All Submission Categories

On Holography and Quantum Mechanics in Yang's Noncommutative Spacetime with a Lower and Upper Scale

Authors: Carlos Castro
Comments: 14 pages, This article appeared in Progress in Physics vol. 2 April (2006) 86-92.

We explore Yang's Noncommutative space-time algebra (involving two length scales) within the context of QM defined in Noncommutative spacetimes; the Holographic principle and the area-coordinates algebra in Clifford spaces. Casimir invariant wave equations corresponding to Noncommutative coordinates and momenta in d-dimensions can be recast in terms of ordinary QM wave equations in d+2-dimensions. It is conjectured that QM over Noncommutative spacetimes (Noncommutative QM) may be described by ordinary QM in higher dimensions. Novel Moyal-Yang-Fedosov-Kontsevich star products deformations of the Noncommutative Poisson Brackets (NCPB) are employed to construct star product deformations of scalar field theories. Finally, generalizations of the Dirac-Konstant and Klein-Gordon-like equations relevant to the physics of D-branes and Matrix Models are presented.
Category: Quantum Gravity and String Theory

On Modified Weyl-Heisenberg Algebras, Noncommutativity Matrix-Valued Planck Constant and QM in Clifford Spaces

Authors: Carlos Castro
Comments: 22 pages, This article appeared in the Journal of Physics A : Math. Gen 39 (2006) 14205-14229.

A novel Weyl-Heisenberg algebra in Clifford-spaces is constructed that is based on a matrix-valued H^AB extension of Planck's constant. As a result of this modifiedWeyl-Heisenberg algebra one will no longer be able to measure, simultaneously, the pairs of variables (x, p_x); (x, p_y); (x, p_z); (y, p_x), ... with absolute precision. New Klein-Gordon and Dirac wave equations and dispersion relations in Clifford-spaces are presented. The latter Dirac equation is a generalization of the Dirac-Lanczos-Barut-Hestenes equation. We display the explicit isomorphism between Yang's Noncommutative space-time algebra and the area-coordinates algebra associated with Clifford spaces. The former Yang's algebra involves noncommuting coordinates and momenta with a minimum Planck scale λ (ultraviolet cutoff) and a minimum momentum p = ℏ/R (maximal length R, infrared cutoff ). The double-scaling limit of Yang's algebra λ → 0, R → ∞, in conjunction with the large n → ∞ limit, leads naturally to the area quantization condition λR = L² = nλ² ( in Planck area units ) given in terms of the discrete angular-momentum eigenvalues n. It is shown how Modified Newtonian dynamics is also a consequence of Yang's algebra resulting from the modified Poisson brackets. Finally, another noncommutative algebra ( which differs from the Yang's algebra ) and related to the minimal length uncertainty relations is presented . We conclude with a discussion of the implications of Noncommutative QM and QFT's in Clifford-spaces.
Category: Quantum Gravity and String Theory

On Time Dependent Black Holes and Cosmological Models from a Kaluza-Klein Mechanism

Authors: Carlos Castro, J. A. Nieto, L. Ruiz, J. Silvas
Comments: 34 pages, This article appeared in the International Journal of Modern Physics A 24, no. 7 (2009) 1383 - 1415.

Novel static, time-dependent and spatial-temporal solutions of Einstein field equations, displaying singularities, with and without horizons, and in several dimensions are found based on a dimensional reduction procedure widely used in Kaluza-Klein type theories. The Kerr-Newman black-hole entropy as well as the Reissner-Nordstrom, Kerr and Schwarzschild black-hole entropy are derived from the corresponding Euclideanized actions. A very special cosmological model based on the dynamical interior geometry of a Black Hole is found that has no singularities at t = 0 due to the smoothing of the mass distribution. We conclude with another cosmological model equipped also with a dynamical horizon and which is related to Vaidya's metric (associated with the Hawking-radiation of black holes) by interchanging t ↔ r which might render our universe as a dynamical black hole.
Category: Relativity and Cosmology

Entropy Growth in the Early Universe and Confirmation of Initial Big Bang Conditions ( Wheeler De Witt Eqn. Results Vs. String Theory ?)

Authors: Andrew Beckwith
Comments: 2 pages, submission to the Blois 2009 conference proceedings

Initial relic entropy growth is presented as a natural outgrowth of relic graviton production, as a generalization of Dr. J.Y Ng's infinite quantum statistics. The adaptation and modification of Ng's (2008) argument, is an outgrowth of string theory cosmology arguments, and is essentially a counting algorithm for relic graviton production. This article is a very abbreviated version of a presentation given in Chongquing, PRC, in April, 2009, at the Chongquing University Physic's department as a guest of Dr. Fangyu Li, and his gravitational research group.
Category: Relativity and Cosmology

The Dirac Equation in a Gravitational Field

Authors: Jack Sarfatti
Comments: 7 pages

Einstein's equivalence principle implies that Newton's gravity force has no local objective meaning. It is an inertial force, i.e. a contingent artifact of the covariantly tensor accelerating (non-zero g's) Local Non-Inertial Frame (LNIF) detector. Indeed, Newton's gravity force disappears in a locally coincident non-accelerating (zero g) Local Inertial Frame (LIF). The presence or absence of tensor spacetime curvature is completely irrelevant to this fact. In the case of an extended test body, these remarks apply only to the Center of Mass (COM). Stresses across separated parts of the test body caused by the local objective tensor curvature are a logically independent separate issue. Garbling this distinction has generated not-even-wrong critiques of the equivalence principle among "philosophers of physics" and even among some venerable confused theoretical physicists. Non-standard terms coupling the spin-connection to the commutator of the Dirac matrices and to the Lorentz group Lie algebra generators are conjectured.
Category: Quantum Gravity and String Theory

Gauge Theories of Kac-Moody Extensions of W_∞ Algebras as Effective Field Theories of Colored W_∞ Strings

Authors: Carlos Castro
Comments: 11 pages, This article appeared in Advanced Studies in Theoretical Physics, 2, no. 17, (2008) 825 - 835.

A novel invariant gauge field theory realization of Kac-Moody extensions of w_∞(w_1+∞) algebras and based on a Lie group G is constructed. The most relevant physical feature of this theory is that it describes an effective field theory of "colored" internal w_∞(w_1+∞) strings when G = SU(3). We conclude with a discussion of how these theories might provide infinite higher conformal-spins extensions of Grand Unified Models and the Standard Model in four dimensions.
Category: Quantum Gravity and String Theory

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

Authors: Carlos Castro
Comments: 61 pages, This article appeared in Foundations of Physics vol 35, no.6 (2005) 971.

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff ). The invariance symmetry leads naturally to the real Clifford algebra Cl(2, 6,R) and complexified Clifford Cl_C(4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale (ℏλ/R). Previous work led us to show from first principles why the observed value of the vacuum energy density (cosmological constant ) is given by a geometric mean relationship ρ ~ L^-2_PlanckR^-2 = L^-4_P(L_Planck/R)² ~ 10^-122M⁴_Planck, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith's 8D model based on the Clifford algebra Cl(1,7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell's Electrodynamics, and Brandt's action related to the 8D spacetime tangentbundle involving coordinates and velocities ( Finsler geometries ). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit.
Category: Quantum Gravity and String Theory

On Timelike Naked Singularities Associated with Noncompact Matter Sources

Authors: Carlos Castro
Comments: 9 pages, This article appeared in Physics Letters B 665, no. 5 (2008) 384-387.

We show the existence of timelike naked singularities which are not hidden by a horizon and which are associated to spherically symmetric (noncompact) matter sources extending from r = 0 to r = ∞. Our asymptotically flat solutions do represent observable timelike naked singularities where the scalar curvature R and volume mass density ρ(r) are both singular at r = 0. To finalize we explain the Finsler geometric origins behind the matter field configuration obeying the weak energy conditions and that leads to a timelike naked singularity.
Category: Relativity and Cosmology

Strings and Membranes from Einstein Gravity, Matrix Models and W_∞ Gauge Theories as Paths to Quantum Gravity

Authors: Carlos Castro
Comments: 49 pages, This article appeared in the Int. J. Mod. Phys. A 23, no. 24 (2008) 3891

It is shown how w_∞,w_1+∞ Gauge Field Theory actions in 2D emerge directly from 4D Gravity. Strings and Membranes actions in 2D and 3D originate as well from 4D Einstein Gravity after recurring to the nonlinear connection formalism of Lagrange-Finsler and Hamilton-Cartan spaces. Quantum Gravity in 3D can be described by aW1 Matrix Model in D = 1 that can be solved exactly via the Collective Field Theory method. We describe why a quantization of 4D Gravity could be attained via a 2D Quantum W_∞ gauge theory coupled to an infinite-component scalar-multiplet. A proof that non-critical W_∞ (super) strings are devoid of BRST anomalies in dimensions D = 27 (D = 11), respectively, follows and which coincide with the critical (super) membrane dimensions D = 27 (D = 11). We establish the correspondence between the states associated with the quasi finite highest weights irreducible representations of W_∞,W_∞ algebras and the quantum states of the continuous Toda molecule. Schroedinger-like QM wave functional equations are derived and solutions are found in the zeroth order approximation. Since higher-conformal spin W_∞ symmetries are very relevant in the study of 2D W_∞ Gravity, the Quantum Hall effect, large N QCD, strings, membranes, ...... it is warranted to explore further the interplay among all these theories.
Category: Quantum Gravity and String Theory

There is no Einstein-Podolsky-Rosen Paradox in Clifford-Spaces

Authors: Carlos Castro
Comments: 8 pages, This article appeared in Adv. Studies in Theor. Phys. 1, no. 12 (2007) 603-610.

It is shown how one can attain the desired locally causal property of QM in Clifford-spaces despite the spacelike separation of two massive spin-½ particles involved in the Einstein-Podolksy-Rosen (EPR) experiment. This is achieved by proving why the addition laws of the particles poly-vector-valued momentum in Clifford-space is null-like. This is the key reason why it is possible to implement a locally causal QM theory in Clifford-spaces despite that QM has a non-local character in ordinary spacetime. The two particles can exchange signals in Clifford-space encoding their respective spin measurement values. Consequently, there is no EPR paradox in the Clifford space associated with the Clifford algebra Cl(3,1) of the underlying 4D spacetime.
Category: Quantum Physics

On Generalized Yang-Mills Theories and Extensions of the Standard Model in Clifford (Tensorial) Spaces

Authors: Carlos Castro
Comments: 31 pages, This article appeared in Annals of Physics vol. 321, no.4 (2006) 813-839.

We construct the Clifford-space tensorial-gauge fields generalizations of Yang-Mills theories and the Standard Model that allows to predict the existence of new particles (bosons, fermions) and tensor-gauge fields of higher-spins in the 10 Tev regime. We proceed with a detailed discussion of the unique D₄ - D₅ - E₆ - E₇ - E₈ model of Smith based on the underlying Clifford algebraic structures in D = 8, and which furnishes all the properties of the Standard Model and Gravity in four-dimensions, at low energies. A generalization and extension of Smith's model to the full Clifford-space is presented when we write explictly all the terms of the extended Clifford-space Lagrangian. We conclude by explaining the relevance of multiple-foldings of D = 8 dimensions related to the modulo 8 periodicity of the real Cliford algebras and display the interplay among Clifford, Division, Jordan and Exceptional algebras, within the context of D = 26, 27, 28 dimensions, corresponding to bosonic string, M and F theory, respectively, advanced earlier by Smith. To finalize we describe explicitly how the E₈ X E₈ Yang-Mills theory can be obtained from a Gauge Theory based on the Clifford ( 16 ) group.
Category: Quantum Gravity and String Theory

Helium-Like Atoms

Authors: Vladislav Konovalov
Comments: 5 pages

In the article the theory of helium-like atoms is given
Category: Nuclear and Atomic Physics

Noncommutative (Super) P-Branes and Moyal-Yang Star Products with a Lower and Upper Scale

Authors: Carlos Castro
Comments: 8 pages, This article appeared in Phys. Letts B 626 (2005) 209.

Noncommutative p-brane actions, for even p+1 = 2n-dimensional world-volumes, are written explicitly in terms of the novel Moyal-Yang ( Fedosov-Kontsevich ) star product deformations of the Noncommutative Nambu Poisson Brackets (NCNPB) that are associated with the noncommuting world-volume coordinates q^A, p^A for A = 1, 2, 3, ...n. The latter noncommuting coordinates obey the noncommutative Yang algebra with an ultraviolet L_P (Planck) scale and infrared (R ) scale cutoff. It is shown why our p-brane actions in the "classical" limit ℏ_eff = ℏL_P/R → 0 still acquire nontrivial noncommutative corrections that differ from ordinary p-brane actions. Super p-branes actions in the light-cone gauge are also amenable to Moyal-Yang star product deformations as well due to the fact that p-branes moving in flat spacetime backgrounds, in the light-cone gauge, can be recast as gauge theories of volume-preserving diffeomorphisms. The most general construction of noncommutative super p-branes actions based on non ( anti ) commuting superspaces and quantum group methods remains an open problem.
Category: Quantum Gravity and String Theory

The Euclidean Gravitational Action as Black Hole Entropy, Singularities and Spacetime Voids

Authors: Carlos Castro
Comments: 41 pages, This article appeared in the Journal of Mathematical Physics, vol 49 (2008) 042501.

