Unified Field Theory
Current paradigms
Physical topics
New paradigms
Dynamic quanta actions
3D-NSE problem solved
Yang-Mills probl. solved
Promising hypotheses
Literature, UFT related
Riemann Hypothesis
Euler-Mascheroni const.
Who I am



The current paradigms of physics to be changed resp. to be replaced appropriately are

Paradigms 1:
The Newton and the Coulomb potentials to deal with continuously distributed mass elements exposed to external (attractive or repulsive) forces; the Debye potentials and the London dispersion interaction potentials

Paradigm 2
Dirac‘s energetical one-component system to model an atom and its radiation field avoiding e.g., two distinct interacting systems to explain the phenomena of emission and absorption of light by matter, the related spin(1/2) hypothesis and the fundamental problem in statistical thermodynamics: the distribution of a given amount of energy E over N identical systems

Paradigms 3:
The Big Bang story, an accelerated expansion of the universe accompanied by a hypothetical substance called "Dark Energy", a gaseous state of the sun, and Newton's theory of "light rays" accompanied by the three forms of redshift in astronomy and cosmology, i.e., a theory of light is not required in current cosmological models


Remark: The article "A Heuristic Approach to General Relativity", (DeH), explains all known tests of Einstein's general relativity theory with variable speed of light, (UnA1) p. 142.

Remark (Einstein's lost key: a variable speed of light): "Nothing forces us to assume that ... clocks have to be seen as running at the same speed", (UnA1) p. 12. ... The formula for gravitational potential he had developed in his variable speed of light article implied that the graviational constant itself could be calculated from the mass distribution of the universe", (UnA1) p. 15. ... Dicke later became famous for his role in the discovery of the cosmic microwave background, and only bad luck prevented him from winning the Nobel Prize. Dicke, who studied Ernst Mach, saw the power of Einstein's formula - and improved it in one crucial respect", UnA1) p. 16.

Remark (General relativity is made up of fields on fields): "General relativity is the discovery that spacetime and the gravitational field are the same entity. What we call „spacetime“ is itself a physical object, in many respects similar to the electromagnetic field. We can say that GR is the discovery that there is no spacetime at all. What Newton called „space“, and Minkowski called „spacetime“, is unmasked: it is nothing but a dynamic object – the gravitational field – in a regime in which we neglect its dynamics. …., the universe is not made up of fields on spacetime; it is made up of fields on fields", (RoC). 

Remark: The key ingredients of Einstein’s field equations are Riemann's differentiable manifolds (whereby the differentiability condition is w/o any physical meaning) in combination with the concept of affine connexion (enabled by the differentiability condition) to build the metric g based (Riemann manifold) metric space (M,g).
 
Remark: Einstein’s field equations are hyperbolic and allow so called „time bomb solutions“ which spreads along bi-characteristic or characteristic hyper surfaces. Actual quantum theories are talking about „inflations“, which blew up the germ of the universe in the very first state. The inflation field due to these concepts are not smooth, but containing fluctuation quanta. The action of those fluctuations create traces into a large area of space.

Remark: Newton's theory of "light rays" basically states that the rays of white light are formed from a finite number of indivisible rays (the prism colors).


Current paradigms and related notes

Paradigms 1:The Newton and the Coulomb potentials to deal with continuously distributed mass elements exposed to external (attractive or repulsive) forces; the Debye potentials and the London dispersion interaction potentials


Note: „Newton’s original law was stated in terms of a system of two particles/bodies attracting each other by the concept of a gravitational force. In order to deal with continuously distributed matter this law has been adopted (regarded as an amplified statement of Newton’s law):

Given two bodies, let them be divided into elements after the manner of the integral calculus, and let the mass of each element be regarded sd concentrated at some point of the element. Then attraction which one body exerts on the other is the limit of the attraction which the corresponding system of particles exerts on the second system of particles, as the maximum chord of the elements approaches zero“, (KeO) pp. 2-3.

