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Any replacements are listed further down
[78] viXra:1202.0001 [pdf] submitted on 2012-02-01 02:19:14
Authors: Victor Katyushchik
Comments: 4 Pages.
The three-dimensional space formatting allows to operate on infinitely large and infinitely small quantities confidently, without any contradictions, paradoxes and uncertainties.
Category: Mathematical Physics
[77] viXra:1201.0119 [pdf] submitted on 2012-01-30 04:01:12
Authors: Prakhar bhatnagar
Comments: 5 Pages.
Magnetic monopole is a hypothetical particle with a single pole. In this paper a new mathematical structure for Dirac string has been proposed .Quantitative aspects and qualitative aspects of a monopole represented as a Dirac string have been highlighted. Magnetic bundle has been defined in a complex form and pole has been defined as composition of that bundle for single pole the pole variable is single. The pole can be considered as a group of threads or a point lying on a monopole magnet bundle for one pole the thread is single and one dimensional. The function is in complex form and defines magnetic bundle.
Category: Mathematical Physics
[76] viXra:1201.0117 [pdf] submitted on 2012-01-29 07:51:38
Authors: Dan Visser
Comments: 10 Pages.
This paper describes what New Dark Energy is, as well as my comment “Nobel Nominations in a New World” to the Nobel Committee. These seemingly different looking subjects are importantly connected in a plead to change the way Nobel-nominations are performed in a changing world with internet and alternative archives, such as viXra. The point is, that institutional established physics and cosmology block new ideas from the public domain. Therefore an appendix has been added to this paper to summarize in a nutshell, relativity, space-expansion, accelerated space-expansion and the one time-direction in the Big Bang Cosmology, in order to explain better what new dark energy is and what its meaning is for physics and new cosmology. That message is meant for the Nobel Committee. Furthermore three-why’s are answered: Why are two extra time-directions needed in a new cosmology? Why is the introduction of dark mass, squared? Why would there be a Double Torus for New Cosmology? Also the basic-formulas are summarized, referring to my papers, such as the dark energy force formula from my thought-experiment, followed by its transformed-version: the force smaller than the smallest gravity. In the end New Dark Energy is formulated as a product of new dark mass (squared) and two extra time-directions from below the Planck scale. This marks that New Dark Energy could recalculate the established dual unitary-entangled quantum-spaces faster backwards in time than time goes forward in the Big Bang Cosmology ! This affects the established quantum dynamics and classical reality towards the past and future differently than Einstein’s General Relativity is prescribing. The letter to the Nobel Committee is send by me, because no other institutions is doing that for me.
Category: Mathematical Physics
[75] viXra:1201.0065 [pdf] submitted on 2012-01-16 10:48:52
Authors: Florentin Smarandache
Comments: 4 Pages.
In a similar way as passing from Euclidean Geometry to Non-Euclidean Geometry, we
can pass from Subluminal Physics to Superluminal Physics, and further to Instantaneous Physics.
In the lights of two consecutive successful CERN experiments with superluminal particles in the
Fall of 2011, we believe that these two new fields of research should begin developing.
Category: Mathematical Physics
[74] viXra:1201.0013 [pdf] submitted on 2012-01-05 06:13:36
Authors: sangwha Yi
Comments: 10 Pages. It is submission.
This article’s purpose is that discover the new inverse-coordinate transformation of the new accelerated theory in the article “The changed coordinate transformation of the constant accelerated coordinate system by tetrad”(vixra:1106,0054).
Category: Mathematical Physics
[73] viXra:1112.0094 [pdf] submitted on 2011-12-31 14:02:34
Authors: DT Froedge
Comments: 12 Pages.
This paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and, though speculative, the mass ratios calculated for elementary particles are very close the observed mass ratios.
Category: Mathematical Physics
[72] viXra:1112.0055 [pdf] submitted on 2011-12-18 14:01:31
Authors: Dan Visser
Comments: 4 Pages. Avalable only for arXiv and informing me by email.
In this paper I give a formulation for why a new Higgs-mass is considered otherwise than is usually done. This leads to an additional explanation of my earlier posted papers about neutrinos-faster-than-light-in-vacuum; I also refer to my earlier calculated new Higgs-mass. The addition is a deeper analysis, which does not change the result in the former paper. It is extending the Higgs-energy. The first prediction is the Higgs-particle is a Limited Boson-Surface, or Higgs-LBS. This means: It is not a singular Higgs-mass boson. The second prediction is: The occurrence of an Higgs-LBS may be about 60 nanoseconds before a proton-proton collision in an accelerator, such as the LHC in CERN. This is possible because the Higgs-energy is related to a new dark energy force squared. These predictions are supposed to fit in a new cosmological hypothesis, called the Double Torus of dark energy and dark matter, wherein a new dark energy force is defined as a force smaller than the smallest gravity, which could act beyond General Relativity.
Category: Mathematical Physics
[71] viXra:1111.0106 [pdf] submitted on 28 Nov 2011
Authors: Dan Visser
Comments: 7 Pages.
In the formulations of this 'paper' speaks the existence of a force smaller than the smallest gravity.
This is a new dark energy force, which affects neutrinos differently than is assumed according to current
physics. The formulations also imply a different look on the Higgs-mass and dark matter-mass. The 'paper'
is also is an overview of recent 'papers' [1] , which already described these issues, but a deeper
analysis became important, because a new cosmological hypothesis is involved. The CERN-experiments on
these issues are the falsification for my formulations, but until now my formulations withstand several
experimental results, and in this case the match with the latest neutrino-faster-than-light experiments
is very convincing (more attention might be given to this 'paper' towards institutional disciplines by
the Arxiv or Nature).
Category: Mathematical Physics
[70] viXra:1111.0091 [pdf] submitted on 1 Nov 2011
Authors: Matti Pitkänen
Comments: 24 pages.
The arguments of this article support the view that in TGD Universe number theoretic and geometric Langlands conjectures could be understood very naturally. The basic notions are following.
There are several steps leading from G to its twisted quantum Yangian. The first step replaces point like particles with partonic 2-surfaces: this brings in Kac-Moody character. The second step brings in finite measurement resolution meaning that Kac-Moody type algebra is replaced with its quantum version. The third step brings in zero energy ontology: one cannot treat single partonic surface or string world sheet as independent unit: always the collection of partonic 2-surfaces and corresponding string worlds sheets defines the geometric structure so that multilocality and therefore quantum Yangian algebra with multilocal generators is unavoidable.
In finite measurement resolution geometric Langlands duality and number theoretic Langlands duality are very closely related since partonic 2-surface is effectively replaced with the punctures representing the ends of braid strands and the orbit of this set under a discrete subgroup of G defines effectively a collection of "rational" 2-surfaces. The number of the "rational" surfaces in geometric Langlands conjecture replaces the number of rational points of partonic 2-surface in its number theoretic variant. The ability to compute both these numbers is very relevant for quantum TGD.
[69] viXra:1111.0090 [pdf] submitted on 1 Nov 2011
Authors: Matti Pitkänen
Comments: 18 pages.
Infinite primes is a purely TGD inspired notion. The notion of infinity is number theoretical and infinite primes have well defined divisibility properties. One can partially order them by the real norm. p-Adic norms of infinite primes are well defined and finite. The construction of infinite primes is a hierarchical procedure structurally equivalent to a repeated second quantization of a supersymmetric arithmetic quantum field theory. At the lowest level bosons and fermions are labelled by ordinary primes. At the next level one obtains free Fock states plus states having interpretation as bound many particle states. The many particle states of a given level become the single particle states of the next level and one can repeat the construction ad infinitum. The analogy with quantum theory is intriguing and I have proposed that the quantum states in TGD Universe correspond to octonionic generalizations of infinite primes. It is interesting to compare infinite primes (and integers) to the Cantorian view about infinite ordinals and cardinals. The basic problems of Cantor's approach which relate to the axiom of choice, continuum hypothesis, and Russell's antinomy: all these problems relate to the definition of ordinals as sets. In TGD framework infinite primes, integers, and rationals are defined purely algebraically so that these problems are avoided. It is not surprising that these approaches are not equivalent. For instance, sum and product for Cantorian ordinals are not commutative unlike for infinite integers defined in terms of infinite primes.
Set theory defines the foundations of modern mathematics. Set theory relies strongly on classical physics, and the obvious question is whether one should reconsider the foundations of mathematics in light of quantum physics. Is set theory really the correct approach to axiomatization?
[68] viXra:1111.0089 [pdf] submitted on 1 Nov 2011
Authors: Matti Pitkänen
Comments: 79 pages.
In this article the goal is to find whether the general mathematical structures associated with twistor approach, superstring models and M-theory could have a generalization or a modification in TGD framework. The contents of the chapter is an outcome of a rather spontaneous process, and represents rather unexpected new insights about TGD resulting as outcome of the comparisons.
1. Infinite primes, Galois groups, algebraic geometry, and TGD
In algebraic geometry the notion of variety defined by algebraic equation is very general: all number fields are allowed. One of the challenges is to define the counterparts of homology and cohomology groups for them. The notion of cohomology giving rise also to homology if Poincare duality holds true is central. The number of various cohomology theories has inflated and one of the basic challenges to find a sufficiently general approach allowing to interpret various cohomology theories as variations of the same motive as Grothendieck, who is the pioneer of the field responsible for many of the basic notions and visions, expressed it.
Cohomology requires a definition of integral for forms for all number fields. In p-adic context the lack of well-ordering of p-adic numbers implies difficulties both in homology and cohomology since the notion of boundary does not exist in topological sense. The notion of definite integral is problematic for the same reason. This has led to a proposal of reducing integration to Fourier analysis working for symmetric spaces but requiring algebraic extensions of p-adic numbers and an appropriate definition of the p-adic symmetric space. The definition is not unique and the interpretation is in terms of the varying measurement resolution.
The notion of infinite has gradually turned out to be more and more important for quantum TGD. Infinite primes, integers, and rationals form a hierarchy completely analogous to a hierarchy of second quantization for a super-symmetric arithmetic quantum field theory. The simplest infinite primes representing elementary particles at given level are in one-one correspondence with many-particle states of the previous level. More complex infinite primes have interpretation in terms of bound states.
This construction would realize the number theoretical, algebraic geometrical, and topological content in the construction of quantum states in TGD framework in accordance with TGD as almost TQFT philosophy, TGD as infinite-D geometry, and TGD as generalized number theory visions.
2. p-Adic integration and cohomology
This picture leads also to a proposal how p-adic integrals could be defined in TGD framework.
3. Floer homology, Gromov-Witten invariants, and TGD
Floer homology defines a generalization of Morse theory allowing to deduce symplectic homology groups by studying Morse theory in loop space of the symplectic manifold. Since the symplectic transformations of the boundary of δ M4+/-× CP2 define isometry group of WCW, it is very natural to expect that Kähler action defines a generalization of the Floer homology allowing to understand the symplectic aspects of quantum TGD. The hierarchy of Planck constants implied by the one-to-many correspondence between canonical momentum densities and time derivatives of the imbedding space coordinates leads naturally to singular coverings of the imbedding space and the resulting symplectic Morse theory could characterize the homology of these coverings.
One ends up to a more precise definition of vacuum functional: Kähler action reduces Chern-Simons terms (imaginary in Minkowskian regions and real in Euclidian regions) so that it has both phase and real exponent which makes the functional integral well-defined. Both the phase factor and its conjugate must be allowed and the resulting degeneracy of ground state could allow to understand qualitatively the delicacies of CP breaking and its sensitivity to the parameters of the system. The critical points with respect to zero modes correspond to those for Kähler function. The critical points with respect to complex coordinates associated with quantum fluctuating degrees of freedom are not allowed by the positive definiteness of Kähler metric of WCW. One can say that Kähler and Morse functions define the real and imaginary parts of the exponent of vacuum functional.
The generalization of Floer homology inspires several new insights. In particular, space-time surface as hyper-quaternionic surface could define the 4-D counterpart for pseudo-holomorphic 2-surfaces in Floer homology. Holomorphic partonic 2-surfaces could in turn correspond to the extrema of Kähler function with respect to zero modes and holomorphy would be accompanied by super-symmetry.
Gromov-Witten invariants appear in Floer homology and topological string theories and this inspires the attempt to build an overall view about their role in TGD. Generalization of topological string theories of type A and B to TGD framework is proposed. The TGD counterpart of the mirror symmetry would be the equivalence of formulations of TGD in H=M4× CP2 and in CP3× CP3 with space-time surfaces replaced with 6-D sphere bundles.
4. K-theory, branes, and TGD
K-theory and its generalizations play a fundamental role in super-string models and M-theory since they allow a topological classification of branes. After representing some physical objections against the notion of brane more technical problems of this approach are discussed briefly and it is proposed how TGD allows to overcome these problems. A more precise formulation of the weak form of electric-magnetic duality emerges: the original formulation was not quite correct for space-time regions with Euclidian signature of the induced metric. The question about possible TGD counterparts of R-R and NS-NS fields and S, T, and U dualities is discussed.
5. p-Adic space-time sheets as correlates for Boolean cognition
p-Adic physics is interpreted as physical correlate for cognition. The so called Stone spaces are in one-one correspondence with Boolean algebras and have typically 2-adic topologies. A generalization to p-adic case with the interpretation of p pinary digits as physically representable Boolean statements of a Boolean algebra with 2n>p>pn-1 statements is encouraged by p-adic length scale hypothesis. Stone spaces are synonymous with profinite spaces about which both finite and infinite Galois groups represent basic examples. This provides a strong support for the connection between Boolean cognition and p-adic space-time physics. The Stone space character of Galois groups suggests also a deep connection between number theory and cognition and some arguments providing support for this vision are discussed.
[67] viXra:1111.0088 [pdf] submitted on 1 Nov 2011
Authors: Matti Pitkänen
Comments: 17 pages.
Witten was awarded by Fields medal from a construction recipe of Jones polynomial based on topological QFT assigned with braids and based on Chern-Simons action. Recently Witten has been working with an attempt to understand in terms of quantum theory the so called Khovanov polynomial associated with a much more abstract link invariant whose interpretation and real understanding remains still open.
The attempts to understand Witten's thoughts lead to a series of questions unavoidably culminating to the frustrating "Why I do not have the brain of Witten making perhaps possible to answer these questions?". This one must just accept. In this article I summarize some thoughts inspired by the associations of the talk of Witten with quantum TGD and with the model of DNA as topological quantum computer. In my own childish manner I dare believe that these associations are interesting and dare also hope that some more brainy individual might take them seriously.
An idea inspired by TGD approach which also main streamer might find interesting is that the Jones invariant defined as vacuum expectation for a Wilson loop in 2+1-D space-time generalizes to a vacuum expectation for a collection of Wilson loops in 2+2-D space-time and could define an invariant for 2-D knots and for cobordisms of braids analogous to Jones polynomial. As a matter fact, it turns out that a generalization of gauge field known as gerbe is needed and that in TGD framework classical color gauge fields defined the gauge potentials of this field. Also topological string theory in 4-D space-time could define this kind of invariants. Of course, it might well be that this kind of ideas have been already discussed in literature.
[66] viXra:1111.0087 [pdf] submitted on 1 Nov 2011
Authors: Matti Pitkänen
Comments: 4 pages.
The vanishing of ordinary determinant tells that a group of linear equations possesses non-trivial solutions. Hyperdeterminant generalizes this notion to a situation in which one has homogenous multilinear equations. The notion has applications to the description of quantum entanglement and has stimulated interest in physics blogs. Hyperdeterminant applies to hyper-matrices with n matrix indices defined for an n-fold tensor power of vector space - or more generally - for a tensor product of vector spaces with varying dimensions. Hyper determinant is an n-linear function of the arguments in the tensor factors with the property that all partial derivatives of the hyper determinant vanish at the point, which corresponds to a non-trivial solution of the equation. A simple example is potential function of n arguments linear in each argument.