We argue why the static spherically symmetric (SSS) vacuum solutions of Einstein's equations described by the textbook Hilbert metric g_μν(r) is not diffeomorphic to the metric g_μν(|r|) corresponding to the gravitational field of a point mass delta function source at r = 0. By choosing a judicious radial function R(r) = r + 2G|M|Θ(r) involving the Heaviside step function, one has the correct boundary condition R(r = 0) = 0 , while displacing the horizon from r = 2G|M| to a location arbitrarily close to r = 0 as one desires, r_h → 0, where stringy geometry and quantum gravitational effects begin to take place. We solve the field equations due to a delta function point mass source at r = 0, and show that the Euclidean gravitational action (in ℏ units) is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions D ≥ 3 . In the Reissner-Nordsrom (massive-charged) and Kerr-Newman black hole case (massive-rotating-charged) we show that the Euclidean action in a bulk domain bounded by the inner and outer horizons is the same as the black hole entropy. When one smears out the point-mass and point-charge delta function distributions by a Gaussian distribution, the areaentropy relation is modified. We postulate why these modifications should furnish the logarithmic corrections (and higher inverse powers of the area) to the entropy of these smeared Black Holes. To finalize, we analyse the Bars-Witten stringy black hole in 1 + 1 dim and its relation to the maximal acceleration principle in phase spaces and Finsler geometries.
Category: Relativity and Cosmology

The Riemann Hypothesis is a Consequence of CT-Invariant Quantum Mechanics

Authors: Carlos Castro
Comments: 17 pages, This article appeared in the Int. Jour. of Geom. Methods of Modern Physics vol 5, no. 1, February 2008

The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form s_n = 1/2 + iλ_n. By constructing a continuous family of scaling-like operators involving the Gauss-Jacobi theta series and by invoking a novel CT-invariant Quantum Mechanics, involving a judicious charge conjugation C and time reversal T operation, we show why the Riemann Hypothesis is true. An infinite family of theta series and their Mellin transform leads to the same conclusions.
Category: Number Theory

Information Mechanics

Authors: John L. Haller Jr.
Comments: 24 pages

Advances in science are brought fourth by hypothesizing that the action of a system is a direct measure of the amount of information in that system. We begin to interpret this governing hypothesis by examining its implications to current research. From this investigation, we find four primary conclusions.

1. To properly and completely quantify the amount of information contained within a particle (or system), one must add the self-information of both the wavefunction and its Fourier transform pair.
2. Information in nature is found in packets quantized to an integer number of the natural units.
3. Over a period of time, the energy of a system acts like an information rate and thus the information needed to describe that system for that period of time is equal to the product of the energy and the time divided by the minimum uncertainty.
4. At a given instant in time, the angular momentum, J, of a system is in direct proportion to the amount of information that is contained within or can be transmitted by that system.

Critic of Notions of Official Physics Concerning a Microcosm

Authors: Vladislav Konovalov
Comments: 11 pages

In the article a critic of the main notions of a modern physics is given
Category: Quantum Physics

An Exceptional E₈ Gauge Theory of Gravity in D = 8, Clifford Spaces and Grand Unification

Authors: Carlos Castro
Comments: 22 pages, This article will appear in the Int J. Geom. Meth in Mod Phys vol 6 , no. 6 (Sept 2009)

A candidate action for an Exceptional E₈ gauge theory of gravity in 8D is constructed. It is obtained by recasting the E₈ group as the semi-direct product of GL(8,R) with a deformed Weyl-Heisenberg group associated with canonical-conjugate pairs of vectorial and antisymmetric tensorial generators of rank two and three. Other actions are proposed, like the quartic E₈ group-invariant action in 8D associated with the Chern-Simons E₈ gauge theory defined on the 7-dim boundary of a 8D bulk. To finalize, it is shown how the E₈ gauge theory of gravity can be embedded into a more general extended gravitational theory in Clifford spaces associated with the Cl(16) algebra and providing a solid geometrical program of a grand-unification of gravity with Yang-Mills theories. The key question remains if this novel gravitational model based on gauging the E8 group may still be renormalizable without spoiling unitarity at the quantum level.
Category: Quantum Gravity and String Theory

Complex Gravitational Theory and Noncommutative Gravity

Authors: Carlos Castro
Comments: 11 pages, This article appeared in Phys Letts B 675, (2009) 226-230

Born's reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity theory in curved spacetimes (without the need to introduce star products) as a local gauge theory of the deformed Quaplectic group that is given by the semi-direct product of U(1,3) with the deformed (noncommutative) Weyl-Heisenberg group corresponding to noncommutative generators [Z_a,Z_b] ≠ 0. The Hermitian metric is complex-valued with symmetric and nonsymmetric components and there are two different complex-valued Hermitian Ricci tensors R_μν, S_μν. The deformed Born's reciprocal gravitational action linear in the Ricci scalars R, S with Torsion-squared terms and BF terms is presented. The plausible interpretation of Z_μ = E_μ^a Z_a as noncommuting p-brane background complex spacetime coordinates is discussed in the conclusion, where E_μ^a is the complex vielbein associated with the Hermitian metric G_μν = g_(μν) + ig_[μν] = E_μ^a Ē_ν^b This could be one of the underlying reasons why string-theory involves gravity.
Category: Quantum Gravity and String Theory

The Cosmological Constant and Pioneer Anomaly from Weyl Spacetimes and Mach's Principle

Authors: Carlos Castro
Comments: 12 pages, This article appeared in Phys Letts B 675, (2009) 226-230

It is shown how Weyl's geometry and Mach's Holographic principle furnishes both the magnitude and sign (towards the sun) of the Pioneer anomalous acceleration a_P ~ -c²/R_Hubble firstly observed by Anderson et al. Weyl's Geometry can account for both the origins and the value of the observed vacuum energy density (dark energy). The source of dark energy is just the dilaton-like Jordan-Brans-Dicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. A nonvanishing value of the vacuum energy density of the order of 10^-123M⁴_Planck is found consistent with observations. Weyl's geometry accounts also for the phantom scalar field in modern Cosmology in a very natural fashion.
Category: Relativity and Cosmology

Energy Creates Particles, the Particles Creates Fields, and the Fields Creates Interplay

Authors: Vladislav Konovalov
Comments: 2 pages

Energy creates particles, the particles creates fields, and the fields creates interplay
Category: High Energy Particle Physics

Polynomials with Rational Roots that Differ by a Non-Zero Constant

Authors: Philip Gibbs
Comments: 6 pages

The problem of finding two polynomials P(x) and Q(x) of a given degree n in a single variable x that have all rational roots and differ by a non-zero constant is investigated. It is shown that the problem reduces to considering only polynomials with integer roots. The cases n < 4 are solved generically. For n = 4 the case of polynomials whose roots come in pairs (a,-a) is solved. For n = 5 an infinite number of inequivalent solutions are found with the ansatz P(x) = -Q(-x). For n = 6 an infinite number of solutions are also found. Finally for n = 8 we find solitary examples. This also solves the problem of finding two polynomials of degree n that fully factorise into linear factors with integer coefficients such that the difference is one.
Category: Number Theory

On the Noncommutative and Nonassociative Geometry of Octonionic Spacetime, Modified Dispersion Relations and Grand Unification

Authors: Carlos Castro
Comments: 23 pages, This article appeared in the J. Math. Phys, 48, no. 7 (2007) 073517.

The Octonionic Geometry (Gravity) developed long ago by Oliveira and Marques is extended to Noncommutative and Nonassociative Spacetime coordinates associated with octonionic-valued coordinates and momenta. The octonionic metric G_μν already encompasses the ordinary spacetime metric g_μν, in addition to the Maxwell U(1) and SU(2) Yang-Mills fields such that implements the Kaluza-Klein Grand Unification program without introducing extra spacetime dimensions. The color group SU(3) is a subgroup of the exceptional G₂ group which is the automorphism group of the octonion algebra. It is shown that the flux of the SU(2) Yang-Mills field strength F_μν through the area momentum Σ^μν in the internal isospin space yields corrections O(1/M²_Planck) to the energy-momentum dispersion relations without violating Lorentz invariance as it occurs with Hopf algebraic deformations of the Poincare algebra. The known Octonionic realizations of the Clifford Cl(8),Cl(4) algebras should permit the construction of octonionic string actions that should have a correspondence with ordinary string actions for strings moving in a curved Clifford-space target background associated with a Cl(3, 1) algebra.
Category: Quantum Gravity and String Theory

The Large N Limit of Exceptional Jordan Matrix Models and M, F Theory

Authors: Carlos Castro
Comments: 14 pages, This article appeared in the Journal of Geometry and Physics, 57 (2007) 1941-1949

The large N → ∞ limit of the Exceptional F₄,E₆ Jordan Matrix Models of Smolin-Ohwashi leads to novel Chern-Simons Membrane Lagrangians which are suitable candidates for a nonperturbative bosonic formulation of M Theory in D = 27 real, complex dimensions, respectively. Freudenthal algebras and triple Freudenthal products permits the construction of a novel E₇ X SU(N) invariant Matrix model whose large N limit yields generalized nonlinear sigma models actions on 28 complex dimensional backgrounds associated with a 56 real-dim phase space realization of the Freudenthal algebra. We argue why the latter Matrix Model, in the large N limit, might be the proper arena for a bosonic formulation of F theory. To finalize we display generalized Dirac-Nambu-Goto membrane actions in terms of 3 X 3 X 3 cubic matrix entries that match the number of degrees of freedom of the 27-dim exceptional Jordan algebra J₃[0].
Category: Quantum Gravity and String Theory

On the Riemann Hypothesis and Tachyons in Dual String Scattering Amplitudes

Authors: Carlos Castro
Comments: 13 pages, This article appeared in the International Journal of Geometric Methods in Modern Physics (IJGMMP) vol 3, no. 2 (2006) 187-199.

It is the purpose of this work to pursue a novel physical interpretation of the nontrivial Riemann zeta zeros and prove why the location of these zeros z_n = 1/2+iλ_n corresponds physically to tachyonic-resonances/tachyonic-condensates, originating from the scattering of two on-shell tachyons in bosonic string theory. Namely, we prove that if there were nontrivial zeta zeros (violating the Riemann hypothesis) outside the critical line Real z = 1/2 (but inside the critical strip), these putative zeros do not correspond to any poles of the bosonic open string scattering (Veneziano) amplitude A(s, t, u). The physical relevance of tachyonic-resonances/tachyonic-condensates in bosonic string theory, establishes an important connection between string theory and the Riemann Hypothesis. In addition, one has also a geometrical interpretation of the zeta zeros in the critical line in terms of very special (degenerate) triangular configurations in the upper-part of the complex plane.
Category: Quantum Gravity and String Theory

Two Large Errors: Newton First Law and Inertial Reference

Authors: Vladislav Konovalov
Comments: 4 pages

In the article one more physical sense of a constant of the Planck is detected and the inaccuracy of notions endured in heading of the article is shown.
Category: Classical Physics

Universe as Whole

Authors: Vladislav Konovalov
Comments: 5 pages

The different versions of the Universe structure are reviewed and it mean density is calculated.
Category: Relativity and Cosmology

The Clifford Space Geometry Behind the Pioneer and Flyby Anomalies

Authors: Carlos Castro
Comments: 23 pages, This article will appear in the IJMPA (2009).

It is rigorously shown how the Extended Relativity Theory in Clifford spaces (C-spaces) can explain the variable radial dependence a_p(r) of the Pioneer anomaly; its sign (pointing towards the sun); why planets don't experience the anomalous acceleration and why the present day value of the Hubble scale R_H appears. It is the curvature-spin coupling of the planetary motions that hold the key. The difference in the rate at which clocks tick in C-space translates into the C-space analog of Doppler shifts which may explain the anomalous redshifts in Cosmology, where objects which are not that far apart from each other exhibit very different redshifts. We conclude by showing how the empirical formula for the Flybys anomalies obtained by Anderson et al. can be derived within the framework of Clifford geometry.
Category: Relativity and Cosmology

The Extended Relativity Theory in Clifford Spaces

Authors: Carlos Castro, M. Pavšič
Comments: 65 pages, This article appeared in Progress in Physics vol 1 (April 2005) 31-64

An introduction to some of the most important features of the Extended Relativity theory in Clifford-spaces (C-spaces) is presented whose "point" coordinates are non-commuting Clifford-valued quantities which incorporate lines, areas, volumes, hyper-volumes.... degrees of freedom associated with the collective particle, string, membrane, p-brane,... dynamics of p-loops (closed p-branes) in target Ddimensional spacetime backgrounds. C-space Relativity naturally incorporates the ideas of an invariant length (Planck scale), maximal acceleration, non-commuting coordinates, supersymmetry, holography, higher derivative gravity with torsion and variable dimensions/signatures. It permits to study the dynamics of all (closed) p-branes, for all values of p, on a unified footing. It resolves the ordering ambiguities in QFT, the problem of time in Cosmology and admits superluminal propagation ( tachyons ) without violations of causality. A discussion of the maximalacceleration Relativity principle in phase-spaces follows and the study of the invariance group of symmetry transformations in phase-space allows to show why Planck areas are invariant under acceleration-boosts transformations . This invariance feature suggests that a maximal-string tension principle may be operating in Nature. We continue by pointing out how the relativity of signatures of the underlying n-dimensional spacetime results from taking different n-dimensional slices through C-space. The conformal group in spacetime emerges as a natural subgroup of the Clifford group and Relativity in C-spaces involves natural scale changes in the sizes of physical objects without the introduction of forces nor Weyl's gauge field of dilations. We finalize by constructing the generalization of Maxwell theory of Electrodynamics of point charges to a theory in C-spaces that involves extended charges coupled to antisymmetric tensor fields of arbitrary rank. In the concluding remarks we outline briefly the current promising research programs and their plausible connections with C-space Relativity.
Category: Quantum Gravity and String Theory

The Exceptional E₈ Geometry of Clifford (16) Superspace and Conformal Gravity Yang-Mills Grand Unification

Authors: Carlos Castro
Comments: 33 pages, This article appeared in the IJGMMP vol 6, no. 3 (2009) 385.

