THE  QUANTUM  SUPERSTRING  IN  CLASSICAL  FLUID  DYNAMICS
by  Anthony  Paul  Bermanseder  {PACIFICAP@hotmail.com};  dated  September 23rd, 2004

This paper shall take the form of a close critique of the paper entitled:  
{Ref.:  http://groups.yahoo.com/group/kiarashniknejad/message/126;
          http://xxx.lanl.gov/abs/gr-qc/0310007} 

Is  a  classical  Euclidean  TOE  reasonable?
by Antonio Arbona, January 6th, 2004 {toniarbona@hotmail.com}

which proposes the universe in the form of Lagrangian functions, modelled on fluid dynamics and termed the 
Spin-Force-Model or SFM.

  We shall support this model in its axiomatic foundation, but extend its applicability in providing a possible
scenario for its Lagrangian Boundary Conditions,  which themselves crystallise as a natural consequence
from the axiomatic foundation of the Arbonaean ether-fluid model.

  In particular, the Lagrangian Boundary Conditions (LBC) become an integral part for the partitioning of the
axiomatic background matrix for the operation of the 'ether-fluid' in modes of self-transformation.
This partitioning serves as an axiomatic reformulation for both, Special- and General Relativity in Mach's Prin-
ciple and allows an explanation for the unquantisability of gravitational mass and the paradox of an collap-
sing wavefunction dependent on an external observer with its associated paradoxes (say, EPR).

The Arbona Assumptions:
a)  The space is Euclidean, governed by deterministic laws in the form of partial differential equations (d) and 
     free of singularities.
b)  The space is isotropic and homogeneous and embodied with an absolute timeframe t.
c)  The observable universe as a blob of fluid is expanding against a selfrelative void and is in local thermodynamic
     equilibrium relative to the quantum-turbulence of the internal noise - this becomes the vacuum.
     [LBC specifies t=n/Ho and the expansion as a topological-  and holographic 3D-surface/4D-volume mapping]. 
d)  Density function r(x*) describes the conservation law for the fluid in the fundamental Lagrangian in its first
     derivative dmr(x*) and the relative fluid characterising acceleration dma(x*).
e)  The vector of coordinates is: x*=(t,x^), ^=1,2,3  for a notational (NonMinkowskian) classical spacetime and
     the evolution of  r(x^) and a(x^) assimilating as the 'ether'-force. 
f)   The 'ether'-force is spindependent for vortex-solutions, i.e. the manifestation of particles is the result of neigh-
     bouring fluidpoints interacting through their aligned spincomponents, (the LBC define this spindependency as
    being intrinsic to SFM). 

Consequences include:
   i)  Lorentz invariance is a property emerging from the fundamental Lagrangian operator.
  ii)  Inertia mirrors the stochastic average forces between the ether and matter for relative accelerations.
 iii)  Gravitation becomes a long distance effect of the ether-force.
 iv)  Quantum Uncertainty is explicable as effect of the random noise of the vacuum.
  v)  The collapse of  the wavefunction is directly inferred from the ether-force in an inertial mechanism.
 vi)   Particles exist not as pointlike entities, but only  as high-density waves operating on a low-density ether.
 vii)  The  properties of particles emerge from the collapse of their wavefunctions.
viii)  At the cosmological level the expanding universe is described with local high-density fluid regions, representing
       the matter distributions in equilibrium with the low-density homogenous fluid of the ether at a boundary con-
       dition (LBC defines this in the the Temperature-Well tunneled at a modular timeinstantenuity tps=fss).
       As the universe expands, the ether density diminishes, modifying the 'soundspeed c' in increasing it, as
       for example in the Scharnhorst effect (LBC sets de Broglie phasespeed parameters in scaled relationships
       to inflationary-runaway mappings in Euclidean space).