Why the notion of hyperdeterminant- or rather its infinite-dimensional generalization- might be interesting in TGD framework relates to the quantum criticality of TGD stating that TGD Universe involves a fractal hierarchy of criticalities: phase transitions inside phase transitions inside... At classical level the lowest order criticality means that the extremal of Kähler action possesses non-trivial second variations for which the action is not affected. The system is critical. In QFT context one speaks about zero modes. The vanishing of the so called Gaussian (of functional) determinant associated with second variations is the condition for the existence of critical deformations. In QFT context this situation corresponds to the presence of zero modes.
The simplest physical model for a critical system is cusp catastrophe defined by a potential function V(x) which is fourth order polynomial. At the edges of cusp two extrema of potential function stable and unstable extrema co-incide and the rank of the matrix defined by the potential function vanishes. This means vanishing of its determinant. At the tip of the cusp the also the third derivative vanishes of potential function vanishes. This situation is however not describable in terms of hyperdeterminant since it is genuinely non-linear rather than only multilinear.
In a complete analogy, one can consider also the vanishing of n:th variations in TGD framework as higher order criticality so that the vanishing of hyperdeterminant might serve as a criterion for the higher order critical point and occurrence of phase transition. Why multilinearity might replace non-linearity in TGD framework could be due to the non-locality. Multilinearty with respect to imbedding space-coordinates at different space-time points would imply also the vanishing of the standard local divergences of quantum field theory known to be absent in TGD framework on basis of very general arguments. In this article an attempt to concretize this idea is made. The challenge is highly non-trivial since in finite measurement resolution one must work with infinite-dimensional system.
[65] viXra:1111.0086 [pdf] submitted on 1 Nov 2011
Authors: Matti Pitkänen
Comments: 45 pages.
There have been impressive steps in the understanding of N=4 maximally sypersymmetric YM theory possessing 4-D super-conformal symmetry. This theory is related by AdS/CFT duality to certain string theory in AdS5× S5 background. Second stringy representation was discovered by Witten and is based on 6-D Calabi-Yau manifold defined by twistors. The unifying proposal is that so called Yangian symmetry is behind the mathematical miracles involved.
In the following I will discuss briefly the notion of Yangian symmetry and suggest its generalization in TGD framework by replacing conformal algebra with appropriate super-conformal algebras. Also a possible realization of twistor approach and the construction of scattering amplitudes in terms of Yangian invariants defined by Grassmannian integrals is considered in TGD framework and based on the idea that in zero energy ontology one can represent massive states as bound states of massless particles. There is also a proposal for a physical interpretation of the Cartan algebra of Yangian algebra allowing to understand at the fundamental level how the mass spectrum of n-particle bound states could be understood in terms of the n-local charges of the Yangian algebra.
Twistors were originally introduced by Penrose to characterize the solutions of Maxwell's equations. Kähler action is Maxwell action for the induced Kähler form of CP2. The preferred extremals allow a very concrete interpretation in terms of modes of massless non-linear field. Both conformally compactified Minkowski space identifiable as so called causal diamond and CP2 allow a description in terms of twistors. These observations inspire the proposal that a generalization of Witten's twistor string theory relying on the identification of twistor string world sheets with certain holomorphic surfaces assigned with Feynman diagrams could allow a formulation of quantum TGD in terms of 3-dimensional holomorphic surfaces of CP3× CP3 mapped to 6-surfaces dual CP3× CP3, which are sphere bundles so that they are projected in a natural manner to 4-D space-time surfaces. Very general physical and mathematical arguments lead to a highly unique proposal for the holomorphic differential equations defining the complex 3-surfaces conjectured to correspond to the preferred extremals of Kähler action.
[64] viXra:1111.0085 [pdf] submitted on 1 Nov 2011
Authors: Matti Pitkänen
Comments: 17 pages.
Shnoll and collaborators have discovered strange repeating patterns of random fluctuations of physical observables such as the number n of nuclear decays in a given time interval. Periodically occurring peaks for the distribution of the number N(n) of measurements producing n events in a series of measurements as a function of n is observed instead of a single peak. The positions of the peaks are not random and the patterns depend on position and time varying periodically in time scales possibly assignable to Earth-Sun and Earth-Moon gravitational interaction.
These observations suggest a modification of the expected probability distributions but it is very difficult to imagine any physical mechanism in the standard physics framework. Rather, a universal deformation of predicted probability distributions would be in question requiring something analogous to the transition from classical physics to quantum physics.
The hint about the nature of the modification comes from the TGD inspired quantum measurement theory proposing a description of the notion of finite measurement resolution in terms of inclusions of so called hyper-finite factors of type II1 (HFFs) and closely related quantum groups. Also p-adic physics -another key element of TGD- is expected to be involved. A modification of a given probability distribution P(nkenovert λi) for a positive integer valued variable n characterized by rational-valued parameters λi is obtained by replacing n and the integers characterizing λi with so called quantum integers depending on the quantum phase qm=exp(i2π/m). Quantum integer nq must be defined as the product of quantum counterparts pq of the primes p appearing in the prime decomposition of n. One has pq= sin(2π p/m)/sin(2π/m) for p≠ P and pq=P for p=P. m must satisfy m≥ 3, m≠ p, and m≠ 2p.
The quantum counterparts of positive integers can be negative. Therefore quantum distribution is defined first as p-adic valued distribution and then mapped by so called canonical identification I to a real distribution by the map taking p-adic -1 to P and powers Pn to P-n and other quantum primes to themselves and requiring that the mean value of n is for distribution and its quantum variant. The map I satisfies I(∑ Pn)=∑ I(Pn). The resulting distribution has peaks located periodically with periods coming as powers of P. Also periodicities with peaks corresponding to n=n+n-, n+q>0 with fixed n-q<0, are predicted. These predictions are universal and easily testable. The prime P and integer m characterizing the quantum variant of distribution can be identified from data. The shapes of the distributions obtained are qualitatively consistent with the findings of Shnoll but detailed tests are required to see whether the number theoretic predictions are correct.
The periodic dependence of the distributions would be most naturally assignable to the gravitational interaction of Earth with Sun and Moon and therefore to the periodic variation of Earth-Sun and Earth-Moon distances. The TGD inspired proposal is that the p-dic prime P and integer m characterizing the quantum distribution are determined by a process analogous to a state function reduction and their most probably values depend on the deviation of the distance R through the formulas Δ p/p≈ kpΔ R/R and Δ m/m≈ kmΔ R/R. The p-adic primes assignable to elementary particles are very large unlike the primes which could characterize the empirical distributions. The hierarchy of Planck constants allows the gravitational Planck constant assignable to the space-time sheets mediating gravitational interactions to have gigantic values and this allows p-adicity with small values of the p-adic prime P.
[63] viXra:1110.0030 [pdf] submitted on 9 Oct 2011
Authors: Dan Visser
Comments: 7 pages
A theoretical calculation with a new dark energy force formula discloses the correctness of the
experimental faster-than-light-neutrinos in the CERN-San Grasso experiment. The formulation in this paper
theoretically confirms that Einstein's Relativity could be violated. This introduces the obligation to accept
a new cosmological model, called the Double Torus hypothesis . The theoretical calculation in this paper
is based on a new momentum of dark energy force, formulated by its new force and two extra time dimensions
below the Planck scale. In detail this completely new perspective shows that the dark energy force starts
to dominate the lowest limit of the Newton-force-acceleration under specific conditions of
neutrino-oscillations. This paper theoretically calculates 62.8 nanosecond for the experimental detected
early-arrival of muon-neutrinos related to how light-in-vacuum would have arrived. This is a marvelous
close match compared to the ((60.7 ± 6.9 (stat.) ± 7.4 (sys.)) nanosecond found during the 'neutrino-flight
path' from CERN to San Grasso.
Category: Mathematical Physics
[62] viXra:1109.0038 [pdf] submitted on 18 Sep 2011
Authors: Markos Georgallides
Comments: 9 pages
This article explains the correlation between Euclidean Geometry , Complex Numbers and Physics .
A Straight line AB is continuous in Points between A and B [ i.e. all points between AB are the elements which fill AB ] , which Points are also , Nothing , Everything , and maybe Anywhere , without any Dimension , and one has to
pass the infinite points between A and B . A point C is on line AB only when exists CA+ CB = AB , or the whole AB is equal to the parts CA , CB , and this
is an equation , which differentiates geometries .
Since points have not any dimension and since only AB has dimension ( the length AB and for ÃC the length AC ) and since on ÃB exist infinite AC → AB , which
have infinite Spaces , Anti-Spaces and Sub-Spaces , then
1. Straight line AB is continuous with points as filling ( Infinitively divisible ) .
2. Straight line AB is discontinuous (discrete) with dimensional Units , ds =AB
as filling ( that is made up of finite divisible or indivisible parts the Monads ds )
or ds → AB / n , where n = 1 , 2 , → ∞ ) , and for n = ∞ then ds = 0 .
3. Straight line AB is discontinuous (discrete) with dimensional Units ds , or
ds = quantum = AB / n [ where n = 1,2,3 → ∞ , = ( a + b.i ) / n , Infinitively
divisible and keeping always the conservation of properties at end points A , B ]
as filling , and continuous with points as filling ( for n = ∞ then ds = 0 i.e.
a point ) . This is the Vector relation of Monads , ds , ( or , as Complex
Numbers in their general form , ds = a + b. i ) , which is the Dual
Nature of lines AB , ( discrete and continuous ) . So travelling on Points
( ds = 0 ) between AB one never comes to B , on the contrary travelling
with ds > 0 one comes in finite time .
4 . Achilles has to pass every point of line AB which is then as passing from
the starting point A , ds =0 , where Velocity of Achilles is v(A) = ds/dt = 0 .
The same happens for Tortoise at point B where Velocity v(T) = ds/dt = 0 .
On the contrary , Achilles passing AB on dimensional Units , ds , then Achilles velocity v(A) = ds/dt(A) is greater than that of Tortoise v(T) = ds / dt(T) .
Since in PNS , v = ∞ , T = 0 , meaning infinite velocity and Time not existing , then
Arrow AB in [PNS] is constant because AB = ds = Constant = u . 0 = ∞ . 0 Straight line AB is discontinuous (discrete) with dimensional Units ds = AB / n
where n = 1 → ∞ and continuous with points [ n = ∞ ] . Continuously on AB happens also with all discrete ds , ( This is the Dual Nature of lines ( Geometry ), discrete and continuous ) .
Monads ds = 0 → ∞ are Simultaneously , actual infinite ( because for n = ∞ then ds = [ AB / n = ∞ ] = 0 i.e. a point ) , and potential infinite , ( because for
n = 0 then ds = [ AB / n=0 ] = ∞ i.e. the straight line through AB .
Category: Mathematical Physics
[61] viXra:1109.0034 [pdf] submitted on 16 Sep 2011
Authors: Giuliano Bettini
Comments: 24 pages.
There is a lot of chattering on the Internet about Tesla waves, vacuum energy, scalar waves and so
on. Professor Meyl says he has a complete theory, experimental evidence and apparatus on these
waves. In a theoretical paper Van Vlaenderen introduced a generalization of classical
electrodynamics for the prediction of scalar field effects. It is said the Monstein has demonstrated
the physical existence of such scalar waves. NASA in a report seems to consider such waves as a
promising item to be studied. Some other papers appeared in arXiv.
I've already showed that such waves are a consequence of "generalized" Maxwell fields which
simply mean space time analytic functions not limited by the Lorenz gauge condition, but accepted
instead in a wide sense.
In this paper I remember my ideas on these waves, together with my doubts about their physical
existence. In fact, the deduction of the scalar waves equations, together with their physical
interpretation, in my opinion demonstrates nothing about the physical existence of scalar waves.
I discuss the experiment of Monstein, and suggest some other experiment.
Obviously I think that the lack of demonstration of the existence doesn't mean the demonstration of
inexistence.
Category: Mathematical Physics
[60] viXra:1108.0048 [pdf] submitted on 29 Aug 2011
Authors: Dan Visser
Comments: 4 pages. Publication is free for any institute or magazine
The Higgs mass is approximately 0.5 TeV/c2 . This is a new predicted value. This
mass value for Higgs is calculated with a new dark energy force formula, which is performing in
the hypothesis of the Double Torus, a new cosmological "model" for the universe. This "model"
embeds the Big Bang framework. The new Higgs mass is theoretically disclosed by implementing the
dimensional features of relativistic spacetime into the dimensions of the dark energy force formula and an
equalization to the lowest limit for acceleration in Newton force, being a transition where Newton breaks down
and the dark energy force takes over. The dark energy force generates gravitational movement and thus mass. This
enables to calculate a Higgs mass differently than in currently used theories.
Category: Mathematical Physics
[59] viXra:1108.0047 [pdf] submitted on 27 Aug 2011
Authors: Giuliano Bettini
Comments: 21 pages.
I present examples of applications of 3-dimensional analytic functions to electrostatics and potential
flows, mainly devoted to engineers and physicists.
Of course, the paper only suggests areas of future development, despite that a persistent idea, from
Sommerfeld on, seems to be "The powerful tool of the theory of complex functions cannot be used
in three-dimensional potential theory" (Sommerfeld, "Mechanics of Deformable Bodies",
Academic Press, 1950)
I summarize here unpublished manuscripts dated 1994.
Category: Mathematical Physics
[58] viXra:1108.0042 [pdf] submitted on 26 Aug 2011
Authors: Valeriy V. Dvoeglazov
Comments: 19 Pages
We introduce the Majorana spinors in the momentum representation.
They obey the Dirac-like equation with eight components, which has been
first introduced by Markov. Thus, the Fock space for corresponding quantum
fields is doubled (as shown by Ziino). Particular attention has been
paid to the questions of chirality and helicity (two concepts which frequently
are confused in the literature) for Dirac and Majorana states.
Category: Mathematical Physics
[57] viXra:1108.0005 [pdf] submitted on 2 Aug 2011
Authors: D.T. Froedge
Comments: 14 pages
In a previous paper we have discussed the conjecture of a variable particle rest mass, as a
function of gravitational potential (Scalar Gravitational Theory with Variable Rest Mass)
This paper discuses the implications of that theory in regard to a large neutron star, and
contrast the difference between the predicted phenomena, and Black Hole theory as put fourth by
standard GR. The validity of this theory would be established by the finding of a neutron star having a
mass greater than allowed by Black Hole theory.
Category: Mathematical Physics
[56] viXra:1107.0062 [pdf] submitted on 31 Jul 2011
Authors: D.T. Froedge
Comments: 16 pages
The purpose of this paper is to present a non-tensor theory of gravitation that
provides the equivalent equations of motion, but does not result in the issue
of black holes, non-localizable energy, or spacetime singularities. The prime
assumption is the notion that the rest mass of a particle entering a
gravitational potential is reduced in proportion to the energy gained by the
velocity increases. One could designate this development as a "catalytic"
theory in that gravitation is a vector catalyst, that converts rest energy into
kinetic energy. The total mass energy will be considered localized with the
individual mass particles, and defined relative to a given observer. No
energy will be ascribed to the field, thus there is no stress energy tensor. We
will develop the energy mass relation, and show that it can result in the
proper orbital precession as demonstrated by GR. The rest mass is not
significantly different from that of a particle defined in a stationary
asymptotically flat GR space-time, when the defining point particles via the
Komar mass. Since rest mass of a particle goes to zero on approaching a
Schwarzschild boundary, the formation of black holes becomes problematic.