We continue to study the Chern-Simons E₈ Gauge theory of Gravity developed by the author which is a unified field theory (at the Planck scale) of a Lanczos-Lovelock Gravitational theory with a E₈ Generalized Yang-Mills (GYM) field theory, and is defined in the 15D boundary of a 16D bulk space. The Exceptional E₈ Geometry of the 256-dim slice of the 256 X 256-dimensional flat Clifford (16) space is explicitly constructed based on a spin connection Ω_M^AB, that gauges the generalized Lorentz transformations in the tangent space of the 256-dim curved slice, and the 256 X 256 components of the vielbein field E_M^A, that gauge the nonabelian translations. Thus, in one-scoop, the vielbein E_M^A encodes all of the 248 (nonabelian) E₈ generators and 8 additional (abelian) translations associated with the vectorial parts of the generators of the diagonal subalgebra [Cl(8) ⊗ Cl(8)]_diag ⊂ Cl(16). The generalized curvature, Ricci tensor, Ricci scalar, torsion, torsion vector and the Einstein-Hilbert-Cartan action is constructed. A preliminary analysis of how to construct a Clifford Superspace (that is far richer than ordinary superspace) based on orthogonal and symplectic Clifford algebras is presented. Finally, it is shown how an E₈ ordinary Yang-Mills in 8D, after a sequence of symmetry breaking processes E₈ → E₇ → E₆ → SO(8, 2), and performing a Kaluza-Klein-Batakis compactification on CP², involving a nontrivial torsion, leads to a (Conformal) Gravity and Yang-Mills theory based on the Standard Model in 4D. The conclusion is devoted to explaining how Conformal (super) Gravity and (super) Yang-Mills theory in any dimension can be embedded into a (super) Clifford-algebra-valued gauge field theory.
Category: Quantum Gravity and String Theory

How to Capture an Electron Into Atomic Orbit

Authors: Vladislav Konovalov
Comments: 3 pages

In the article the capture bar of an electron into atomic orbit and mechanism for analysis of screw motion of an electron is described.
Category: Condensed Matter

The Clifford Space Geometry of Conformal Gravity and U(4) X U(4) Yang-Mills Unification

Authors: Carlos Castro
Comments: 22 pages, This article will appear in the Int J. of Mod. Phys A.

It is shown how a Conformal Gravity and U(4) X U(4) Yang-Mills Grand Unification model in four dimensions can be attained from a Clifford Gauge Field Theory in C-spaces (Clifford spaces) based on the (complex) Clifford Cl(4,C) algebra underlying a complexified four dimensional spacetime (8 real dimensions). Upon taking a real slice, and after symmetry breaking, it leads to ordinary Gravity and the Standard Model in four real dimensions. A brief conclusion about the Noncommutative star product deformations of this Grand Unified Theory of Gravity with the other forces of Nature is presented.
Category: Quantum Gravity and String Theory

P-Branes as Antisymmetric Nonabelian Tensorial Gauge Field Theories of Diffeomorphisms in P + 1 Dimensions

Authors: Carlos Castro
Comments: 44 pages, This article has been submitted to the Journal of Mathematical Physics, Aug 2009

Long ago, Bergshoeff, Sezgin, Tanni and Townsend have shown that the light-cone gauge-fixed action of a super p-brane belongs to a new kind of supersymmetric gauge theory of p-volume preserving diffeomorphisms (diffs) associated with the p-spatial dimensions of the extended object. These authors conjectured that this new kind of supersymmetric gauge theory must be related to an infinite-dim nonabelian antisymmetric gauge theory. It is shown in this work how this new theory should be part of an underlying antisymmetric nonabelian tensorial gauge field theory of p+1-dimensional diffs (upon supersymmetrization) associated with the world volume evolution of the p-brane. We conclude by embedding the latter theory into a more fundamental one based on the Clifford-space geometry of the p-brane configuration space.
Category: Quantum Gravity and String Theory

On the Riemann Hypothesis, Area Quantization, Dirac Operators, Modularity and Renormalization Group

Authors: Carlos Castro
Comments: 33 pages, This article will appear in the Int. J. of Geom. Methods in Mod Phys vol 7, no. 1 (2010)

Two methods to prove the Riemann Hypothesis are presented. One is based on the modular properties of Θ (theta) functions and the other on the Hilbert-Polya proposal to find an operator whose spectrum reproduces the ordinates ρ_n (imaginary parts) of the zeta zeros in the critical line : s_n = 1/2 + iρ_n A detailed analysis of a one-dimensional Dirac-like operator with a potential V(x) is given that reproduces the spectrum of energy levels E_n = ρ_n, when the boundary conditions Ψ_E (x = -∞) = ± Ψ_E (x = +∞) are imposed. Such potential V(x) is derived implicitly from the relation x = x(V) = π/2(dN(V)/dV), where the functional form of N(V) is given by the full-fledged Riemann-von Mangoldt counting function of the zeta zeros, including the fluctuating as well as the O(E^-n) terms. The construction is also extended to self-adjoint Schroedinger operators. Crucial is the introduction of an energy-dependent cut-off function Λ(E). Finally, the natural quantization of the phase space areas (associated to nonperiodic crystal-like structures) in integer multiples of π follows from the Bohr-Sommerfeld quantization conditions of Quantum Mechanics. It allows to find a physical reasoning why the average density of the primes distribution for very large x (O(1/logx)) has a one-to-one correspondence with the asymptotic limit of the inverse average density of the zeta zeros in the critical line suggesting intriguing connections to the Renormalization Group program.
Category: Number Theory

Colloid Systems

Authors: Vladislav Konovalov
Comments: 19 pages

In the article the equations of a kinetics of coagulation of disperse systems and theory of a solvate layer of colloidal particles are given.
Category: Condensed Matter

Dark Energy is Needed for the Consistency of Quantum Electrodynamics Heisenberg's Biggest Blunder?

Authors: Jack Sarfatti
Comments: 4 pages

The argument that virtual photons can be globally gauged away I think is spurious. Indeed, the inconsistency with the boson commutation rules in Heisenberg and Pauli's historic 1929 attempt to quantize the electromagnetic field disappears once one uses the recently discovered dark energy density.
Category: Quantum Gravity and String Theory

Quantum Signatures of Solar System Dynamics

Authors: Arkady L. Kholodenko
Comments: 61 pages.

Let ω(i) be period of rotation of the i-th planet around the Sun (or ω_j(i) be period of rotation of j-th satellite around the i-th planet). From empirical observations it is known that within margins of experimental errors Σ_i n_iω(i) = 0 (or Σ_j n_jω_j(i) = 0) for some integers n_i (or n_j ), different for different satellite systems. These conditions, known as resonance conditions, make uses of theories such as KAM difficult to implement. The resonances in Solar System are similar to those encountered in old quantum mechanics where applications of methods of celestial mechanics to atomic and molecular physics were highly successful. With such a successes, the birth of new quantum mechanics is difficult to understand. In short, the rationale for its birth lies in simplicity with which the same type of calculations can be done using methods of quantum mechanics capable of taking care of resonances. The solution of quantization puzzle was found by Heisenberg. In this paper new uses of Heisenberg?s ideas are found. When superimposed with the equivalence principle of general relativity, they lead to quantum mechanical treatment of observed resonances in the Solar System. To test correctness of theoretical predictions the number of allowed stable orbits for planets and for equatorial stable orbits of satellites of heavy planets is calculated resulting in good agreement with observational data. In addition, the paper briefl?y discusses quantum mechanical nature of rings of heavy planets and potential usefulness of the obtained results for cosmology.
Category: Astrophysics

Conditions for Entanglement

Authors: Dieter Gernert
Comments: 6 pages. Journal reference: Frontier Perspectives, vol. 14, no. 2, 8-13 (2005)

Whereas entanglement and nonlocality belong to the fundamental findings of quantum theory, possible extensions to macroscopic systems outside the quantum laboratory are scarcely studied. This paper analyses conditions for entanglement to occur on a macrophysical level. An empirical basis is given by historic episodes and modern quantitative data. Theoretical understanding can start from the concept of perspective notions; the crucial new term is "common prearranged context", which characterizes the preparation to be made in advance (or naturally given conditions) in order to enable entanglement. A mathematical formalization is possible and gives some insight about how to handle perspective notions.
Category: Quantum Physics

Ockham's Razor and Its Improper Use

Authors: Dieter Gernert
Comments: 6 pages. Journal reference: Cognitive Systems, vol.7, nr. 2, 133-138 (2009)

"Ockham's razor" is a methodical principle, due to the medieval philosopher William of Ockham, who mainly opposed an unjustified creation of new terms in philosophy. Since this principle and its later versions are frequently quoted in discussions about anomalies, it will be studied here in some detail. After a short look on the historical roots, the principal modern formulations are summarized. It will be shown that a demand for "simplicity" cannot be generally maintained. Rather, striving for simplicity can conflict with other essentials of scientific method. Ockham's principle - no matter whether in its original or in a modified version - cannot be helpful in a rational decision between competing explanations for the same empirical facts. An incorrect use of Ockham's razor only leads to a perpetuation and corroboration of existing prejudice, and this principle should not be used to easily get rid of unwelcome data or concepts.
Category: History and Philosophy of Physics

Magnetic Processing of Water

Authors: Vladislav Konovalov
Comments: 8 pages

In the article the in-depth arguing is given, that takes place at magnetic processing of water.
Category: Classical Physics

Formation of Galaxies and Stars

Authors: Vladislav Konovalov
Comments: 9 pages

In the article some features of formation of galaxies and stars are considered
Category: Astrophysics

A Wave-Based Polishing Theory

Authors: Hamid V. Ansari
Comments: 3 pages

The molecules of the reflecting surface are sources of Huygens' wavelets which make the reflected wavefront. These molecules can be nonplanar to the extent of a fraction of the wavelength while yet there exists practically reflected plane wavefront.
Category: Classical Physics

"Proposition for Performing a Series of Important Electromagnetic Experiments" and "Why Two Parallel Currents Exert Force on Each Other"

Authors: Hamid V. Ansari
Comments: 6 pages

The real causes of force existent between two current-carrying wires are searched. Some electromagnetic experiments are proposed to verify these causes and other similar material.
Category: Classical Physics

Primary Proof that the Torque Exerted on a Stationary Body is Zero

Authors: Hamid V. Ansari
Comments: 3 pages

In a primary manner it is shown that if a body is stationary the torque exerted on it is zero, while at present avoiding the analytical proof of this theorem, this theorem is presented to the student unprovenly and almost as an axiom.
Category: Classical Physics

Why Evaporation Causes Coldness; a Challenge to the Second Law of Thermodynamics

Authors: Hamid V. Ansari
Comments: 11 pages

In surface evaporation the liquid increases the potential energy of its molecules by taking heat while their kinetic energies remain unchanged. In such state the molecules are in the form of a gas (vapor). We know that in an isothermal system of a liquid and a gas adjacent to it, the temperature of the gas decreases due to the surface evaporation while some net heat is transferred from the gas to the liquid. So, if the temperature of the gas is lower than the temperature of the liquid only in a sufficiently small extent, some net heat will be still transferred from the gas to the liquid due to the surface evaporation and finally the gas and liquid (and vapor) will be isothermal (in a temperature lower than the initial temperature). This matter violates the Clausius (or refrigerator) statement of the second law of thermodynamics.
Category: Classical Physics

A Deliberation on the Surface Tension Theory

Authors: Hamid V. Ansari
Comments: 16 pages

It is shown that surface tension is not the reason causing minimization of the surface of a liquid pile. It is shown that there exists a pressure inside the liquid arising from the inward intermolecular resultant force on the surface molecules exerted by the liquid molecules adjacent to the surface. We call it as cohesion pressure. A method is presented for measuring the intermolecular attraction which will be also a means for testing the theory in comparison with the current theory of surface tension. It is proven that the surface tension is not what causes the horizontal wire sliding on the two limbs of a U-shaped wire to be in equilibrium in any position when a liquid film forms the area of the U-shaped wire. In a sure manner, incorrectness of the current relation Δp = 4 γ/R, for the pressure difference between inside and outside of a bubble having radius R, and Δp = 4 γ/R, for the one related to a solid drop having radius R, is proven. It is shown that the adhesion reduces the pressure inside the liquid, because a part of the liquid weight is sustained by the walls of the container. The mechanism of capillarity is discussed in detail in terms of intermolecular attraction and cohesion pressure. Dependence of rise altitude on depth of dipping and dependence of fall depth on depth of dipping are properties in capillarity; this is predicted by the theory presented in this paper and not by the theory of surface tension, and then can be a practical test for the theory.
Category: Classical Physics

A Critique of the Definitions of Mass and Force

Authors: Hamid V. Ansari
Comments: 18 pages

It is not necessary to distinguish between inertial and gravitational masses believing that the nature has chosen them quite proportional to each other by chance, and not necessary to believe that the nature by chance has chosen the power of distance in inverse-square forces exactly equal to two, and not necessary that in trying to define mass (and force) to become involved in a vicious circle using presupposition of existence of inertial reference frame which itself requires pre-definition of mass. Newton's laws of motion are rewritten in a logical manner. Some primary models are presented as guides for discovering the essence of known forces. A model for justifying the force between two electric and magnetic charges, moving relative to each other, is presented. In fact energy has only one form: kinetic energy. The law of action-reaction holds completely and undoubtedly only during the direct collisions of particles.
Category: Classical Physics

Does Really Stellar Aberration Contradict Ether Drag

Authors: Hamid V. Ansari
Comments: 7 pages

As we know the Michelson-Morley experiment proves that there is no ethereal wind on the ground. It is thought at present that the existence of the stellar aberration necessitates existence of ethereal wind on the ground if the ether is to exist. Comparison of these two experiments results in believing that the ether does not exist. We prove that if the ether exists the stellar aberration can occur with the ether drag and then does not necessitate existence of the ethereal wind.
A new model in the form of undiscovered tiny particles is presented for the ether. With accepting this model and by using the results of the Michelson-Morley and Michelson-Gale experiments a model consisting of an ethereal stack stuck with the earth in its motion in the space is presented such that the earth can rotate axially inside this stack freely. We shall also see why atomic clocks are slow when are in (fast) motion.
Category: Classical Physics

Optical Deviation of Stars Light by Sun

Authors: Hamid V. Ansari
Comments: 9 pages

We consider the sun and its atmosphere as a spherical lens causing deviation of stars light and also decrease of its speed in the lens. Such a lens can probably make a multiple image of a star. It is also shown that the sun, because of its atmosphere, is in fact smaller than what an observer measures. We show that the above-mentioned spherical lens is non-dispersive practically.
Category: Astrophysics

