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Why Dark Energy has an Antigravitational effect

Antidimensional space intersects with ndimensional space (normative dimensional space) resulting in the cancellation of gravitational effect.

Intersection of Space and Antidimensional Space and the Cancellation of Gravity

Entropy increases due to the Intersection of ndimensional and antidmensional space. Intersection of ndimensional and antidmensional space is a decrease in potential energy.

Imbalance of Matter and Antimatter

While matter and antimatter particles are defined in equal quantities, because definition is equal and opposite. When intersection occurs, antiparticles and particles enter the cancelled vacuum space. This does not have to occur in equal quantities.

Defining Dimensions of Space

Definition is a function of equal and opposite relativity. Dimensions of space are defined as a function of equal and opposite relativity. One point is defined relative to another. A point is defined relative to an anti-point. Mutual cancellation is non-definition. Definition is defined relative to non-definition and non-definition is cancellation .

No gravity.

A point is where any three axis converge. its virtual.

When dimension and antidimension cancel, then there is vacuum space.

Dimensional Interaction: Equations

[Submitted on 11 Mar 1998]

Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity

D. J. Broadhurst

In each of the 10 cases with propagators of unit or zero mass, the finite part of the scalar 3-loop tetrahedral vacuum diagram is reduced to 4-letter words in the 7-letter alphabet of the 1-forms Ω:=dz/z and ωp:=dz/(λ−p−z), where λ is the sixth root of unity. Three diagrams yield only ζ(Ω3ω0)=1/90π4. In two cases π4 combines with the Euler-Zagier sum ζ(Ω2ω3ω0)=∑m>n>0(−1)m+n/m3n; in three cases it combines with the square of Clausen’s Cl2(π/3)=Iζ(Ωω1)=∑n>0sin(πn/3)/n2. The case with 6 masses involves no further constant; with 5 masses a Deligne-Euler-Zagier sum appears: Rζ(Ω2ω3ω1)=∑m>n>0(−1)mcos(2πn/3)/m3n. The previously unidentified term in the 3-loop rho-parameter of the standard model is merely D3=6ζ(3)−6Cl22(π/3)−1/24π4. The remarkable simplicity of these results stems from two shuffle algebras: one for nested sums; the other for iterated integrals. Each diagram evaluates to 10 000 digits in seconds, because the primitive words are transformable to exponentially convergent single sums, as recently shown for ζ(3) and ζ(5), familiar in QCD. Those are SC∗(2) constants, whose base of super-fast computation is 2. Mass involves the novel base-3 set SC∗(3). All 10 diagrams reduce to SC∗(3)∪SC∗(2) constants and their products. Only the 6-mass case entails both bases.

Comments:41 pages, LaTeX
Subjects:High Energy Physics – Theory (hep-th); High Energy Physics – Phenomenology (hep-ph); Classical Analysis and ODEs (math.CA)
Journal reference:Eur.Phys.J.C8:311-333,1999
Report number:OUT–4102–72
Cite as:arXiv:hep-th/9803091
 (or arXiv:hep-th/9803091v1 for this version)

Figure Eight Knot

DOWNLOAD Mathematica Notebook

The figure eight knot, also known as the Flemish knot and savoy knot, is the unique prime knot of four crossings 04-001. It has braid word .

The figure eight knot is implemented in the Wolfram Language as KnotData[“FigureEight”].

It is a 2-embeddable knot, and is amphichiral as well as invertible. It has Arf invariant 1. It is not a slice knot (Rolfsen 1976, p. 224).

del (x)

The Alexander polynomial , BLM/Ho polynomial , Conway polynomial , HOMFLY polynomial , Jones polynomial , and Kauffman polynomial F  of the figure eight knot are


There are no other knots on 10 or fewer crossings sharing the same Alexander polynomialBLM/Ho polynomialbracket polynomialHOMFLY polynomialJones polynomial, or Kauffman polynomial F.

The figure eight knot has knot group


(Rolfsen 1976, p. 58).