Note: „Auf Grund der angegebenen Tatsachen kommt man notgedrungen zu der Auffassung, daß die Definition „Kraft = Ableitung des Impulses“ das Wesen der Kraft nicht richtig wiedergibt. Der wirkliche Sachverhalt ist vielmehr umgekehrt: Die Kraft ist der Ausdruck für eine selbständige, die Körper zufolge ihrer inneren Natur und ihrer gegenseitigen Lage und Bewegungsbeziehung verknüpfende Potenz, welche die zeitliche Änderung des Impulses verursacht. …. So wird der Kraftbegriff zu einer Quelle neuer meßbarer physikalischen Kennzeichen der Materie, welche ebenso wie die Masse mit den im ersten Abschnitt besprochenen, aus der Substanzvostellung entsprungenen Merkmalen nichts mehr zu tun haben. … Man sieht an diesem Beispiel, dasß die Entdeckung der „dynamischen“ Eigenschaften der Materie von selber dazu führt, ihre substanziellen zu verdrängen, die zur Erklärung der Naturerscheinungen überflüssig werden. …. Hier sollte uns der Kraftbegriff nur als Vorbereitung dienen auf die Idee des Feldes“, (WeH2) S. 28-29.

Note: The Coulomb potential model is a generalization of the Coulomb force law, where there are two Coulomb forces F(1) and F(2) acting in the direction of the connecting line between two charged particles, whereby F(1)=-F(2).

Note: In classical electricity theory the electric current is a flux of charges (measured in the unit "Coulomb") transported by the electrons in metals. The „pressure“ by which the electrons are pushed into the conductive wire is called electric tension or electric potential. Ohm's law is U = R * I, where U denotes the potential, R denotes the resistance of the metal to the current, and I denotes the strength of the current.

Note: In electromagnetism the Biot–Savart law is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The magnetic field can also be calculated as a consequence of the Lorentz transformation for the electromagnetic force acting from one charged particle on another particle, Wikipedia

Note: In electrodynamics the matter equations (Maxwell equations in discharged areas) are prescribed by the hyperbolic telegraph equations.They are wave equations for a lossy dieletric, which correspond to standard wave equations in case of an isolator. The dielectric constant governs the resistence and the frequency depending damping phenomena. The magnetic permeability is defined by the ratio of the magnetic flux density and the magnetic field strength.

Note: The solution of time-harmonic Maxwell equations in a vacuum leads to the Helmholtz equation. The fundamental solution of the Helmholtz equation at the origin is given by spherical wave fronts. The time-dependent magnetic field has the form of the Hertz dipole centered at the origin, (KiA) p. 14.

Note (Newtonian dynamics): The Newtonian dynamics is governed by the gravitational (Newton) potential at a „point“ in space equipped with a mass. The reference point, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance. The field of gravity potentials  is called the gravitational field. If the field is nearly independent of position the gravitational accelleration (the standard gravity on the surface of the earth) can be considered constant.

Note: The mathematical model of the „mass element“ concept govering the Newton/Coulomb potentials is called the Dirac function. It is an element of the distributional Sobolev space H(-n/2-c), where c>0, and n denotes the dimension of the Euclidian space. The "potential function" is given by the fundamental (potential function) solution of the (mechanical) Laplacian operator equation with given Dirac function.

Note: London dispersion forces (instantaneous dipole–induced dipole forces, fluctuating induced dipole bonds) are a type of intermolecular force acting between atoms and molecules are symmetrically distributed with respect to the nucleus. They are part of the van der Waals forces. London dispersion interactions are weak, temporary attractive forces between molecules caused by fluctuating electron distributions that induce temporary dipoles. The "potential" of these interactions refers to their strength, which is influenced by molecular surface area, shape, and the polarizability of the molecule, making them a significant factor in nonpolar interactions and molecular aggregation, Wikipedia.

Note: London dispersion forces are temporary, induced attractions between molecules arising from electron cloud fluctuations, while a Debye potential describes the interaction between a permanent dipole and an induced dipole in a neighboring molecule. London forces are universal and the weakest van der Waals force, whereas Debye forces are a specific type of interaction that requires a molecule with permanent dipoles, Wikipedia

Note: The physical interpretation of the Debye potential enabled by the concept of a Debye length is the following:

"The statistical attraction of electrons and repulsion of ions shield the potential of any ion, reducing the Coulomb value at large r by an exponential factor", (ShF) p. 9.