Category: Mathematical Physics
[55] viXra:1107.0042 [pdf] submitted on 21 Jul 2011
Authors: Dan Visser
Comments: 4 pages
September 1 2009 a new cosmological hypothesis was proposed to imagine the
universe otherwise. Many institutional scientists still try to implement their results into the
commonly accepted Big Bang theory. I am one of the two scientists who propose a
Double Torus as a new shape for the universe. Several 'papers' are hosted at 'vixra' about
this subject. This paper adds an explanaition to these afore published papers and in
particular explains the 'dominance of matter over anti-matter', deduced from the earlier
derived 'dark energy force formula' and the perspective of the Double Torus.
Category: Mathematical Physics
[54] viXra:1107.0017 [pdf] submitted on 10 Jul 2011
Authors: Dan Visser
Comments: 5 pages
Here in this 'paper' a deeper analysis of the 'dark energy force formula' in the
Double Torus Cosmology is made. Earlier 'papers' were posted as 'pre-papers' in the
vixra-archive. These are subject to a new cosmological hypothesis, being further described
in higher order mathematics in the near future by Christopher Forbes. I have found
evidence through an unexpected interpretation of CMB results, that the 'dark energy force
formula' appears to be a functional 'recalculation-mechanism' for quantum gravity.
Category: Mathematical Physics
[53] viXra:1106.0059 [pdf] submitted on 27 Jun 2011
Authors: Sangwha-Yi
Comments: 6 pages.
In the special relativity theory, study the gauge theory in the Electro-magnetic field theory.Using that the
Electro-magnetic potential is 4-vector, treat invariant potential. And the Electro-Magnetic field theory's
the gauge theory expand.
Category: Mathematical Physics
[52] viXra:1106.0054 [pdf] submitted on 27 Jun 2011
Authors: Sangwha-Yi
Comments: 12 pages.
In the general relativity theory, instead of in the present accelerated system theory, the
coordinate transformation that the inertial coordinate system and the accelerated
coordinate system, find the new relation's coordinate transformation that used the tetrad
on the new method.And using the new relation's coordinate transformation of the new
accelerated system, organize the expansive accelerated system, the relation of the
inertial coordinate system and an accelerated system that accelerated constantly on an
inertial coordinate system.
Category: Mathematical Physics
[51] viXra:1106.0018 [pdf] submitted on 11 Jun 2011
Authors: Sergey V. Ershkov
Comments: 6 pages
Here is presented a new exact solution of Ice dynamics in Glaciers in terms of viscousplastic
theory of movements, for 2-dimensional case: x (t) = y (t). In general case, 2-D
solution of Ice dynamics could be classified as Riccati's type. Due to a very special
character of Riccati's type equation, it's general solution is proved to have a proper gap
of components of such a solution.
Category: Mathematical Physics
[50] viXra:1106.0011 [pdf] submitted on 8 Jun 2011
Authors: Giuseppe Iurato
Comments: 14 pages
In this paper, we explain the existence of a possible first-order
phase transition that may occur over the external solid crust of a pulsar,
by means of an interpretation of a particular formal model (drew from
Theoretical Astrophysics) whose thermodynamical phenomenology shows
a possible first-order phase transition (according to Landau's
Phenomenological Theory).
Category: Mathematical Physics
[49] viXra:1105.0033 [pdf] submitted on 23 May 2011
Authors: Dan Visser
Comments: 5 pages
Three new cosmological models are 'circling' the science-community: a 'Bouncing
Universe', a 'Conformal Cyclic Cosmology and a 'Double Torus Cosmology'. All new
ideas, commented anonymously and discussed institutionally. This paper wants more
cosmologists and physicists to involve the discussion openly in the media, without walking
save roads. The authors and readers are invited to involve this discussion. Which model is
true and can the mathematics be matched?
Category: Mathematical Physics
[48] viXra:1105.0022 [pdf] submitted on 15 May 2011
Authors: Dan Visser
Comments: 6 pages
This paper shows how a 'dark energy force formula' emerges five more space- and
two more time-dimensions in nature. The 'formula' is earlier described in vixra-papers,
announcing the universe is a double torus of dark energy and dark matter. The 'formula' is
a completely different force than the cosmological constant of Einstein used to explain
accelerated expansion in the big bang. With this in mind, two independent experimental
investigations has given additional proof, that the 'dark energy force formula' correlates
the independent investigations, because: 1) Five extra space-dimensions have to exist,
according to how electrons behave in graphene-experiments. 2) Computer-simulation
shows a double torus geometry, that emerges from two colliding blackholes involving a
third torus during pulsation. These results match with the postulate that the universe exists
of a double torus of dark energy and dark matter, including a 'dark energy force formula'.
Category: Mathematical Physics
[47] viXra:1105.0016 [pdf] submitted on 12 May 2011
Authors: Subhajit Ganguly
Comments: 10 pages.
Considering transport of light through space-time, following the laws of physical transactions
(viXra:1101.0035) it may be said that there must be a spreading effect on it. Over suitable distances from
a source of light, an observer's perception is bound to be affected due to this spreading. In the following
paper, these effects on the reception of a signal, due to the spreading of light are studied. Experimental
set-ups are desired to verify the actual angles of spread with their theoretical values. An experiment
regarding the minimum distance between two disturbances for them to be distinguishable is also carried
out. The energy quantum is also studied in a new light.
Category: Mathematical Physics
[46] viXra:1104.0085 [pdf] submitted on 28 Apr 2011
Authors: Dan Visser
Comments: 8 pages
For the first time an announcement is made in this paper to have found
fundamental evidence for the flyby-anomalies of six satelites earlier investigated by John
Anderson and coworkers of the Jet Propulsion Laboratory (JPL) in Pasadena USA. The
central part of this theoretical evidence exists of a 'dark matter impuls flow' being the
cause of a velocity-change for satelites during their 'flyby' along the earth. A formula is
given to calculate the velocity-change caused by dark matter. Also a dark matter constant
is suggested. The origin of the evidence is related to a 'dark energy force formula', which
is a new force in a new proposed cosmological model describing dark energy and dark
matter in a double torus geometry (TTM). Originally the 'dark energy force formula' is
discovered by an independent cosmologist and E-ingenieur, Dan Visser from Almere, the
Netherlands. Then afterwards a few 'papers' have been published in the vixra-archive
since September 1 2009 in colaboration with mathematician and physicist Christopher
Forbes (UK). These 'papers' could be considered as 'pre-exercises' in awaiting for a more
robust mathematical framework for the new proposed double torus cosmological model.
Category: Mathematical Physics
[45] viXra:1103.0115 [pdf] submitted on 30 Mar 2011
Authors: José Francisco García Juliá
Comments: 3 pages
We consider that the action at a distance is carried out by virtual carriers of the force,
which are created and annihilated in the vacuum by the field in a time less than that of
the Heisenberg's uncertainty.
Category: Mathematical Physics
[44] viXra:1103.0114 [pdf] submitted on 30 Mar 2011
Authors: Jalil Olia, Vahid Afshinmehr
Comments: 20 pages
In this paper we applied a finite element method to finding the effects on the
reverberation times of common irregularities like curved surfaces, non-parallel walls
and large open-walled ante-rooms, found in auditoria. The number of modes having
a reverberation time in a specified time interval is expressed as a function of the
total allowed degrees of freedom and it is shown that even when the number of
degrees of freedom of the model is large there is, in general, no one dominant group.
Curved surfaces in particular lead to a situation where some modes have very long
reverberation times, leading to bad acoustics. In such situations a knowledge of the
offending mode shapes give an indication on where to position absorptive material
for optimum effect.
Category: Mathematical Physics
[43] viXra:1103.0012 [pdf] submitted on 3 Mar 2011
Authors: Dan Visser, Chris Forbes
Comments:
7 pages.
Particularly this paper announces dark energy could be measured as a
cosmic backround (CMB)-frame related to a specific quantumstate of dark
energy and dark matter conform a double torus cosmology (TTM[1,2,3,4,5,6,7]).
In addition this paper also refers to a planned dark energy interferometerproject
expected to be operational in 2014[8]. Both aspects can be combined
in order to get a better expectation and interpretation of the detection of dark
energy. This paper shows dark energy to interact differently than in the
planned experiments of the dark energy interferometer-project. That is the
motive to publish this paper. Benchmark is dark energy and dark matter are
not considered in a big bang cosmology, but in a double torus universe of one
torus of dark energy, which encloses and intertwines a second torus of dark
matter (TTM-cosmology). In derivations is shown that dark energy will affect
falling (super positioned) Cesium atoms in the dark energy interferometerproject
unexpectedly: 1. It will touch the super-positioned atoms twice! ; the
cause will be the torus-geometry of the TTM-derived CMB-frame. 2. The
'Twice-touching' will vary subsequently; the cause will be a dependency on
'expansion or contraction' of the CMB-torus geometry through dynamics that
are caused by the "+" and "-" strength of the dark energy force in the TTM
and which is produced by the dark energy torus. This has motivated me to
calculate a specific value for TTM-dark energy on about 4 x 10-114 [X.s] in
6.4 x 10-48 [m2] as a new sort of spin-quantumstate [X.s], which drives the
expansion of big bang cosmology analogue to how elementary spin is a
'generator for rotation' in conventional quantumphysics. Probably this paper
might be of interest to the dark energy interferometer-project at least.
Category: Mathematical Physics
[42] viXra:1102.0037 [pdf] submitted on 21 Feb 2011
Authors: Ayind T Mahamba
Comments:
8 Pages. Submissions for FQXi essay contest.
The quest to explain the true nature of reality is one of the great scientific goals. In fact, this essay contest
asks: is Nature fundamentally continuous or discrete and how can these two different but very useful concepts be
fully reconciled? Physical science is vast, complex and remains mysterious [10]. Since long ago, the great thinkers
and scholars have dedicated their lives to the attempted comprehension1 of this reality that has become so abstract.
Throughout the centuries and through experimentation, they have established numerous laws, concepts, theories,
and principles concerning the fundamental notions of reality (centered on matter-energy and spacetime). I propose a
central theory (MIT), based on the information of, and compatible with, the contemporary scientific knowledge; the
existing fundamental relation between the "physical entities" passes through the determined quantitative
transmission (quantity) of this preserved transcendent greatness (quality). In addition to a "formal" relationship
(existence) which creates an informal description of what is real, there is a causal relationship between
"phenomena" (relativity). My informational approach has been productive in several domains where many enigma
persist; solutions for these problems must be envisaged globally, using ideas and concepts from numerous different
fields, with a coherent schema...
The "Theory of Universal Relativity" (TUR as a ToE) proposed here lays bridges between domains which, at first
glance, have nothing to do with each other; it also provides insight into how we can improve our knowledge by
understanding the interplay of complexity and simplicity. Therefore emerging from simplexity (contraction of
simplicity and complexity), reality is both digital and analogue (and between) and also more! We know there is a
strange and mysterious world that surrounds us, a world largely hidden from our senses with extra dimensions and
as a mathematical concept of reality, MIT may confirm that we are part of a cosmic hologram (a paradigm shift).
My theory has the advantage of being extremely simple, not limited to scientists because everyone can understand it
(I = 1 ± i). So, in this essay, I will try to explain why and how [1][13][48][51].
Category: Mathematical Physics
[41] viXra:1102.0032 [pdf] submitted on 19 Feb 2011
Authors: Malcolm Macleod
Comments:
3 pages.
This paper suggests a 'quantity of momentum', a square root of Planck momentum,
here referred to as Quintessence-momentum, as a natural unit that is common to both
mass and charge. In terms of this Quintessence momentum Q, alpha (Sommerfeld fine
structure constant) and c; geometrical formulas for the natural physical constants and
the electron mass are proposed. Results are consistent with CODATA 2006.
Category: Mathematical Physics
[40] viXra:1102.0027 [pdf] submitted on 17 Feb 2011
Authors: Sergey G. Fedosin
Comments:
5 pages. In Russian
The scale dimension which is discovered in the theory of infinite nesting of matter is studied from the
perspective of the physical implementation of well-studied four-and n-dimensional geometric objects.
Adding of the scale dimension to Minkowski space means the need to use the five-dimensional spacetime.
Category: Mathematical Physics
[39] viXra:1102.0009 [pdf] submitted on 7 Feb 2011
Authors: Daniele Sasso
Comments: 7 pages, 5 figures.
The criteria of stability defined in the standard theory of linear systems aren't
exhaustive and show some inconsistencies. In this article we define new
criteria of stability more consistent with real physical situations. In particular
we distinguish between static stability and dynamic stability in order to analyse
the stability of systems in the time domain and in Laplace's equivalent
domain. Let introduce then the frequency stability in order to analyse the
stability of systems in the Fourier domain.
Category: Mathematical Physics
[38] viXra:1101.0096 [pdf] submitted on 29 Jan 2011
Authors: Dan Visser, Christopher Forbes
Comments: 10 pages
This paper postulates a theoretical structure within entangled photons.
The postulate is introduced within the framework of the cosmological
Twin-Tori Model (TTM). Related papers are to be found in viXra[1,2,3,4,5,6]. After
generally derived equations and interpretations, a mass (mt) per 2π is
calculated on ~ 2.6 x 10-34 [(J.s) m2 / s]. Such a tiny spinning-forward surface
per second (torus geometry) has an energy much smaller than the Planckenergy
in Joule, suggesting a subdivision of 1043 surfaces below the
Planckscale: If one photon changes spin, the entangled photon could follow
by means of the spinning-forward tiny surface-structure within the torus
geometry (per 2π), being an information-flux for entanglement in general
below the Planckscale.
Category: Mathematical Physics
[37] viXra:1101.0052 [pdf] submitted on 16 Jan 2011
Authors: Giuliano Bettini
Comments: 10 pages
In a preceding paper we introduced a conjecture: the classification of the 32 crystal classes with 5
bits. In the present paper we will review our preceding result, and continue showing some further
interesting issues. In the paper, it is argued that bits should be identified with five basic unknown
symmetries generating these 32 groups. Probably it is not merely a coincidence that 32 means 5
bits. And probably is it not merely a coincidence that each complete subset of bits (properties)
means the holohedry of a crystal system; and each new bit means a new crystal system.
The purpose of this article was of course not to draw a conclusive theory, but to suggest ideas that,
we hope, will be useful for researchers in mathematics, group theory and crystallography.
Category: Mathematical Physics
[36] viXra:1101.0037 [pdf] submitted on 11 Jan 2011
Authors: Ke Xiao
Comments: 5 pages
The fine structure constant α = e2/hc ~ 1/137.036 and the blackbody
radiation constant αR = e2(aR/k4B)1/3 ~ 1/157.555
are linked by prime numbers. The blackbody radiation constant is a new method to measure
the fine structure constant. It also links the fine structure constant to the
Boltzmann constant.
Category: Mathematical Physics
[35] viXra:1101.0035 [pdf] submitted on 10 Jan 2011
Authors: Subhajit Ganguly
Comments: 15 pages
Considering transport or tendency ... (see paper)
Category: Mathematical Physics
[34] viXra:1012.0052 [pdf] submitted on 29 Dec 2010
Authors: Giuliano Bettini
Comments: 9 pages, in Italian
There are 32 possible combinations of symmetry operations that define the external symmetry of
crystals. These 32 possible combinations result in the 32 crystal classes.
But for a radar engineer it is inevitable to associate "32" to "5 bits".
I submit a tentative classification of the 32 crystal classes with a 5 bit classification, obviously with
a (tentative) physical meaning of each bit.