Helaman Ferguson’s sculpture “Figure-Eight Complement II” illustrates the knot complement of the figure eight knot (Borwein and Bailey 2003, pp. 54-55, color plate IV, and front cover; Bailey et al. 2007, p. 37). Furthermore, Ferguson has carved the BBP-type formula for the hyperbolic volume of the knot complement (discussed below) on both figure eight knot complement sculptures commissioned by the Clay Mathematics Institute (Borwein and Bailey 2003, p. 56; Bailey et al. 2007, pp. 36-38).

The hyperbolic volume of the knot complement of the figure eight knot is approximately given by


(OEIS A091518). Exact expressions are given by the infinite sums


where  is a harmonic number.


 has a variety of BBP-type formulas including


with additional identities for coefficients of  of the form  (E. W. Weisstein, Sep. 30, 2007). Higher-order identities are


(E. W. Weisstein, Aug. 11, 2008).

Additional classes of identities are given by


with additional identities for coefficients of  of the form  (E. W. Weisstein, Sep. 30, 2007). Another BBP-type formula is given by


 is also given by the integrals


and the analytic expressions


(Broadhurst 1998; Borwein and Bailey 2003, pp. 54 and 88-92; Bailey et al. 2007, pp. 36-38 and 265-266), where  is a generalized hypergeometric function,  is the trigamma function,  is the dilogarithm and  is Clausen’s integral.SEE ALSO:BBP-Type FormulaKnotPrime KnotREFERENCES:

Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. Experimental Mathematics in Action. Wellesley, MA: A K Peters, 2007.


Bar-Natan, D. “The Knot .”

Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, 2003.


Broadhurst, D. J. “Massive 3-Loop Feynman Diagrams Reducible to  Primitives of Algebras of the Sixth Root of Unity.” March 11, 1998.

Francis, G. K. A Topological Picture Book. New York: Springer-Verlag, 1987.

Kauffman, L. Knots and Physics. Teaneck, NJ: World Scientific, pp. 8, 12, and 35, 1991.


KnotPlot. “.”

Livingston, C. Knot Theory. Washington, DC: Math. Assoc. Amer., pp. 21 and 153, 1993.

Owen, P. Knots. Philadelphia, PA: Courage, p. 16, 1993.

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 58 and 224, 1976.

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. Middlesex, England: Penguin Books, pp. 78-79, 1991.CITE THIS AS:

Weisstein, Eric W. “Figure Eight Knot.” From MathWorld–A Wolfram Web Resource.

350 Meluzzi·Smith·Arya
Annu. Rev. Biophys. 2010.39:349-366. Downloaded from by University of California – San Diego on 05/31/10. For personal use only.
31 Trefoil
41 Figure-eight
Closed curve Open curve



f Square knot
Granny knot
q–1 + q–3 – q–4
q2 – q + 1 –q–1 + q–2
q–2 + q–4 – q–5 + q–6 – q–7
q–1 – q–2 + 2q–3 – q–4 + q–5 – q–6
Figure 1 Knot types and features. (a) Knots formally exist only in 3D curves (left). Knot projections are 2D representations of knots (right). (b) Knot-like conformations in open curves are often encountered in biophysics (left). To analyze such knots, their loose ends must be connected, according to some procedure, to obtainaclosedcurve(right).(c)Projectionsofthefoursimplestnontrivialknottypes,withthecorresponding CS denominations and Jones polynomials (see text for definition of CS) (adapted from http://katlas.math. Page). (d) The size of a knot, SK, in a polymer may be less than the size of the polymer, SP, containing the knot. (e) In a slip link arrangement, entropic competition between the knotted loops causes the ring to squeeze one of the knots. The size of the latter can be deduced from the position of the ring. Adapted from Reference 64. (f ) The size of a tight knot can be estimated from the volume of the enclosing ideal knot representation: SK ∼(D2L)1/3, where D and L are the diameter and length of the outer tube. Adapted from Reference 39. (g) Square and granny knots can tie


AntiDimensional space interacts with Spatial Dimensions to Produce a Plasma

Equations for a Plasma Consisting of Matter and Antimatter

Fluctuations of space have lobes in every dimension. Six normative spatial dimensions and six antispatial dimensions exist because definition is a function of equal and opposite relativity.

