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Quantum Relativity

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Mathematical physicist

Tony Bermanseder's

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Dear Forum!

Allow me to indicate the dimensional orthogonality in quantum
geometric terms. This should help in elucidating the confusions
about higher dimensional spaces, as proposed in superbrane theories.

The First Dimension is called a 1-brane and utilises the 0-brane as
generator of itself.

This Zero-Dimension becomes an equidistant displacement from some
origin, let us call it Wolford-Centre about which some abstract or
imaginary radius could be drawn, say to negative and positive
infinity. Let us term this the Y-axis, following conventional

This imaginary displacement is modelled as the Planck-Length in
contemporary physics, but could theoretically be some other parameter
of minimal and quantisable displacement.

Now consider the Wolford-Centre to be the origin for the positive
and the negative Y-coordinate.
A simultaneous expansion from this Wolford-Centre, say to +a and -a
as displacement coordinates then defines the diameter of a circle
radius a in the XY-plane say.
This is the 1-sphere in brane quantum geometry, defined as the locus
of an equidistant point from the Wolford-Centre or origin.

Rotating the 1-sphere into the Z-plane then generates the 2-sphere
as the 2-brane, defined as the locus of an equidistant point from
the Wolford-Centre and as the surface of a sphere with radius a.

Now the question as to the origin of the Z-axis as orthogonality to
the XY-plane arises.

We return to the 0-brane and its definition to examine orthogonality
of X to Y to Z.

To generate the 1-sphere, the Wolford-Centre extended itself
simultaneously into the positive and negative Y-directions.

We qualify this and allow the positive Y-coordinate to describe a
halfcircle, say the X-positive XY-plane for half the circle's or 1-
sphere's surface area.

We introduce orthogonality in phaseshifting the negative Y-
coordinate in say rotation by 90 degrees to define the positive Z-
axis and obtain a subsequent halfcircle in the positive ZY-plane
with negative and positive z-coordinates.

The identity of the 1-sphere is then obtained in rotating the ZY-
halfplane 90 degrees anticlockwise as the ZY-plane with positive and
negative y-coordinates; followed by a clockwise 90 degree rotation
(into the -ve x-coordinated axis) as the X-negative XY-plane for the
then completed circle of the 1-sphere.

This manipulation of the 0-brane to construct the 1-brane introduces
the complex number plane to the real number plane and represents the
physical significance for the representation of physical parameters
in the Argand Diagrams of Vectors representing metricated systems.

The underpinning quantum geometry deriving from this is
the 'Twisting of Space', say in the Moebius Strip and the Klein
Bottle, leading directly to the quantisation of space in toroidal

To obtain a torus, one of only three minimally connected manifold
topologies (Plane, Catenoid, Helicoid), the plane is folded to meet
opposing edges. Pasting say upper and lower edges and then
folding/curving the resulting tube to join left and right edges
gives the torus/doughnut topology, which is not simply connected,
but multiconnected.

To obtain a Klein Bottle, one joins left and right edges but then
only the lower edge is folded with the upper edge becoming
'stretched' gooseneckwise and twisted in the 0-brane/1-brane
transform to othogonally 'meet' a 'wormhole' point someplace
on the OUTER surface of the folded tube of the right and left
Now the INNER surface connects to the initially folded lower edge
stretching towards this wormhole connection from the INSIDE.
Connecting the INSIDE gooseneck to the OUTSIDE gooseneck then
renders the Klein Bottle as a ONESIDED SURFACE or Manifold as the
EXTENDED FORM of the Moebius Strip.
And because the Klein Bottle is a torus derivative (via the folding
mechanism), the cosmology of toroidal spacequanta is applicable.

The 3-sphere or 3-brane hence becomes a Riemannian Hypersphere as a
3-dimensional surface, which also is a 4-dimensional
volume, connected by the curvature factor 3pi/2 (derived in a
previous post).
The 3-brane also depicts the rotation of the 2-sphere, incorporating
the orthogonality as described to combine the negative and positive
curvatures in summation to Euclidean perfect flatness.