Each bit means a physical property.
Category: Mathematical Physics
[33] viXra:1012.0031 [pdf] submitted on 14 Dec 2010
Authors: Elemér E Rosinger
Comments: 9 pages
A class of non-Cartesian physical systems, [7], are those whose
composite state spaces are given by significantly extended tensor products.
A more detailed presentation of the way such extended tensor products
are constructed is offered, based on a step by step comparison with the
construction of usual tensor products. This presentation clarifies the
extent to which the extended tensor products are indeed more general
than the usual ones.
Category: Mathematical Physics
[32] viXra:1012.0020 [pdf] submitted on 8 Dec 2010
Authors: Elemer E Rosinger
Comments: 6 pages
The following open problem is presented and motivated : Are there
physical systems whose state spaces do not compose according to either
the Cartesian product, as classical systems do, or the usual tensor
product, as quantum systems do ?
Category: Mathematical Physics
[31] viXra:1012.0014 [pdf] submitted on 4 Dec 2010
Authors: Elemer E Rosinger
Comments: 28 pages
Much of Mathematics, and therefore Physics as well, have been
limited by four rather consequential restrictions. Two of them are ancient
taboos, one is an ancient and no longer felt as such bondage, and the
fourth is a surprising omission in Algebra. The paper brings to the
attention of those interested these four restrictions, as well as the fact
that each of them has by now ways, even if hardly yet known ones, to
overcome them.
Category: Mathematical Physics
[30] viXra:1012.0002 [pdf] submitted on 1 Dec 2010
Authors: Arkadiusz Jadczyk
Comments: 7 pages, To appear in Advances in Applied Clifford Algebras
We study in some detail the structure of the projective quadric Q'
obtained by taking the quotient of the isotropic cone in a standard pseudohermitian
space Hp,q with respect to the positive real numbers R+ and,
further, by taking the quotient ~Q = Q'/U(1). The case of signature (1. 1)
serves as an illustration. ~Q is studied as a compactification of RxHp-1,q-1
Category: Mathematical Physics
[29] viXra:1011.0039 [pdf] submitted on 17 Nov 2010
Authors: Guy Moore, Richard Moore
Comments: 40 pages
Our obtaining the analytical equations for the gravitation of a particular type of
mathematical annulus, which we called a 'Special Gravitating Annulus' (SGA), greatly
facilitates studying its orbital properties by computer programming. This includes
isomorphism, periodic and chaotic polar orbits, and orbits in three dimensions.
We provide further insights into the gravitational properties of this annulus and
describe our computer algorithms and programs. We study a number of periodic orbits,
giving them names to aid identification.
'Ellipses extraordinaires' which are bisected by the annulus, have no gravitating
matter at either focus and represent a fundamental departure from the normal association
of elliptical orbits with Keplerian motion. We describe how we came across this type of
orbit and the analysis we performed. We present the simultaneous differential equations
of motion of 'ellipses extraordinaires' and other orbits as a mathematical challenge. The
'St.Louis Gateway Arch' orbit contains two 'instantaneous static points' (ISP).
Polar elliptical orbits can wander considerably without tending to form other kinds
of orbit. If this type of orbit is favoured then this gives a similarity to spiral galaxies
containing polar orbiting material.
Annular oscillatory orbits and rotating polar elliptical orbits are computed in
isometric projection. A 'daisy' orbit is computed in stereo-isometric projection.
The singularity at the centre of the SGA is discussed in relation to mechanics and
computing, and it appears mathematically different from a black hole.
In the Appendix, we prove by a mathematical method that a thin plane self-gravitating
Newtonian annulus, free from external influence, exhibiting radial gravitation that varies
inversely with the radius in the annular plane, must have an area mass density which
also varies inversely with the radius and this exact solution is the only exact solution.
Category: Mathematical Physics
[28] viXra:1010.0063 [pdf] submitted on 29 Oct 2010
Authors: Dan Visser
Comments: 7 pages
A new surface energy-value for dark matter is calculated, derivated from a
perspective of a "higher order universe". A universe of dark energy, dark- and visible
matter, and a dark energy force. A fundamental connection between dark matter and
visible matter is related to dark energy (viXra-paper 1010.0014 in particular is the
reference for this novum [5]. The surface energy-density of dark matter seems to be a
factor 5 to 20 times higher than earlier predicted value-ranges by the CDMS-project and
the Fermi-satelite. Also the produced energies through particle-collissions by LHC CERN
will not be enough to achieve the dark matter surface energy-value. The "fact" some of
these projects have announced some vaque "bliebs" might be due to a new phenomenon in
the search of dark matter. It could be caused by "three dimensional time", which is
embedded as a "new duality" in the new model, the "Twin-Tori cosmological Model
(TTM)"[1,2,3,4]. The "three dimensional time" might cause dark matter taking unknown
paths before detection. This paper has calculated the surface energy-density value for
dark matter on 1 TeV in a surface of 6.4 x 10 -48 [m2].
Category: Mathematical Physics
[27] viXra:1010.0036 [pdf] submitted on 24 Oct 2010
Authors: Debayan Dasgupta
Comments: 10 pages
The main purpose of this paper is to show the application of mathematical system
of quaternions in physics. We show a basic way of generating a quaternion
operator and a method of obtaining the Schrodinger's equation using this
operator matrix. Then we investigate the various probable uses of the coefficient
matrix to scale relativity and spacetime quantization.
Category: Mathematical Physics
[26] viXra:1010.0014 [pdf] submitted on 7 Oct 2010
Authors: Dan Visser
Comments: 5 pages
A new cosmological model, named the Twin-Tori Model (TTM)[1], postulates a
dark energy force Fde , which empowers the dynamic of a lower order universe, well
known as the big bang. In this paper I introduce the 1st derivative F'de of this dark energy
force to reveal deeper properties of the TTM, such as: why quantummechanics exists in
the big bang, why dark matter and visible matter are equally responsible for gravity in
galaxies for 1/4 of the density of dark matter at a specific length, why the big bang universe
is recalculated by subquantumlevel-information below the Plancklength, and why the
impression of space-expansion is due to the higher order cosmological model TTM.
Category: Mathematical Physics
[25] viXra:1009.0007 [pdf] submitted on 3 Sep 2010
Authors: D.T. Froedge
Comments:
16 pages 38 equations 98kb
The purpose of this paper is to illustrate a fundamental, multiple particle,
system equation for which the Klein-Gordon-Dirac-Schrödinger equations are
single particle special cases. In the same manner that eigenvalues of the
Schrödinger equation represents energy levels of an interacting atomic system,
eigenvalues represent particle energies in an interacting system of particles. An
equation is proposed that has vector solutions defined in Dirac, or Clifford
algebra, that treats a collection of particles as a single system..The proposed
solution is a descriptor of a symmetric, light speed expanding group of
interacting particles having real, as well as the familiar QM constituents.
Category: Mathematical Physics
[24] viXra:1007.0031 [pdf] submitted on 19 Jul 2010
Authors: T. E. Raptis
Comments: 13 pages.
We report on a new general class of solutions of the Beltrami equation, with
special characteristics. We also provide examples of solutions that also satisfy Maxwell equations.
A subset of these solutions can be isolated which corresponds to "gauge" fields. A special
projective geometry of vacuum fields is also revealed and discussed.
Category: Mathematical Physics
[23] viXra:1006.0070 [pdf] submitted on 30 Jun 2010
Authors: Carey R Carlson
Comments: 16 pages.
Quantum theory is reconstructed using standalone causal sets. The frequency ratios
inherent in causal sets are used to define energy-ratios, implicating the causal link as the
quantum of action. Space-time and its particle-like sequences are then constructed from
causal links. A 4-D time-lattice structure is defined and then used to model neutrinos and
electron clouds, which together constitute a 4-D manifold. A 6-D time-lattice is used to
model the nucleons. The integration of the nucleus with its electron cloud affords
calculation of the mass-ratio of the proton (or the neutron) with respect to the electron.
Arrow diagrams, along with several ball-and-stick models, are used to streamline the
presentation.
Category: Mathematical Physics
[22] viXra:1006.0052 [pdf] submitted on 21 Jun 2010
Authors: Fredy Zypman
Comments:
2 pages
Formulas connecting toroidal functions and elliptical functions are useful in
various areas of physics. In solving a problem in electrostatics we run across
an error in the Handbook of mathematical functions of Abramowitz and
Stegun. In this paper we report the details.
Category: Mathematical Physics
[21] viXra:1006.0042 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 13 Pages.
This appendix contains basic facts about CP2 as a symmetric space and Kähler manifold. The
coding of the standard model symmetries to the geometry of CP2, the physical interpretation of
the induced spinor connection in terms of electro-weak gauge potentials, and basic facts about
induced gauge fields are discussed
Category: Mathematical Physics
[20] viXra:1006.0041 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 5 Pages.
The original justification for the hierarchy of Planck constants came from the indications that
Planck constant could have large values in both astrophysical systems involving dark matter and
also in biology. The realization of the hierarchy in terms of the singular coverings and possibly also
factor spaces of CD and CP2 emerged from consistency conditions. It however seems that TGD
actually predicts this hierarchy of covering spaces. The extreme non-linearity of the field equations
defined by Kähler action means that the correspondence between canonical momentum densities
and time derivatives of the imbedding space coordinates is 1-to-many. This leads naturally to the
introduction of the covering space of CD x CP2, where CD denotes causal diamond defined as
intersection of future and past directed light-cones.
Category: Mathematical Physics
[19] viXra:1006.0040 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 13 Pages.
The notion of electric magnetic duality emerged already two decades ago in the attempts to
formulate the Kähler geometry of the "world of classical worlds". Quite recently a considerable
step of progress took place in the understanding of this notion. This concept leads to the
identification of the physical particles as string like objects defined by magnetic charged wormhole
throats connected by magnetic
ux tubes. The second end of the string contains particle having
electroweak isospin neutralizing that of elementary fermion and the size scale of the string is
electro-weak scale would be in question. Hence the screening of electro-weak force takes place
via weak confinement. This picture generalizes to magnetic color confinement. Electric-magnetic
duality leads also to a detailed understanding of how TGD reduces to almost topological quantum
field theory. A surprising outcome is the necessity to replace CP2 Kähler form in Kähler action
with its sum with S2 Kähler form.
Category: Mathematical Physics
[18] viXra:1006.0039 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 16 Pages.
Generalized Feynman diagrams have become the central notion of quantum TGD and one might even say that space-time surfaces can be identified as generalized Feynman diagrams. The challenge is to assign a precise mathematical content for this notion, show their mathematical existence, and develop a machinery for calculating them. Zero energy ontology has led to a dramatic progress in the understanding of generalized Feynman diagrams at the level of fermionic degrees of freedom. In particular, manifest finiteness in these degrees of freedom follows trivially from the basic identifications as does also unitarity and non-trivial coupling constant evolution. There are however several formidable looking challenges left.
[17] viXra:1006.0038 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 37 Pages.
Physics as a generalized number theory program involves three threads: various p-adic physics
and their fusion together with real number based physics to a larger structure, the attempt to
understand basic physics in terms of classical number fields, and infinite primes discussed in this
article.
The construction of infinite primes is formally analogous to a repeated second quantization of
an arithmetic quantum field theory by taking the many particle states of previous level elementary
particles at the new level. Besides free many particle states also the analogs of bound states
appear. In the representation in terms of polynomials the free states correspond to products of
first order polynomials with rational zeros. Bound states correspond to nth order polynomials
with non-rational but algebraic zeros.
The construction can be generalized to classical number fields and their complexifications
obtained by adding a commuting imaginary unit. Special class corresponds to hyper-octonionic
primes for which the imaginary part of ordinary octonion is multiplied by the commuting
imaginary unit so that one obtains a sub-space M8 with Minkowski signature of metric. Also in this
case the basic construction reduces to that for rational or complex rational primes and more
complex primes are obtained by acting using elements of the octonionic automorphism group which
preserve the complex octonionic integer property.
Can one map infinite primes/integers/rationals to quantum states? Do they have space-time
surfaces as correlates? Quantum classical correspondence realized in terms of modified Dirac
operator implies that if infinite rationals can be mapped to quantum states then the mapping of
quantum states to space-time surfaces automatically gives the map to space-time surfaces. The
question is therefore whether the mapping to quantum states defined by WCW spinor fields is
possible. A natural hypothesis is that number theoretic fermions can be mapped to real fermions
and number theoretic bosons to WCW ("world of classical worlds") Hamiltonians. The crucial
observation is that one can construct infinite hierarchy of hyper-octonionic units by forming
ratios of infinite integers such that their ratio equals to one in real sense: the integers have
interpretation as positive and negative energy parts of zero energy states. One can construct also
sums of these units with complex coefficients using commuting imaginary unit and these sums
can be normalized to unity and have interpretation as states in Hilbert space. These units can
be assumed to possess well defined standard model quantum numbers. It is possible to map the
quantum number combinations of WCW spinor fields to these states. Hence the points of M8
can be said to have infinitely complex number theoretic anatomy so that quantum states of the
universe can be mapped to this anatomy. One could talk about algebraic holography or number
theoretic Brahman=Atman identity.
One can also ask how infinite primes relate to the p-adicization program and to the hierarchy of
Planck constants. The key observation is that infinite primes are in one-one correspondence with
rational numbers at the lower level of hierarchy. At the first level of hierarchy the p-adic norm
with respect to p-adic prime for this rational gives power p-n so that one has two powers of p - pn+
and pn- since two infinite primes corresponding to fermionic vacua X±1, where X is the product
of all primes at given level of hierarchy, characterize the partonic 2-surface. The proposal inspired
by the p-adicization program is that Δφ = 2π/pn defines angle measurement resolution crucial in
the construction of p-adic variants of WCW ("world of classical world") as a union of symmetric
coset spaces by starting from discrete variants of the real counterpart of symmetric space having
common points with tis p-adic variant. The two measurement resolutions correspond to CD and
CP2 degrees of freedom. The hierarchy of Planck constants generalizes imbedding space to a
book like structure with pages identified in terms of singular coverings and factor spaces of CD
and CP2. There are good arguments suggesting that only coverings characterized by integers na
and nbare realized. The identifications n
Category: Mathematical Physics
[16] viXra:1006.0037 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 28 Pages.
Physics as a generalized number theory program involves three threads: various p-adic physics
and their fusion together with real number based physics to a larger structure, the attempt to
understand basic physics in terms of classical number fields discussed in this article, and infinite
primes whose construction is formally analogous to a repeated second quantization of an arithmetic
quantum field theory.
In this article the connection between standard model symmetries and classical number fields
is discussed. The basis vision is that the geometry of the infinite-dimensional WCW ("world of
classical worlds") is unique from its mere existence. This leads to its identification as union of
symmetric spaces whose Kähler geometries are fixed by generalized conformal symmetries. This
fixes space-time dimension and the decomposition M4 x S and the idea is that the symmetries
of the Kähler manifold S make it somehow unique. The motivating observations are that the
dimensions of classical number fields are the dimensions of partonic 2-surfaces, space-time surfaces,
and imbedding space and M8 can be identified as hyper-octonions- a sub-space of complexified
octonions obtained by adding a commuting imaginary unit. This stimulates some questions.
Could one understand S = CP2 number theoretically in the sense that M8 and H = M4 x CP2
be in some deep sense equivalent ("number theoretical compactification" or M8 - H duality)?
Could associativity define the fundamental dynamical principle so that space-time surfaces could
be regarded as associative or co-associative (defined properly) sub-manifolds of M8 or equivalently
of H.
