In a nutshell: scope & conceptual design elements The scope of the Unified Field Theory (UFT) includes the scope of the three (independent, just "linked because they seem to have similar characteristics", (GlJ) p. 433) quantum field theories (strong interactions, weak interactions, and electromagnetics) and the scope of the relativity theory.
The Hilbert space theory provides the mathematical framework of quantum mechanics. The extended Krein space theory (accompanied by the concepts of an indefinite norm and an intrinsic self adjoint potential operator) provides the mathematical framework of the proposed UFT. While quantum mechanics is governed by the physical concept of mechanical energy, the proposed quanta dynamics is governed by mechanical and (newly) dynamic energy. There are several dynamic quanta systems, which are governed by an appropriately defined deductive quanta numbers scheme. The underlying quanta numbers are appropriately defined to reflect a kind of "potential difference" between affected underlying implicate (in the sense of D. Bohm, (BoD1)) (particle,anti-particle) quanta pairs.
The real Lorentz group L has three subgroups
(orthochronous, proper, orthochorous). Associated with the restricted
Lorentz group is the group of 2x2 complex matrices of determinant one,
which is denoted by SL(2,C). It is isomophic to the symmetry group
SU(2) and
the unit quaternions S(3). It plays a key
role in the special relativity theory (accompanied by the concept of the Minkowski space) and is a characteristic of the
beta-decay process.
The complex
Lorentz group L(C) is associated with SU(2)xSU(2). It is essential in
the proof of the PCT theorem, (StR) p. 13. It is also the (hidden)
symmetry group of the
Coulomb problem, (BrK0) p. 58 ff., (BrK14) pp. 14, 28. In contrast to
the real Lorentz group the complex Lorentz group has just two connected (!)
components accompanied by a multiplication law for pairs of 2x2
matrices, (StR) p. 14. It is supposed to govern the conservation of
energy laws of the dynamic quanta systems, (BrK0) p. 31.
There are two a priori 2-component mathematical dynamic quanta systems: the a priori dynamic electrino-positrino based ground state quanta system and the electron-positron based perfect
plasma quanta system, see also (BrK14) p. 26. The most aggregated Krein space based energetical systems built from those a priori systems are three types of explicate 1-component mechanical atomic nucleus quanta systems accompanied by implicate 1-component dynamic quanta systems (ref. Bohm's "wholeness and implicate & explicate orders", (BoD1)). They may be interpreted as conductor, semi-conductor, and non-conductor atomic nucleus types.
The UFT provides a
- 2-component a priori dynamic "Ground State" Model (GSM) - 2-component a priori dynamic "Perfect Plasma" Model (PPM) - 2-component mechanical "Electro-Magnetic" Maxwell-Mie Theory (EMT) - 1-component mechanical "Dirac 2.0 Atomic Nucleus" Theory (ANT) - 1-component Dynamic Fluid Theory (DFT).
It enables
- a well-posed
3D-NSE system for dynamic fluid particles by the DFT - an enhanced Schrödinger 2.0 operator by the Riesz transform - a "Yang-Mills" SU(2)-invariance for Dirac 2.0 (mass) particles by the ANT - an integrated Plasma Dynamics Theory (PDT).
The symmetry break down from the complex Lorentz group transform
to the (real) restricted Lorentz transform may become a characteristic
of the transformation process from 2-component quanta systems to
1-component quanta systems accompanied by the concept of the Minkowski space-time continuum.
GSM & PPM The a priori 2-component dynamic "Ground State" Model (GSM) and the a priori dynamic "Perfect Plasma" Model (PPM) may be interpreted as an Einstein-Lorentz
ether, (EiA5). We note that
- the CMBR (currently interpreted as the "echo of the early universe", (LaM)) is an essential element of theoretical and observational cosmology and one of the foundation stones of the big bang models; to the author's humble opinion, those models are extremely unrealistic because they are based on an a priori required mathematical singularity which caused for whatever reason the biggest explosion ever, (PeR) p. 444
- there are currently two different (!) physical explanation models for the Landau damping phenomenon depending from the considered
linear or nonlinear mathematical model, (BrK14) p. 18.
The cosmic microwave background
radiation (CMBR) and the Landau damping phenomena may be interpreted as
characteristic (echo) phenomena of the EMT electroton-magneton quanta
creation process from the GSM and PPM, see also (BrK14) p. 26.