Wrong Construing of the Boltzmann Factor; e = Hν is Wrong

Authors: Hamid V. Ansari
Comments: 13 pages

As we know probability of finding a system in one of its accessible states is proportial to the Boltzmann factor. It is shown that contrary to what is thought at present in this proportion the energy appearing in the Boltzmann factor is not a variable but it is a constant and the variable is the state accessible for the system having this constant energy. So, what at present is accepted as Boltzmann factor is not real. Deduction of the Maxwell velocity distribution as an instance of the consequences of the real Boltzmann factor, and the first deduction of the relation E = hν as an instance of the consequences of the wrong Boltzmann factor are presented. A logical review of some of the fundamental elements of the statistical mechanics, that also contains some new viewpoints, has been necessary. A factor is introduced in a general expression for molar specific heat which plays the role of partition (not equipartition) of energy and giving suitable amounts to it all the practical cases including ones related to ideal gases and crystalline solids are coveredν
Category: Classical Physics

Classical Justification of the Stern-Gerlach Experiment

Authors: Hamid V. Ansari
Comments: 8 pages

It is shown that contrary to what is thought the classical physics does not predict a uniform distribution for the magnetic dipoles (silver atoms) in a nonuniform magnetic field in the Stern-Gerlach experiment. Its prediction for a concentrated beam is obtained in the form of a circular surface such that the density of the dipoles is much more near the edge than near the center. Some experiments are proposed for testing the contents of the article.
Category: Classical Physics

Compton Effect as a Doppler Effect

Authors: Hamid V. Ansari
Comments: 4 pages

An electromagnetic wave with the wavelength λ, which has some energy, descends on an electron and makes it move in the same direction of propagation of the wave. The wave makes the moving electron oscillate with a lower frequency. A very much simple analysis shows that this moving oscillating electron radiates, in the direction making angle θ with the direction of the incident wave, an electromagnetic wave which its wavelength is bigger by a factor proportional to λ(1 - cosθ).
Category: Classical Physics

Actual Justification of the Crooks and Nichols Radiometers

Authors: Hamid V. Ansari
Comments: 6 pages

Radiation energy causes fluctuation of the molecules in vanes of the Crooks radiometer. Through this fluctuation the molecules of the vanes strike the adjacent air molecules and as reaction cause recoil of the vanes. It seems that this is also the mechanism of Nichols radiometer.
Category: Classical Physics

Geomagnetic Field Reason

Authors: Hamid V. Ansari
Comments: 6 pages

Conductive core of the earth is as hot as causing freedom of the valence electrons after which these released electrons distribute themselves toward the core surface and move along with the rotation of the earth causing that magnetic field which forms the big magnet inside the earth. This is the summary of the article which also includes presentation of some experiments for testing the validity of the presented theory and a conclusion justifying the magnetic inversions of the earth. Based on the presented discussions a practical way for direct determination of ionization energies of different elements is proposed.
Category: Classical Physics

Classical Analysis of the Electric Conductivity

Authors: Hamid V. Ansari
Comments: 8 pages

Action mechanism of a conductor is presented in a simple manner. It is proven that this is not the charges themselves that are distributed in the conductor but their substitutes do this act. Also we conclude that probably the electron doesn't have a size so small compared with the dimensions of a molecule. In a discussion relating directly to the subject of surface tension we see why a net negative charge in a conductor cannot leave it.
Category: Classical Physics

Electric Current Similar to Water Current

Authors: Hamid V. Ansari
Comments: 20 pages

A perfect comparison between a closed circuit of water current and a closed circuit of electric current is made and Ohm's law is obtained in this manner and it is shown that, contrary to the current belief, existence of conduction current is not because of the existence of any electric field in the conductor, and the linear relation J = gE cannot be valid. The relaxation time (necessary for the current to reach its final speed) and the final speed (drift velocity) of the current are obtained in the above-mentioned manner, and it is shown that, contrary to what is believed at present, both of them are independent of the chosen standard unit charge (eg electron charge or coulomb) and its mass. It is also shown that, contrary to the current belief, alternating current is steady. We also prove the existence of a kind of resistance arising from the configuration of the circuit. Action mechanism of transistor is explained and a hydrodynamical analogue for it is introduced: both confirming the material presented earlier.
Category: Classical Physics

A Deliberation on the Limits of the Validity of Newton's Third Law in Electromagnetism

Authors: Hamid V. Ansari
Comments: 7 pages

It is shown that as Newton's third law holds in static discussions of Electromagnetism it holds also in dynamic discussions of it, ie where the motion of electric charge in the magnetic field arising from the magnetic static (or magnetostatic) poles is under consideration. In addition, it is shown that in this recent case the forces of action and reaction are not collinear. In other words as we know there is some force exerted on a current-carrying wire in the magnetic field of a magnet. It is shown that this magnet is in fact the same enlarged magnetic needle in Oersted's experiment, and then there exists also some force exerted on the magnet due to the electric current in the wire. These two action and reaction forces are in opposite directions but are not collinear.
Category: Classical Physics

Role of Air Pressure in the Force Between Currents

Authors: Hamid V. Ansari
Comments: 9 pages

Density of lines of the magnetodynamic field arising from two parallel currents is more in the regions out of the distance between the two wires and then the molecular magnetic dipoles of air are pulled toward these regions and create a bigger pressure there which causes the two wires to be pushed (or to be attracted) toward each other. A similar reasoning applied conversely to two antiparallel currents justifies their repulsion arising from the created air pressure difference. Thus, most probably, railgun will not work very well in the absence of the air.
Category: Classical Physics

Electromagnetic Theory Without the Lorentz Transformations

Authors: Hamid V. Ansari
Comments: 32 pages

We consider point magnetic charges as the sources of the magnetostatic fields, like the point electric charges for the electrostatic fields. Forms of the mutual effects of electric and magnetic charges on themselves and on each other are presented in the forms of vectorial relations. Using these relations incorrectness of a usual manner which eventually leads to the deviation from the classical physics and to the rejection of the Galilean transformations and to the resort to the special relativity is proven. Static potential energy of a distribution of electric and magnetic charges is presented with a careful view on the actual essence of each involved term; this itself shows a sample of the usual carelessness existing in the present current electromagnetic theory even in its static discussions. Almost all the fundamental relations in the present current electromagnetic theory are rewritten in new forms by using the fundamental vectorial relations presented at the beginning of the paper. In a more detailed argument the proportion of the curl of the dynamic field of one kind (ie magnetodynamic or electrodynamic) to the time derivative of the static field of the other kind (ie electrostatic or magnetostatic) is established; meanwhile the proportion of the current density of one kind to the time derivative of the field of the same kind is also shown. Lenz's law is obtained in its new form. Static and dynamic inductances are presented. By presenting an aspect which views the space full of much tiny electrostatic and magnetostatic dipoles, the possibility of the proportion of the static fields to the dynamic fields is shown. The way in which the electromagnetic wave propagates through these dipoles is easily explained by using the mentioned fundamental relations, and by obtaining the new form of Maxwell's equations and deducing the wave equations from them, this simple explanation is endorsed. By deducing the dynamic potential energy and explaining its difference with the static potential energy of a set of charges, the Poynting vector is obtained in its new form. It is shown that the fields of an electromagnetic wave are continuous across the boundary interfaces. Fresnel coefficients are obtained in their quite new forms, and it is explained that the coefficient appearing in the fundamental relations showing the relations between two electric and magnetic charges moving relative to each other, μ, must be construed as a world constant. The reflectance and transmittance are introduced in this new approach, and it is shown that sum of them is identical with one.
Category: Classical Physics

Odd Algebraic Bases, and Their Utility in Computer

Authors: Hamid V. Ansari
Comments: 3 pages

It is shown that we can take all numbers to odd bases such that we require only about half of the digits required in the current method provided that we introduce negative mark for each digit. Most probably this method will have various applications in the computer technology.
Category: Data Structures and Algorithms

Solution to Four-Color Problem

Authors: Hamid V. Ansari
Comments: 15 pages

To color a given map we first find its related map with the most mutual adjacencies and color it by only four colors, then we trace back.
Category: Combinatorics and Graph Theory

A Proof for Goldbach's Conjecture

Authors: Hamid V. Ansari
Comments: 5 pages

For a large even number there are a large number of pairs of odd numbers sum of the members of each being the even number. We eliminate those pairs that none of the members of each of them is prime and show that the number of the remaining pairs is still large. The process of proof shows that there can be no drop to zero in the function of the number of the mentioned prime pairs.
Category: Number Theory

A Design for Making a New Simple Coil Trap

Authors: Hamid V. Ansari
Comments: 2 pages

It seems that for some applications we require to decrease the drifting velocity of atomic or molecular beams, and seemingly various methods have been designed to achieve this purpose. I propose to select a relatively big coreless solenoid through which we can give an intense direct (probably impulsive) electric current. Set the whole instrument which is to create the beam in the space interior to the solenoid, and create the beam parallel to the solenoid. There is no magnetic field gradient inside a current-carrying solenoid. So, the drift velocity of the beam is not changed inside the solenoid, but when it is leaving the solenoid its drift velocity decreases. (If we use this method conversely we can increase the drift velocity of the beam.)
Category: Nuclear and Atomic Physics

Classical Justification of the Photoelectric Effect

Authors: Hamid V. Ansari
Comments: 6 pages

It is said that empirical results of the photoelectric effect have no classical justification and then are used for deduction of the famous relation E = hν as an alternative way to Planck's deduction. We show that these results are in fact justifiable by the classical theory of electromagnetism and then this way can not be a valid manner for obtaining this relation. Using the presented discussions simple justification of the Rayleigh scattering and of the action mechanism of laser are presented in support of the validity of the discussion.
Category: Nuclear and Atomic Physics

Classical Justification of the Franck-Hertz Experiment

Authors: Hamid V. Ansari
Comments: 6 pages

By increasing the voltage in the Franck-Hertz experiment we reach a breakdown voltage in which the current existent between the grid and anode is canceled. This breakdown voltage will be repeated at equal intervals by increasing the voltage.
Category: Nuclear and Atomic Physics

Classical Justification of the Wave-Like Behavior of Electron Beams

Authors: Hamid V. Ansari
Comments: 17 pages

Relying on this fact that not only role of the medium (intermediate gas) cannot be ignored in the electric discharge between cathode and anode, but also it is very important, the diffraction and interference phenomena which an electron beam can reveal are justified. This act is done after analyzing the manner in which stroke propagates via the gas valence electrons. In this respect an experiment is proposed as a test. We conclude that the cathodic ray does not carry charge, ie is not a ray of electrons being shot but is a longitudinal wave arising from the vibration of the valence electrons of the molecules of the carrying-wave medium. In this way the mechanism of production of and the difference between the longitudinal and transverse waves and that our longitudinal wave is only due to compression (not expansion) impacts are explained.
Our ability for complete deflecting and making away the electron beam (behind the anode), existence of sharp shadow of anode in the electric discharge tube, existence of dark-bright striated columns in this tube (similar to Kundt tube in acoustics), and the action mechanism of image intensifying in the image intensifier tubes are all described as witnesses to confirm the wave-like motion for electron beam proposed in this paper and reject the shooting motion for it.
Deflection of the trajectory of electron beams in electric and magnetic fields is justified in wave-like motion of "going" and "backing" for evaluation of which an experiment has been proposed. It is shown that how for transferring of momentum there is no necessity to suppose shooting motion for electron in the cathodic ray.
Two separate parallel cathodic rays repel each other. This will be contrary to what the electromagnetism predicts if a cathodic ray is to carry charge. This phenomenon is justified by the model presented here.
Category: Nuclear and Atomic Physics

Cylindrical Wave, Wave Equation, and Method of Separation of Variables

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

Classical Justification of the Hall Effect

Authors: Hamid V. Ansari
Comments: 7 pages

By exerting a magnetic field normal to a current-carrying strip we cause a deviation in the path of moving electrons as if our conducting path is a wire along an edge of the strip which at a point is deflected normal to the edge and reaches the other edge and afterwards is continued along this other edge in the same direction as before. It is clear that connecting the two end points of the transverse part of such a wire by a minor wire we expect a part of the main current to pass through this minor wire. The direction of such a current flowing in the minor wire is such that as if the current-carrying charges in the main current-carrying strip are positive charges. This is the basis of this article. A quite practical experiment is proposed for testing the presented theory.
Category: Condensed Matter

Role of Air Pressure in Diamagnetism

Authors: Hamid V. Ansari
Comments: 7 pages

In a gradient of magnetic field, magnetic dipoles of the air are attracted toward the region of intense field such that the air pressure is more in the regions of more intense field. The formed pressure gradient exerts a net force on a body placed in the air in this gradient of magnetic field toward the region of low pressure or the region having weaker field. This is like what takes place in sink-float separation.
Category: Condensed Matter

Independence of Capacitance from Dielectric

Authors: Hamid V. Ansari
Comments: 30 pages

It is shown that there exists a uniqueness theorem, stating that the charges given to a constant configuration of conductors take a unique distribution, which contrary to what is believed does not have any relation to the uniqueness theorem of electrostatic potential. Using this theorem we obtain coefficients of potential analytically. We show that a simple carelessness has caused the famous formula for the electrostatic potential to be written as U = 1/2 ∫D.Edv while its correct form is U = 1/2 ∫D.E_ρdv in which E_ρ is the electrostatic field arising only from the external charges not also from the polarization charges.
Considering the above-mentioned material it is shown that, contrary to the current belief, capacitance of a capacitor does not at all depend on the dielectric used in it and depends only on the configuration of its conductors. We proceed to correct some current mistakes resulted from the above-mentioned mistakes, eg electrostatic potential energy of and the inward force exerted on a dielectric block entering into a parallel-plate capacitor are obtained and compared with the wrong current ones.
It is shown that existence of dielectric in the capacitor of a circuit causes attraction of more charges onto the capacitor because of the polarization of the dielectric. Then, in electric circuits we should consider the capacitor's dielectric as a source of potential not think wrongly that existence of dielectric changes the capacitor's capacitance. Difference between these two understandings are verified completely during some examples, and some experiments are proposed for testing the theory. For example it is shown that contrary to what the current theory predicts, resonance frequency of a circuit of RLC will increase by inserting dielectric into the capacitor (without any change of the geometry of its conductors). It is also shown that what is calculated as K (dielectric constant) is in fact 2 - (1/K).
Category: Condensed Matter

Will Solar Oscillations Spoil the Lisa Experiment?

