Ian Miller

The purpose of theory is to try to understand, and understanding means more than being able to calculate. My recommended procedure for forming theories follows Aristotle, where observation provides the problem, the use of set theory helps induce propositions, these are worked through, then we see whether what we have agrees with observation. However, set theory analysis only works if we start with the complete set of what we know, and a separate set of what we think we know. It is important to include ALL the awkward data, because these indicate where the current theory might be wrong. Details of this procedure are in my ebook Aristotelian Methodology in the Physical Sciences (Elements of Theory)

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The standard theory of planetary formation assumes that in the stellar accretion disk, dust and solids accrete into a reasonably uniform distribution of planetesimals, which then gravitationally accrete into planets by what is called oligarchic accretion.

However, there is no known mechanism for planetesimal formation and there is no real way the planets could have formed in time. I propose the overlooked monarchic growth, which in certain regions specific chemical effects are accelerated due to the local temperature. This explains why every planetary system in our solar system has a different overall composition from the others. The giant cores arise from melt fusion of ices and therefore four giants are -predicted for every system with enough matter, and a further planet is possible at greater distance, depending on the initial temperature of the disk gas and the rate of inflow. The rocky planets are similarly dependent on temperatures in the disk, but it is more complicated because there are three different periods with different temperatures and hence more variation is possible.

No evidence was found in the ten years following the first edition to contradict the proposed mechanism, but the second edition was published to include a lot of additional information gathered by the research community over those ten years. Details can be found in my ebook “Planetary Formation and Biogenesis”

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The two-slit experiment shows unambiguously the presence of wave-particle duality. Either there is a physical wave or there is not, and while standard physics concludes there is not, I follow de Broglie and Bohm in asserting there is. The standard theory assumes that despite the fact there is no wave, the quantum systems are defined by the Schrödinger equation, which in its more basic form, free of operator formalism, is

The wave function ψ is given by

where A is the amplitude, S the action, and h is Planck's quantum of action. It is generally held that ψ is complex, but from Euler's complex number theory, when S (the time integral of the Lagrangian, and which hence evolves with time) equals h, then ψ = A, which is real. Accordingly, my interpretation assumes the antinode of the wave defines the expectation dynamical properties. My second assumption is that if the wave is to cause the diffraction in the two-slit experiment, it has to arrive at the slits at the same time. If so, the wave must transmit energy, and since the Born rule has to be false because the phase velocity and particle velocity are not the same, ψ.ψ* is not defined by probability. Instead, A 2 defines the energy of the motion. From this I obtain, the Uncertainty Principle and the Exclusion Principle. What follows is that atomic orbitals do not correspond to hydrogen-like solutions of the Schrodinger equation, but rather the wave function is a combination of all possible paths, and the screening constant is a function of quantum numbers. A possible explanation is given for the delayed choice quantum eraser, which, if correct, predicts the results of further experiments. I also argue that the assertion that Alain Aspect proved violations of Bell's Inequality is not correct. The experimental results are fine, but there is a logic error in reaching the conclusion. (See Miller, I. J. (2023). Non-Violations in Bell's Inequality. J Math Techniques Comput Math, 2(6), 209-210 .) Details are in my ebook “Guidance Waves”

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If we accept the principles of the guidance wave, the energy of electrons is determined by the potential fields at the antinodes of the wave component between the nuclei, which produces analytical results.. As a simple example, the hydrogen molecule formed by linear combination of wave components has the bond energy of one third the Rydberg energy. For elements Li and heavier, the atomic orbitals do not correspond to the simple excited states of hydrogen, but rather linear combination of waves occurs, which gives ionization energies that are reasonably accurate with no arbitrary constants such as screening constants. The net result of this, however, is that on linear combination of orbitals, a further quantum effect is required, essentially to remove the effect of wave nodes on the component between the nuclei. Calculated energies and bond lengths are generally in good agreement with observation without any empirical correction through validation and without arbitrary constants. Details can be found in my ebook “The Covalent Bond From Guidance Waves”

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My approach has been to assume the critical step is to convert the solid biomass to a liquid. Hydrothermal liquefaction of lignocellulose rapidly produces an oil containing hydrocarbons suitable for high-octane petroleum and jet fuel, together with a phenolic fraction that can be further hydrotreated for fuel. Microalgae are one promising feedstock, and besides fuel, some highly valuable chemical feedstocks can be isolated. Details can be found in my ebook “Biofuels. An Overview”.