 The Arbona-Partitioning is described in a fourfold scaling of the Lagrangian operators:

1. The Subthermal Realm, modelled on a 'Brownian Motion' of Smoothness, is mapped as a prePlanck-Fluid-Scale,
    where density, speed and acceleration vary smoothly and are well behaved in the [Planck-Plasma]-Lagrangian:

                    Lag{x*}=Lag[r(x*), dnr(x*), dna(x*)]       (and  with higher derivatives as required)            [Equation.#1]

                                                                                -1-
      Arbona introduces the "Jerk" e(x^) (=)dta(x^), which with  r(x^), speed v(x^) and  a(x^) provides the dynamics for
    this range; completing the Cauchy problem by adding the continuity equation with initial data for the parameters.

2. The Thermal Realm, modelled on a 'Brownian Motion' of Turbulence, maps as the Planck-Scale, where here
    the ether-fluid is in a thermal equilibrium, against a stochastic background of quantised parameter-space.
    This is the [Planck-Gas, where magnetopolic charges become unified with electropolic charges; both elementary 
    force charges, which are separated in the Planck-Plasma, defined in the LBC].

    Arbona considers the mean values for this thermal range in a comoving reference frame, such that:
    <v>th=<a>th=<e>th=0 with momentum orders <X^2>th,...,<X^n>th  for  X=r, v,a,e ; the same which are invariant
   under spatial and temporal variations described in  realm#3.
   The maximum order, depending on the form of [Equation.#1], describes invariant momenta in cosmological
   ranges however.
   The applicable Lagrangian would describe the dynamics of the perturbations upon the static background provided
   by the thermodynamic quantities.
   The mean values for density, speed, acceleration, jerk, their standard deviations and higher orders of momentum
   for those magnitudes with the perturbation variables would describe the dynamics of the system.
   The n-th order momentum of  X is defined by <X^n> in:     

    Lag{th}=Lagth[dthr(x*), dndthr(x*), dndtha(x*), <r^n>th ,<v^n>th, <a^n> th,  <e^n>th,  N(x*)], n=1,...m [Equation.#10]

    Here N(x*) represents a source of noise, dth is the derivative relative to the background means and  m derives
    from [Equation.#1].
    Assuming isotropy, these means are given in scalar fields.
    The addition of initial conditions for the perturbations in density (dthr(x^)), speed (dthv(x^), acceleration (dtha(x^) 
    and jerk (dthe(x^) then solves the Cauchy problem for the fluid.

      Arbona then considers the probabilistic thermodynamical background to provide a reservoir of fluid noise, par-
    ticularly expressed in thermodynamic quantities like energy, temperature and entropy and interprets this as the
    uncertainty in quantum theory. (This becomes defined in the LBC as the finestructure in Heisenberg's Principle).
    The virtual particles in Quantum Field Theory so derive from the ether-vortex-field, for which Arbona specifies
    an indeterminacy in  the equations for dthX(x*).
    
3. The Macroscopic Realm, modelled on a homogeneous ether-fluid; where no stable vortex solutions exist for the
    neighbourhood of vortices within the ether; is represented as a simple non-dynamical background of constant
    density, speed and acceleration; without the thermal fluctuations characterising realm#2.
    Arbona  then proposes the emergence of a new space-time from that macroscopic range, a continuum, which
    can ignore the details of the underpinning ether-noise and is then described through appropriately derived
    quantities.
    
      The assumed equilibrium requires the macroscopic range to engage integral standard deviations (and higher
    order  momentums) of a(x^) to be small enough across the ether(e) to allow a local null-state acting on typical
    volumes.
    The kinematical quantities (<X(e)>m) match those in the Thermal range:  <X(e)>m = <X>th,   for X=v,a,e.

    For the comoving frame:  <X>th = 0;  as are the higher momentum orders: <X^n(e)> = 0,  for X=v,a,e for any n>1. 
 
      Corollarily, the neighbourhood of vortex solutions becomes assimilated in parameter numbers for the particles(p),
    which are surrounded by standard unperturbed ether. [The LBC describes the particle-caused ether perturbations
    to derive from the interaction between the now macrodifferentiated magnetopole- and electropole charges in the
    'Brownian Motion' of the Planck-Liquid].

      Here then, the macroscopic means have well defined values in the comoving reference system, which differ in
    general  from those of the ether. 
    The particles are described in statistical distributions of thermal averages, summed over the particle distribution.
    Those functions are neither isotropic nor homogenous in general.
  