Note (On the present (1909) status of the radiation problem; the different opinions of W. Ritz and A. Einstein, (RiW)): „To clarify the differences of opinion that came to the light in our respective publications, we note the following.   

In the special cases in which an electromagnetic process remains restricted to a finite field, the process can be represented in the form  …  as well as in the form  …  and in other forms.  

While Einstein believes that one could restrict oneself to the case of retarded potentials without substantially limiting the generality of the consideration, Ritz considers this restriction not to be permissble in principle. If one takes this standpoint, then experience compels one to consider the representation by means of retarded potentials as the only one possible. If one inclined to the view that the fact of irreversibility of radiation processes must already find its expression in the fundamental equations. Ritz considers the restriction to the form of retarded potentials as one of the roots of the second law, while Einstein believes that irreversibility is exclusively due to reasons of probability“.

Note: The Eulerian Equations for Perfect Fluids
In order to get nearer to the behavior of real matter we must add to the energy tensor a term which corresponds to the pressures. The simplest case is that of a perfect fluid in which the pressure is determined by a scalar p“, (EiA1) p. 30.

Note: The d’Alembert “paradox” is not about a real paradox but it is about the failure of the Euler equation (the model of an ideal incompressible fluid) as a model for fluid-solid interaction. The difficulty with ideal fluids and the source of the d’Alembert paradox is that in incompressible fluids there are no frictional forces. Two neighboring portions of an ideal fluid can move at different velocities without rubbing on each other, provided they are separated by streamline. It is clear, that such a phenomenon can never occur in a real fluid, and the question is how frictional forces can be introduced into a model of a fluid.

Note: Hydrodynamical Equations 
We know that matter is built up of electrically charged particles, but we do not know the laws which govern the constitution of these particles. In treating mechanical problems, we are therefore obliged to make use of an inexact description of matter, which corresponds to that of classical mechanics“, (EiA1) p. 29.

Note: Energy Tensor of the Electromagnetic Field
We (therefore) conclude from these considerations that the energy per unit volume has the character of a tensor. This has been proved directly only for an electromagnetic field, although we may claim universal validity for it. Maxwell's equations determine the electromagnetic field when the distribution of electric charges and currents is known. But we do not know the laws which govern the currents and charges. We do know, indeed, that electricity consists of elementary particles (electrons, positive nuclei), but from a theoretical point of view we cannot comprehend this. We do not know the energy factors which determine the distribution of electricity in particles of definite size and charge, and all attempts to complete the theory in this direction have failed. If then we can build upon Maxwell's equations at all, the energy tensor of the electromagnetic field is known only outside the charged particles (It has been attempted to remedy this lack of knowledge by considering the charged particles as proper singularities. But in my opinion this means giving up a real understanding of the structure of matter. It seems to me much better to admit our present inability rather than to be satisfied by a solution that is only apparent.) In these regions, outside of charged particles, the only regions in which we can believe that we have the complete expression for the energy tensor in the form … =0", (EiA1) p. 28.

Note: „Lorentz succeeded in reducing all electromagnetic happenings to Maxwell’s equations for free space“, (EiA5). 

Note: The cosmological microwave background radiation (CMBR) is currently interpreted as the "echo of the early universe". It is an essential element of theoretical and observational cosmology and one of the foundation stones of the big bang models:

(LaM) p. 7: "Big bang models are based on the theory of relativity and follow from a number of assumptions. These are the following:

(1) homogeneity of space applies
(2) isoptopy of space applies
(3) that the matter in the universe can be described very simple in terms of what is called a perfect fluid. In this case its properties are completely given by its density and its pressure
(4) that the laws of physics are the same everywhere.

The assumptions (1) and (2) make up what is called the cosmological principle."

Note: "A stellar system is a gravitationally bound assembly of stars or other point masses. Stellar systems vary over more than fourteen orders of magnitude in size and mass, from binary stars, to stars clusters containing 10 exp(2) to 10 exp(6) stars, through galaxies containing 10 exp(5) to 10 exp(12) stars, to vast clusters containing thousands of galaxies.