One can indeed define the associativite (co-associative) 4-surfaces using octonionic representation
of gamma matrices of 8-D spaces as surfaces for which the modified gamma matrices span
an associate (co-associative) sub-space at each point of space-time surface. Also M8 - H duality
holds true if one assumes that this associative sub-space at each point contains preferred plane of
M8 identifiable as a preferred commutative or co-commutative plane (this condition generalizes
to an integral distribution of commutative planes in M8). These planes are parametrized by CP2
and this leads to M8 - H duality.
WCW itself can be identified as the space of 4-D local sub-algebras of the local Clifford
algebra of M8 or H which are associative or co-associative. An open conjecture is that this
characterization of the space-time surfaces is equivalent with the preferred extremal property of
Kähler action with preferred extremal identified as a critical extremal allowing infinite-dimensional
algebra of vanishing second variations.
Category: Mathematical Physics
[15] viXra:1006.0036 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 51 Pages.
Physics as a generalized number theory program involves three threads: various p-adic physics
and their fusion together with real number based physics to a larger structure, the attempt to
understand basic physics in terms of classical number fields (in particular, identifying associativity
condition as the basic dynamical principle), and infinite primes whose construction is formally
analogous to a repeated second quantization of an arithmetic quantum field theory. In this article
p-adic physics and the technical problems relates to the fusion of p-adic physics and real physics
to a larger structure are discussed.
The basic technical problems relate to the notion of definite integral both at space-time level,
imbedding space level and the level of WCW (the "world of classical worlds"). The expressibility
of WCW as a union of symmetric spacesleads to a proposal that harmonic analysis of symmetric
spaces can be used to define various integrals as sums over Fourier components. This leads to the
proposal the p-adic variant of symmetric space is obtained by a algebraic continuation through a
common intersection of these spaces, which basically reduces to an algebraic variant of coset space
involving algebraic extension of rationals by roots of unity. This brings in the notion of angle
measurement resolution coming as Δφ = 2π/pn for given p-adic prime p. Also a proposal how
one can complete the discrete version of symmetric space to a continuous p-adic versions emerges
and means that each point is effectively replaced with the p-adic variant of the symmetric space
identifiable as a p-adic counterpart of the real discretization volume so that a fractal p-adic variant
of symmetric space results.
If the Kähler geometry of WCW is expressible in terms of rational or algebraic functions, it
can in principle be continued the p-adic context. One can however consider the possibility that
that the integrals over partonic 2-surfaces defining
ux Hamiltonians exist p-adically as Riemann
sums. This requires that the geometries of the partonic 2-surfaces effectively reduce to finite
sub-manifold geometries in the discretized version of δM+4. If Kähler action is required
to exist p-adically same kind of condition applies to the space-time surfaces themselves. These
strong conditions might make sense in the intersection of the real and p-adic worlds assumed to
characterized living matter.
Category: Mathematical Physics
[14] viXra:1006.0035 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 34 Pages.
There are three separate approaches to the challenge of constructing WCW Kähler geometry
and spinor structure. The first approach relies on a direct guess of Kähler function. Second
approach relies on the construction of Kähler form and metric utilizing the huge symmetries
of the geometry needed to guarantee the mathematical existence of Riemann connection. The
third approach discussed in this article relies on the construction of spinor structure based on the
hypothesis that complexified WCW gamma matrices are representable as linear combinations of
fermionic oscillator operator for the second quantized free spinor fields at space-time surface and
on the geometrization of super-conformal symmetries in terms of spinor structure. This implies a
geometrization of fermionic statistics.
The basic philosophy is that at fundamental level the construction of WCW geometry reduces
to the second quantization of the induced spinor fields using Dirac action. This assumption
is parallel with the bosonic emergence stating that all gauge bosons are pairs of fermion and
antifermion at opposite throats of wormhole contact. Vacuum function is identified as Dirac
determinant and the conjecture is that it reduces to the exponent of Kähler function. In order
to achieve internal consistency induced gamma matrices appearing in Dirac operator must be
replaced by the modified gamma matrices defined uniquely by Kähler action and one must also
assume that extremals of Kähler action are in question so that the classical space-time dynamics
reduces to a consistency condition. This implies also super-symmetries and the fermionic oscillator
algebra at partonic 2-surfaces has intepretation as N = 1 generalization of space-time supersymmetry
algebra different however from standard SUSY algebra in that Majorana spinors are
not needed. This algebra serves as a building brick of various super-conformal algebras involved.
The requirement that there exist deformations giving rise to conserved Noether charges requires
that the preferred extremals are critical in the sense that the second variation of the Kähler action
vanishes for these deformations. Thus Bohr orbit property could correspond to criticality or at
least involve it.
Quantum classical correspondence demands that quantum numbers are coded to the properties
of the preferred extremals given by the Dirac determinant and this requires a linear coupling
to the conserved quantum charges in Cartan algebra. Effective 2-dimensionality allows a measurement
interaction term only in 3-D Chern-Simons Dirac action assignable to the wormhole
throats and the ends of the space-time surfaces at the boundaries of CD. This allows also to
have physical propagators reducing to Dirac propagator not possible without the measurement
interaction term. An essential point is that the measurement interaction corresponds formally
to a gauge transformation for the induced Kähler gauge potential. If one accepts the weak form
of electric-magnetic duality Kähler function reduces to a generalized Chern-Simons term and the
effect of measurement interaction term to Kähler function reduces effectively to the same gauge
transformation.
The basic vision is that WCW gamma matrices are expressible as super-symplectic charges at
the boundaries of CD. The basic building brick of WCW is the product of infinite-D symmetric
spaces assignable to the ends of the propagator line of the generalized Feynman diagram. WCW
Kähler metric has in this case "kinetic" parts associated with the ends and "interaction" part
between the ends. General expressions for the super-counterparts of WCW
ux Hamiltoniansand
for the matrix elements of WCW metric in terms of their anticommutators are proposed on basis
of this picture.
Category: Mathematical Physics
[13] viXra:1006.0034 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 26 Pages.
There are three separate approaches to the challenge of constructing WCW Kähler geometry
and spinor structure. The first one relies on a direct guess of Kähler function. Second approach
relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry
needed to guarantee the mathematical existence of Riemann connection. The third approach relies
on the construction of spinor structure assuming that complexified WCW gamma matrices are
representable as linear combinations of fermionic oscillator operator for the second quantized free
spinor fields at space-time surface and on the geometrization of super-conformal symmetries in
terms of spinor structure.
In this article the construction of Kähler form and metric based on symmetries is discussed.
The basic vision is that WCW can be regarded as the space of generalized Feynman diagrams with
lines thickned to light-like 3-surfaces and vertices identified as partonic 2-surfaces. In zero energy
ontology the strong form of General Coordinate Invariance (GCI) implies effective 2-dimensionality
and the basic objects are pairs partonic 2-surfaces X2 at opposite light-like boundaries of causal
diamonds (CDs).
The hypothesis is that WCW can be regarded as a union of infinite-dimensional symmetric
spaces G/H labeled by zero modes having an interpretation as classical, non-quantum
uctuating
variables. A crucial role is played by the metric 2-dimensionality of the light-cone boundary
δM+4
+ and of light-like 3-surfaces implying a generalization of conformal invariance. The group
G acting as isometries of WCW is tentatively identified as the symplectic group of
δM+4 x CP2
localized with respect to X2. H is identified as Kac-Moody type group associated with isometries
of H = M+4 x CP2 acting on light-like 3-surfaces and thus on X2.
An explicit construction for the Hamiltonians of WCW isometry algebra as so called
ux
Hamiltonians is proposed and also the elements of Kähler form can be constructed in terms of
these. Explicit expressions for WCW
ux Hamiltonians as functionals of complex coordinates of
the Cartesisian product of the infinite-dimensional symmetric spaces having as points the partonic
2-surfaces defining the ends of the the light 3-surface (line of generalized Feynman diagram) are
proposed.
Category: Mathematical Physics
[12] viXra:1006.0033 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 38 Pages.
There are two basic approaches to quantum TGD. The first approach, which is discussed in
this article, is a generalization of Einstein's geometrization program of physics to an infinitedimensional
context. Second approach is based on the identification of physics as a generalized
number theory. The first approach relies on the vision of quantum physics as infinite-dimensional
Kähler geometry for the "world of classical worlds" (WCW) identified as the space of 3-surfaces
in in certain 8-dimensional space. There are three separate approaches to the challenge of constructing
WCW Kähler geometry and spinor structure. The first approach relies on direct guess
of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing
the huge symmetries of the geometry needed to guarantee the mathematical existence of
Riemann connection. The third approach relies on the construction of spinor structure based on
the hypothesis that complexified WCW gamma matrices are representable as linear combinations
of fermionic oscillator operator for second quantized free spinor fields at space-time surface and
on the geometrization of super-conformal symmetries in terms of WCW spinor structure.
In this article the proposal for Kähler function based on the requirement of 4-dimensional General
Coordinate Invariance implying that its definition must assign to a given 3-surface a unique
space-time surface. Quantum classical correspondence requires that this surface is a preferred extremal
of some some general coordinate invariant action, and so called Kähler action is a unique
candidate in this respect. The preferred extremal has intepretation as an analog of Bohr orbit
so that classical physics becomes and exact part of WCW geometry and therefore also quantum
physics.
The basic challenge is the explicit identification of WCW Kähler function K. Two assumptions
lead to the identification of K as a sum of Chern-Simons type terms associated with the ends of
causal diamond and with the light-like wormhole throats at which the signature of the induced
metric changes. The first assumption is the weak form of electric magnetic duality. Second
assumption is that the Kähler current for preferred extremals satisfies the condition jK ^ djK = 0
implying that the
ow parameter of the
ow lines of jK defines a global space-time coordinate.
This would mean that the vision about reduction to almost topological QFT would be realized.
Second challenge is the understanding of the space-time correlates of quantum criticality.
Electric-magnetic duality helps considerably here. The realization that the hierarchy of Planck
constant realized in terms of coverings of the imbedding space follows from basic quantum TGD
leads to a further understanding. The extreme non-linearity of canonical momentum densities as
functions of time derivatives of the imbedding space coordinates implies that the correspondence
between these two variables is not 1-1 so that it is natural to introduce coverings of CD x CP2.
This leads also to a precise geometric characterization of the criticality of the preferred extremals.
Category: Mathematical Physics
[11] viXra:1006.0032 [pdf] submitted on 16 Jun 2010
Authors: Matti Pitkänen
Comments: 32 Pages.
There are two basic approaches to the construction of quantum TGD. The first approach
relies on the vision of quantum physics as infinite-dimensional Kähler geometry for the "world of
classical worlds" identified as the space of 3-surfaces in in certain 8-dimensional space. Essentially
a generalization of the Einstein's geometrization of physics program is in question. The second
vision is the identification of physics as a generalized number theory. This program involves
three threads: various p-adic physics and their fusion together with real number based physics
to a larger structure, the attempt to understand basic physics in terms of classical number fields
(in particular, identifying associativity condition as the basic dynamical principle), and infinite
primes whose construction is formally analogous to a repeated second quantization of an arithmetic
quantum field theory. In this article brief summaries of physics as infinite-dimensional geometry
and generalized number theory are given to be followed by more detailed articles.
Category: Mathematical Physics
[10] viXra:1003.0027 [pdf] submitted on 6 Mar 2010
Authors: Florentin Smarandache, V. Christianto, Fu Yuhua, Radi I. Khrapko, J. Hutchison
Comments: 147 pages
The reader will find herein a collection of unsolved problems in mathematics
and the physical sciences. Theoretical and experimental domains have each
been given consideration. The authors have taken a liberal approach in their
selection of problems and questions, and have not shied away from what
might otherwise be called speculative, in order to enhance the opportunities
for scientific discovery.
Progress and development in our knowledge of the structure, form and function
of the Universe, in the true sense of the word, its beauty and power, and
its timeless presence and mystery, before which even the greatest intellect is
awed and humbled, can spring forth only from an unshackled mind combined
with a willingness to imagine beyond the boundaries imposed by that
ossified authority by which science inevitably becomes, as history teaches
us, barren and decrepit.
Revealing the secrets of Nature, so that we truly see 'the sunlit plains extended,
and at night the wondrous glory of the everlasting stars', requires
far more than mere technical ability and mechanical dexterity learnt form
books and consensus. The dustbin of scientific history is replete with discredited
consensus and the grand reputations of erudite reactionaries. Only
by boldly asking questions, fearlessly, despite opposition, and searching for
answers where most have not looked for want of courage and independence
of thought, can one hope to discover for one's self. From nothing else can
creativity blossom and grow, and without which the garden of science can
only aspire to an overpopulation of weeds.
Category: Mathematical Physics
[9] viXra:1001.0044 [pdf] submitted on 28 Jan 2010
Authors: Constantinos Ragazas
Comments: 8 pages
We derive a characterization of simple exponential functions that has the exact
mathematical form to Planck's Formula for blackbody radiation in Quantum Physics.
Category: Mathematical Physics
[8] viXra:1001.0002 [pdf] submitted on 6 Jan 2010
Authors: Elemér E Rosinger
Comments: 17 pages.
A simple and rather general mathematical model of the phenomenon
of information is presented, followed by several examples and
comments.
Category: Mathematical Physics
[7] viXra:0910.0069 [pdf] submitted on 31 Oct 2009
Authors: Vladimir I. Smirnov
Comments: 34 pages, Russian and English versions included
It is identified the new class of invariants which values are constant at change of value of an inde-pendent variable.
Their properties and a deriving method are shown on already known and still un-known instances, concerning to various
areas of physics. In particular, new invariants (50), (55) and (57) for the straight lines intersected in one point on
a plane have been discovered. Besides, the re-quest for detection of the third (not dependent on two already known) an
invariant (31) electromag-netic fields for a special case of the special theory of relativity is made.
Category: Mathematical Physics
[6] viXra:0910.0016 [pdf] submitted on 11 Oct 2009
Authors: Chris Forbes
Comments: 10 pages
In this, a follow up to a previous paper 'A Short Article On A Newly
Proposed Model Of Cosmology' (viXra:0909.0005), some of the basic
mathematical structures to be used in the formulation of the model are
shown, and several advantages are discussed. The paper then takes a
more phenomenological approach and several simple (1+1) dimensional
models are explored.
Category: Mathematical Physics
[5] viXra:0909.0026 [pdf] submitted on 9 Sep 2009
Authors: Bruce Rout
Comments: 13 pages
This paper examines the difference between infinite and finite domains
of a Stefan Problem. It is pointed out that attributes of solutions
to the Diffusion Equation suggest assumptions of an infinite domain
are invalid during initial times for finite domain Stefan Problems. The
paper provides a solution for initial and early times from an analytical
approach using a perturbation. This solution can then easily be applied
to numerical models for later times. The differences of the two domains
are examined and discussed.
Category: Mathematical Physics
[4] viXra:0908.0045 [pdf] submitted on 10 Aug 2009
Authors: Hamid V. Ansari
Comments: 7 pages
It is shown that the wave equation cannot be solved for the general
spreading of the cylindrical wave using the method of separation of variables.
But an equation is presented in case of its solving the above act
will have occurred. Also using this equation the above-mentioned general
spreading of the cylindrical wave for large distances is obtained which
contrary to what is believed consists of arbitrary functions.
Category: Mathematical Physics
[3] viXra:0908.0001 [pdf] submitted on 1 Aug 2009
Authors: Vladislav Konovalov
Comments: 12 pages
In the article the new calculuses are offered similar differential and integral, but differing,
that in them the analysis of the previous and subsequent values of a function is made. The
new calculuses allow to decide problems, the solution which one with usage customary
differential and integral calculus is impossible.