Authors: John Hunter
Comments: 2 pages

A conjecture is discussed whereby the gravitational mass of an object depends on its mass/radius ratio. If the conjecture is true then solar oscillations of the sun would cause large signals for LISA. These signals would be greater than those produced by gravitational waves from distant sources, and potentially spoil the experiment.
Category: Relativity and Cosmology

Unified Theory's Non-Expanding Universe Replaces Big Bang & Steady State Theories of Expanding Universe

Authors: Rati Ram Sharma
Comments: 11 pages

In a universe expanding as per the Big Bang or Steady State theory the cosmic redshifts should increase exponentially with time, which is not actually observed. So the universe is NOT expanding. In Unified Theory's non-expanding universe the total energy-mass content is eternally conserved with NO 'initial creation of matter from nothing' in a single big explosive event of the Big Bang theory or continuously as in the Steady State theory. The cosmic redshift is caused not by Doppler effects of receding velocities of stellar light sources but by depletion of photon energy during long passage through the sharmon medium due to non-Doppler effects of gravitational, electromagnetic & viscous losses. Cosmic microwave background follows naturally and plausible explanation given to the observation on Ia type supernovae, which has amazed & horrified the astronomers. Halton Arp's observation of high-redshift quasars in the vicinity of low-redshift parent star systems is also explained. There is no antigravity force permeating space and no likelihood for the universe to become empty ever in future. Age of the non-expanding universe is about 45 billion years. Dark energy and dark matter are related to the Sharmon medium. Realistic theory of Nonexpanding universe replaces Big Bang & Steady State theories of expanding universe.
Category: Relativity and Cosmology

Unified Theory's New Principle of Null Action

Authors: Rati Ram Sharma
Comments: 6 pages

Quantum Theory's Uncertainty Principle violates conservation of energy & momentum and invokes matter's unrealistic creation from, and dissolution into, nothing. In Unified Theory action is an evolute of sharmon with Planck constant h as its quantum. The inviolable conservations of energy and momentum ordain conservation of action, invalidation of the Uncertainty Principle and introduction of the new Principle of Null Action. It has universal applications and is conceptually superior to the old Hamilton's Principle of Least Action as the latter unrealistically associates turnover of action NOT with variations in but with constant energy & momentum. In Nature, the path chosen by an isolated closed system during a real physical change through a succession of intermediate states from the initial equilibrium state 'a' to the final equilibrium state 'b' is such that the summation or integration of action covering all variations of energy or momentum is zero or null. Hence the name: "Principle of Null Action". The new principle has successfully derived the generally accepted equations for the following: Schwinger's Quantum Dynamical Principle, Klein-Gorden Field Equations, Schrodinger Wave Equation, Special and General Relativity, Euler's Equations, Lagrange's Equations, Maxwell Equations for Electromagnetic Radiation, Newton's laws of motion, Thermodynamic Equation of State, Discharge of Capacitance through Inductance & Resistance.
Category: High Energy Particle Physics

Unified Theory's Elements, Basic Substance & Absolute Reference Frame

Authors: Rati Ram Sharma
Comments: 8 pages

An element composes other particles but it itself is non-composite. The basic substance composes all and it itself is composed by the basic element(s). The Modern Standard Model with Supersymmetry has over 200 basic particles but none of them satisfies the definition of 'element'. Inter-conversions of various forms of energies and/or with mass and the equation E=mc² compellingly needs a 'basic substance' composing all forms of E & m, otherwise E & m could not interconvert. Real Sharmon Medium propagating light as wave-quantum UNITY at constant velocity invariant to source-observer motion is the 'absolute reference frame' and all-composing and all-pervading 'basic substance' composed by the new particle 'sharmon', which comprises a positive positrino & a negative negatrino, the two basic elements named cosminos. They compose all forms of energy & mass, material particles and energy-quanta in the Cosmos. Their electric charge is ± 1.37x 10^-30 esu; mass 2.596x10^-48 gm & spin ½. Sharmon's mass is 5.192x10-48 gm, spin 0 & 1. As a kinetic gas, the sharmon medium is irremovable by any means since the ~10^-33 cm Sharmon can pass thru interatomic spaces and between orbital electrons. Its number density is ~10¹⁵ sharmons per cm³, mass density 0.519x10^-33 gm.cm^-3. Its inter-sharmon distance of ~ 10,sup>-5 cm compares with Mean Free Path for real gasses e.g. 1.12x 10^-5 cm for Hydrogen. An element is singly charged since multiple charges imply that many constituents. Cosmino's single unified charge manifests as mass & electric charge via the mediation of gravitational and electromagnetic fields/forces, which also unify into a single gravitoelectromagnetic field/force. No particle is massless or sizeless point; neutrinos have mass, size & electric charge. Cosmino compositions of quarks, leptons, neutrinos and photon are worked out.
Category: High Energy Particle Physics

Multiple Stars and Problem of Jupiter

Authors: Vladislav Konovalov
Comments: 4 pages

In the article is shown, than the largest planet can threaten to mankind.
Category: Astrophysics

Mass Equivalent of Electrostatic and Gravidynamic Interplay

Authors: Vladislav Konovalov
Comments: 2 pages

In the article the concept of a gravitational equivalent electrostatic and gravidynamic of interplay is entered.
Category: Classical Physics

Interplay of Fields

Authors: Vladislav Konovalov
Comments: 15 pages

In the article the different aspects of interplay of fields with field carriers are reviewed.
Category: Quantum Physics

About "SURFACE GAS" of Liquids and Solids

Authors: Vladislav Konovalov
Comments: 5 pages

Many characteristics of fluids and solids it is possible to calculate, using notion about existence of "surface gas".
Category: Condensed Matter

A Novel Window Function

Authors: John Fanson
Comments: 2 pages

A novel window function, also known as an apodization or tapering function is proposed. The window is similar in shape, spectral response and interpretation to the Hanning window.
Category: Digital Signal Processing

Mechanism of Formation of Universe and Galaxies

Authors: Vladislav Konovalov
Comments: 10 pages

As the galaxies are formed and the Universe as a whole is reviewed in this article.
Category: Relativity and Cosmology

Some Thoughts on Big Science

Authors: J W Cahill
Comments: 2 pages

Original insights for the most part emanate from the minds of single individuals. Consequently, institutions, no matter how well funded, cannot expect to enjoy a monopoly on creativity. Hwever, the individual without institutional affiliation is most likely to be ignored. The situation is counterproductive to scientific progress and the world economy. This article recounts one person's experience and offers a potential solution.
Category: History and Philosophy of Physics

The Law of the Habble Cosmogonic Error

Authors: Vladislav Konovalov
Comments: 8 pages

In the article the problems, bound with the law Habble are reviewed
Category: Relativity and Cosmology

TGD and EEG

Authors: Matti Pitkänen
Comments: 538 Pages.

The TGD based general view about EEG developed in this book relies on the following general picture. </p><p> <OL> <LI> Magnetic body is the key actor in TGD inspired model of EEG and nerve pulse. Magnetic body acts as intentional agent using biological body as motor instrument and sensory receptor. There would be entire hierarchy of magnetic bodies associated with various body parts and characterized by the p-adic length scale and the level of dark matter hierarchy labeled by the value of Planck constant. The hierarchy of counterparts of EEGs associated with photons, Z⁰ and W bosons, and gluons at various frequency scales involving dark bosons with energies above thermal threshold by the large value of hbar would make possible communication and control. In particular, cyclotron radiation from Bose-Einstein condensates at magnetic body and Josephson radiation from Josephson junctions associated with cell membrane and other bio-electrets would be involved and cyclotron and Josephson frequencies would correspond to EEG frequencies. <LI> DNA as topological quantum computer vision suggests a rather detailed view about how genome and cell membrane interact. Nucleotides and lipids would be connected by magnetic flux tubes carrying dark matter with varying values of Planck constant and define braiding affected by the 2-D flow of the lipids in liquid crystal state and giving rise to a topological quantum computation with program modules defined by liquid flow patterns resulting via self organization process in presence of metabolic energy feed. <LI> Sensory qualia could be associated with the generalized di-electric breakdowns between sensory organ and its magnetic body. The cyclotron phase transitions of Bose-Einstein condensates of biologically important ions generated by the dark EEG photons at the magnetic body could generate the analogs of somatosensory qualia identifiable as our cognitive and emotional qualia. Long ranged charge entanglement made possible by W MEs (topological light rays) could be essential element of motor control and generate exotic ionization of nuclei (new nuclear physics predicted by TGD) in turn inducing classical electric fields at space-time sheets carrying ordinary matter. These fields generate various responses such as ionic waves and nerve pulses yielding the desired physiological responses. The recent view about cell membrane as almost vacuum extremal of K&auml;hler action explains large parity breaking effects in living matter and also the peak frequencies of photoreceptors in retina. Also a model for the cell membrane as a kind of sensory homunculus with lipids identified as pixels of a sensory map representing basic qualia follows naturally. Furthermore, EEG photons and biophotons can be identified as decay products of same dark photons. </OL> </p><p> The plan of the book is roughly following. The chapter describing the magnetic sensory canvas hypothesis is followed by a model for nerve pulse and by three chapters devoted to EEG.
Category: Mind Science

TGD Inspired Theory of Consciousness

Authors: Matti Pitkänen
Comments: 800 Pages.

This book tries to give an overall view about TGD inspired theory of consciousness as it stands now. </p><p> The basic notions TGD inspired theory of consciousness are quantum jump identified as a moment of consciousness, self identified as sequence of quantum jumps analogous to bound state of particles, self hierarchy with sub-selves experienced by self as mental images, and sharing and fusion of mental images by quantum entanglement. The topics of the book are organized in the following manner. </p><p> <OL> <LI> In the first part of the book TGD inspired theory of consciousness is discussed. There are three summarizing chapters giving a view about how ideas have evolved. There are also chapter about Negentropy Maximization Principle, about the notion of self, and about sensory representations. <LI> The second part of the book contains two chapters about the relationship between experienced and geometric time. The first one is more than decade old. The second one - inspired by zero energy ontology and written quite recently - provides a rather detailed vision about how the arrow of geometric time correlating with the arrow of experienced time and the localization of the contents of sensory experience to a narrow time interval emerge. The chapter explaining TGD based view about long term memory is also included. <LI> The third part of the book summarizes roughly decade old view about intelligence and cognition. p-Adic physics as physics of cognition and intentionality and many-fermion states as representations of Boolean statements are the key notions. In zero energy ontology also quantal versions of logical rules A&rarr; B realized as quantum variants of Boolean functions emerge at the fundamental level. A chapter about the role of dark matter hierarchy, in particular about topological quantum computation as a universal information processing tool, would be needed to make the picture more complete. <LI> The fourth chapter is devoted to remote mental interactions. The theoretical motivation for taking remote mental interactions seriously is that exactly the same mechanisms which are involved with the interaction between magnetic body and biological body apply also to remote mental interactions in TGD Universe. One could also understand why these phenomena are rare: a kind of immune system making it impossible for foreign magnetic bodies to control and communicate with the biological body possessed by a particular magnetic body would be a highly probable (but perhaps not unavoidable) outcome of evolutionary process. </OL>
Category: Mind Science

Mathematical Aspects of Consciousness Theory

Authors: Matti Pitkänen
Comments: 632 Pages.

This book discusses general mathematical ideas behind TGD inspired theory of consciousness. </p><p> <I> PART I: New Physics And Mathematics Involved With TGD</I> </p><p> The Clifford algebra associated with point of configuration space ("world of classical worlds") decomposes to a direct integral of von Neumann algebras known as hyper-finite factors of type II₁. This implies strong physical predictions and deep connections with conformal field theories, knot-, braid- and quantum groups, and topological quantum computation. <br> In TGD framework dark matter forms a hierarchy with levels characterized partially by the value of Planck constant labeling the pages of the book like structure formed by singular covering spaces of the imbedding space M⁴&times; CP₂ glued together along four-dimensional back. Particles at different pages are dark relative to each other since purely local interactions (vertices of Feynman diagram) involve only particles at the same page. The phase transitions changing the value of Planck constant having interpretation as tunneling between different pages of the book would induce phase transitions of gel phases abundant in living matter. </p><p> <I> Part II: TGD Universe as topological quantum computer</I> </p><p> The braids formed by magnetic flux tubes are ideal for the realization of topological quantum computations (tqc). Bio-systems are basic candidates for topological quantum computers. In DNA as tqc vision nucleotides and lipids are connected by flux tubes and the flow of lipids induces tqc programs. </p><p> <I> Part III: Categories, Number Theory And Consciousness</I> </p><p> Category theory could reflect the basic structures of conscious thought. The comparison of the inherent generalized logics associated with categories to the Boolean logic naturally associated with the configuration space spinor fields is also of interest. <br> The notion of infinite prime was the first mathematical invention inspired by TGD inspired theory of consciousness. The construction of infinite primes is very much analogous to a repeated second quantization of a super-symmetric arithmetic quantum field theory (with analogs of bound states included). Infinite primes form an infinite hierarchy and the physical realization of this hierarchy imply infinite hierarchy of conscious entities and that we represent only a single level in this hierarchy looking infinitesimal from the point of view of higher levels. The notion of infinite rational predicts an infinite number of real units with infinitely rich number theoretical anatomy and single space-time point becomes a Platonia able to represent every quantum state of the entire Universe in its structure: kind of algebraic Brahman=Atman identity.
Category: Mind Science

Magnetospheric Consciousness

Authors: Matti Pitkänen
Comments: 514 Pages.