Tony Bermanseder Quantum Relativity





Message 17240 in

The Machian Momentum for the Universe

We consider the universe to be a Quantum Universe; that is we sum all fermionic spin-states (N) as

Intrinsic Angular Momenta to become the Intrisic Spin Angular Momentum for the Universe as a

quantised protoverse.

This rather naturally engages the Heisenbergian Uncertainty Principle in the form of the fermionic

(or halfspin) intrinsic angular momentm given in h/4p as the limit for measurement regarding dynamical


1. Moments of Inertia and the nested curvatures of dimension mappings

The Moment of Inertia of a solid sphere mass M and radius R is (2/5).MR^2 and that of a spherical

shell of the same dimensions is (2/3).MR^2 as determined by integration across the geometries.

We consider the universe to be the Hypersphere of Riemann of 4D-Volume [2p^2Rmax^3], which is also

a 3D-surface of toroidal derivative, i.e. a KleinBottle as Moebian extension in 2D.

As precisely 8 spheres radius (a) fit into a sphere radius (2a) and volume (4p/3)(8a^3)=(32p/3)(a^3);

we define the curvature factor (3p/2) to relate toroidal volume [(2p^2)a^3] to spherical volume [(4p/3)a^3].

Considering now the topology of such a torus, defined in radii a and 2a; we can observe a positive spherical

curvature encompassing a negative hyperbolic curvature in a 3D perspective, the latter which we expand

into 4D as the hypersphere of Riemann.

The encompassment or enveloping of a lower surface dimension by a volume dimension is however twosided.

We must consider the mapping of volumes onto both the inner and outer surfaces in the same dimensional


Whilst the inner volume of the earth, say is mapped onto the inner manifold comprising the earth's surface;

the outer volume of the earth (the outer space) is mapped onto the outer manifold as the encompassing

volume and as given in the 4D hypersphere, which is a 3D surface.

This consideration then allows us to extend the 3D/4D scenario in the application of conifolded or enfolded

higher dimensional geometries.

Especially, there exist toroidal derivatives in 6D, which are called Calabi-Yau manifolds and their

extensions into 7D are termed Joycian shaped topologies.

We so invoke here the nomenclature of superbrane theory, without its mathematical formalism.

In our analysis of the Machian observer, we shall find the principle behind higher dimensional M-Theory of

the superbranes.

The underlying principle is the Principle of Quantum Relativity (QR) as a natural extension for the Principle

of General Relativity (GR), itself a natural consequence for the Principle of Special Relativity (SR).

We rename M-Theory in 11 dimensions as FMC-Theory of Quantum Relativity in 12 dimensions for this


The elementary precept of modular duality in M-Theory shall also be the defining foundation for QR.

We then consider 3D-surfaces as 4D-volumes to conifold 6D-Calabi-Yau shapes and 7D-Joyce manifolds in

the connector dimensions of their enfolding.

This process renders the Minkowski-Riemann spacetime metric as a scalerelative enfolding of space within

time, thus leading to the 'sharing of dimensions' and any object moving through time with maximum speed 'c',

requiring to be necessarily at rest relative to its scale relative spacial dimensions.

Any motion of the object relative to the space dimensions, would decompose the Minkowski 4-vector and

reduce the speed c via the formalisms of Special Relativity and its postulates.

For simplicity, we define the 12 dimensions as a simple superpositioning of four worlds superimposed upon

one another, say as:

LineSpace (1-2-3)HyperSpace(4-5-6)QuantumSpace(7-8-9)OmniSpace(10-11-12)(13=1-2-3)..

Each of the four worlds is the Riemann hypersphere with 3 spacial dimensions and a connector time

dimension, which forms however a spacial dimension for the adjacent superimposed world.

So LineSpace connects to HyperSpace via a convenient, but ultimately imaginary timedimension and as

say expressed in the Minkowsi 4-vector.