          <X^n(p)>m  not= <X^n(e)>m,  where X=r ,v,a,e          &        <X^n(p)>th (x^) not= <X^n(e)>m, where X=r ,v,a,e

  Here x^ is an element in  C ,   where  C  represents the neighbourhood, comprising the particle and x^ is expressed
 in the comoving reference frame and is so independent of t.
    
                                                                         -2-
The thermal Lagrangian for a particle then becomes:                        (for n=1...m  and  x^ an element in  C).

              Lagth = Lagth[ dmr(p)(x*), dmdnr(p)(x*), dmdna(p)(x*),                                                 [Equation.#28]
              <X^n(p)>th (x^)   &   <X^n(e)>th,  for X=r,v,a,e                          (for n=1...m  and x^ an element in  C)

An isolated particle (Lagm) in the macroscopic range interacts with the background in its deviations from that
background, thus determining its dynamics.
Arbona  calls this the mean effect of minimising relative acceleration between the particle and the ether, so
defining inertia.
Inertia is so describable through the relativistic kinematics.
Particles perturbing each other so modify the equilibrium in the true dynamics of the <X(p)>m values.
Here the ether neighbourhoods are not dynamical as the Minkowskian space-time.
  
4. The Cosmological Realm, the ether fluid is not homogeneous, but spherical and in expansion.
    Arbona proposes a violation of energy in 'runaway' scenarios of cosmic accelerations, say in the dark energy,
    acting akin a constant addition of classical energy.
    [LBC shall define the dark energy as an intrinsic parameter for  the equilibrium of the ether-fluid and as given
    in its expansion to satisfy the selfsame boundary conditions; any cosmological force-deviations appearing as an
    addition of energy to the fluid background, hence is balanced in a finestructuring of the parameters constituent
    to the force laws].
    
  The LBC's are certain relationships and ratios between fundamental constants, which allow a one-to-one 
correspondence  between the Arbona Ranges and the boundary conditions separating the latter in qualitative and
quantitative definitions.

  The Subthermal Range is modelled on a PrePlanckian Phasetransition, which phenomenologically can be des-
cribed as the Planck-Plasma; which is upper bounded in a parameter called the Planck-Length-Oscillation, where
(OlPlanck=lPlanck(Alpha)^1/2=[e/c^2]u, where []u depicts an unified, dimensionless and algorithmic quantity).

  It is absolutely smooth and continuous and defined in an algorithmic (Platonic-Penrosian) Null-SpaceTime, 
where all potential definitions of physical parameters are dimensionless and therefore require to be invented.
This Null-Continuum is the Nothing of the Perennial Philosophy, but can be likened to the 'Awakening Thought' of an
Eigenstate or Selfaware Sentience of a selfprogramming computer, processing itself in inventing and manifesting
both of the necessary software (Natural Laws, Constants etc) and the required hardware (the laws manifested).

  Arbona's omission of velocity in the elementary Lagrangian becomes a natural consequence from the definition 
process in the Null-Continuum, which assimilates a modular duality between displacement standards in a nume-
rical and dimensionless form for velocity in 'c' (actually in the form c^2).
Velocity and Acceleration  so become derived consequences, but whereas acceleration has a direct link to angular 
acceleration in the form of the timedifferential for frequency, velocity AS angular frequency requires definition via  a
constancy 'c' in its dimensionless numeracy.