This book is about the notion of magnetic body, which is one of the key notions in TGD inspired model of living matter and predicts a hierarchy of generalized EEGs associated with the magnetic bodies responsible for communication and control. Not only personal magnetic bodies of living systems need to be relevant and the idea about entire magnetosphere as a conscious system controlling the behavior of biosphere emerges naturally. </p><p> <OL> <LI> Part I discusses the idea about magnetosphere as a fractally scaled up version of biological body and brain. p-Adic fractality and dark matter hierarchy give some plausibility to this idea. Also a vision about evolution in many-sheeted space-time is discussed. <LI> Part II introduces the notion of semitrance involving quantum entanglement of subself of self, say subsystem of brain, with remote system. The entanglement of sub-systems of two unentangled systems possible in many-sheeted space-time means sharing and fusion of mental images (say stereo vision). The notion of finite measurement resolution justifies this concept.<br> Semitrance could have been basic control and communication tool of collective levels of consciousness during the period of human consciousness which Jaynes calls bicamerality. The idea that human consciousness might have had totally different character for only few millenia ago, finds additional support from the notions of super- and hyper genome implicated naturally by the dark matter hierarchy and the notion of magnetic body. The identification of memes as hyper-genes looks attractive. The evolution of hyper-genome could have driven the explosive evolution of human civilizations during last two millenia. <LI> Part III entitled "Crazy Stuff" discusses the idea that crop circles are due to intentional action of magnetospheric higher level self or a higher level self using magnetosphere as a tool to build them. Two special crop circles, Chilbolton and Crabwood crop circles, are discussed. The proposal is that they provide information about the genomes of life forms responsible for them. The most science fictive identification for these life-forms would be ourselves in distant geometric future using time mirror mechanism to affect geometric past. </OL> </p><p> Most of the material of this book has been written much before the dark matter revolution and formulation of the zero energy ontology and that I have only later added comments to the existing text. I hope that I can later add new material in which the implications of the dark matter hierarchy are discussed in more detail.
Category: Mind Science

Bio-Systems as Conscious Holograms

Authors: Matti Pitkänen
Comments: 766 Pages.

Brain as a hologram is an old idea and it emerges naturally also in TGD framework both at quantum and classical level, which by quantum classical correspondence is expected to reflect what happens at the deeper quantum level. The book is organized as follows. </p><p> <OL> <LI> The new view about the relationship between experienced and geometric time underlies the notion of 4-D dynamical hologram. Therefore the first part of the book contains three chapters about this topic reflecting the development of ideas. The first one is more than decade old. The third one written quite recently is inspired by zero energy ontology and provides a rather detailed vision about how the arrow of geometric time correlating with the arrow of experienced time and the localization of the contents of sensory experience to a narrow time interval emerge. It must be emphasized that the details of the model for the relationship between experienced and geometric time are still uncertain. <LI> Second part of the book is devoted to the development of hologram idea. Also a general model of sensory qualia and a model for sensory receptor as electret, which are very abundant in living matter, are discussed. The recent view about cell membrane as almost vacuum extremal of K&auml;hler action explains large parity breaking effects in living matter and also the peak frequencies of photoreceptors in retina. Also a model for the cell membrane as a kind of sensory homunculus with lipids identified as pixels of a sensory map representing basic qualia follows naturally. Furthermore, EEG photons and biophotons can be identified as decay products of same dark photons. <LI> The third part of the book is devoted to water memory and metabolism. The title suggests a connection between these two and this kind of connection has indeed emerged. A discovery - certainly one of the greatest surprises of my professional life - popped up as an outcome of an attempt to understand the mechanism behind water memory for which rather strong support exists now. The idea was that dark nuclei which sizes zoomed up to atomic size scale could provide a representation of genes with dark nucleons consisting of three quarks representing DNA codons. It turned out that the model for dark nucleon consisting of three quarks predicts counterparts of 64 DNAs, 64 RNAs, and 20 aminoacids and allows to identify vertebrate genetic code as a natural mapping of DNA type states to amino-acid type states. The population of dark nuclei would be new life-form possibly responsible for the water memory. The chapter about metabolism represents a model of metabolism based on the identification of universal metabolic energy quanta as increments of zero point kinetic energies emitted or absorbed as particles are transferred between space-time time sheets characterized by different p-adic primes. </OL>
Category: Mind Science

Genes and Memes

Authors: Matti Pitkänen
Comments: 910 Pages.

The first part of book discusses the new physics relevant to biology and the vision about Universe as topological quantum computer (tqc). </p><p Second part describes concrete physical models. </p><p> <OL> <LI> The notion of many-sheeted DNA and a model of genetic code inspired by the notion of Combinatorial Hierarchy predicting what I call memetic code are introduced. The almost exact symmetries of the code table with respect to the third letter inspire the proposal that genetic code could have evolved as fusion of two-letter code and single-letter code. <LI> A model for how genome and cell membrane could act as tqc is developed. Magnetic flux tubes containing dark matter characterized by large value of Planck constant would make living matter a macroscopic quantum system. DNA nucleotides and lipids of the cell membrane would be connected by magnetic flux tubes and the flow of the 2-D liquid formed by lipids would induce dynamical braiding defining the computation. <LI> The net of magnetic flux tubes could explain the properties of gel phase. Phase transitions reducing Planck constant would induce a contraction of the flux tubes explaining why bio-molecules manage to find each other in a dense soup of bio-molecules. The topology of the net would be dynamical and ADP &harr; ATP transformation could affect it. The anomalies related to ionic currents, nerve pulse activity, and interaction of ELF radiation with vertebrate brain find an explanation in this framework. The number theoretic entanglement entropy able to have negative values could be seen as the real quintenssence associated with the metabolic energy transfer, and the poorly understood high energy phosphate bond could be interpreted in terms of negentropic entanglement rather than ordinary bound state entanglement. <LI> The discoveries of Peter Gariaev about interaction of ordinary and laser light with genome combined with ideas about dark matter and water memory lead to a model for the interaction of photons with DNA. Dark &harr; ordinary transformation for photons could allow to "see" dark matter by allowing ordinary light to interact with DNA. <LI> A physical model for genetic code emerged from an attempt to understand the mechanism behind water memory. Dark nuclei which sizes zoomed up to atomic size scale could represent genes. The model for dark nucleon consisting of three quarks predicts counterparts of 64 DNAs, 64 RNAs, and 20 aminoacids and allows to identify genetic code as a natural mapping of DNA type states to amino-acid type states and consistent with vertebrate genetic code. </OL> </p><p> The third part of the book discusses number theoretical models of the genetic code based on p-adic thermodynamics and maximization of entropy or negentropy. These models reproduce the genetic code but fail to make killer predictions.
Category: Quantum Gravity and String Theory

Quantum Hardware of Living Matter

Authors: Matti Pitkänen
Comments: 602 Pages.

This book represents a view about quantum hardware of living systems in TGD framework. Since the vision is bound to look highly speculative, it is good to emphasize that the most important predictions follow almost without any reference to the classical field equations using only quantum classical correspondence. </p><p> The new conceptual elements are the notion of many-sheeted space-time having fractal hierarchical structure, 4-D spin glass degeneracy of the preferred extremals of K&auml;hler action providing huge information storage capacity, topological field quantization, the notion of magnetic/field body serving as intentional agent using biological body as sensory receptor and motor instrument, zero energy ontology leading to a new view about energy and about the relationship between experienced and geometric time, dark matter hierarchy realized in terms of book like structure of 8-D imbedding space with pages labeled by values of Planck constant, the assumption that the phase transitions changing the value of Planck constant provide a key control tool in living matter, and p-adic length scale hypothesis allowing quantitative grasp to the situation. </p><p> <OL> <LI> Three chapters of this book are devoted to the model of high $T_c$ super-conductivity relying strongly on the notions of quantum criticality and dark matter. <LI> Two chapters discuss quantum antenna hypothesis inspired by topological light rays (M(assless) E(xtremals)) and the notion of wormhole magnetic fields. Notice that the notion of wormhole magnetic field was introduced much before the hypothesis that bosons and also interaction fermions have a natural identification as wormhole contacts emerged. The recent view about quantum TGD suggests the interpretation wormhole magnetic fields as dark scaled up versions of elementary particles identified as K&auml;hler magnetic flux tubes identified as pairs of magnetically charged wormhole contacts carrying at the second wormhole throat neutrino pair neutralizing the weak isospin of the fermion at the second wormhole throat. For ordinary value of Planck constant the length of is flux would be given by weak length scale. Therefore weak interactions in biological length scales are involved giving rise to large parity breaking effects. Also scaled up QCD is involved and implying hadron like states in biological length scales. <LI> Two chapters are devoted to the possible biological implications of the hypothesis that dark matter corresponds to macroscopic quantum phases characterized by a large value of Planck constant and is the key actor in living matter. <LI> A possible identification of quantum correlates of sensory qualia is discussed assuming that qualia are in one-one correspondence with the increments of quantum numbers in quantum jump. Also a simple model for sensory receptor is introduced. The recent view about cell membrane as almost vacuum extremal of K&auml;hler action explains large parity breaking effects in living matter and also the peak frequencies of photoreceptors in retina. Also a model for the cell membrane as a kind of sensory homunculus with lipids identified as pixels of a sensory map representing basic qualia follows naturally. Furthermore, EEG photons and biophotons can be identified as decay products of same dark photons. </OL>
Category: Physics of Biology

Bio-Systems as Self-Organizing Quantum Systems

Authors: Matti Pitkänen
Comments: 397 Pages.

The quantum theory of self organization represents a rather old layer of TGD inspired theory of consciousness. <p></p> <OL><LI> Self organization is a non-deterministic process and corresponds to the evolution of conscious entities - selves - to asymptotic self-organization patterns via quantum jumps. This requires macroscopic quantum coherence. <LI> Space-time surfaces are analogous to Bohr orbits and the failure of the classical non-determinism in the conventional sense of the word makes it possible to interpret space-time surfaces as representations of both quantum states and sequences of quantum states assignable to the sequences of quantum jumps. The huge vacuum degeneracy of K&auml;hler action implies spin glass degeneracy in 4-dimensional sense providing maximal resources to represent information about external world by mapping its states to its own internal states. Space-time sheets would be four-dimensional statues gradually carved by a sequence of quantum jump to a shape representing asymptotic self-organization pattern. <LI> Magnetic body is the intentional agent controlling the biological body. The fractal hierarchy of copies of standard model physics involving in particular a hierarchy of electro-weak bosons and gluons with increasingly longer weak/confinement length scale is an essential piece of the story. The concrete quantum model for how intentions are transformed to actions provides additional insights to quantum self-organization. <LI> The new view about time and energy justifying time mirror mechanism involving sending of negative energy phase conjugate photons to geometric past is crucial for the models of long term memory, intentional action, and remote metabolism. <LI> The model of self organization involves cyclotron radiation from the cyclotron transitions assignable with the Bose-Einstein condensates of charged bosons at the magnetic bodies and Josephson radiation from Josephson junctions assignable to the cell membrane and also other layer like structures (electrets). <LI> The vision about life residing in the intersection of real and p-adic worlds is central for the approach. In particular, the existence of number theoretic entanglement entropy, which can have negative values, makes possible to identify a measure of conscious information and negentropic entanglement replaces metabolic energy feed as the basic prequisite of life. </OL> Zero energy ontology and hierarchy of Planck constants complete this vision. Zero energy ontology justifies time mirror mechanism and explains how arrow of subjective time emerges. Dark matter hierarchy implies macroscopic quantum coherence, inspires vision about bio-catalysis and quantum computation in living matter, explains evolutionary leaps, and suggests generalization of the notion of genome and new realizations of genetic code. </p><p> The topics of the book are following. The first chapters explain the vision about biological self organization in TGD framework. The last chapters of the book discuss quantum control and coordination in living matter according to TGD.
Category: Physics of Biology

P-Adic Length Scale Hypothesis and Dark Matter Hierarchy

Authors: Matti Pitkänen
Comments: 1204 Pages.

The book is devoted to the applications of p-adic length scale hypothesis and dark matter hierarchy. </p><p> <OL> <LI> p-Adic length scale hypothesis states that primes p&asymp; 2^k, k integer, in particular prime, define preferred p-adic length scales. Physical arguments supporting this hypothesis are based on the generalization of Hawking's area law for blackhole entropy so that it applies in case of elementary particles. A deeper number theory based justification for this hypothesis is based on the generalization of the number concept fusing real number fields and p-adic number fields among common rationals or numbers in their non-trivial algebraic extensions. This approach also justifies the notion of multi-p-fractality and allows to understand scaling law in terms of simultaneous p&asymp; 2^k- and 2-fractality. <LI> In TGD framework the levels of dark matter hierarchy are labeled by the values of dynamical quantized Planck constant. The justification for the hypothesis provided by quantum classical correspondence and the fact the sizes of space-time sheets identifiable as quantum coherence regions can be arbitrarily large. <LI> The weak form of electric-magnetic duality is the newest building brick of the vision and leads to a detailed view about electro-weak screening and color confinement and predicts new physics below weak scales. The weak form of electric-magnetic duality allows to identify Higgs bosons and to understand how they provide the longitudinal polarizations of gauge bosons. The most natural option is that photon eats the remaining Higgs scalar and receives a small mass. This true for all bosons regarded as massless and allows to have exact Yangian symmetry requiring the vanishing of IR divergences. Higgs potential and vacuum expectation of Higgs are not needed in the model. <LI> Twistors emerge naturally in TGD framework and several proposal for twistorialization of TGD is discussed in two chapters devoted to the topic. Twistorial approach combined with zero energy ontology, bosonic emergence, and the properties of the Chern-Simons Dirac operator leads to the conjecture that all particles -also string like objects- can be regarded as bound states of massless particles identifiable as wormhole throats. Also virtual particles would consist of massles wormhole throats but bound state property is not assumed anymore and the energies of wormhole throats can have opposite signs so that space-like momentum exchanges become possible. This implies extremely strong constraints on loop momenta and manifest finiteness of loop integrals. </OL> </p><p> The first part of the book is about the description of elementary particle massivation in terms of p-adic thermodynamics and Higgsy contribution affecting the vacuum conformal weight. In the first chapter the view about quantum TGD from particle physics perspective is discussed and the remaining chapters are devoted to the detailed calculation of masses of elementary particles and hadrons, and to various new physics suggested or predicted by the resulting scenario. </p><p> Second part of the book is devoted to the application of p-adic length scale hypothesis above elementary particle length scales. The so called leptohadron physics, originally developed on basis of experimental anomalies, is discussed as a particular instance of an infinite fractal hierarchy of copies of standard model physics, predicted by TGD and consistent with what is known about ordinary elementary particle physics. TGD based view about nuclear physics involves light exotic quarks as a essential element, and dark nuclear physics could have implications also at the level of condensed matter physics and biology. TGD based view about high T_c superconductors involves also in an essential manner dark matter and is summarized in the closing chapter.
Category: High Energy Particle Physics

Towards M-Matrix

Authors: Matti Pitkänen
Comments: 1137 Pages.