EMT Quote: „…. light beams must have electric stationary
components in the direction of the wave front normal, and that consequently
there must be stationary electric potential differences between different
points along the beam; and that there must be also a stationary magnetic field
in the beam of light with potential differences. Hence, the light beam must
have a magnetizing effect, and the charge of a magnet should be changed by
light“, (EhF1).
We note that the mechanical energy based 2-component electro-magnetic quanta field of the EMT is in line with the "photopheresis" phenomenon discovered by F. Ehrenhaft, (BrJ), (BrK14) p. 22.
ANT In
the ANT the term "Dirac 2.0 Atomic Nucleus" is chosen to anticipate
that Dirac's single mechanical energy system is extended to a mechanical
x dynamic energy system concept.
Quote: "Dirac's theory of radiation
is based on a very simple idea; he treats an atom and the radiation
field as a single system whose energy is the sum of three terms: one
representing the energy of the atom, a second representing the
electromagnetic energy of the radiation field, and a small term
representing the coupling energy of the atom and the radiation field", (FeE).
The Dirac 2.0 systems provide a mechanical atomic nucleus concept accompanied by the concept of implicate dynamic quanta (in the sense of D. Bohm, (BoD1)). The potential between this implicate quanta pair defines the dynamic energy of the mechanical atomic nucleus. Those systems neither require the hypothesis
of an electron spin nor the existence of the fine structure constant.
The ANT puts the spot on the "Mach 2.0" principle as proposed in (UnA1) p. 156,
which is essentially the Mach principle + Dirac's two large number
hypotheses in the context of his "new basis for cosmology", (DiP2).
DFT The Krein space based 1-component mechanical atomic
nucleus quanta systems can be further aggregated/approximated by the
purely Hilbert (energy) space system H(1/2), which is an extension of
the variational mechanical standard energy Hilbert space H(1). The
mechanical H(1) energy system is the domain of the Friedrichs extension
of the Laplacian (potential) operator accompanied by the domain H(2),
i.e. it is an extension of the classical mechanical standard energy
Hilbert space H(2).
The standard Hilbert space systems H(1) resp.
H(2) provides the variational resp. the classical framework for
classical and quantum mechanics accompanied by the concept of Fourier
waves. The complementary sub-space of the extended H(1/2) Hilbert space
with respect to the H(1)-norm provides an appropriate Hilbert space
based framework for quantum dynamics accompanied by the concept of
wavelets. The latter ones may be interpreted as "a mathematical
microscope", (BrK0) p. 19, (BrK14) p. 37, (HoM) 1.2.
Physically speaking, the compact embedding of H(1) into H(1/2) addresses "the
problem of matter in the Maxwell equations, by explaining why the field
possesses a granular structure and why the knots of energy remain
intact in spite of the back-and-forth flux of (mechanical!) energy and
momentum", (WeH) p. 171.
PDT Plasma is that state
of matter in which the atoms or molecules are found in an ionized state. The number of neutral particles (atomes or molecules) in a gas is
irrelevant for the definition of a plasma. The number of positively and
negatively charged particles per considered volume element may be arbitrarily
small oder arbitrarily large, but both numbers need to be approximately
identical (in order to have no internal macroscopic electrostatic fields. The
interactions of electrons and ions are determined by long-range electrical
forces. 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“,(BrK0) p. 60.
The a priori GSM & PPM in combination with the EMT, ANT and DFT enable an integrated Plasma Dynamics Theory (PDT) avoiding the concept of a Debye sphere.
Further notes Note (Nature constants): The UFT indicates a new role of Nature constants.
They may provide physical characterizations of the borderlines within
the hierarchical quanta system structure of the above five dynamic
quanta systems. The obvious characteristic borderline constant between
ANT and PDT is Planck's quantum of action. In this context we refer to
Robitaille’s „blackbody radiation and
the loss of universality:
implications for Planck’s formulation and Boltzman’s constant“,
(RoP3). The observed duration for the beta-decay (about 15 min) might
become another Nature constant with respect to the borderline between
EMT and ANT. The magnetic moment interpretation of an electroton might
become another characteristic constant. Basically Unzicker's approach
investigating constants of nature and questioning their origin is
reversed, (UnA2) p. 3. In other words, Planck's quantum of action
become the most rough "approximation" constant within the deductive
structure as its formula contains the generic term "temperature" for
"energy". It also contains the speed of light, which can be calculated from the two electromagnetic Nature constants, the vacuum permittivity and the vacuum permeability resp. the Bohr magneton, i.e. the size of atomic magnetic moments, (BlS) p. 4.