   This then can be utilised to quantitatively establish Arbona's vorticity in the Azimuthal-Toroidal Speed Ratio of:
wq/wt=2 [Equation.#B1] to explain the spinproperty for elementary particles; (Transformation under the Lorentz 
group derives Dirac's equation as a macroscopic approximation).
Since Thermal Spacequanta are toroidally defined by the LBC, the property of elementary spin must necessarily
derive from the Lagrangians who define the particle interactions/genesis at the ether-singularities or vortex points.
Those points then are the Null-State definitions from the subthermal range manifesting as quantifiable and finite 
vortices at the boundary condition between the thermal range and the macroscopic range.
The LBC defines this boundary as the intersections of 12 magnetopolic current-loops, which as 'magnetocharge-
knots' allow the eventuation of quantum geometric bluebrints, abstractly defined in the prePlanckian phase.
The vortex speed wq about the azimuthal axis is twice the internal toroidal speed wt, because two degrees of
freedom are established in an internal superpositioning of the LBC wavefunctions from the initiatory Planck-
Plasma phase, (similarly the graviton's wavefunction is a halfphase of the source-photonic wavefunction) .
Arbona's subthermal realm, so 'invented' the fermionic hierarchies via its algorithmic selfdefinitions as derivatives
from an primordial bosonic and unitised spinstate.	  
The cosmogenetic algorithm is selfiterative and in a sense programs itself in certain modes of binary eigenstates.
A crucial algorithmic definition becomes the statement: Minimum/Maximum=Cycletime=1/Frequency.
This leads to a definition process, which can crystallise related energy concepts, such as Temperature, Frequency 
and Mass, all however subject to their correlation to the ForceCharges.

                                                                         -3-
  In the Subthermal Arbona Range, those ForceCharges are subject to their unique genesis, but unified in an all
encompassing Action Law [Action=Charge-Squared], manifesting in the later ranges in concepts of superconduc-
tivity and the intrinsic relationship between inertial mass and electromagnetric charge.

  The Thermal Range then becomes the Planckian Phasetransition, characterised in 5 classes of superstring and 
their various relationships to GUT Unitary Symmetries.
This is the Planck-Gas, where the magnetopolecharges (e*) are now unified with the electropolecharges (e).
The transition from the Thermal Range of QuantumTurbulence to the Macroscopic Range of physical measurement
is given by the LBC as the macroquantisation of the heterotic superstring, that is an heterosis of the Bosonic Super-
string in 26 dimensions with the heterotic superstring classes HO(32)  and HE(8x8).

  The former member defines the XL-Bosonic Quark-Lepton Kernel-Ring coupling from a pentagonal supersymmetry
and as defined in the algorithms manifesting the Thermal Range from the Subthermal Range.
The latter heterosis becomes the crucial manifestation of the LBC in specifying the wormhole parameters for
the macroscopic range however.
The appropriate supermembrane here is the heterotic HE(8x8) with its link to SO(27) GUT-models and the Magnetic
Monopole spectra, explixitely bounded in the Gamma-Ray-Burster limit of 27x10^15 GeV-units.

  This phasetransition crystallises at an LBC of 10^-22 metre-units (Ng-Van Dam limit), as the linearised wavelength
for the toroidal internal angular speed of {fps=3x10^30} inverse time units, which however apply the modular dualities
for the thermal phase in defining Timeinstantenuity at {fss=tss=1/(3x10^30)} second-units.
Other important parameters for that transition, include the de Broglie Phase-Speed {VdB=fps.rmax} and the de Broglie
Phase-Acceleration {AdB=fps^2.rmax}, specifying the LBC for the cosmological range in the inflationary mechanisms.
 
  The Arbona argument of 'c' defining an 'acoustic' speedlimit, rather than an universal one, is herewith justified on
both phenomenological and quantitative grounds.
The 11-dimensional boundary (Witten-Mirror) for the expanding 4-dimensional Hypersphere of closed curvature is
defined in the scalelimit {rmax=c/Ho}, where Ho defines a 'Nodal Hubble-Constant' for a Half-Hubble-Oscillation with 
a duration calculated by the LBC as so 16.9 Billion year-units.

  The generalised boundary conditions are applied locally and hence result in a local compactification of the
higher dimensions, as mathematically modelled in the superbrane scenarios, especially the conifoldment of 
Calabi-Yau and Joyce-manifolds in 6 and 7 dimensions respectively.

  The 11-D mirror so becomes an envelope for a 10-D spacetime mirror (which is Arbona's new space-time), which
has conifolded the appropriate 6- and 7-dimensional quantum geometric shapes within the thermal range, mani-
festing with the LBC of the lower bounded absolute timeframe fps modular dual to the upper bounded 
'Nodal Hubble-Time' of: {1/Ho=rmax/c=rmax/(fps.lps)=(tss)Maximum/Minimum}, thus satisfying the boundary con-
ditions set in Arbona's subthermal range of the Planck-Plasma-StatePhase.