This book is devoted to a detailed representation of the recent state of quantum TGD. </p><p> The first part of the book summarizes quantum TGD in its recent form. </p><p> <OL> <LI> General coordinate invariance and generalized super-conformal symmetries are the basic symmetries of TGD and Equivalence Principle can be generalized using generalized coset construction. <LI> In zero energy ontology the basis of classical WCW spinors fields forms unitary U-matrix having M-matrices as its orthogonal rows. M-matrix defines time-like entanglement coefficients between positive and negative energy parts of the zero energy states. M-matrix is a product of a hermitian density matrix and unitary S-matrix commuting with it. The hermitian density matrices define infinite-dimensional Lie-algebra extending to a generalization of Kac-Moody type algebra with generators defined as products of hermitian density matrices and powers of S-matrix. Yangian type algebra is obtained if only non-negative powers of S are allowed. The interpretation is in terms of the hierarchy of causal diamonds with size scales coming as integer multiples of CP₂ size scale. Zero energy states define their own symmetry algebra. For generalized Feynman diagrams lines correspond to light-like 3-surfaces and vertices to 2-D surfaces. <LI> Finite measurement resolution realized using fractal hierarchy of causal diamonds (CDs) inside CDs implies a stringy formulation of quantum TGD involving replacement of 3-D light-like surfaces with braids representing the ends of strings. Category theoretical formulation leads to a hierarchy of algebras forming an operad. <LI> Twistors emerge naturally in TGD framework and several proposal for twistorialization of TGD is discussed in two chapters devoted to the topic. Twistorial approach combined with zero energy ontology, bosonic emergence, and the properties of the Chern-Simons Dirac operator leads to the conjecture that all particles -also string like objects- can be regarded as bound states of massless particles identifiable as wormhole throats. Also virtual particles would consist of massles wormhole throats but bound state property is not assumed anymore and the energies of wormhole throats can have opposite signs so that space-like momentum exchanges become possible. This implies extremely strong constraints on loop momenta and manifest finiteness of loop integrals. </p><p> An essential element of the formulation is exact Yangian symmetry obtained by replacing the loci of multilocal symmetry generators of Yangian algebra with partonic 2-surfaces so that conformal algebra of Minkowski space is extened to infinite-dimensional algebra bringing in also the conformal algebra assigned to the partonic 2-surfaces. Yangian symmetry requires the vanishing of both UV and IR divergences achieved if the physical particles are bound states of massless wormhole throats. </p><p> Rather general arguments suggest the formulation of TGD in terms of holomorphic 6-surfaces in the product CP₃&times; CP₃ of twistor spaces leading to a unique partial differential equations determining these surfaces in terms of homogenous polynomials of the projective complex coordinates of the two twistor spaces. </OL> </p><p> Second part of the book is devoted to hyper-finite factors and hierarchy of Planck constants. </p><p> <OL> <LI> The Clifford algebra of WCW is hyper-finite factor of type II₁. The inclusions provide a mathematical description of finite measurement resolution. The included factor is analogous to gauge symmetry group since the action of the included factor creates states not distinguishable from the original one. TGD Universe would be analogous to Turing machine able to emulate any internally consistent gauge theory (or more general theory) so that finite measurement resolution would provide TGD Universe with huge simulational powers. <LI> In TGD framework dark matter corresponds to ordinary particles with non-standard value of Planck constant. The simplest view about the hierarchy of Planck constants is as an effective hierarchy describable in terms of local, singular coverings of the imbedding space. The basic observation is that for K&auml;hler action the time derivatives of the imbedding space coordinates are many-valued functions of canonical momentum densities. If all branches for given values of canonical momentum densities are allowed, one obtains the analogs of many-sheeted Riemann surfaces with each sheet giving same contribution to the K&auml;hler action so that Planck constant is effectively a multiple of the ordinary Planck constant. Dark matter could be in quantum Hall like phase localized at light-like 3-surfaces with macroscopic size and analogous to black-hole horizons. </OL>
Category: Quantum Gravity and String Theory

TGD as a Generalized Number Theory

Authors: Matti Pitkänen
Comments: 1197 Pages.

The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts. </p><p> <OL><LI> The fusion of real physic and various p-adic physics to a single coherent whole by generalizing the number concept by fusing real numbers and various p-adic number fields along common rationals. Extensions of p-adic number fields can be introduced by gluing them along common algebraic numbers to reals. Algebraic continuation of the physics from rationals and their their extensions to various number fields (generalization of completion process for rationals) is the key idea, and the challenge is to understand whether how one could achieve this dream. A profound implication is that purely local p-adic physics would code for the p-adic fractality of long length length scale real physics and vice versa, and one could understand the origins of p-adic length scale hypothesis. <LI> Second part of the vision involves hyper counterparts of the classical number fields defined as subspaces of their complexificationsnwith Minkowskian signature of metric. Allowed space-time surfaces would correspond to what might be callednhyper-quaternionic sub-manifolds of a hyper-octonionic space and mappable to M⁴&times; CP₂ in natural manner. One could assign to each point of space-time surface a hyper-quaternionic 4-plane which is the plane defined by the induced or modified gamma matrices defined by the canonical momentum currents of K&auml;hler action. Induced gamma matrices seem to be preferred mathematically: they correspond to modified gamma matrices assignable to 4-volume action, and one can develop arguments for why K&auml;hler action defines the dynamics. </p><p> Also a general vision about preferred extremals of K&auml;hler action emerges. The basic idea is that imbedding space allows octonionic structure and that field equations in a given space-time region reduce to the associativity of the tangent space or normal space: space-time regions should be quaternionic or co-quaternionic. The first formulation is in terms of the octonionic representation of the imbedding space Clifford algebra and states that the octonionic gamma "matrices" span a complexified quaternionic sub-algebra. Another formulation is in terms of octonion real-analyticity. Octonion real-analytic function f is expressible as f=q₁+Iq₂, where q_i are quaternions and I is an octonionic imaginary unit analogous to the ordinary imaginary unit. q₂ (q₁) would vanish for quaternionic (co-quaternionic) space-time regions. The local number field structure of the octonion real-analytic functions with composition of functions as additional operation would be realized as geometric operations for space-time surfaces. The conjecture is that these two formulations are equivalent. <LI> The third part of the vision involves infinite primes identifiable in terms of an infinite hierarchy of second quantized arithmetic quantum fields theories on one hand, and as having representations as space-time surfaces analogous to zero loci of polynomials on the other hand. Single space-time point would have an infinitely complex structure since real unity can be represented as a ratio of infinite numbers in infinitely many manners each having its own number theoretic anatomy. Single space-time point would be in principle able to represent in its structure the quantum state of the entire universe. This number theoretic variant of Brahman=Atman identity would make Universe an algebraic hologram. </p><p> 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. </OL> </p><p> Besides this holy trinity I will discuss in the first part of the book loosely related topics such as the relationship between infinite primes and non-standard numbers. </p><p> Second part of the book is devoted to the mathematical formulation of the p-adic TGD. The p-adic counterpart of integration is certainly the basic mathematical challenge. Number theoretical universality and the notion of algebraic continuation from rationals to various continuous number fields is the basic idea behind the attempts to solve the problems. p-Adic integration is also a central problem of modern mathematics and the relationship of TGD approach to motivic integration and cohomology theories in p-adic numberfields is discussed. </p><p> The correspondence between real and p-adic numbers is second fundamental problem. The key problem is to understand whether and how this correspondence could be at the same time continuous and respect symmetries at least in discrete sense. The proposed explanation of Shnoll effect suggests that the notion of quantum rational number could tie together p-adic physics and quantum groups and could allow to define real-p-adic correspondence satisfying the basic conditions. </p><p> The third part is develoted to possible applications. Included are 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: Quantum Gravity and String Theory

Physics in Many-Sheeted Space-Time

Authors: Matti Pitkänen
Comments: 1091 Pages.

This book is devoted to what might be called classical TGD. </p><p> <OL> <LI> Classical TGD identifies space-time surfaces as kind of generalized Bohr orbits. It is an exact part of quantum TGD. <LI> The notions of many-sheeted space-time, topological field quantization and the notion of field/magnetic body, follow from simple topological considerations. Space-time sheets can have arbitrarily large sizes and their interpretation as quantum coherence regions implies that in TGD Universe macroscopic quantum coherence is possible in arbitrarily long scales. Also long ranged classical color and electro-weak fields are predicted. <LI> TGD Universe is fractal containing fractal copies of standard model physics at various space-time sheets and labeled by p-adic primes assignable to elementary particles and by the level of dark matter hierarchy characterized partially by the value of Planck constant labeling the pages of the book like structure formed by singular covering spaces of the imbedding space M⁴&times; CP₂ glued together along four-dimensional back. Particles at different pages are dark relative to each other since local interactions defined in terms of the vertices of Feynman diagram involve only particles at the same page. </p><p> The simplest view about the hierarchy of Planck constants is as an effective hierarchy describable in terms of local, singular coverings of the imbedding space. The basic observation is that for K&auml;hler action the time derivatives of the imbedding space coordinates are many-valued functions of canonical momentum densities. If all branches for given values of canonical momentum densities are allowed, one obtains the analogs of many-sheeted Riemann surfaces with each sheet giving same contribution to the K&auml;hler action so that Planck constant is effectively a multiple of the ordinary Planck constant. <LI> Zero energy ontology brings in additional powerful interpretational principle. </OL> </p><p> The topics of the book are organized as follows. <OL> <LI> In Part I extremals of K&auml;hler action are discussed and the notions of many-sheeted space-time, topological field quantization, and topological condensation and evaporation are introduced. <LI> In Part II many-sheeted-cosmology and astrophysics are summarized. p-Adic and dark matter hierarchies imply that TGD inspired cosmology is fractal. Cosmic strings and their deformations giving rise to magnetic flux tubes are basic objects of TGD inspired cosmology. Magnetic flux tubes can in fact be interpreted as carriers of dark energy giving rise to accelerated expansion via negative magnetic "pressure". The study of imbeddings of Robertson-Walker cosmology shows that critical and over-critical cosmology are unique apart from their duration. The idea about dark matter hierarchy was originally motivated by the observation that planetary orbits could be interpreted as Bohr orbits with enormous value of Planck constant, and this picture leads to a rather detailed view about macroscopically quantum coherent dark matter in astrophysics and cosmology. </p><p> <LI> Part III includes old chapters about implications of TGD for condensed matter physics. The phases of CP₂ complex coordinates could define phases of order parameters of macroscopic quantum phases manifesting themselves in the properties of living matter and even in hydrodynamics. For instance, Z⁰ magnetic gauge field could make itself visible in hydrodynamics and Z⁰ magnetic vortices could be involved with super-fluidity. </OL>
Category: Quantum Gravity and String Theory

Physics as Infinite-Dimensional Geometry

Authors: Matti Pitkänen
Comments: 476 Pages.

The topics of this book is a vision about physics as infinite-dimensional K&auml;hler geometry of the "world of classical worlds" (WCW), with "classical world" identified either as light-like 3-D surface X³ of a unique Bohr orbit like 4-surface X⁴(X³) or X⁴(X³) itself. The non-determinism of K&auml;hler action defining K&auml;hler function forces to generalize the notion of 3-surface. Zero energy ontology allows to formulate this generalization elegantly using a hierarchy of causal diamonds (CDs) defined as intersections of future and past directed light-cones, and a geometric realization of coupling constant evolution and finite measurement resolution emerges. </p><p> The general vision about quantum dynamics is that the basis for WCW spinor fields defines in zero energy ontology unitary U-matrix having as orthogonal rows M-matrices. Given M-matrix is expressible as a product of hermitian square root of density matrix and S-matrix. M-matrices define time-like entanglement coefficients between positive and negative energy parts of zero energy states represented by the modes of WCW spinor fields. </p><p> One encounters two challenges. <OL><LI> Provide WCW with K&auml;hler geometry consistent with 4-dimensional general coordinate invariance. Clearly, the definition of metric must assign to given light-like 3-surface X³ a 4-surface X⁴(X³) as kind of Bohr orbit. <LI> Provide WCW with spinor structure. The idea is to express configuration space gamma matrices using super algebra generators expressible using second quantized fermionic oscillator operators for induced free spinor fields at X⁴(X³). Isometry generators and contractions of Killing vectors with gamma matrices would generalize Super Kac-Moody algebra. </OL> </p><p> The condition of mathematical existence poses stringent conditions on the construction. </p><p> <OL> <LI> The experience with loop spaces suggests that a well-defined Riemann connection exists only if this space is union of infinite-dimensional symmetric spaces. Finiteness requires that vacuum Einstein equations are satisfied. The coordinates labeling these symmetric spaces do not contribute to the line element and have interpretation as non-quantum fluctuating classical variables. <LI> The construction of the K&auml;hler structure requires the identification of complex structure. Direct construction of K&auml;hler function as action associated with a preferred extremal for K&auml;hler action leads to a unique result. The group theoretical approach relies on direct guess of isometries of the symmetric spaces involved. Isometry group generalizes Kac-Moody group by replacing finite-dimensional Lie group with the group of symplectic transformations of &delta; M⁴₊&times; CP₂, where &delta; M⁴₊ is the boundary of 4-dimensional future light-cone. The generalized conformal symmetries assignable to light-like 3-surfaces and boundaries of causal diamonds bring in stringy aspect and Equivalence Principle can be generalized in terms of generalized coset construction. <LI> Configuration space spinor structure geometrizes fermionic statistics and quantization of spinor fields. Quantum criticality can be formulated in terms of the modified Dirac equation for induced spinor fields allowing a realization of super-conformal symmetries and quantum gravitational holography. <LI> Zero energy ontology combined with the weak form of electric-magnetic duality led to a breakthrough in the understanding of the theory. The boundary conditions at light-like wormhole throats and at space-like 3-surfaces defined by the intersection of the space-time surface with the light-like boundaries of causal diamonds reduce the classical quantization of K&auml;hler electric charge to that for K&auml;hler magnetic charge. The integrability of field equations for the preferred extremals reduces to the condition that the flow lines of various isometry currents define Beltrami fields for which the flow parameter by definition defines a global coordinate. The assumption that isometry currents are proportional to the instanton current for K&auml;hler action reduces K&auml;hler function to a boundary term which by the weak form of electric-magnetic duality reduces to Chern-Simons term. This realizes TGD as almost topological QFT. <LI> There are also number theoretical conjectures about the character of the preferred extremals. The basic idea is that imbedding space allows octonionic structure and that field equations in a given space-time region should reduce to the associativity of the tangent space or normal space so that space-time regions should be quaternionic or co-quaternionic. The first formulation is in terms of the octonionic representation of the imbedding space Clifford algebra and states that the octonionic gamma "matrices" span a quaternionic sub-algebra. Another formulation is in terms of octonion real-analyticity. Octonion real-analytic function f is expressible as f=q₁+Iq₂, where q_i are quaternions and I is an octonionic imaginary unit analogous to the ordinary imaginary unit. q₂ (q₁) would vanish for quaternionic (co-quaternionic) space-time regions. The local number field structure of octonion real-analytic functions with composition of functions as additional operation would be realized as geometric operations for space-time surfaces. The conjecture is that these two formulations are equivalent. <LI> An important new interpretational element is the identification of the K&auml;hler action from Minkowskian space-time regions as a purely imaginary contribution identified as Morse function making possible quantal interference effects. The contribution from the Euclidian regions interpreted in terms of generalized Feynman graphs is real and identified as K&auml;hler function. These contributions give apart from coefficient identical Chern-Simons terms at wormhole throats and at the space-like ends of space-time surface: it is not clear whether only the contributions these 3-surfaces are present. <LI> Effective 2-dimensionality suggests a reduction of Chern-Simons terms to a sum of real and imaginary terms corresponding to the total areas of of string world sheets from Euclidian and Minkowskian string world sheets and partonic 2-surfaces, which are an essential element of the proposal for what preferred extremals should be. The duality between partonic 2-surfaces and string world sheets suggests that the total area of partonic 2-surfaces is same as that for string world sheets. <LI> The approach leads also to a highly detailed understanding of the Chern-Simons Dirac equation at the wormhole throats and space-like 3-surfaces and K&auml;hler Dirac equation in the interior of the space-time surface. The effective metric defined by the anticommutators of the modified gamma matrices has an attractive interpretation as a geometrization for parameters like sound velocity assigned with condensed matter systems in accordance with effective 2-dimensionality and strong form of holography. </OL>
Category: Quantum Gravity and String Theory