We could also extend our 4 worlds in ascribing Translation to LineSpace, Rotation to Hyperspace, Vibration to

QuantumSpace and Quantization to OmniSpace, the decisive constant being the speed of light in 'free space',

denoted as 'c'.

2. The Machian observer and the principles of relativity and the Weyl nullification

The rotational frames of references of HyperSpace will become elucidated in the Machian observer.

Consider the rotation of a dynamical system about its axis of rotation, say a solid circular disk radius R

with angular velocity w=v/R=2pf; f the frequency of rotation and v the tangential velocity linked to angular

centripetal acceleration ac =v^2/R.

The postulates of SR lead to Time-Dilation and Lorentz-Contraction and invoke the notion of no absolute

motion being measurable between two oberservers moving uniformely or at rest with respect to one another.

This and the invariance of 'c', irrespective as to the dynamical motion of the observer, forms the Principle of

Special Relativity.

The Principle of General Relativity states, that a dynamical system of SR, that is in uniform motion of an

inertial frame of reference and which is experiencing a gravitational field; is indistinguishable from a non-

inertial system subject to accelerations, which is not experiencing such a gravitational field.

This is known as the Principle of Equivalence.

Our rotating disk above so experiences both inertial and non-inertial frames of references, so applying both SR

and GR in the one dynamical system.

In particular the radius vector musty remain invariant, being normal to the central force, causing the

centripetal acceleration.

The tangent vector experiences Lorentz-Contraction relative to a Bird's Eye Observer (BEO), which remains

stationary relative to the rotating frame of reference (FOR).

Using SR and allowing an observer to rotate with the FOR must produce the invariance of 'c'.

Now any 'observation point' for the corotating FOR must be somewhere on the disk, resolved in the

radius vector and the tangent vector.

We 'shrink' the radius vector using GR until we encounter the Weyl-Limit.

The Riemann Tensor of GR's field equations consists of two parts; the Weyl-Tidal-Tensor and the

Ricci-Density-Tensor with the g-metric.

The Weyl-Tensor preserves volume, but deforms the volume, whilst the Ricci-Tensor reduces volume in

accelerating the particles comprising the warping surface inwards.

But our radius vector must remain invariant and when the limit for measurement is reached in the

'point-limit', then there can be no deformation by the Weyl-Tensor, because this would violate the

invariance of the radius vector.

Subsequently, the Weyl-Curvature must be 0 and the 'point limit' must be a dewarped singularity, which

we now rename as the wormhole perimeter lps=rps/2p.

As mensuration limit, no further Lorentz-Contraction below the wormhole perimeter is possible.

This is a consequence of QR in the modular duality definitions for heterotic superstring HE(8x8), which we

rename here as the Supermembrane EpsEss.

3. Quantum Relativity definitions for the Mach observer

The Identity coupling the macrorealm to the microrealm is given in the inverse properties of SourceBoson

Eps and SinkBoson Ess, the subscripts denoting ps=primary sourcesink and ss=secondary sinksource.

QR defines the following:......Energy:..........E = moc^2 = hf

.........................................................................................E=hf iff mo=0

.........................................................................................E=mo iff f=fss=1/fps=lps/c

All elementary particles/wavelets thus carry an intrinsic EigenFrequency or Lightequivalent fss=1/fps=tps,

which is the TimeInstanton, the beginning of the universe as described by GR and the metricated scenarios

of mensuration, observation and scalerelative measurements.

This gives the inverse proportionality for lightspeed 'c' to the coupling between the vibratory Eps of high

frequency/small radius source-part, modular dual to the winded Ess of low frequency/big radius sink-part.

Gravitational Radiation is the modular inverse of Electromagnetic Radiation, differing in the scaleindependent

and algorithmnically QR-derived supersonstant c^2.