  Arbona-Spacetime is hyperbolically curved, the ether-field expanding, but decelerating towards its 11-D boundary
asymptotically.
The LBC's definition of a nodal Hubble-Constant results in the intradimensional intersection of electromagnetic
parameters, enfolding the 11-D Witten-Spacetime in the 10-D Arbona-Spacetime.
As a consequence, there will be certain redshift intervals in the n-cyclic (n=Ho.t) cosmoevolution, where the 11D
parameters, which are mapped onto the 3D-surface of the Riemannian hypersphere as information, superimpose
upon the linearly unique 10D-parameters.
This allows a multivalued spectrum of 'light-related' measurements, resulting in certain cosmological redshifts
appearing quasi-blueshifted and in a seeming 'dip' in related constants, such as the Alpha-Finestructure for the
said intervals.

  The definition for a demetrication of General Relativistic parameters then explicitely define this Hubble-Oscillation
as a special solution in the Einstein-Friedmann model and the Schwarzschild formulation for the universe as an
encompassing Mother Black Hole.

 Arbona's Macroscopic- and Cosmological Range so become the ether-fluid as the Planck-Liquid-Crystal,
manifesting  as phaseshifted macroquantisation of the Thermal- and Subthermal Range in the form of the
Planck-Plasma-Gas.  

  The Lagrangian for Arbona's Cosmological Range, must so be based on Black Hole parameters and as mapped
onto the fermionic hierarchies defined in the monopole spectra, mapped onto the particle templates (which are
defined in supersymmetries, based on the interaction of colour-magnetocharges and Coulombic electrocharges).

                                                                           -4-
   Both the Principle of  Special Relativity and the Principle of Equivalence are reformulated as emergent pheno-
mena, and derive from the rotational symmetries or vorticity of the 'ether-fluid' in the axiomatic definition of the
vortex-space as a Zero-Point-Energy (ZPE or Vortex-Potential-Energy (VPE)).
This renders inertial mass as the vortex-parameter, which upon a local geometrodynamic force interaction manifests
as gravity through the Principle of Equivalence and the General Relativistic Riemannian Field.

   Henceforth, General Relativity with its geometrical and classical underpinning does not require a quantum form
for the gravitational interaction, but the locally applied Riemann metric is scaled in a quantum geometry from the
macroscopic maximum of the cosmological range to the macroscopic minimum for that range, the latter becoming
the thermal maximum in the quantumised range, that are the Planckian gas-liquid-solid phasal transitions.     

   A close examination of that partitioning then allows a synthesis between unification parameters  in relation to the
boundaries of the boundary conditions themselves.
This creates the model for synthesing not only a boundary for the higher-dimensional supermembrane scenarios
with Supersymmetric Grand-Unification-Theories, but also a reparametrication of the Riemann metric in terms of the
parameters of the partitioned fluid dynamics of the background matrix (which we might term the vorticity of space-
quanta in selfreferential frames of references).

 I.  Arbonaean Vortex Dynamics and the Particles

  Particles exist not as point-like structures, but as wavelets which travel freely out of matter to fill the space sto-
chastically (and as described in the wavefunctions of Quantum Field Theory).
Stable configurations of matter, such as atoms, represent the collapse of the wavelets wavefunctions into density
concentrations, in a singularity-free ether fluid.
Vortices on the fluid are interpreted as fermionic halfspin states, travelling slower than phononic fullspin states. 
Part of the bounding phononic speed limit 'c' is used to manifest the internal rotation in fermionic spin properties.
Fermions so have generally a well-defined subsonic phononspeed and Bosons travel at the phonon speedlimit 'c'.
Supersonic speeds can then occur for invalid macroscopic approximations.

  Inertial  mass becomes a consequence from the interaction of the fermionic internally rotating (or spinning) 
vortices, necessarily creating an acceleration field with the corresponding spin-components of the background
ether-fluid. 
Ether Forces so emerge from the relative accelerations and the dynamics of the fluid vortex lines should allow
the computation of specific inertia masses, say in numerical simulations of parameters in (Francom) adjacency.
The longrange effect of these vortex structures, depending again on the spin-ether coupling, must recover the 
Principle of Equivalence.