When a lobe in a normative dimension interacts with a lobe in an antidimensional spatial lobe, a void forms; the dimensions cancel out. Knotted fluctuations in dimension rush in. A plasma is produced from matter / antimatter annihilation.

Dark Energy

Matter and anti-matter are created in equal quantities because definition is a function of equal and opposite relativity. Quantities of normative fluctuations and anti-dimensional fluctuations intersect creating a void. An increase in entropy occurs when the void is filled. The void is filled with unequal quantities definition and anti-definition, with definition being a knotted fluctuations of space. As knotted normative and anti-normative dimensions cancel out, which is the cancelling out of matter and antimatter a plasma results. While normative and anti-normative fluctuation are equivalently defined, the filling of the intersectional void occurs asymmetrically. If there is a preponderance of normative knotted dimensions in fluctuations, matter will persist.

The interaction of the antidimensionl lobe enters the space of the normative dimensional lobe producing, an expansionary effect on the universe. This may be what has been identified as Dark Energy.

Anti-Dimension/Dimension Intersectional Interchange Produces Plasmatic Flow

Anti-dimensional space and normative dimensional space intersect. Dimensions rotate around the intersection creating an interchange.

The intersectional interchange generates a void. The void is filled as anti-dimension and normative dimension rush in; the lobes pass through each other and the void is filled. The circles represent lobes which are fluctuations in dimension. In figure 2, the lobes are passing through each other; anti-dimension space and normative dimensional space slice through each other.

In figure 2, knotted fluctuations of space, represented by the ‘+’, happen to outnumber the knotted fluctuations of anti-dimensional space ‘-‘ in the intersected space. The ‘+’ and ‘-‘ annihilate, creating a plasma.

Proportionately, ‘+’ remains.   Such a scenario illustrates how matter particles could outnumber anti-matter particles. The intersection of lobes creates a void in which knotted dimensions enter. This results in the expansion of the normative dimension and the expansion of anti-dimensional space, anti-dark energy.  The expansion of normative dimension is attributed to dark energy. What we refer to as dark energy is the expansion of anti-dimensional lobes into normative dimensional space.  Gravitational effects in the area of intersection between the lobes are cancelled out.  Thus, there is an anti-gravitational effect associated with dark energy.

When the lobes knot the normative dimensional lobe and the anti-dimensional lobe loop through each other, dimensional space knots. The lobes are already part of interrelated lobes. So, lobes knot within lobes. And those lobes may already be knotted. The looping within lobes, which occurs because this occurrence is a reduction in entropy, is an expansion of the universe. The occurrence of the expansion of the uniiverse, is attributed to dark energy.

So, six dimensions of normative space are knotted with six anti-dimensions of anti-space. Knotted with another six dimensions. The knots change the flow of dimension and thus produce the gravitational effect which is attributed to dark matter.

Plasma flow induces electro-magnetic field which results in magnetic bubbles.

From Yahoo link below:

As the plasma travels, the magnetic field forms odd, “bubble-like structures” called magnetic islands.

“These may be produced from helical current perturbations in the plasma,” Oak Ridge National Laboratory published in a report from—wait for it—1974. “Physically the islands are a result of having a harmonic component of the radial component of the perturbed magnetic field in resonance with the unperturbed rational surface field lines, in the presence of shear.”

Researchers realized then that blasting the plasma with radio waves went a long way toward stabilizing the stream and reducing the factors that led to disruptions from islands. In 2019, a new generation of researchers identified a way to improve just how stabilizing those radio waves could be, boosting them using tiny temperature fluctuations called perturbations.