The behavior of these systems is determined by Newton's laws of motion and Newton's law of gravity, and the study of this behavior is the branch of theoretical physics called stellar dynamics", ((BiJ) p. 1.

Note: The Landau damping phenomenon is a characteristic of collisionless plasma dynamics. It is a wave damping without energy dissipation by elementary particle collisions.

Note: In plasma physics the Debye (shielding) length is derived from the Poisson equation for the electrostatic (Coulomb) potential of the related Debye ball resp. Debye sphere.

Note: "The Debye length provides a measure of the distance over which the influence of the electric field of an individual charged particle (or of a surface at some nonzero potential) is felt by the other charged particles inside the plasma. The charged particles arrange themselves in such a way as to effectively shield any electrostatic fields within a distance of the order of the Debye length. … It is convenient to define a Debey sphere as a sphere inside the plasma of radius equal to the Debye length", (BiJ) p. 8.

Note: Vlasov’s argument against the Landau equation (supporting his Vlasov equation) was, that “the Landau model of pair collisions is formally not applicable to Coulomb interaction due to the divergence of the kinetic terms”. Because of its comparative simplicity, the Vlasov equation is the equation most commonly studied in kinetic plasma theory.

Note: Superconductivity, Superfluids and Condensates
Ever since their original discovery nearly 100 years ago superconductors and superfluids have lead to an incredible number of unexpected and surprising new phenomena. The theories which eventually explained superconductivity in metals and superfluid helium-4 count among the greatest achievements in theoretical physics, and have had profound implications in many other areas, such as in the construction of the „Higgs mechanism“ and the standard model of particle physics“, (AnJ), Preface.

Key words
Bose-Einstein statistics, Bose-Einstein condensate (BEC), BEC temperature, BEC in ultra-cold atomic gases, superfluid helium-4, classical and quantum fluids, macroscopic wave function, momentum distribution, superconducting metals, zero-resistivity, perfect diamagnetism, the (classical) London equation, the London vortex, the Ginzburg-Landau model, bosonic quantum fields, weakly interacting Bose gas, the electron-phonon interaction governed by strongly electrostatic Coulomb repulsion, electron-phonon coupling parameter, (AnJ).

Note: There are only two superfluids which can be studied in laboratory. These are the two isotopes of helium. Unlike all other substances they are unique because they remain in the liquid state even down to absolute zero in temperature, (AnJ) p. 21.


Paradigm 2
Dirac‘s energetical one-component system to model an atom and its radiation field avoiding e.g., two distinct interacting systems to explain the phenomena of emission and absorption of light by matter, the related spin(1/2) hypothesis and the fundamental problem in statistical thermodynamics: the distribution of a given amount of energy E over N identical systems


Note: Only one problem in statistical thermodynamics
“There is, essentially, only one problem in statistical thermodynamics: the distribution of a given amount of energy E over N identical systems. Or perhaps better: to determine the distribution of an assembly of N identical systems over the possible states in which this assembly can find itself, given that the energy of the assembly is a constant E. The idea is that there is weak interaction between them, so weak that the energy of interaction can be disregarded, that one can speak of the “private” energy of every one of them and that the sum of their “private” energies has to equal E", (ScE) p. 1.

Note (E. Fermi): „Dirac‘s theory of radiation is based on a very simple idea; instead of considering an atom and the radiation field with which it interacts as two distinct systems, he treats them as a single system whose energy is the sum of three terms: one representing the energy of the atom, a second representating the electromagnetic energy of the radiation field, and a small term representing the coupling energy of the atom and the radiation field“, (FeE).

Note (E. Fermi): "Dirac's quantum theory of radiation explains the phenomena of emission and absorption of light by matter", (FeE).

Note: Pauli‘s spin(1/2)-concept is about a „rotation“ concept of an elementary particle, which looks the same only after the second „rotation“. This „spin(1/2)-rotation“ concept is the model for an angular (non-kinematical) momentum. However, in the current quantum theory translation and rotation operators are not interchangeable, which is a consequence of the quantification process of classical partial differential equations (PDE). Therefore, in order to characterize the angular momentum of a system about an axis by a quantum number it is neccessary that the perpendicular translation momentum vanishes or is unknown, (DüH), (HeW).