   The LBC defines the spin-ether coupling as the superpositioning of two subthermally defined wavefunctions.
The first manifests the even-odd-pi vorticity for electromagnetic- and gravitational junction-points respectively.
This is the source relative mapping of a 11/2-dimensional surface onto itself in a 'Moebian' connectivity (say).
A trisected colourcharge permutation Red-Green-Blue of a clockwise rotational symmetry on one half of the
onesided surface (say a Klein-Bottle as a toroidal derivative) is mapped as an anticlockwise spin symmetry
relative to a primary sourcesink frame(ps) of reference, but is clockwise to a secondary sinksource(ss) relativity.

  A triple-120 degree rotation hence mixes the colourcharge sectors into Yellow-Cyan-Magenta for a Matter-
Template at the 60- and 120-degree point and manifests the blueprint for Antimatter Magenta-Cyan-Yellow
following inflection (at 180 degrees) at the 240- and 300 degree points.
This first full phononic rotational symmetry conserves angular spin properties.

  Then the subthermal symmetry is broken, in the sinksource relativity assuming the sourcesink relativity.
Instead of inflecting from clockwise to anticlockwise relative to the sourcesink at the 0pi=2pi-junction, the 
sinksource 'copies' the sourcesink relativity, which duly inflects at the alpha=omega point from anticlockwise to
clockwise.
The resulting 'conflict of the sources' hence results in a clockwise doublespin, which demands the creation of a new 
phononic template in the Graviton, spinning double-opposite the now established unified field photonic/antiphotonic
fieldagent, (suppressing the Antiphoton template in the Graviton, linked to a Restmass-Induction-Higgs-Template).
This then created the Temperature/Energy well, manifesting in timeinstantenuity, following the quantum tunneling
of the temperature-gradient in the de Broglie phasal inflation of the Arbonaean thermal phase of the Planck-Fluid.

  So the second of the wavefunctions, now incorporating a gravitational blueprint, superimposes onto the previously
odd-even-pi specified bosonic wavefunction and with it allows the YCM-MCY matter/antimatter templates to manifest
in the expansion of the Planckian Liquid-Crystal as the mensurative universe.

                                                                              -5-
Conclusions and Consequences:

   Arbona's postulates are well justified and quantitatively established in the Lagrangian Boundary Conditions.
The spin properties of both fermionic- and bosonic particle states derive as consequences from the reharmonisation
of the unified field conditions established in the algorithmic-subthermal range.
Inertial parameters become manifested in the energisation of primary and secondary colourcharges, using funda-
mental quantum geometric templates as guiding VPE-envelopes to transform magnetocharge-definitions for
massinduced wavelets into electrocharged mappings of the former.  

  The LBC defines a precise atomic definition from the thermal-macroscopic boundary as the Classical Electronic
Radius (re) containing exactly {10^10/360}  linearised wavelengths of the macroquantised vibrating part of the super-
membrane EpsEss. 
This is also the wormhole perimeter of macroquantised superstring HE(8x8), defined in (rps=lps/2p  =2p/lss=1/rss)
in modular duality: (EpsEss=h^2; Eps/Ess=fps^2; lps.lss=fpsfss=1; lpsfps=c=1/lssfss in their coupling constants).                           

II. Arbonaean Special Relativity and Invariance

a. The Speed of Light 'c'

  Special Relativity is valid in the Macroscopic Range, where the ether is both isotropic and homogeneous.
Causality is given in the absolute timeframe of the underlying theory.
Macroscopic wavelets travel with averaged dynamical quantities on the thermal range,  determined by the mean,
variance and possible higher orders of density, speed and acceleration,

  i.e. the macroscopic Lagrangian Lagm  derived from:    c=(<X^n>th, for X=r,v,a,e)                            [Equation.#29].

The phonon speed of the azimuthal vorticity describes lightspeed 'c' as the phononic acoustic speed-limit.
 