By “depositing” accumulating radio frequency waves within the magnetic islands, scientists can suspend the islands and prevent them from growing. And in the new paper, researchers suggest that by carefully controlling and varying the temperature of the plasma, they can magnify the controlling effect of radio waves.

This nonlinear treatment of the temperature introduces new variables, too. The scientists say they’re excited about the possibilities for new control schemes and other subsequent research.

Density in Dimension due to the Folding and Intersection of Dimensions

Fluctuations in dimension fold over on each other.

Folding, undulating Dimensions form a plasma. As the plasma travels, a magnetic field is induced. The magnetic field forms odd, “bubble-like structures” called magnetic islands.

“These may be produced from helical current perturbations in the plasma,” Oak Ridge National Laboratory published in a report from 1974. “Physically the islands are a result of having a harmonic component of the radial component of the perturbed magnetic field in resonance with the unperturbed rational surface field lines, in the presence of shear.”

Current is Induced Along Twisted Dimensions

Frayed, unwound, strands of dimension are high potential energy (Live Wires) looking to connect (twist together) with strands of frayed dimensions to induce (a current of) fluctuations in dimension

When normative dimensions interact with anti-dimensions, interlooped stranded dimensions blow apart (short out).

Dimensions that are fluctuating with polarity induce fluctuation in dimension. When dimensions phase, normative dimensions and anti-dimensional space do not interact. And do not blow each other’s dimensions apart.

Dimension Flow

Kinks in the Fabric

As dimensions fold, twist and knot, flow is impeded. A field is constrained dimensions. This is manifested as a force. Gravity may be manifested as tightly woven dimensions which slow and constrict movement of knots in dimension.

Knots which aggregate have increased entropy and lower potential energy. Aggregated knots in dimension slow the flow of dimension in that space.

A Decrease in the Potential of Spatial Dimensions Results in Knots

Knot Formation is an Increase in Entropy

Let me offer a solution to the Paradox of the First Moment

The decrease in potential energy of a stretched rubber band results in an increase in entropy and kinetic energy which is manifested as a knot in space.

How are the dimensions of space stretched? I am able to understand a question at a deeper level when I resolve a paradox. In this case, the paradox of the First Moment. In resolving this paradox, we can understand how the Big Bang would occur.

Definition is a function of equal and opposite relativity. Space has twelve dimensions. Three potential positive matter dimensions, three potential negative matter dimensions, three potential positive antimatter dimensions and three potential negative antimatter dimensions. I can graph that for you, if you like.

These dimensions are fluctuating in and out of relative definition. Which means in and out of equilibrium, in and out of potential; defined and expressed as positive and negative potential … fluctuating definitions interphase. When dimensions interphase, picture intertwining, the first moment of persistent dimensional change occurs for that unit of space, a unit of space being the wavelength equal to the amplitude. As areas develop, persistent, non-potential changes in spatial dimensions, the changes gravitate toward each other. Interphased fluctuations are dispersed, forming a network matrix of negative potential nodes; stretching and tugging on space. Picture the change in spatial dimension which is one area being stretched due to network attractor affects; picture dispersed areas tug on a central point. Stretching space. Space becomes entangled. Due to the the ongoing fluctuation of space, stretched space snaps back.

Lower Potential Energy, Increased Entropy

As space lurches in another direction, as stretched dimensions of space snap back, dimensions twist and turn, forming nodes.

What about the Paradox of the First Moment? The paradox of a first moment is that if a first moment did occur, why didn’t occur before then? And if it could occur then, why didn’t occur before that moment?

Resolving the paradox reveals a fundamental: The first moment had to have been sourced from an ongoing event that canceled itself out. An event that was ongoing, but did not persist. This ongoing event must have had the capability, the potential, of interacting with itself such that the ongoing event would persist.

The ongoing event is a fluctuation of space. A virtual fluctuation. When fluctuations interphase they persist. In multiple spatial dimensions. These fluctuations may then gravitate toward each other and eventually erupt in the Big Bang. …