 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
In the context of the term "paradigm change" we refer to (KuT), (UnA6).
A. The three considered groups of current physical paradigms
The three considered groups of physical paradigms to be changed are
Paradigm group 1:
The Newton and the Coulomb
potentials dealing with continuously distributed mass elements exposed to external (attractive or repulsive) forces; the Debye potentials and the London dispersion interaction potentials
Paradigm group 2:
Dirac‘s energetical one-component system to model an
atom and its radiation field explaining the phenomena of emission and absorption of light by
matter, the spin(1/2) hypothesis, time reversal invariance, and the fundamental problem in
statistical thermodynamics, i.e., the distribution of a given amount of energy
E over
N identical systems, Two- (mechanical)
particle systems, (RoH) p. 147/ 166 ff.
Paradigm group 3:
The Big Bang story, an accelerated expansion of the
universe accompanied by a hypothetical substance called "Dark Energy", direction of time, a
gaseous state of the sun, and Newton's theory of "light
rays" accompanied by the three types of redshift in astrophysics (Doppler, gravitational, and cosmological redshift), i.e., a theory of light is not required, neither in current cosmological models nor in current quantum field models
B. The conceptual math. tool sets supporting the current paradigms
... re paradigm group 1
Coulomb
resp. Newton potential function in a 3D space continuum (i.e., a single layer singulat integral
operator), Dirac’s point charge particle model mathematically modelled as Dirac distribution "function" d(x) with related Sobolev space (distributional) regularity depending from the space dimension n=3, i.e., the Dirac distribution „function“ d is an
element of H(-n/2-e), the H(0)/H(1) based variational Lagrange/Hamiltonian
formalism and related energy methods based on the Hamiltonian mechanical Laplace potential operator, e.g. (LaC),
(VeW).
... re paradigm group 2
The Schrödinger harmonic quantum operator accompanied by case specificly defined potential functions, Dirac’s
theory of radiation based on a single quanta system accompanied by two "energy" attributes, the energy of the atom and the electromagnetic enenergy of the radiation
field, while the coupling energy between atom and radiation field is neglected (BrK0) p. 5, (FeE), renormalization groups (BrK10) pp. 45, 86, (BrK14)
p. 9, (DeP) p. 551, the Yang Mills theory with the related mass gap problem, (BrK10) pp. 40, 43, 59.
... re paradigm group 3
Geometrodynamics
and the boundary of the boundary principle, i.e., the GRT is made up of fields on fields, (BrK0) p. 53
(RoC), (BrK10) p. 166, (CiI) p. 49, accompanied by Einstein
(differentiable manifold) spaces, black (and newly also white) holes, inflations, time bombs, the evolution problem of GRT, and a "Big Bang", (BrK10) pp. 42-44, Newton’s (optic) theory of light radiation based on the current physical paradigm of indivisible (prism) baseline colors, (MüO).
C. Related notes
Paradigm group 1
The Newton and the Coulomb potentials dealing 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 group 2
Dirac‘s energetical one-component system to model an
atom and its radiation field explaining the phenomena of emission and absorption of light by
matter, the spin(1/2) hypothesis, time reversal invariance, and the fundamental problem in
statistical thermodynamics, i.e., the distribution of a given amount of energy
E over
N identical systems, Two- (mechanical)
particle systems, (RoH) p. 147/ 166 ff.
Note: Dirac’s relativistic
quantum mechanics is only concerned with the main part between the interaction
effects between electro-spin and nuclear spin governed by the Coulomb
potential. The „Lamb shift“ phenomenon is interpreted as the radiation
correction term of this approximation.
Note: There is 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..
Paradigm group 3
The Big Bang story, an accelerated expansion of the
universe accompanied by a hypothetical substance called "Dark Energy", direction of time, a
gaseous state of the sun, and Newton's theory of "light
rays" accompanied by the three types of redshift in astrophysics (Doppler, gravitational, and cosmological redshift), i.e., a theory of light is not required, neither in current cosmological models nor in current quantum field models
Note: 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).
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: 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, Wikipedia.
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 |