  This speed 'c' is homogeneous in the neighbourhood of homogeneous X-distributions.
This is generally the case for macroscopic ranges, but fails in the thermal regimes and background variations (say
in particular  changes in the background boundary conditions) and can result in superluminous signals, such as
observed in the Scharnhorst effect in the Casimir vacuum, the wormhole, the Alcubierre warp drive and the
Krasnikov tube.

b. Lorentz Invariance

  A fermionic wavelet can so travel with speeds in the range from 0 to 'c' with respect to the ether's (<v>m  & <a>m).
We consider a reference frame comoving with the fermion, the latter incorporating an internal toroidal-thermal 
structure, thus distinguishing it from the background.
Henceforth the integration on times (dt >>Tth  of <diaj >th) differs from 0 on different regions in the comoving refe-
rence system, while the background remains chaotically invariant and concealed from the simplified macroscopic
Lagrangian Lagm.

  Should the particle accelerate relative to the background, the gradient of acceleration is decomposed into the
internal particle gradient derived from the internal structure and the gradient from the acceleration relative to the
background.
The second term defines a dynamical effect, according to the fundamental Lagrangian, which only disappears
when the relative acceleration is inertialised (smeared).
Decomposing the speed of the particle in like manner, does not provide any dynamical effect, since the fundamental
Lagrangian remains invariant under boosts, rendering the background-ignoring equations as Lorentz invariant.
The underlying ether-force only depends on relative accelerations (ao) to the ether, but not on relative speeds (vo).
All typical speeds in the stochastic fluid motion (<v>th) and the phonon speed 'c' can enter the effective Lagrangian,
but remain independent of the relative speed of the reference system to the ether background.

   Relative speed and position of particles relative to each other can perturb the particle fields and their equilibrium
values, so resulting in dynamical effects.
The perturbations must be accomodated in the internal gradients for the accelerations.

Conclusions and Consequences:

  The phenomenology of Special Relativity is given in the interaction of a stable particle with the ether background.
This approximation can then be described kinematically in the assumption of a background Minkowskian spacetime;

                                                                             -6-
but when considering more than a single particle, the vortex-wavelets (as particle equivalents) affect each other in
their internal gradients and (still considering the particle as isolated), additional forces or interactions are introduced
to account for the phenomena, not accounted for in the Minkowskian description.

  The underlying space is Euclidean and coexists with an absolute timeframe.
This is the Liberati-Sonego-Visser (LSV) approach for a fluid universe, occupied by hypothetical beings, whose
internal structure is completely mediated by phonon exchange, oblivious to electromagnetic parameters.
They would so discover an acoustic Lorentz invariance in measurements of an acoustic special relativity.
Motion would become undetectable, the fluid playing the role of an ether, whose presence is masked by length-
contraction and time dilation (there are no frictional speed effects).

The LBC defines an additional internal force term in the extension of the classical Newtonian forcelaw.
Differentiating the momentum in the form (mv=mo/(1-v^2/c^2)^1/2=hf/(c^2(1-v^2/c^2)^1/2) introduces the additional
Alpha-Force {Falpha=hv.(df/dt)/(c^2.(1-v^2/c^2)^1/2} in addition to the inertial {F=mo.(dv/dt)/(1-v^2/c^2)^3/2}.

  Speed v is decomposed into the external groupspeed vgroup and the internal phasespeed vphase.
For an Minkowskian isolated particle, vgroup is observed, and we apply the initial LBC for Lorentz invariance in the
de Broglie phase inflation.

Phasespeed {vphase=f.lgroup=(mc^2/h).(h/mvgroup)=c^2/vgroup > c  "  v < c "  vgroup for the de Broglie matter wave}.

Falpha = h[vphase](df/dt)/(c^2{1-vphase ^2/c^2}^1/2), reducing to {h[vphase](df/dt)/c^2} in the limit (vgroup=vphase) at the
instanton tps, where  {1-c^4/(vphase.c)^2}={1-c^2/vdB^2}={1- lps^2/rmax^2}~1, for =Nulltime=Minimum/Maximum=nps=6.2591x10^-49. 
Scalefactor R(n)=v(n)/f is bounded in the inflation parameters R(n,fmax)=rmax=vdB/fps=adB/fps^2 for n=nps=Ho.tps;
and generalises in {Falpha=h.v(n)(df/dt)/c^2=h.R(n,f).f(df/dt)/c^2=(hf/c^2).R(n,f)(df/dt)=mo.R(n,f).(df/dt)}.