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.
Note: Sommerfeld’s fine
structure constant is „just“ mathematically required to ensure convergent power
series representations of the solutions of Dirac equation.
Note (The self-energy problem of an electroton): The UFT solves the baseline "self-energy
problem" of an electroton, avoiding the spin and the iso-spin hypotheses,
(UnA6) p. 100.
Note: The UFT provides an appropriate modelling framework explaining
the decay of a neutron into an electron and a proton (as part of the
PPM).
Note: In (RoP2) it is shown
that hydrogen bonds within water should be able to produce thermal spectra in
the far infrared and microwave regions of the electromagnetic spectrum. This
simple analysis reveals that the oceans have a physical mechanism at their
disposal, which is capable of generating the microwave background.
Note: The
pressure p in the NSE (which may be interpreted as a "potential") can be expressed in terms of the velocity u by the
formula p = R(u x u), where R denotes the Riesz operator and u x u denotes a
3x3 matrix.
Note: The H(1/2) Hilbert space plays also a key role in the
Teichmüller theory and the universal period mapping via quantum calculus accompanied
by a canonical complex structure for H(1/2), (NaS). Also,
the degree or a winding number of maps of the unit circle into itself corresponds
to a related H(1/2) -norm
enabling the statement „one cannot her the winding number“, (BoJ).
Note (The Mie theory of matter): The UFT
framework supports Mie’s theory of matter, (MiG0,(MiG1),(MiG2), and his project „to
derive electromagnetism, gravitation, and aspects of the emerging quantum
theory from a single variational principle and a well-chosen Lagrangian, governing
the state of the aether and its dynamical evolution, and conceiving of
elementary particles as stable “knots” in the aether rather than independent
entities“, (SmC). Mie’s nonlinear
field equations allow for stable particle-like solutions using
variational principles in the context of special relativity, (SmC). This
is in line with Klainerman’s proof of a global nonlinear stability of
the
Minkowski space, (ChD). Technically speaking, the eigenpairs of the
standard self-adjoint (mechanical!) Laplace operator with H(1)-domain
become the model of Mie's (mechanical!) energy knots. The
"complementary" (dynamic) operator with the complementary domain in
H(1/2) with respect to the H(1)-norm becomes the model of the
"implicate" dynamic energy field, which is governed by the Schrödinger
2.0 operator. Technically speaking the Schrödinger 2.0 operator is
"just" the Riesz transformed Schrödinger operator. For the appreciated
properties of the Riesz transforms we refer to (BrK14) p. 33.
Note (Einstein's lost key, UnA1)): All
known tests of the GRT can be explained with the concept of a variable speed of
light, (DeH), (UnA1) p. 142. Additionally, there is a „nonlinear stability
of the Minkowski space“, (ChD). Approximation theory of a nonlinear
operator equation in
Hilbert scales is enabled by an appropriate decomposition of the
nonlinear operator N=L+R into a lineralized operator L and a remaining
nonlinear operator R. In this context "nonlinear energy stability" is
ensured if the nonlinear variational equation representation fulfills
the
Garding inequality with respect to the underlying „energy norm“ induced
by the
linearized term L. In this case the remaining nonlinear operator R may
be interpreted as a compact
disturbance of the linear operator, (BrK0) pp. 11, 26, (BrK13). Note (Mechanical mass-energy equivalence): Einstein's
famous formula E = m*c*c may be interpreted as approximation formula,
where the energy terms on both sides of the equation are interpreted as
norms of the underlying weak variational representation in an
appropriately defined Hilbert-Krein space framework. In other words, the
Hilbert-Krein space framework (accompanied by the concept of indefinite
norms) avoids the problem of infinite negative eigenvalues. This problem
occurs in Dirac's relativistic invariant wave equation for an
one-electron system, which allows electrons to traverse very high
potential thresholds with a certain probability, e.g. (HeW1) S. 76.