebraically.

First-order

First-order

Coulomb force directions within the Hydrogen atom.

Thomas rotation. When the particle traverses the full circle, its internal frame of reference rotates 180°.

Illustration of Two-Step Light propagation.

Numerical relationships among three speed concepts.

Attraction between two like charges orbiting at superluminal speed

Electron redistributions in relatively stable molecules to give to all of the atoms an electron count equal to that of a noble gas, or else zero.

Name | Chemical formula | Electron contributions | Electron redistributions |
---|---|---|---|

Ammonia | NH_{3} |
N: 7, H’s: 1 each total 10 | N : 10, H’s: all 0 total 10 |

Sodium hydroxide | NaOH | Na : 11, O: 8, H : 1 total 20 | Na : 10, O: 10, H : 0 total 20 |

Potassium carbonate | K_{2}CO_{3} |
K’s: 19 each, total 38 | K’s: 18 each; total 36 |

O’s: 8 each, total 24 | O’s: 10 each, total 30 | ||

C: 6; total 68 | C: 2; total 68 | ||

Bornyl acetate | CH_{3}CO_{2}C_{10}H_{17} |
C’s: 6 each, total 72 | C’s: 6@2, 6@10; total 72 |

H’s: 1 each, total 20 | H’s: 8@2, 8@0, total 16 | ||

O’s: 8 each, total 16 | O’s: 10 each, total 20 | ||

total 108 | total 108 | ||

Lead acetate | (CH_{3}CO_{2})_{2}Pb · 3H_{2}O |
C’s: 6 each, total 24 | C’s: 2 each: total 8 |

H’s: 1 each, total 12 | H’s: 5@2, 7@0, total 10 | ||

O’s: 8 each, total 56 | O’s: 10 each, total 70 | ||

Pb: 82; total 174 | Pb: 86; total 174 | ||

Calcium stearate | (C_{17}H_{35}CO_{2})_{2}Ca |
C’s: 6 each; total 216 | C’s: 18@10, 18@2, total 216 |

H’s: 1 each, total 70 | H’s: 38@0, 32@2, total 64 | ||

O’s: 8 each, total 32 | O’s: 10 each, total 40 | ||

Ca : 20 total 338 | Ca : 18; total 338 |