  This shows the internal PhaseForce (Fa) acting in addition to the Newtonian external GroupForce (Fa).
This also allows a further definition for the dynamic Lagrangians in associating the Timedifferential of Frequency as
a quasiangular acceleration acting upon a toroidal spacequantum, defining the VPE in terms of the EpsEss wormhole
definitions from the limiting thermal range.

  The LBC defines the Magnetocharge (e*) as function of the Awareness (df/dt) in {e*=1/Eps=2Re.c^2} in units of the 
StarCoulomb (C*=cubicmetre-units/second-units^2), and as higher dimensional subthermal mapping of the Planck-
Length-Oscillation {llPlanckAlpha^1/2},  where [lPlanckAlpha^1/2]=[e/c^2]u=[l]u and mapping electropole {(e)= [l]u.c^2}
onto an atomic diameter in {(e*)=2Re.c^2}, the internal scalefactor R(n,f) so becoming fixed in an elementary and
limiting application of the characteristic Lagrangians.

  Arbona's Jerk as the differential for the acceleration hence relates to a second order of  'Awareness', describing the
change in the change of frequency as an internal  phaserelated parameter , which allows a qualitative and quan-
titative analysis for the phenomenon of 'consciousness' as the timerate-change of awareness as a scaleindependent
form of angular acceleration.

Arbonaean Gravity and General Relativity

a. The Origin of Inertia

   The equilibrium state in the macroscopic range demands there be no relative acceleration between the phonon waves
and the ether background.
If this equilibrium is broken in relative acceleration, then either the macroscopic wavelet drags its supporting inertial framework
of the thermal-range with it, causing wave function collapse or the ether background manages to stop the accelerating wavelet. 

  In the first case, a metastable vortex or particle can materialise, if enough substance mass/energy/charge/current becomes
available for such a transformation, regulated by the Lagrangians and the LBC.
The dragging collapse must have a central point and develop radially for a condensed 'particle-state' to manifest.
This Arbona calls the existence of a condensed wavestructure (or wavelet) in the framework of the SFM.

   In the second case, the resistance to relative acceleration manifests as inertia.
                                                    
                                                                         -7-
In the frame of the accelerating wave, it is stopped and the rest of the universe accelerated homogeneously, now 
dragging the wave and linearly accelerating it towards the coframed equilibrium of the local universe.
This follows the Haisch-Rueda-Puthoff (HRP) model, where inertia emerges from an interaction between the Zero-
Point-Field and the testparticles, possibly also involving the emergence of geometrodynamic principles.
It is the local force (FAlpha),which generates a spinrelated inertia, which is Mach's position, considering the entire
universe as the absolute frame of reference; the interaction being provided by the fluid-field in equilibrium with the 
universal boundary (the 11D-Wittenmirror, manifesting as the doublesided 3D-surface of an Riemannian hyper-
sphere, scaled in a longranged oscillating Black Hole boundary following the min/max evolution set in the LBC).

  Subsequently, inertia cannot be derived from graviatation, as it is itself the fundamental mechanism, giving rise to
the appearance of gravity as an inertial force.
Rather than deriving gravity from a particular quantum field, we derive it from the longrange properties of the averaged
ether forces; but inertia manifests as a stochastic short-range fundamental force.
The Principle of Equivalence forces us to associate the origin of with that force and to search for an explanation
for the geometrodynamic nature of General Relativity in local and general application.   
  
b. The Origin of Gravity   

Conclusions and Consequences

Arbonaean Indeterminism and Heisenbergian Uncertainty
a. The Origin of Indeterminism
b. The Origin of the Wave Function Collapse 
Conclusions and Consequences:

The Dynamics of the Ether and the Vacuum (ZPE)
a. The EPR-Paradox
b. Real and Virtual Particles
c. Conservation Laws
d. Gravity and the ZPF
e. Cosmic Evolution
f. Beyond the Observable Universe

Summary for the  Arboraean Spin-Force-Model 

Summary and 

The Arbona Jerk