My PhD work related to whether there is electron delocalization from the strained ring cyclopropane to adjacent unsaturation. Standard theory says it does, and this was "confirmed" by quantum computations, however the same code was used to "verify" the stability of polywater. My interpretation was to consider staring the system produced polarization fields. To illustrate the basics of what followed, consider two charges at A and B on one side of a wall W, and an observer O, thus

A     B     |W|     O     (Note to web editor – use the diagram already there)

The observer O can detect a combined electric field E from A and B. Now, suppose charge A moves closer to B; O now sees a change in electric field, and two interpretations are possible: charges have moved closer, or further charge was added. In each case, the same work has to be done (the strain energy) on the charge. The two possibilities are indistinguishable, and while we know charge moved in the strained molecule, it is impossible to calculate by how much. If, however, we assume a constant structure and we add a pseudocharge, the calculation is much easier. (This is like using centrifugal force in a calculation; in principle there is no such force, but it does make calculations easier.) I have put a review on the web that shows there are about 60 different types of observation that show that the unusual effects of strained rings are due to such polarization fields resulting from moving charge rather than from electron delocalization.

If there is a physical wave, as per my guidance wave theory, chemical bonds are localized if the delocalized path is bent such that wave refraction is required, but the required impedance differences are not exactly present. Aromaticity arises as a consequence of the Exclusion Principle not permitting a classical structure because of the phase relationships, and the bond lengths are determined by the weighting of the canonical structures. Aromatic bond localization can occur through the alteration of the refractive index for quantal waves by the focusing of polarization fields.

Resonance energy is not a consequence of some "quantum mechanical effect with no classical equivalent", but rather a consequence of the de Broglie wave equation, and the requirement that momentum be conserved between canonical structures.

I have proposed that the gas-phase stabilities of carbenium ions are determined by the polarization of adjacent bonds by the ionic charge. The required relative permittivity for the given bonds are in good accord with bond refractivities. Accordingly, I argue the concept of hyperconjugation is unnecessary.

The stability of the atomic nucleus with respect to radioactive decay can be expressed in terms of phase relationships of electro-weak quark-quark interaction wave functions. The relevant journal no longer functions and the article has not seemingly been put onto the web, however information is available on request. The proposal requires a slight modification to account for nuclear spin.

The electric field vector from the rest of the molecule is directed along the line of a bond with zero deformation, I proposed that the mechanics of bond bending is not simple harmonic, but approximates to the mechanics of a pendulum. The differences become more significant as the amplitude of the vibration increases, and anharmonicities for some molecules were obtained in good agreement with observation.

(1) Processes have been developed for manufacturing agar from unsorted seaweed, high gel strength agars, agaroses and agaroid derivatives, including an agarose-like material the gel of which does not melt at ambient pressure; a xylosylated pyruvylated 'agarose'; agaroses with low gel melting temperatures but with gel strengths higher than most current examples, and Nemidon gels. More details are found here.

(2) An improved method has been developed to desulphate sulphated polysaccharides. Alkaline desulfation also occurs in the presence of reducing agents, and some materials such as ferric oxide, which requires the removal of such agents when carrying out methylation analyses.

(3) The use of set theory logic applied to a number of simple procedures was used to develop a faster means of determining the structures of red algal galactans. This was applied to standard agars and carrageenans, mixed diads, and then more complicated galactans such as Chladhymenia oblongifolia. The method was extended to a number of further phycocolloids, and samples that have potential biological activity are available.