Category: Mathematical Physics
[2] viXra:0907.0002 [pdf] submitted on 9 Jul 2009
Authors: Philip Gibbs
Comments: 5 pages, published in Prespacetime Journal, V5
We prove that any 3x3 unitary matrix can be transformed to a magic matrix by multiplying its rows
and columns by phase factors. A magic matrix is defined as one for which the sum of the elements in any row
or column add to the same value. This result is relevant to recent observations on particle mixing matrices.
Category: Mathematical Physics
[1] viXra:0812.0008 [pdf] submitted on 21 Dec 2008
Authors: R. M. Kiehn
Comments: recovered from sciprint.org
Finally, I have found time to think about, and the incentive to study, how the
field theory of Topological thermodynamics, electrodynamics, and hydrodynamics
can be compared to field theory concepts that have been developed by Lagrangian
methods, for both the classic and quantum mechanical varieties. For more than
30 years I have known that Cartan's topological methods could be applied to
dissipative systems; the methods based on diffeomorphic-invariant Lagrangian
field theories can not. The incentive came when I realized that the topological
methods of Cartan gave dynamical results that can explain "symmetry breaking"
and quantization in terms of continuous topological evolution.
Category: Mathematical Physics
[41] viXra:1111.0105 [pdf] replaced on 2012-01-25 05:58:47
Authors: Jose Javier garcia
Comments: 25 Pages.
We give a possible interpretation of the Xi-function of Riemann as the Functional determinant
for a certain Hamiltonian quantum operator in one dimension for a real-valued function V(x) , this
potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function,
through the paper we will assume that the reduced Planck constant is defined in units where and that the
mass is .In this case the Energies of the Hamiltonian operator will be the square of the imaginary part
of the Riemann Zeros Also trhough this paper we may refer to the Hamiltonian Operator whose Energies are
the square of the imaginary part of the Riemann Zeros as or (square) in the same case we will refer to
the potential inside this Hamiltonian either as or to simplify notation.
Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical
Approximation , Trace formula , Quantum chaos.
Category: Mathematical Physics
[40] viXra:1111.0105 [pdf] replaced on 2011-12-14 13:56:54
Authors: Jose Javier Garcia Moreta
Comments: 23 Pages. there is an ERROR, whenever it says 'Whose zeros' should we put 'Whose Energies' (A Hamiltonian has no zeros)H
We give a possible interpretation of the Xi-function of Riemann as the Functional determinant for a certain Hamiltonian quantum operator in one dimension for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where and that the mass is .In this case the Energies of the Hamiltonian operator will be the square of the imaginary part of the Riemann Zeros Also trhough this paper we may refer to the Hamiltonian Operator whose Energies are the square of the imaginary part of the Riemann Zeros as or (square) in the same case we will refer to the potential inside this Hamiltonian either as or to simplify notation.
Category: Mathematical Physics
[39] viXra:1111.0105 [pdf] replaced on 2011-12-04 07:54:17
Authors: Jose Javier Garcia Moreta
Comments: 23 Pages.
We give a possible interpretation of the Xi-function of Riemann as the Functional determinant for a certain Hamiltonian quantum operator in one dimension for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where and that the mass is
Category: Mathematical Physics
[38] viXra:1111.0091 [pdf] replaced on 2012-01-30 08:18:27
Authors: Matti Pitkänen
Comments: 24 Pages.
The arguments of this article support the view that in TGD Universe number theoretic and geometric Langlands conjectures could be understood very naturally. The basic notions are following.
There are several steps leading from G to its twisted quantum Yangian. The first step replaces point like particles with partonic 2-surfaces: this brings in Kac-Moody character. The second step brings in finite measurement resolution meaning that Kac-Moody type algebra is replaced with its quantum version. The third step brings in zero energy ontology: one cannot treat single partonic surface or string world sheet as independent unit: always the collection of partonic 2-surfaces and corresponding string worlds sheets defines the geometric structure so that multilocality and therefore quantum Yangian algebra with multilocal generators is unavoidable.
In finite measurement resolution geometric Langlands duality and number theoretic Langlands duality are very closely related since partonic 2-surface is effectively replaced with the punctures representing the ends of braid strands and the orbit of this set under a discrete subgroup of G defines effectively a collection of "rational" 2-surfaces. The number of the "rational" surfaces in geometric Langlands conjecture replaces the number of rational points of partonic 2-surface in its number theoretic variant. The ability to compute both these numbers is very relevant for quantum TGD.
[37] viXra:1111.0090 [pdf] replaced on 2012-01-30 08:22:30
Authors: Matti Pitkänen
Comments: 16 Pages.
Infinite primes is a purely TGD inspired notion. The notion of infinity is number theoretical and infinite primes have well defined divisibility properties. One can partially order them by the real norm. p-Adic norms of infinite primes are well defined and finite. The construction of infinite primes is a hierarchical procedure structurally equivalent to a repeated second quantization of a supersymmetric arithmetic quantum field theory. At the lowest level bosons and fermions are labelled by ordinary primes. At the next level one obtains free Fock states plus states having interpretation as bound many particle states. The many particle states of a given level become the single particle states of the next level and one can repeat the construction ad infinitum. The analogy with quantum theory is intriguing and I have proposed that the quantum states in TGD Universe correspond to octonionic generalizations of infinite primes. It is interesting to compare infinite primes (and integers) to the Cantorian view about infinite ordinals and cardinals. The basic problems of Cantor's approach which relate to the axiom of choice, continuum hypothesis, and Russell's antinomy: all these problems relate to the definition of ordinals as sets. In TGD framework infinite primes, integers, and rationals are defined purely algebraically so that these problems are avoided. It is not surprising that these approaches are not equivalent. For instance, sum and product for Cantorian ordinals are not commutative unlike for infinite integers defined in terms of infinite primes.
Set theory defines the foundations of modern mathematics. Set theory relies strongly on classical physics, and the obvious question is whether one should reconsider the foundations of mathematics in light of quantum physics. Is set theory really the correct approach to axiomatization?
[36] viXra:1111.0089 [pdf] replaced on 2012-01-30 08:24:00
Authors: Matti Pitkänen
Comments: 80 Pages.
In this article the goal is to find whether the general mathematical structures associated with twistor approach, superstring models and M-theory could have a generalization or a modification in TGD framework. The contents of the chapter is an outcome of a rather spontaneous process, and represents rather unexpected new insights about TGD resulting as outcome of the comparisons.
1. Infinite primes, Galois groups, algebraic geometry, and TGD
In algebraic geometry the notion of variety defined by algebraic equation is very general: all number fields are allowed. One of the challenges is to define the counterparts of homology and cohomology groups for them. The notion of cohomology giving rise also to homology if Poincare duality holds true is central. The number of various cohomology theories has inflated and one of the basic challenges to find a sufficiently general approach allowing to interpret various cohomology theories as variations of the same motive as Grothendieck, who is the pioneer of the field responsible for many of the basic notions and visions, expressed it.
Cohomology requires a definition of integral for forms for all number fields. In p-adic context the lack of well-ordering of p-adic numbers implies difficulties both in homology and cohomology since the notion of boundary does not exist in topological sense. The notion of definite integral is problematic for the same reason. This has led to a proposal of reducing integration to Fourier analysis working for symmetric spaces but requiring algebraic extensions of p-adic numbers and an appropriate definition of the p-adic symmetric space. The definition is not unique and the interpretation is in terms of the varying measurement resolution.
The notion of infinite has gradually turned out to be more and more important for quantum TGD. Infinite primes, integers, and rationals form a hierarchy completely analogous to a hierarchy of second quantization for a super-symmetric arithmetic quantum field theory. The simplest infinite primes representing elementary particles at given level are in one-one correspondence with many-particle states of the previous level. More complex infinite primes have interpretation in terms of bound states.
This construction would realize the number theoretical, algebraic geometrical, and topological content in the construction of quantum states in TGD framework in accordance with TGD as almost TQFT philosophy, TGD as infinite-D geometry, and TGD as generalized number theory visions.
2. p-Adic integration and cohomology
This picture leads also to a proposal how p-adic integrals could be defined in TGD framework.
3. Floer homology, Gromov-Witten invariants, and TGD
Floer homology defines a generalization of Morse theory allowing to deduce symplectic homology groups by studying Morse theory in loop space of the symplectic manifold. Since the symplectic transformations of the boundary of δ M4+/-× CP2 define isometry group of WCW, it is very natural to expect that Kähler action defines a generalization of the Floer homology allowing to understand the symplectic aspects of quantum TGD. The hierarchy of Planck constants implied by the one-to-many correspondence between canonical momentum densities and time derivatives of the imbedding space coordinates leads naturally to singular coverings of the imbedding space and the resulting symplectic Morse theory could characterize the homology of these coverings.
One ends up to a more precise definition of vacuum functional: Kähler action reduces Chern-Simons terms (imaginary in Minkowskian regions and real in Euclidian regions) so that it has both phase and real exponent which makes the functional integral well-defined. Both the phase factor and its conjugate must be allowed and the resulting degeneracy of ground state could allow to understand qualitatively the delicacies of CP breaking and its sensitivity to the parameters of the system. The critical points with respect to zero modes correspond to those for Kähler function. The critical points with respect to complex coordinates associated with quantum fluctuating degrees of freedom are not allowed by the positive definiteness of Kähler metric of WCW. One can say that Kähler and Morse functions define the real and imaginary parts of the exponent of vacuum functional.
The generalization of Floer homology inspires several new insights. In particular, space-time surface as hyper-quaternionic surface could define the 4-D counterpart for pseudo-holomorphic 2-surfaces in Floer homology. Holomorphic partonic 2-surfaces could in turn correspond to the extrema of Kähler function with respect to zero modes and holomorphy would be accompanied by super-symmetry.
Gromov-Witten invariants appear in Floer homology and topological string theories and this inspires the attempt to build an overall view about their role in TGD. Generalization of topological string theories of type A and B to TGD framework is proposed. The TGD counterpart of the mirror symmetry would be the equivalence of formulations of TGD in H=M4× CP2 and in CP3× CP3 with space-time surfaces replaced with 6-D sphere bundles.
4. K-theory, branes, and TGD
K-theory and its generalizations play a fundamental role in super-string models and M-theory since they allow a topological classification of branes. After representing some physical objections against the notion of brane more technical problems of this approach are discussed briefly and it is proposed how TGD allows to overcome these problems. A more precise formulation of the weak form of electric-magnetic duality emerges: the original formulation was not quite correct for space-time regions with Euclidian signature of the induced metric. The question about possible TGD counterparts of R-R and NS-NS fields and S, T, and U dualities is discussed.
5. p-Adic space-time sheets as correlates for Boolean cognition
p-Adic physics is interpreted as physical correlate for cognition. The so called Stone spaces are in one-one correspondence with Boolean algebras and have typically 2-adic topologies. A generalization to p-adic case with the interpretation of p pinary digits as physically representable Boolean statements of a Boolean algebra with 2n>p>pn-1 statements is encouraged by p-adic length scale hypothesis. Stone spaces are synonymous with profinite spaces about which both finite and infinite Galois groups represent basic examples. This provides a strong support for the connection between Boolean cognition and p-adic space-time physics. The Stone space character of Galois groups suggests also a deep connection between number theory and cognition and some arguments providing support for this vision are discussed.
[35] viXra:1111.0088 [pdf] replaced on 2012-01-30 08:34:19
Authors: Matti Pitkänen
Comments: 17 Pages.
Witten was awarded by Fields medal from a construction recipe of Jones polynomial based on topological QFT assigned with braids and based on Chern-Simons action. Recently Witten has been working with an attempt to understand in terms of quantum theory the so called Khovanov polynomial associated with a much more abstract link invariant whose interpretation and real understanding remains still open.
The attempts to understand Witten's thoughts lead to a series of questions unavoidably culminating to the frustrating "Why I do not have the brain of Witten making perhaps possible to answer these questions?". This one must just accept. In this article I summarize some thoughts inspired by the associations of the talk of Witten with quantum TGD and with the model of DNA as topological quantum computer. In my own childish manner I dare believe that these associations are interesting and dare also hope that some more brainy individual might take them seriously.
An idea inspired by TGD approach which also main streamer might find interesting is that the Jones invariant defined as vacuum expectation for a Wilson loop in 2+1-D space-time generalizes to a vacuum expectation for a collection of Wilson loops in 2+2-D space-time and could define an invariant for 2-D knots and for cobordisms of braids analogous to Jones polynomial. As a matter fact, it turns out that a generalization of gauge field known as gerbe is needed and that in TGD framework classical color gauge fields defined the gauge potentials of this field. Also topological string theory in 4-D space-time could define this kind of invariants. Of course, it might well be that this kind of ideas have been already discussed in literature.
[34] viXra:1111.0086 [pdf] replaced on 2012-01-30 08:45:30
Authors: Matti Pitkänen
Comments: 61 Pages.
There have been impressive steps in the understanding of N=4 maximally sypersymmetric YM theory possessing 4-D super-conformal symmetry. This theory is related by AdS/CFT duality to certain string theory in AdS5× S5 background. Second stringy representation was discovered by Witten and is based on 6-D Calabi-Yau manifold defined by twistors. The unifying proposal is that so called Yangian symmetry is behind the mathematical miracles involved.
In the following I will discuss briefly the notion of Yangian symmetry and suggest its generalization in TGD framework by replacing conformal algebra with appropriate super-conformal algebras. Also a possible realization of twistor approach and the construction of scattering amplitudes in terms of Yangian invariants defined by Grassmannian integrals is considered in TGD framework and based on the idea that in zero energy ontology one can represent massive states as bound states of massless particles. There is also a proposal for a physical interpretation of the Cartan algebra of Yangian algebra allowing to understand at the fundamental level how the mass spectrum of n-particle bound states could be understood in terms of the n-local charges of the Yangian algebra.
Twistors were originally introduced by Penrose to characterize the solutions of Maxwell's equations. Kähler action is Maxwell action for the induced Kähler form of CP2. The preferred extremals allow a very concrete interpretation in terms of modes of massless non-linear field. Both conformally compactified Minkowski space identifiable as so called causal diamond and CP2 allow a description in terms of twistors. These observations inspire the proposal that a generalization of Witten's twistor string theory relying on the identification of twistor string world sheets with certain holomorphic surfaces assigned with Feynman diagrams could allow a formulation of quantum TGD in terms of 3-dimensional holomorphic surfaces of CP3× CP3 mapped to 6-surfaces dual CP3× CP3, which are sphere bundles so that they are projected in a natural manner to 4-D space-time surfaces. Very general physical and mathematical arguments lead to a highly unique proposal for the holomorphic differential equations defining the complex 3-surfaces conjectured to correspond to the preferred extremals of Kähler action.
[33] viXra:1111.0085 [pdf] replaced on 2012-01-30 08:52:00
Authors: Matti Pitkänen
Comments: 17 Pages.
Shnoll and collaborators have discovered strange repeating patterns of random fluctuations of physical observables such as the number n of nuclear decays in a given time interval. Periodically occurring peaks for the distribution of the number N(n) of measurements producing n events in a series of measurements as a function of n is observed instead of a single peak. The positions of the peaks are not random and the patterns depend on position and time varying periodically in time scales possibly assignable to Earth-Sun and Earth-Moon gravitational interaction.
These observations suggest a modification of the expected probability distributions but it is very difficult to imagine any physical mechanism in the standard physics framework. Rather, a universal deformation of predicted probability distributions would be in question requiring something analogous to the transition from classical physics to quantum physics.