A derived minimum/maximum coupling relates the frequency of the 11D-oscillating universe with nodally

fixed Hubble Constant Ho=58.04 (km/Mpc.s) and maximum curvature radius Rmax=c/Ho to the wormhole in

the constancy for c in: c = Ho.Rmax = fps.lps

Also, the dimensionless TauTime(t) in GR, applied to the curvature Rc=c.dt/dt, becomes the cycletime

n in our descriptions as dn/dt=Ho, n=Ho.t.

The wormhole perimeter is directly quantised in terms of the classical electron radius Re=e^2/(4peo.mec^2),

which is proportional to the Compton Radius of quantum-atomic-structure in RCompton=Re/Alpha.

Alpha is the electromagnetic finestructure given as Alpha=e^2/2eohc and as Alpha=60pe^2/h in QR, and

denotes the interaction probability between matter and light.

(QR derives a superconductive form for the Action Law: Action = Charge^2, electrical conductance quantum,

Quantum Hall effect and Josephson Constant).

There are exactly 10^10 lps/360 wormholeperimeters in one Re; relating to the finestructure of Planck's

Constant h as: h=lps/[8p.Rec^3] in dimensionless Action-Units (relating to the monopole superstring class IIB).

{The 360 count is not arbitrary, because the QR derivation for transcendental p, engages trigonometric series which lead to the

cipher 180 as a limit in Archimedean polygon approximations, also related to QR definitions for magnetic permeability and

electric permittivity}.

The nodal and 11D oscillating universe grows under agency of 'c' in electromagnetic parameters, encompassing

the asymptotically expanding, but decelerating 10D hyperbolically curved 4D-volumed hypersphere as its inner

surface mapping in say the 5D-Anti DeSitter hyperspace.

The volume as 4D-information becomes the 3D-surface of the inner LineSpace mapping the 5D-surface

of the outer HyperSpace.

The volume is nested between the surfaces of two worlds, an ekpyrotic universe of LineSpace blending with

the Hyperspace, encompassed in the cyclicity of the 10th dimension , reflecting off the M-Space of the


Thus the connector-time dimensions are 4-7-10-13=1 and the four worlds are defined in perfect supersymmetry.

Maxwell's equations are introduced to the magnetic monopole(as selfdual superstring class IIB) and 12

magnetopolic junction points within a fourfolded propagation of the wormhole toroidal spacequantum define

the Unified Field of Quantum Relativity (UFoQR).

And yet, this fourfoldedness is just the one world of our Machian Observer.

The singularity is no more; it has become the selfrelative BEO at the centre of rotation as the Machian


It is irrelevant if the BEO rotates with the Perimeter FOR or is stationary relative to it.

As Machian BEO, shehe is located literally at the centre of the universe, with everything else rotating or

moving relatively to himher.

The uniform motion of SR implies invariance of c, should the perimeter FOR rotate with the FOR.

It is only at the now demetricated singularity, that this corotation becomes arbitrary.

Demetricating the field equations of GR blends QuantumTheory with Classical Mechanics, culminating in

General Relativity, itself emerged from Special Relativity and the physics of Newton and Galileo.

The nullification of the Weyl-Tensor hence dewarps Minkowskian spacetime into the Schwarzschild

solutions for the overall cosmic evolution, from the wormhole singularity as limit for the g-metric onto the

Sarkar-architecture of the fractal universe in 236.5 million lightyears, then onwards towards the asymptotic

boundary defined by the Spherical Standing Wave defined by the Hubble-Oscillation and c-invariance.

Meanwhile so the oscillating cosmos as returned in its cyclicity to intersect the dimensions 2.2 Billion

years ago, superposing its blueshift onto the cosmological redshif and giving the 'appearance' of an

accelerating cosmic expansion, linked to a 'dip' in the Alpha-Electromagnetic Finestructure Constant to

about 80 parts per million in a redshift interval from 1.08 to 1.84, mapped again around an Arpian present

cycle value of 0.2505.

But the finite cosmos is enfolded within the infinite one, creating space and time as it moves ever onwards

under invariance of 'c'.