Note: One basic problem in the quantum interpretation is the „wave function“ to be defined by problem adequate wave equations, based on the imitations of various classical physical processes. Thereby, the Schrödinger and the Pauli equations are non-relativistic equations, while the Klein-Gordon and the Dirac equations are relativistic, (XiK).

Note: The electromagnetic interaction has gauge invariance for the probability density and for the Dirac equation. The wave equation for the gauge bosons, i.e. the generalization of the Maxwell equations, can be derived by forming a gauge-invariant field tensor using generalized derivative. There is a parallel to the definition of the covariant derivative in general relativity.

Note: In (HeW) the deviation from iso-spin-symmetry in electrodynamics is taken as indication for an asymmetry of the ground state, (DüH).

Note (Gauge invariance): The gauge invariance is the main principle in current SMEP theory.   

Note (the mass gap problem of the Yang-Mills theory): The Maxwell fields can carry energy from one place to another. The classical Yang-Mills theory is a generalization of the Maxwell theory of electromagnetism where the invented chromo-electromagnetic field also carries charges for low energy scales. As a classical field theory it has solutions which travel at the speed of light so that its quantum version should describe massless particles (gluons). However, the postulated phenomenon of color confinement permits only bound states of gluons, forming massive particles. This is the mass gap.
 
Note (The Higgs boson): The Higgs boson is supposed to be a heavy elementary particle (with non-zero rest mass of about 125 GeV with spin 0). The Higgs field is supposed to fill the whole universe interacting with each particle, which “moves” through it by a kind of frictional resistance, i.e. which has kinetic energy. Therefore, the Higgs effect (explaining the mass of the gauge (weak interaction) bosons of the weak „nuclear-force“) requires a Higgs field with not vanishing amplitudes in the ground state.
     
Note (Higgs mechanism, (HiP)): The Higgs effect (or mechanism) builds on an extended from global to local U(1) transformations symmetry group of the underlying Lagrangian. It explains the mass of the gauge W- and Z- (weak interaction) bosons of the weak “nuclear-force”.     

Note (Higgs mechanism, (HiP): “It is fine that the gauge field of electromagnetism has zero mass because there the force is mediated by photons, which are massless. However, Yang-Mills type forces must arise from the exchange of massive particles because of the observed short range of these forces. The Higgs mechanism helps in two ways. First, gauge fields can acquire mass by the symmetry breaking. Second, the undesirable Goldstone bosons (which arise in the symmetry-breaking process) can be usually gauged away”, (BlD) 10.3.    

Note: “Within the framework of quantum field theory a “spontaneous” breakdown of symmetry occurs if a Lagrangian, fully invariant under the internal symmetry group, has such a structure that physical vacuum is a member of a set of (physically equivalent) states which transform according to a nontrivial representation of the group. This degeneracy of the vacuum permits non-trivial multiplets of scalar fields to have nonzero vacuum expectation values (or “vacuons”), whose appearance leads to symmetry-breaking terms in propagators and vertices. … When the symmetry group of the Lagrangian is extended from global to local transformations by introduction of coupling with a vector gauge field the original scalar massless boson as a result of spontaneous breakdown of symmetry then becomes the longitudinal state of a massive vector (Higgs) boson whose transverse state sare the quanta of the transverse gauge field. A perturbative treatment of the model is developed in which the major features of these phenomena are present in zero order”, (HiP).

Note: Based on the magnitude of the angular momentum of the electron performing a circular orbit around the nucleus of a hydogen atom in the ground state the magnetic moment value of the electron can be derived, (BlS) p. 4. Note that the sign of the magnetic moment is negative. Because of the negative charge of the electron, its magnetic moment is antiparallel to its angular momentum.The absolute value of the magnetic moment is called „Bohr magneton“. The size of the „Bohr magneton“ can be calculated from the charge e of the electron, the Planck action constant h and the mass of the electron.

Note: Currently there is no explanation for the ratio of the mass of the proton and the mass of the electron (about 1836,15 ..).