The hint about the nature of the modification comes from the TGD inspired quantum measurement theory proposing a description of the notion of finite measurement resolution in terms of inclusions of so called hyper-finite factors of type II1 (HFFs) and closely related quantum groups. Also p-adic physics -another key element of TGD- is expected to be involved. A modification of a given probability distribution P(nkenovert λi) for a positive integer valued variable n characterized by rational-valued parameters λi is obtained by replacing n and the integers characterizing λi with so called quantum integers depending on the quantum phase qm=exp(i2π/m). Quantum integer nq must be defined as the product of quantum counterparts pq of the primes p appearing in the prime decomposition of n. One has pq= sin(2π p/m)/sin(2π/m) for p≠ P and pq=P for p=P. m must satisfy m≥ 3, m≠ p, and m≠ 2p.
The quantum counterparts of positive integers can be negative. Therefore quantum distribution is defined first as p-adic valued distribution and then mapped by so called canonical identification I to a real distribution by the map taking p-adic -1 to P and powers Pn to P-n and other quantum primes to themselves and requiring that the mean value of n is for distribution and its quantum variant. The map I satisfies I(∑ Pn)=∑ I(Pn). The resulting distribution has peaks located periodically with periods coming as powers of P. Also periodicities with peaks corresponding to n=n+n-, n+q>0 with fixed n-q<0, are predicted. These predictions are universal and easily testable. The prime P and integer m characterizing the quantum variant of distribution can be identified from data. The shapes of the distributions obtained are qualitatively consistent with the findings of Shnoll but detailed tests are required to see whether the number theoretic predictions are correct.
The periodic dependence of the distributions would be most naturally assignable to the gravitational interaction of Earth with Sun and Moon and therefore to the periodic variation of Earth-Sun and Earth-Moon distances. The TGD inspired proposal is that the p-dic prime P and integer m characterizing the quantum distribution are determined by a process analogous to a state function reduction and their most probably values depend on the deviation of the distance R through the formulas Δ p/p≈ kpΔ R/R and Δ m/m≈ kmΔ R/R. The p-adic primes assignable to elementary particles are very large unlike the primes which could characterize the empirical distributions. The hierarchy of Planck constants allows the gravitational Planck constant assignable to the space-time sheets mediating gravitational interactions to have gigantic values and this allows p-adicity with small values of the p-adic prime P.
[32] viXra:1106.0054 [pdf] replaced on 2011-12-18 18:29:41
Authors: sangwha Yi
Comments: 15 Pages. It is replacement
In the general relativity theory, instead of in the present accelerated system theory, the
coordinate transformation that the inertial coordinate system and the accelerated
coordinate system, find the new relation’s coordinate transformation that used the tetrad
on the new method.And using the new relation’s coordinate transformation of the new
accelerated system, organize the expansive accelerated system, the relation of the
inertial coordinate system and an accelerated system that accelerated constantly on an
inertial coordinate system.
Category: Mathematical Physics
[31] viXra:1106.0054 [pdf] replaced on 2011-12-11 05:27:27
Authors: Sangwha Yi
Comments: 12 Pages. It is replacement
In the general relativity theory, instead of in the present accelerated system theory, the
coordinate transformation that the inertial coordinate system and the accelerated
coordinate system, find the new relation’s coordinate transformation that used the tetrad
on the new method.And using the new relation’s coordinate transformation of the new
accelerated system, organize the expansive accelerated system, the relation of the
inertial coordinate system and an accelerated system that accelerated constantly on an
inertial coordinate system.
Category: Mathematical Physics
[30] viXra:1106.0054 [pdf] replaced on 5 Dec 2011
Authors: Sangwha-Yi
Comments: 12 pages.
In the general relativity theory, instead of in the present accelerated system theory, the
coordinate transformation that the inertial coordinate system and the accelerated
coordinate system, find the new relation's coordinate transformation that used the tetrad
on the new method.And using the new relation's coordinate transformation of the new
accelerated system, organize the expansive accelerated system, the relation of the
inertial coordinate system and an accelerated system that accelerated constantly on an
inertial coordinate system.
Category: Mathematical Physics
[29] viXra:1106.0054 [pdf] replaced on 22 Nov 2011
Authors: Sangwha-Yi
Comments: 12 pages.
In the general relativity theory, instead of in the present accelerated system theory, the
coordinate transformation that the inertial coordinate system and the accelerated
coordinate system, find the new relation's coordinate transformation that used the tetrad
on the new method.And using the new relation's coordinate transformation of the new
accelerated system, organize the expansive accelerated system, the relation of the
inertial coordinate system and an accelerated system that accelerated constantly on an
inertial coordinate system.
Category: Mathematical Physics
[28] viXra:1106.0018 [pdf] replaced on 23 Jun 2011
Authors: Sergey V. Ershkov
Comments: 9 pages
Here is presented a new exact solution of Ice dynamics in Glaciers in terms of viscousplastic
theory of movements, for 2-dimensional case: x (t) = y (t). In general case, 2-D
solution of Ice dynamics could be classified as Riccati's type. Due to a very special
character of Riccati's type equation, it's general solution is proved to have a proper gap
of components of such a solution.
Category: Mathematical Physics
[27] viXra:1106.0018 [pdf] replaced on 20 Jun 2011
Authors: Sergey V. Ershkov
Comments: 7 pages
Here is presented a new exact solution of Ice dynamics in Glaciers in terms of viscousplastic
theory of movements, for 2-dimensional case: x (t) = y (t). In general case, 2-D
solution of Ice dynamics could be classified as Riccati's type. Due to a very special
character of Riccati's type equation, it's general solution is proved to have a proper gap
of components of such a solution.
Category: Mathematical Physics
[26] viXra:1103.0115 [pdf] replaced on 2012-01-26 10:29:23
Authors: José Francisco García Juliá
Comments: 3 Pages.
We consider that the action at a distance is carried out by virtual carriers of the force,
which are created and annihilated in the vacuum by the field in a time less than that of
the Heisenberg's uncertainty.
Category: Mathematical Physics
[25] viXra:1102.0032 [pdf] replaced on 3 Oct 2011
Authors: Malcolm Macleod
Comments:
3 pages. v1 in Russian, v4 in English
The natural constants, G; h; e, μ0 and me are presented as geometrical shapes in terms
of Planck momentum, α (Sommerfeld fine structure constant) and c. A square root
solution of Planck momentum denoted Quintessence-momentum Q links the mass and
charge constants. The electron formula describes a dimensionless magnetic monopole.
The Rydberg constant R1, the most accurate of the natural constants, is used for crossreference,
the solutions are consistent with CODATA 2010 precision.
Category: Mathematical Physics
[24] viXra:1102.0032 [pdf] replaced on 18 May 2011
Authors: Malcolm Macleod
Comments:
3 pages. v1 in Russian, v3 in English
A mathematical description of the natural constants, G, h, e, μ0 me R∞, is presented in
terms of momentum Q, alpha (Sommerfeld fine structure constant) and c. This momentum
is referred to as Quintessence-momentum and is the square root of Planck
momentum. The formulas describe geometrical forms, the units are consistent with
corresponding SI units and the numerical values, including the Rydberg constant and
the vacuum permeability, are consistent with CODATA 2006.
Category: Mathematical Physics
[23] viXra:1102.0032 [pdf] replaced on 20 Feb 2011
Authors: Malcolm Macleod
Comments:
3 pages. v1 in Russian, v2 in English
This paper suggests a 'quantity of momentum', a square root of Planck momentum,
here referred to as Quintessence-momentum, as a natural unit that is common to both
mass and charge. In terms of this Quintessence momentum Q, alpha (Sommerfeld fine
structure constant) and c; geometrical formulas for the natural physical constants and
the electron mass are proposed. Results are consistent with CODATA 2006.
Category: Mathematical Physics
[22] viXra:1102.0027 [pdf] replaced on 18 Feb 2011
Authors: Sergey G. Fedosin
Comments:
4 pages. v1 in Russian, v2 in English
The scale dimension which is discovered in the theory of infinite nesting of matter is studied from the
perspective of the physical implementation of well-studied four-and n-dimensional geometric objects.
Adding of the scale dimension to Minkowski space means the need to use the five-dimensional spacetime.
Category: Mathematical Physics
[21] viXra:1101.0037 [pdf] replaced on 12 Jan 2011
Authors: Ke Xiao
Comments: 5 pages
The fine structure constant α = e2/hc ~ 1/137.036 and the blackbody
radiation constant αR = e2(aR/k4B)1/3 ~ 1/157.555
are linked by prime numbers. The blackbody radiation constant is a new method to measure
the fine structure constant. It also links the fine structure constant to the
Boltzmann constant.
Category: Mathematical Physics
[20] viXra:1012.0052 [pdf] replaced on 17 Jan 2011
Authors: Giuliano Bettini
Comments: 9 pages, v3 in Italian, v2 in English, corrections to the tables, and a new table added.
There are 32 possible combinations of symmetry operations that define the external symmetry of
crystals. These 32 possible combinations result in the 32 crystal classes.
But for a radar engineer it is inevitable to associate "32" to "5 bits".
I submit a tentative classification of the 32 crystal classes with a 5 bit classification, obviously with
a (tentative) physical meaning of each bit.
Each bit means a physical property.
Category: Mathematical Physics
[19] viXra:1012.0052 [pdf] replaced on 1 Jan 2011
Authors: Giuliano Bettini
Comments: 9 pages, v1 in Italian, v2 in English, corrections to the tables, and a new table added.
There are 32 possible combinations of symmetry operations that define the external symmetry of
crystals. These 32 possible combinations result in the 32 crystal classes.
But for a radar engineer it is inevitable to associate "32" to "5 bits".
I submit a tentative classification of the 32 crystal classes with a 5 bit classification, obviously with
a (tentative) physical meaning of each bit.
Each bit means a physical property.
Category: Mathematical Physics
[18] viXra:1012.0031 [pdf] replaced on 16 Dec 2010
Authors: Elemér E Rosinger
Comments: 9 pages
A class of non-Cartesian physical systems, [7], are those whose
composite state spaces are given by significantly extended tensor products.
A more detailed presentation of the way such extended tensor products
are constructed is offered, based on a step by step comparison with the
construction of usual tensor products. This presentation clarifies the
extent to which the extended tensor products are indeed more general
than the usual ones.
Category: Mathematical Physics
[17] viXra:1010.0014 [pdf] replaced on 1 Jun 2011
Authors: Dan Visser
Comments: 5 pages
A new cosmological model, named the Twin-Tori Model (TTM)[1], postulates a
dark energy force Fde , which empowers the dynamic of a lower order universe, well
known as the big bang. In this paper I introduce the 1st derivative F'de of this dark energy
force to reveal deeper properties of the TTM, such as: why quantummechanics exists in
the big bang, why dark matter and visible matter are equally responsible for gravity in
galaxies for 1/4 of the density of dark matter at a specific length, why the big bang universe
is recalculated by subquantumlevel-information below the Plancklength, and why the
impression of space-expansion is due to the higher order cosmological model TTM.
Category: Mathematical Physics
[16] viXra:1009.0007 [pdf] replaced on 2011-12-21 11:44:45
Authors: DT Froedge
Comments: 39 Pages.
The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are single particle special cases. The basic concept is that there is a broader picture, based on a more general equation that includes the entire system of particles. The first part will be to postulate an equation, and then, by modifying the methods of Path Integrals, develop a solution which describes the internal dynamics as well as particle interactions of quantum particles. The complete function has both real and imaginary, as well as timelike and spacelike parts, each of which are separable into independent expressions that define particle properties. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an atomic system, particle are eigenvalues in an interacting universe of particles. The Dirac massive and massless equation and solution will be shown as factorable independent components. A clear distinction between the classical and quantum properties of particles is made, increasing the scope of QM.
Category: Mathematical Physics
[15] viXra:1009.0007 [pdf] replaced on 2 Jul 2011
Authors: D.T. Froedge
Comments:
30 pages.
The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for
which the Klein-Gordon-Dirac-Schrödinger equations are single particle special cases. In the
same manner that eigenvalues of the Schrödinger equation represents energy levels of an
interacting atomic system, eigenvalues represent particle energies in an interacting system of
particles. An equation and a solution is proposed that treats all of the particles in the universe
as a single system. The proposed solution is a descriptor of a symmetric, light speed
expanding group of interacting particles having familiar constituents.
Category: Mathematical Physics
[14] viXra:1009.0007 [pdf] replaced on 5 Mar 2011
Authors: D.T. Froedge
Comments:
17 pages 38 equations 98kb
The purpose of this paper is to illustrate a fundamental, multiple particle,
system equation for which the Klein-Gordon-Dirac-Schrödinger equations are
single particle special cases. In the same manner that eigenvalues of the
Schrödinger equation represents energy levels of an interacting atomic system,
eigenvalues represent particle energies in an interacting system of particles. An
equation is proposed that has vector solutions defined in Dirac, or Clifford
algebra, that treats all of the particles in the universe as a single system. The
proposed solution is a descriptor of a symmetric, light speed expanding group
of interacting particles having real, as well as the familiar QM constituents.
Category: Mathematical Physics
[13] viXra:1006.0042 [pdf] replaced on 2012-01-30 21:36:44
Authors: Matti
Comments: 13 Pages.
This appendix contains basic facts about CP2 as a symmetric space and Kähler manifold. The
coding of the standard model symmetries to the geometry of CP2, the physical interpretation of
the induced spinor connection in terms of electro-weak gauge potentials, and basic facts about
induced gauge fields are discussed
Category: Mathematical Physics
[12] viXra:1006.0041 [pdf] replaced on 2012-01-30 21:40:48
Authors: Matti Pitkänen
Comments: 5 Pages.
The original justification for the hierarchy of Planck constants came from the indications that
Planck constant could have large values in both astrophysical systems involving dark matter and
also in biology. The realization of the hierarchy in terms of the singular coverings and possibly also
factor spaces of CD and CP2 emerged from consistency conditions. It however seems that TGD
actually predicts this hierarchy of covering spaces. The extreme non-linearity of the field equations
defined by Kähler action means that the correspondence between canonical momentum densities
and time derivatives of the imbedding space coordinates is 1-to-many. This leads naturally to the
introduction of the covering space of CD x CP2, where CD denotes causal diamond defined as
intersection of future and past directed light-cones.
Category: Mathematical Physics
[11] viXra:1006.0040 [pdf] replaced on 2012-01-30 21:49:56
Authors: Matti Pitkänen
Comments: 25 Pages.
The notion of electric magnetic duality emerged already two decades ago in the attempts to
formulate the Kähler geometry of the "world of classical worlds". Quite recently a considerable
step of progress took place in the understanding of this notion. This concept leads to the
identification of the physical particles as string like objects defined by magnetic charged wormhole
throats connected by magnetic
ux tubes. The second end of the string contains particle having
electroweak isospin neutralizing that of elementary fermion and the size scale of the string is
electro-weak scale would be in question. Hence the screening of electro-weak force takes place
via weak confinement. This picture generalizes to magnetic color confinement. Electric-magnetic
duality leads also to a detailed understanding of how TGD reduces to almost topological quantum
field theory. A surprising outcome is the necessity to replace CP2 Kähler form in Kähler action
with its sum with S2 Kähler form.
Category: Mathematical Physics
[10] viXra:1006.0039 [pdf] replaced on 2012-01-30 21:53:06
Authors: Matti Pitkänen
Comments: 16 Pages.