4. The Mach momentum for the universe

Let us now calculate the Machian Momentum for the Universe and the intrinsic angular momentum for it

as a Quantum Universe, a Protouniverse or monosong.

The geometry can be modelled on a prolate ellipsoid with major axis invariance under rotation.

The focalpoints would remain mathematical singularities as the 0-brane of Quantum Relativity.

Any minor axis rotation would merge the focus points in a pointcircle and the 1-brane of QR would define

an oblate ellipsoid of phaseshifted multiverses; integrated as angular function of the complex OmniSpace

as the Omniverse.

As there is no gravitational field outside the enfolded protouniverse, uniform motion of the protoverse in

inertial frames is not equivalent to accelerated motion in noninertial frames by the postulates of GR.

Subsequently, rotating the protouniverse in the nongravitational undefined spacetime without does not

cause centripetally forces balanced by centrifugal (coriolis) forces within the enfolded and metrically defined


The Machian and Einsteinian postulates of 'Relativity of Inertia' hence becomes the BEO -frame within the

protoverse as referring to the centre of rotation as the Machian observer, a reference previously known as

'relative to the fixed stars'.

It is only in that FOR, that the BEO becomes independent from any other coexisting relative rotational

systems in the measurement of the invariance of light, say as in the Sagnac Effect.

The monosongs become tunes, melodies and a symphony of the supermembranes as particle/wavelets of

the UFoQR.

The Total Momentum for the Universe is given in:..................(2/3)M.Rmax^2.w = N.h/4p

We consider the Universe's mass M to be the surface mapping of 10D onto the inside of the 11D-manifold

and use the moment of inertia of a spherical shell.

We incorporate all fermionic particles, including the (anti)neutrinos, whose number is given in the

baryon/photon ratio (Eta h) and a number which increases N by a factor of about 10^9.

QR calculates, for a present cycletime np=1.1324.., the following parameters:

Deceleration Parameter qo=0.014015 for Sarkar-Architecture at cosmological redshift z=7.477 or 236.5 Mly.

Critical Density rc=3Ho^2/8pG=Rmax.c^2/2GVmax ....(rc=Ho^2/4p^2.G for 11D-curvature)

Mo=1.81371262x10^51 kg*

M8=6.47061227x10^52 kg*

Rmax=1.59767545x10^26 m*; R10D(n)=Rmax(1 - n/(n+1)) m*; R11D(n)=n.Rmax(n) m*





w = 2pf = 2p /T = 3Nh/{8phMRmax^2} = 3.06x10^-50 1/s for the asymptotic 10D-massparametric universe

(T=Period)....................................................................= 5.08x10^-50 1/s for the oscillating 11D-electromagnetic universe

The QR definition for time sets the natural limit for this in the minimum/maximum ratio of lps/Rmax=nps.

The Timeinstanton tps=fss=3.333..x10^-31 s thus relates nps=1/lssRmax=6.26x10^-49; mapping the 'real'

time tps onto the 'imaginary' time Ho.tps=1.17x10^-66 s/s.

This analysis has lead us into the realms of the poets and dreamers.

Leonardo de Vinci's 'Vitruvian Man' has literally become the Machian Observer, encompassing the

entire universe as 'Cosmic Man', the Adam Kadmon of Lurianic-Hebrew Kabbalah or the Purusha of Hindu cosmology.

Molecules are mapped as star systems from the 'inner space' and biovital cells become the galaxies

of 'outer space'.

Every sentient being is mapped holographically as a neuron in all other 'immortalised' non-telomere

depleted 'neuronal brains'.

The monosongs become tunes, melodies and a symphony of the supermembranes as particle/wavelets of

the UFoQR.

Anthony Paul Bermanseder, BSc.

Love from the DragonHeart!

As a mathematical physicist, I also study ancient scrolls and the signature can be evaluated on a number of levels; from childishly naive to profoundly esoteric---Tony Whynot, Unicorn of SophiaGnosis !

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