Note: Ultimately, Sommerfeld’s fine structure constant is a mathematical requirement to ensure convergent power series representations when separating the radial part of the solution of the Dirac equation for the hydrogen atom into two parts to determine the eigenstates of the electron governed by the Coulomb potential, (MaW) S. 71 ff. Sommerfeld's formula calculates the fine structure value from the charge e constant, the permittivity constant, the speed of light constant, and the Planck action constant, (MaW) S. 75. 

Note: From the wave equation in a „vacuum“ (which is mathematically derived from the Maxwell equations by differentiation accompanied by a loss of physical information (!)) the square of the speed of light constant can be calculated by the inverse of the product of the „vacuum“ (free space) permittivity (electric polarization) and the vacuum permeability (magnetization in a material applied to a magnetic field).

Note: Originally, the Planck action constant was introduced as an auxiliary constant to ensure a mathematical bounded energy density function in case of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T. However, the concept of temperature is the measure of the physical energy of the most aggregated closed physical system, while Planck’s black body radiation has lost its universal significance becoming restricted to perfect absorbers, (RoP1).

Note: The behavior of a physical system depends on a scale (of energies, distances, momenta, etc.) at which the behavior is studied. The change of behavior when the scale is changed, is described by the renormalization group equation. In quantum field theory, the dependence of the behavior on the scale is often expressed mathematically by the fact that in order to regularize (i.e., render finite) Feynman diagram integrals one must introduce auxiliary scales, cutoffs, etc. The effect of these choices on the physics is encoded into the renormalization group equation. The "case" if there is no related (G-invariant) renormalization realisation (example ground state energy) is called "symmetry break down", (DeP1) p. 1119 ff.. 
                           

Paradigms 3:
The Big Bang story, an accelerated expansion of the universe accompanied by a hypothetical substance called "dark Energy", a gaseous state of the sun, and Newton's theory of "light rays" accompanied by the three forms of redshift in astronomy and cosmology, i.e., a theory of light is not required in current cosmological models


Note: "Crucial cosmological observations support Einstein's idea of variable speed of light. It also illuminates how difficult it is to correct existing misconceptions that have been firmly anchored in the scientific community for decades.

The most important cosmological discovery in recent times is the so-called "accelerated expansion of the universe", also well konwn as "Dark Energy", a hypothetical substance postulated to explain the acceleration that up until then, nobody could account for. As questionable and as suspicious as these terms might be, a significant discovery lay behind them. ....

... The key to an explanation of "dark energy" is not to be found in his (Einstein) idea from 1917 but in a completely different idea that goen back to 1911: variable speed of light", (UnA1) pp. 199/200.

Note: Most of our understanding of the universe is based on the lights by stars we observe by telescopes (like the Hubble telescope). One of the main conclusions is made based on the Doppler effect phenomenon in optics. The photosphere of the sun appears as a surface, i.e. the upper layers of the sun do not permit that the observed sun light passes from the interior of the sun to Earth. Technically speaking, a gaseous structure of the sun do not allow blackbody radiations, (RoP), (UnA4).

Note: Newton's concept of light rays is based on the "prism" experiment, where the "light" (brightness) became white light. Goethe's so-called "theory of color" is not a physical theory but the discovery of the phenomenon, that there are in a certain sense symmetric series to the prism colors caused by "darkness", (MüO), ((NuI). If there is a theory of light based on an unified quanta dynamics field theory (including "ground state & plasma" dynamics) how the explanation of Newton's (white light) prism phenomenon and Goethe's "dark light" prism phenomenon would look like?

Note: (Einstein & Lorentz and the Michelson-Morley experiment): "People often wonder whether Einstein’s declaration that „c is a law of physics“ was based on theoretical insight or prior experimental results – in particular the Michelson-Morley experiment. Einstein himself claimed that he was not aware of Michelson’s and Morley’s result …Einstein took Maxwell’s equations to be the law of physics.  … In modern language, Einstein’s great accomplishment was to recognize that the symmetry structure of Maxwell’s equations is not a Galileo transformation but a Lorentz transformation. He encapsulated all of this in a single principle. … All he needed to know is that Maxwell’s equations are a law of physics, and that the law of physics requires light to move with a certain velocity. From there he could just work with the motion of light rays.   ..... Lorentz did know about the Michelson-Morley experiment. He came up with the same transformation equations but interpreted them differently. He envisioned them as effects on moving objects caused by their motion through the ether. Because of various kinds of ether pressures, objects would be squeezed and therefore shortened", (SuL) pp. 60-62.