TGD and Fringe Physics

Authors: Matti Pitkänen
Comments: 392 Pages.

The topics of this book could be called fringe physics involving claimed phenomena which do not have explanation in terms of standard physics. </p><p> Many-sheeted space-time with p-adic length scale hierarchy, the predicted dark matter hierarchy with levels partially characterized by quantized dynamical Planck constant, and the prediction of long ranged color and weak forces alone predict a vast variety of new physics effects. Zero energy ontology predicts that energy can have both signs and that classical signals can propagate in reversed time direction at negative energy space-time sheets and an attractive identification for negative energy signals would be as generalizations of phase conjugate laser beams. This vision leads to a coherent view about metabolism, memory, and bio-control and it is natural to ask whether the reported anomalies might be explained in terms of the mechanisms giving hopes about understanding the behavior of living matter. </p><p> <OL> <LI> The effects involving coin words like antigravity, strong gravity, and electro-gravity motivate the discussion of possible anomalous effects related to long range electro-weak fields and many-sheeted gravitation. For instance, TGD leads to a model for the strange effects reported in rotating magnetic systems. <LI> Tesla did not believe that Maxwell's theory was an exhaustive description of electromagnetism. He claimed that experimental findings related to pulsed systems require the assumption of what he called scalar waves not allowed by Maxwell's electrodynamics. TGD indeed allows scalar wave pulses propagating with light velocity. The dropping of particles to larger space-time sheets liberating metabolic energy, transformation of ordinary charged matter to dark matter and vice versa, dark photons, etc... might be needed to explain Tesla's findings. Also phase conjugate, possibly dark, photons making possible communications with geometric past might be involved. <br> These speculative ideas receive unexpected support from the TGD inspired view about particle physics. The recent TGD inspired view about Higgs mechanism suggests strongly that photon eats the remaining component of Higgs boson and in this manner gets longitudinal polarization and small mass allowing to avoid infrared divergences of scattering amplitudes. <LI> The reports about ufos represent a further application for TGD based view about Universe. Taking seriously the predicted presence of infinite self hierarchy represented by dark matter hierarchy makes it almost obvious that higher civilizations are here, there, and everywhere, and that their relationship to us is like that of our brain to its neurons, so that Fermi paradox (Where are they all?) would disappear. Although the space travel might be quite too primitive idea for the civilizations at higher levels of hierarchy, ufos might be real objects representing more advanced technology rather than plasmoid like life forms serving as mediums in telepathic communications. </OL>
Category: Quantum Gravity and String Theory

Topological Geometrodynamics: Overview

Authors: Matti Pitkänen
Comments: 1536 Pages.

This book tries to give an overall view about quantum TGD as it stands now. The topics of this book are following. <OL><LI> Part I: An overall view about the evolution of TGD and about quantum TGD in its recent form. Two visions about physics are discussed at general level. According to first vision physical states of the Universe correspond to classical spinor fields in the world of the classical worlds (WCW) identified as 3-surfaces or equivalently as corresponding 4-surfaces analogous to Bohr orbits and identified as special extrema of K&auml;hler action. TGD as a generalized number theory vision leading naturally also to the emergence of p-adic physics as physics of cognitive representations is the second vision. <LI> Part II: The vision about physics as infinite-dimensional configuration space geometry. The basic idea is that classical spinor fields in WCW describe the quantum states of the Universe. Quantum jump remains the only purely quantal aspect of quantum theory in this approach since there is no quantization at the level of the configuration space. Space-time surfaces correspond to special extremals of the K&auml;hler action analogous to Bohr orbits and define what might be called classical TGD discussed in the first chapter. The construction of the configuration space geometry and spinor structure are discussed in remaining chapters. <LI> Part III: Physics as generalized number theory. Number theoretical vision involves three loosely related approaches: fusion of real and various p-adic physics to a larger whole as algebraic continuations of what might be called rational physics; space-time as a hyper-quaternionic surface of hyper-octonion space, and space-time surfaces as a representations of infinite primes. <LI> Part IV: The first chapter summarizes the basic ideas related to von Neumann algebras known as hyper-finite factors of type II₁ about which configuration space Clifford algebra represents canonical example. Second chapter is devoted to the basic ideas related to the hierarchy of Planck constants and related generalization of the notion of imbedding space to a book like structure. <LI> Part V: Physical applications of TGD. Cosmological and astrophysical applications are summarized and applications to elementary particle physics are discussed at the general level. TGD explains particle families in terms of generation-genus correspondence (particle families correspond to 2-dimensional topologies labeled by genus). The general theory for particle massivation based on p-adic thermodynamics is discussed at the general level. </OL>
Category: Quantum Gravity and String Theory

Units Unification

Authors: António Saraiva
Comments: 3 pages

Everything is made of speed and distance.
Category: Classical Physics

Unified Force

Authors: António Saraiva
Comments: 3 pages

There's only one force, the electric one that can be expressed by only one formula.
Category: Classical Physics

Multielectronic Atoms

Authors: Vladislav Konovalov
Comments: 5 pages

In the article the constitution of multielectronic atoms is reviewed and the new form of the Mendeleyev's table is offered.
Category: Nuclear and Atomic Physics

Electron Motion in a Field of Two Nuclei and Chemical Bond

Authors: Vladislav Konovalov
Comments: 7 pages

In the article the different types of a chemical bond are reviewed.
Category: Nuclear and Atomic Physics

Unified Theory Replaces Relativity.

Authors: Rati Ram Sharma
Comments: 14 pages

F A wave exists only in its propagating medium but Einstein erred to discard the physical medium for light wave and to introduce the non-existent 4-D spacetime continuum instead. It denied him the chance to address the intrinsic wave-quantum Unity of light and predict the new entity of 'basic substance' to compose all forms of E & m so compellingly demanded for the inter-conversions of E & m by the eqn. E=mc², which is now re-derived. Unified Theory gives cogent arguments and experimental support for the existence of a real physical medium in space, the all-composing & allpervading 'sharmon medium' as Basic Substance. It propagates light as a wave-quantum UNITY, the particle aspect showing up at short wavelength e.g. from ~ 7000 A° downward in photochemical effects and below ~ 3000 A° in photoelectric effects. The non-substantive abstract concepts of space & time evolve from our perceptions of successive motions & changes in the surrounding objects and cannot fuse into any concrete spacetime continuum. If existent it would retard motion of heavenly bodies, which is not actually observed. Any non-composite static spacetime cannot undulate to transmit light. Various multidimensional spacetime continua are mere mathematical constructs bereft of physical existence and theories based on them unrealistic. Unified Theory explains from sharmon medium the constancy & invariance to source-observer motion, the two pillar postulates of Special Relativity without validating SR. It explains the Michelson-Morley and Sagnac experiments as also the observed variability of light velocity and superluminality, which invalidate Relativity Theories. Lorentz transformations do not describe any natural motion since no velocity can vary (like v) with, and be invariant (like c) to, a source-observer motion at the same time. The actual length of an object, viewed by say, 100 differently moving observers cannot undergo 100 different objective contractions at the same time, making 'contraction of length' an unrealistic concept. So is 'dilatation of time'. Unified Theory derives from sharmon medium the Maxwell equations and the time containing and time free equations for the propagation of wave-quantum unity in gravitational and electromagnetic radiation. The Schrodinger wave equation is also derived. It explains the photoelectric effect. Explanation of the bending of light in a gravitational field shows that photon has mass and gravitation is not a curvature in 4-D spacetime. All particles and energy-quanta have definite mass & size.
Category: Relativity and Cosmology

Unified Theory Replaces Quantum Theory & Uncertainty Principle

Authors: Rati Ram Sharma
Comments: 12 pages

Heisenberg argued that wave and particle are too exclusively different in properties, making the intrinsic wave-quantum unity of light impossible to visualize and describe by the language. He invented mathematical Quantum Theory to circumvent visualization and inadequacy of language. But mathematics too is a language to supplement description. He used it to superimpose hidden concepts leading to the Uncertainty Principle. In Unified Theory the wave & particle aspects of electromagnetic radiation and moving material particle coexist blended together as wave-quantum UNITY. This is also supported by experiments. The wave-or-quantum DUALITIES of Quantum Theory appear due to experimental limitations to observe only one and not both of the two aspects simultaneously. Conservation of mass & momentum are inviolable. Matter's creation from, or dissolution into, 'nothing' is unrealistic. So the Heisenberg's Uncertainty Principle is rejected as unrealistic and new Principle of Null Action with universal applications is introduced. The Copenhagen interpretation of Quantum Theory is reappraised critically.
Category: Quantum Physics

Composition-Structure of Electron, Proton & Neutron

Authors: Rati Ram Sharma
Comments: 8 pages

An element is non-composite but composes other particles. The elementary quarks & leptons of the Modern Standard Model are found to be compressible and assembleable, hence having composition. These in Unified Theory are composed by two elementary cosminos, positrino & negatrino. The cosmino-sharmon composition-structures of electron, proton and neutron presented for the first time are defined by Form Factors and concentric regions. It is shown that no ½-spin Fermion can be neutral. Electric Dipole Moment of neutron calculated from Unified Theory agrees with observations. An almost neutral neutron emits electron, never positron, because its outer region is negative. Hofstadter's positive outer region in neutron is inconsistent with negatron decay. Effect of superimposed magnetic field on neutron's negatron decay is explained without Electroweak Theory's weak charge and W^± & Z⁰ particles. A new Hook's law mediated short-range nuclear force is suggested.
Category: High Energy Particle Physics

The Rescaling Symmetry Principle.

Authors: John Hunter
Comments: 9 pages

A symmetry principle is discussed whereby the whole universe can change scale. It is shown that a reinterpretation of 'expansion' of the universe, (due to changing scale factor), as a 'rescaling', can lead to a redshift of light, due to a changing of Plancks constant with time. Predictions for the magnitudes of supernovae against redshift are made and found to be in good agreement with supernovae data, without recourse to dark energy. Matter density, of one quarter critical density, occurs naturally from Einsteins equations, with an equation of state parameter of -1 (in accordance with values inferred from WMAP data). It is concluded that the reinterpretation of a solution of the equations of General Relativity, for the universe, may be necessary. The question of inertia is considered, and the new interpretation of General Relativity is found to support modern views on its cause.
Category: Relativity and Cosmology

On Gravity and the Motion of Dark Matter.

Authors: John Hunter
Comments: 4 pages

It has proved problematic, within General Relativity, to form a general definition of mass. The results of singularity theorems also seem to indicate an incompleteness of General Relativity. A simple model of the effect of the gravitational self binding energy of masses, on both gravitational and inertial mass, is considered. The result is a reduction in gravitational mass for compact objects, consequently it is proposed that General Relativity, or its successor, will ultimately show that singularities cannot form. As another consequence it is found that dark matter can best account for the flat shape of galactic rotation curves, if it is moving continuously towards the galactic centre. It is proposed that dark matter is ejected periodically from galactic centres. These proposals may best be tested by computer simulation, and if found to give a realistic match to observations, they may act as a guide to those attempting a fully formulated theory.
Category: Relativity and Cosmology

Demonstration

Authors: António Saraiva
Comments: 2 pages

Einstein's spacetime doesn't exist because the Lorentz's invariance equation is equal to a constant.
Category: Relativity and Cosmology

The Corona Effect

Authors: André Michaud
Comments: 20 pages

It can be shown that positron production and nucleosynthesis in the corona could be much more extensive than assumed from current theories. It can be shown also that there is a possibility that the extreme temperatures observed in the corona may be due to nucleon genesis within the corona and that most heavy elements in the planetary system could be indigenous to our system and could have been produced in the corona by nucleosynthesis.
Category: Astrophysics

New Calculuses

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