Generalized Feynman diagrams have become the central notion of quantum TGD and one might even say that space-time surfaces can be identified as generalized Feynman diagrams. The challenge is to assign a precise mathematical content for this notion, show their mathematical existence, and develop a machinery for calculating them. Zero energy ontology has led to a dramatic progress in the understanding of generalized Feynman diagrams at the level of fermionic degrees of freedom. In particular, manifest finiteness in these degrees of freedom follows trivially from the basic identifications as does also unitarity and non-trivial coupling constant evolution. There are however several formidable looking challenges left.
[9] viXra:1006.0038 [pdf] replaced on 2012-01-30 21:55:27
Authors: Matti Pitkänen
Comments: 38 Pages.
The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts.
Number theoretical vision suggests that infinite hyper-octonionic or -quaternionic primes could could correspond directly to the quantum numbers of elementary particles and a detailed proposal for this correspondence is made. Furthermore, the generalized eigenvalue spectrum of the Chern-Simons Dirac operator could be expressed in terms of hyper-complex primes in turn defining basic building bricks of infinite hyper-complex primes from which hyper-octonionic primes are obtained by dicrete SU(3) rotations performed for finite hyper-complex primes.
Besides this holy trinity I will discuss loosely related topics. Included are possible applications of category theory in TGD framework; TGD inspired considerations related to Riemann hypothesis; topological quantum computation in TGD Universe; and TGD inspired approach to Langlands program.
Category: Mathematical Physics
[8] viXra:1006.0038 [pdf] replaced on 3 Nov 2010
Authors: Matti Pitkänen
Comments: 695 Pages.
The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts.
Number theoretical vision suggests that infinite hyper-octonionic or -quaternionic primes could could correspond directly to the quantum numbers of elementary particles and a detailed proposal for this correspondence is made. Furthermore, the generalized eigenvalue spectrum of the Chern-Simons Dirac operator could be expressed in terms of hyper-complex primes in turn defining basic building bricks of infinite hyper-complex primes from which hyper-octonionic primes are obtained by dicrete SU(3) rotations performed for finite hyper-complex primes.
Besides this holy trinity I will discuss loosely related topics. Included are possible applications of category theory in TGD framework; TGD inspired considerations related to Riemann hypothesis; topological quantum computation in TGD Universe; and TGD inspired approach to Langlands program.
Category: Mathematical Physics
[7] viXra:1006.0037 [pdf] replaced on 2012-01-30 21:56:36
Authors: Matti Pitkänen
Comments: 28 Pages.
Physics as a generalized number theory program involves three threads: various p-adic physics
and their fusion together with real number based physics to a larger structure, the attempt to
understand basic physics in terms of classical number fields discussed in this article, and infinite
primes whose construction is formally analogous to a repeated second quantization of an arithmetic
quantum field theory.
In this article the connection between standard model symmetries and classical number fields
is discussed. The basis vision is that the geometry of the infinite-dimensional WCW ("world of
classical worlds") is unique from its mere existence. This leads to its identification as union of
symmetric spaces whose Kähler geometries are fixed by generalized conformal symmetries. This
fixes space-time dimension and the decomposition M4 x S and the idea is that the symmetries
of the Kähler manifold S make it somehow unique. The motivating observations are that the
dimensions of classical number fields are the dimensions of partonic 2-surfaces, space-time surfaces,
and imbedding space and M8 can be identified as hyper-octonions- a sub-space of complexified
octonions obtained by adding a commuting imaginary unit. This stimulates some questions.
Could one understand S = CP2 number theoretically in the sense that M8 and H = M4 x CP2
be in some deep sense equivalent ("number theoretical compactification" or M8 - H duality)?
Could associativity define the fundamental dynamical principle so that space-time surfaces could
be regarded as associative or co-associative (defined properly) sub-manifolds of M8 or equivalently
of H.
One can indeed define the associativite (co-associative) 4-surfaces using octonionic representation
of gamma matrices of 8-D spaces as surfaces for which the modified gamma matrices span
an associate (co-associative) sub-space at each point of space-time surface. Also M8 - H duality
holds true if one assumes that this associative sub-space at each point contains preferred plane of
M8 identifiable as a preferred commutative or co-commutative plane (this condition generalizes
to an integral distribution of commutative planes in M8). These planes are parametrized by CP2
and this leads to M8 - H duality.
WCW itself can be identified as the space of 4-D local sub-algebras of the local Clifford
algebra of M8 or H which are associative or co-associative. An open conjecture is that this
characterization of the space-time surfaces is equivalent with the preferred extremal property of
Kähler action with preferred extremal identified as a critical extremal allowing infinite-dimensional
algebra of vanishing second variations.
Category: Mathematical Physics
[6] viXra:1006.0036 [pdf] replaced on 2012-01-30 21:58:07
Authors: Matti Pitkänen
Comments: 51 Pages.
Physics as a generalized number theory program involves three threads: various p-adic physics
and their fusion together with real number based physics to a larger structure, the attempt to
understand basic physics in terms of classical number fields (in particular, identifying associativity
condition as the basic dynamical principle), and infinite primes whose construction is formally
analogous to a repeated second quantization of an arithmetic quantum field theory. In this article
p-adic physics and the technical problems relates to the fusion of p-adic physics and real physics
to a larger structure are discussed.
The basic technical problems relate to the notion of definite integral both at space-time level,
imbedding space level and the level of WCW (the "world of classical worlds"). The expressibility
of WCW as a union of symmetric spacesleads to a proposal that harmonic analysis of symmetric
spaces can be used to define various integrals as sums over Fourier components. This leads to the
proposal the p-adic variant of symmetric space is obtained by a algebraic continuation through a
common intersection of these spaces, which basically reduces to an algebraic variant of coset space
involving algebraic extension of rationals by roots of unity. This brings in the notion of angle
measurement resolution coming as Δφ = 2π/pn for given p-adic prime p. Also a proposal how
one can complete the discrete version of symmetric space to a continuous p-adic versions emerges
and means that each point is effectively replaced with the p-adic variant of the symmetric space
identifiable as a p-adic counterpart of the real discretization volume so that a fractal p-adic variant
of symmetric space results.
If the Kähler geometry of WCW is expressible in terms of rational or algebraic functions, it
can in principle be continued the p-adic context. One can however consider the possibility that
that the integrals over partonic 2-surfaces defining
ux Hamiltonians exist p-adically as Riemann
sums. This requires that the geometries of the partonic 2-surfaces effectively reduce to finite
sub-manifold geometries in the discretized version of δM+4. If Kähler action is required
to exist p-adically same kind of condition applies to the space-time surfaces themselves. These
strong conditions might make sense in the intersection of the real and p-adic worlds assumed to
characterized living matter.
Category: Mathematical Physics
[5] viXra:1006.0035 [pdf] replaced on 2012-01-30 22:01:55
Authors: Matti Pitkänen
Comments: 95 Pages.
There are three separate approaches to the challenge of constructing WCW Kähler geometry
and spinor structure. The first approach relies on a direct guess of Kähler function. Second
approach relies on the construction of Kähler form and metric utilizing the huge symmetries
of the geometry needed to guarantee the mathematical existence of Riemann connection. The
third approach discussed in this article relies on the construction of spinor structure based on the
hypothesis that complexified WCW gamma matrices are representable as linear combinations of
fermionic oscillator operator for the second quantized free spinor fields at space-time surface and
on the geometrization of super-conformal symmetries in terms of spinor structure. This implies a
geometrization of fermionic statistics.
The basic philosophy is that at fundamental level the construction of WCW geometry reduces
to the second quantization of the induced spinor fields using Dirac action. This assumption
is parallel with the bosonic emergence stating that all gauge bosons are pairs of fermion and
antifermion at opposite throats of wormhole contact. Vacuum function is identified as Dirac
determinant and the conjecture is that it reduces to the exponent of Kähler function. In order
to achieve internal consistency induced gamma matrices appearing in Dirac operator must be
replaced by the modified gamma matrices defined uniquely by Kähler action and one must also
assume that extremals of Kähler action are in question so that the classical space-time dynamics
reduces to a consistency condition. This implies also super-symmetries and the fermionic oscillator
algebra at partonic 2-surfaces has intepretation as N = 1 generalization of space-time supersymmetry
algebra different however from standard SUSY algebra in that Majorana spinors are
not needed. This algebra serves as a building brick of various super-conformal algebras involved.
The requirement that there exist deformations giving rise to conserved Noether charges requires
that the preferred extremals are critical in the sense that the second variation of the Kähler action
vanishes for these deformations. Thus Bohr orbit property could correspond to criticality or at
least involve it.
Quantum classical correspondence demands that quantum numbers are coded to the properties
of the preferred extremals given by the Dirac determinant and this requires a linear coupling
to the conserved quantum charges in Cartan algebra. Effective 2-dimensionality allows a measurement
interaction term only in 3-D Chern-Simons Dirac action assignable to the wormhole
throats and the ends of the space-time surfaces at the boundaries of CD. This allows also to
have physical propagators reducing to Dirac propagator not possible without the measurement
interaction term. An essential point is that the measurement interaction corresponds formally
to a gauge transformation for the induced Kähler gauge potential. If one accepts the weak form
of electric-magnetic duality Kähler function reduces to a generalized Chern-Simons term and the
effect of measurement interaction term to Kähler function reduces effectively to the same gauge
transformation.
The basic vision is that WCW gamma matrices are expressible as super-symplectic charges at
the boundaries of CD. The basic building brick of WCW is the product of infinite-D symmetric
spaces assignable to the ends of the propagator line of the generalized Feynman diagram. WCW
Kähler metric has in this case "kinetic" parts associated with the ends and "interaction" part
between the ends. General expressions for the super-counterparts of WCW
ux Hamiltoniansand
for the matrix elements of WCW metric in terms of their anticommutators are proposed on basis
of this picture.
Category: Mathematical Physics
[4] viXra:1006.0034 [pdf] replaced on 2012-01-30 22:03:21
Authors: Matti Pitkänen
Comments: 26 Pages.
There are three separate approaches to the challenge of constructing WCW Kähler geometry
and spinor structure. The first one relies on a direct guess of Kähler function. Second approach
relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry
needed to guarantee the mathematical existence of Riemann connection. The third approach relies
on the construction of spinor structure assuming that complexified WCW gamma matrices are
representable as linear combinations of fermionic oscillator operator for the second quantized free
spinor fields at space-time surface and on the geometrization of super-conformal symmetries in
terms of spinor structure.
In this article the construction of Kähler form and metric based on symmetries is discussed.
The basic vision is that WCW can be regarded as the space of generalized Feynman diagrams with
lines thickned to light-like 3-surfaces and vertices identified as partonic 2-surfaces. In zero energy
ontology the strong form of General Coordinate Invariance (GCI) implies effective 2-dimensionality
and the basic objects are pairs partonic 2-surfaces X2 at opposite light-like boundaries of causal
diamonds (CDs).
The hypothesis is that WCW can be regarded as a union of infinite-dimensional symmetric
spaces G/H labeled by zero modes having an interpretation as classical, non-quantum
uctuating
variables. A crucial role is played by the metric 2-dimensionality of the light-cone boundary
δM+4
+ and of light-like 3-surfaces implying a generalization of conformal invariance. The group
G acting as isometries of WCW is tentatively identified as the symplectic group of
δM+4 x CP2
localized with respect to X2. H is identified as Kac-Moody type group associated with isometries
of H = M+4 x CP2 acting on light-like 3-surfaces and thus on X2.
An explicit construction for the Hamiltonians of WCW isometry algebra as so called
ux
Hamiltonians is proposed and also the elements of Kähler form can be constructed in terms of
these. Explicit expressions for WCW
ux Hamiltonians as functionals of complex coordinates of
the Cartesisian product of the infinite-dimensional symmetric spaces having as points the partonic
2-surfaces defining the ends of the the light 3-surface (line of generalized Feynman diagram) are
proposed.
Category: Mathematical Physics
[3] viXra:1006.0033 [pdf] replaced on 2012-01-30 22:05:03
Authors: Matti Pitkänen
Comments: 29 Pages.
There are two basic approaches to quantum TGD. The first approach, which is discussed in
this article, is a generalization of Einstein's geometrization program of physics to an infinitedimensional
context. Second approach is based on the identification of physics as a generalized
number theory. The first approach relies on the vision of quantum physics as infinite-dimensional
Kähler geometry for the "world of classical worlds" (WCW) identified as the space of 3-surfaces
in in certain 8-dimensional space. There are three separate approaches to the challenge of constructing
WCW Kähler geometry and spinor structure. The first approach relies on direct guess
of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing
the huge symmetries of the geometry needed to guarantee the mathematical existence of
Riemann connection. The third approach relies on the construction of spinor structure based on
the hypothesis that complexified WCW gamma matrices are representable as linear combinations
of fermionic oscillator operator for second quantized free spinor fields at space-time surface and
on the geometrization of super-conformal symmetries in terms of WCW spinor structure.
In this article the proposal for Kähler function based on the requirement of 4-dimensional General
Coordinate Invariance implying that its definition must assign to a given 3-surface a unique
space-time surface. Quantum classical correspondence requires that this surface is a preferred extremal
of some some general coordinate invariant action, and so called Kähler action is a unique
candidate in this respect. The preferred extremal has intepretation as an analog of Bohr orbit
so that classical physics becomes and exact part of WCW geometry and therefore also quantum
physics.
The basic challenge is the explicit identification of WCW Kähler function K. Two assumptions
lead to the identification of K as a sum of Chern-Simons type terms associated with the ends of
causal diamond and with the light-like wormhole throats at which the signature of the induced
metric changes. The first assumption is the weak form of electric magnetic duality. Second
assumption is that the Kähler current for preferred extremals satisfies the condition jK ^ djK = 0
implying that the
ow parameter of the
ow lines of jK defines a global space-time coordinate.
This would mean that the vision about reduction to almost topological QFT would be realized.
Second challenge is the understanding of the space-time correlates of quantum criticality.
Electric-magnetic duality helps considerably here. The realization that the hierarchy of Planck
constant realized in terms of coverings of the imbedding space follows from basic quantum TGD
leads to a further understanding. The extreme non-linearity of canonical momentum densities as
functions of time derivatives of the imbedding space coordinates implies that the correspondence
between these two variables is not 1-1 so that it is natural to introduce coverings of CD x CP2.
This leads also to a precise geometric characterization of the criticality of the preferred extremals.
Category: Mathematical Physics
[2] viXra:1006.0032 [pdf] replaced on 2012-01-30 22:06:21
Authors: Matti Pitkänen
Comments: 33 Pages.
There are two basic approaches to the construction of quantum TGD. The first approach
relies on the vision of quantum physics as infinite-dimensional Kähler geometry for the "world of
classical worlds" identified as the space of 3-surfaces in in certain 8-dimensional space. Essentially
a generalization of the Einstein's geometrization of physics program is in question. The second
vision is the identification of physics as a generalized number theory. This program involves
three threads: various p-adic physics and their fusion together with real number based physics
to a larger structure, the attempt to understand basic physics in terms of classical number fields
(in particular, identifying associativity condition as the basic dynamical principle), and infinite
primes whose construction is formally analogous to a repeated second quantization of an arithmetic
quantum field theory. In this article brief summaries of physics as infinite-dimensional geometry
and generalized number theory are given to be followed by more detailed articles.
Category: Mathematical Physics
[1] viXra:0907.0002 [pdf] replaced on 10 Jul 2009
Authors: Philip Gibbs
Comments: 5 pages
We prove that any 3x3 unitary matrix can be transformed to a magic matrix by multiplying its rows
and columns by phase factors. A magic matrix is defined as one for which the sum of the elements in any row
or column add to the same value. This result is relevant to recent observations on particle mixing matrices.
Category: Mathematical Physics