Note (Ehrenhaft's photophoresis phenomenon): „The light induces electric and magnetic charges (poles) upon the particles if they are illuminated by concentrated light preponderantly shorter wave lengths“, (EhF) p. 242.

Note (solar wind, magnetopause, magnetosphere; when highly conducted tenuous plasma manifests itself in space-time): „A highly conducted tenuous plasma called the solar wind, composed mainly of protons and electrons, is continuously emitted by the sun at very high speeds into interplanetary space, as a result of the supersonic expansion of the hot solar corona. The solar magnetic field tends to remain frozen in the streaming plasma due to its very high conductivity. Because of solar rotation, the field lines are carried into Archimedian spirals by the radial motion of the solar wind. … As the higly conducted solar wind impinges on the Earth’s magnetic field, it compresses the field on the sunward side and flows around it at supersonic speeds. This creates a boundary, called the magnetopause, which is roughly spherical on the sunward side and roughly cylindrical in the anti-sun direction. The inner region, from which the solar wind is excluded and which contains the Earth’s magnetic field, is called the magnetosphere", (BiJ) pp. 13-14.

Note (Wikipedia): The term "van der Waals force" is used to describe any dipole-dipole interactions in atom/molecules. Since hydrogen bonds involve interactions between permanent dipoles, they can be considered as a type of van der Waals force (and would fall under the category of Keesom interactions). The strength of van der Waals forces varies, with dipole-dipole interactions typically being stronger than covalent or ionic bonds. "London dispersion forces" are a specific type of intermolecular force present in nonpolar molecules. They are the weakest of all molecular forces. Molecules like noble gases (e.g., He, Ar), diatomic molecules (e.g., H2), and nonpolar organic molecules experience these forces.


1. Phenomena specific physical theories

Anticipating the validity of the conservation law of total energy per considered system the consequences of the two paradigms above are phenomena specific physical theories. Moreover, even within such a phenomena specific theory there may be incompatible mathematical models to "explain" the same phenomenon.

Example: 
Plasma physics, one phenomenon, statistical fluid mechanics & classical fluid dynamics, multiple application areas

About 95% of the universe is about the phenomenon „vacuum“. The same proportion applies to the emptyness between a proton and an electron. The remaining 5% of universe’s vacuum consists roughly of 5% matter, of 25% sophisticated „dark matter“, and of 70% sophisticated „dark energy“. Nearly all (about 99%) of the 5% matter in the universe is in "plasma state". A presumed physical concept of „dark matter“ „explains“ the phenomenon of the spiral shapes in the universe. A presumed physical concept of „dark energy“ explains the phenomenon of the cosmic microwave background radiation (CMBR).

Plasma physics is about classical statistical fluid mechanics and classical fluid dynamics. The underlying related mathematical models are grouped by different physical application areas resp. chosen mathematical tools accompanied by correspondingly defined different types of „plasma matter gases“ („hot“, „medium“, „cold“), e.g., there are

- neutral and plasma gas models, (BiJ), (ChF), (DeR) 
- radiation fluid hydrodynamics, (MiD) 
- gas dynamics and radiation hydrodynamics in astrophysics (ShF)
- magnetodynamics in plasma physics (CaF) 
- flow radiation and vortices in superfluids (AnJ) 
- condensation energy in the Ginzburg-Landau model (AnJ) 
- magnetism in condensed matter, (BlS).   

Note (electro-magnetohydrodynamics): MHD is concerned with the motion of electrically conducting fluids in the presence of electric or magnetic fields. In MHD one does not consider velocity distributions. It is about notions like number density, flow velocity and pressure. The MHD equations are derived from continuum theory of non-polar fluids with three kinds of balance laws:   

- conservation of mass/energy   
- balance of angular momentum (Maxwell equations)    
- balance of linear momentum.

Note: The most advanced mathematics of “galactic dynamics” is about collisionsless Boltzmann and Poisson equations accompanied by the probability of a given star to be found in unit phase-space volume near the phase-space position (x,v), (BiJ) p. 555.

Note (non-relativistic resp. relativistic gravitational instability of the universe): The two magic tricks to analyse the (non-relativistic resp. the relativistic) gravitational instability of the universe is based on a simple continuity equation of fluid elements in combination with a related fluid-particle Lagrangian, (BiJ) p. 722.

                            The Landau damping phenomenon

The Landau damping phenomenon is a characteristic of collisionless plasma dynamics. It is a wave damping without energy dissipation by elementary particle collisions.

Landau damping is a characteristic of collisionless plasmas, but it may also have application in other fields. For instance, in the kinetic treatment of galaxy formation, stars can be considered as atoms of a plasma interaction via gravitational rather then electromagnetic forces“, (ChF) p. 245.   

Landau damping models are applied to model the capability of stars to organize themselves in a stable arrangement as resonances in an inhomogeneous medium producing wave absorption (in space rather than in time) (ShF). If stars are considered as atoms of a plasma interacting via gravitational forces rather than electromagnetic forces (as a model for kinetic treatment of galaxy formation), instabilities of the gas of stars can cause spiral arms to form, but this process is limited by Landau damping“, (ChF) p. 245. 

There are actually two kinds of Landau damping: linear Landau damping, and nonlinear Landau damping. Both kinds are independent of dissipative collisional mechanisms. If a particle is caught in the potential well of a wave, the phenomenon is called „trapping“. As in case of a surfer, particles can indeed gain or lose energy in trapping. However, trapping does not lie within the purview of the linear theory. …. , trapping is not in the linear theory. When a wave grows to a larger amplitude, collisonless damping with trapping occur. One then finds that the wave does not decay monotonically; rather the amplitutes fluctuates during the decay as the trapped particles bounce back and forth in the potential wells. This is nonlinear Landau damping.  .. Since the linear Landau damping is derived from a linear theory, … the nonlinear Landau damping must arise from a different physical effect. The question is: Can untrapped electrons moving close to the phase velocity of the wave exchange energy with the wave?“, (ChF) p. 248-249.

2. Scale dependent physical theories

Anticipating the validity of the conservation law of total energy per considered system the consequences of the two paradigms above are scale specific physical theories. 
                                                                 
(DeP) p. 551: "At each scale there are different degrees of freedom and different dynamics. Therefore, at each scale level to be studied, there is the need for a different theory (e.g. classical continuum mechanics, theory of granular structure, nucleus + electronic cloud, nuclear physics, QED, free-electron theory, modelling, e.g. the properties of metals, semiconductors, and insulators) to describe the behavior of the considered physical system depending on a scale (of energies, distances, momenta, etc.). For example, in quantum field theory, the dependence of the behavior on the scale is often expressed mathematically by the fact that in order to regularize (i.e. render finite) Feynman diagram integrals one must introduce auxiliary scales, cutoffs, etc. The effect of these choices on the physics is encoded into the renormalization group equation. This equation then becomes an important tool for the study of physical theories.

When passing from a smaller scale to a larger scale irrelevant degrees of freedom are averaged over. Mathematically this means that they become integration variables and thus disappear. 

- In classical mechanics one deals with three scales according to its three basic measurements: distance D, time (better called duration) T, mass M

- in non-relativistic quantum theory and classical relativity it has two scales: D & T resp. D & M (mass M can be expressed through T & D using the Planck constant resp. T can be expressed via D using the speed of light) 

- in relativistic quantum theory there is only one scale: distance D."

Example 
The "standard model" of elementary particles, which is in fact about three independent theories with one common similarity, the symmetry groups SU(3), SU(2), and U(1), (GlJ) p. 433.


                                              Supporting data


Braun, K., Current physical and mathematical realities regarding an unified field theory
  


Braun, K., A Krein space based quanta energy field model, supporting mathematics



                          

Braun K., Looking back, part B, (B1)-(B17)



                             

Braun K., 3D-NSE, YME, GUT solutions
                                          

                               

Braun K., UFT related list of papers