E-infinity Theory Research Articles

From E-eight to E-Infinity

The paper discusses the recently uncovered connections between certain finite Exceptional Lie symmetry group hierarchy and the standard model of elementary particles as well as the unification of all fundamental interactions including gravity. We start from the E 8 Exceptional Lie group and proceed by reviewing various alternatives including E 10 and E 11. We conclude by proposing that the hierarchical E ∞ is the true average fractal symmetry of E-Infinity theory and consequently the proper extension of the Exceptional Lie groups to the transfinite setting of E-Infinity spacetime.

A generalized poincaré-invariant action with possible application in strings and E-infinity theory

Using the semi-inverse method [He. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos Solitons & Fractals 2004;19(4):847–851], a generalized Poincaré-invariant action using the tetrad in any number of dimensions is obtained. The so-obtained generalized action with a free parameter might find potential applications in bosonic strings and E-infinity theory.

Noether’s theorem, exceptional Lie groups hierarchy and determining 1/α≅137 of electromagnetism

Noether’s theorem relating conservation laws with symmetry is applied in conjunction with the exceptional Lie group hierarchy, the holographic principles and E-infinity theory to calculate the electromagnetic fine structure constant. Various schemes are suggested utilizing the fundamentals of heterotic strings as well as P-Brane theory leading to essentially the same value of 1/α ≅ 137 in complete agreement with the well-established experimental evidences.

Symmetry group prerequisite for E-infinity in high energy physics

Abstract The work addresses the question of extending certain symplectic and exceptional Lie Symmetry groups to the realm of chaotic dynamics. Using a collection of simple examples, the technique of transfinite continuation is illustrated and various physically relevant results are obtained. The paper is intended as an elementary introduction to the use of symmetry groups in transfinite physics and as such is a sequel to a series of previous papers constituting the elementary and advanced mathematical prerequisite for a proper understanding of E-infinity theory.

Space–time symmetry violation, configuration mixing model and E-infinity theory

We have studied the time reversal symmetry violation on the bases of the configuration mixing model and E-infinity theory. With the use of the Cabibbo angle approximation, we have presented the transformation matrix in terms of the golden ratio ( ϕ), and shown that the time reversal symmetry violation is described by the configuration mixing of the unstable and stable manifolds ( W u, W s). The magnitude of the mixing for the weak interaction field is given by the expression sin 2 θ T(theor) ≈ sin 4 θ C(theor) ≈ ( ϕ) 12 = 3.105 × 10 −3, which is compared to the Kaon decay experiment ∼2.3 × 10 −3. We have also discussed the space–time symmetry violation by using the CPT theorem.

From pointillism to E-infinity electromagnetism

Pretty much like in a pointillism masterpiece of say Georges Seurat or Paul Signac, quantum space-time, which is in reality a collection of transfinite discrete set of points, appears when observed at a distance to be a nowhere disjoined continuum. This geometry which is best described by its Hausdorff dimension leads us ultimately to a radical change of some of our most basic mathematical assumptions with regard to the corresponding symmetry groups. Thus instead of being restricted to an integer value of the order of these symmetry groups, it seems natural to extend this order to the realm of irrational transfinite numbers. This step is not as strange as it may seem when we consider the role played by the factorial function n! in elementary group theory and its extension for non-integer value of n using the well-known Gauss’ Gamma function. Proceeding in this way, we find that the space-time of E-infinity theory constitutes a transfinite pointillism setting in which all fundamental interactions could be accounted for via the corresponding transfinite order of its symmetry groups and finally we find a conservation equation from which the exact inverse fine structure constant α ¯ o may be accurately determined.

Complex dynamics in diatomic molecules. Part II: Quantum trajectories

The second part of this paper deals with quantum trajectories in diatomic molecules, which has not been considered before in the literature. Morse potential serves as a more accurate function than a simple harmonic oscillator for illustrating a realistic picture about the vibration of diatomic molecules. However, if we determine molecular dynamics by integrating the classical force equations derived from a Morse potential, we will find that the resulting trajectories do not consist with the probabilistic prediction of quantum mechanics. On the other hand, the quantum trajectory determined by Bohmian mechanics [Bohm D. A suggested interpretation of the quantum theory in terms of hidden variable. Phys. Rev. 1952;85:166–179] leads to the conclusion that a diatomic molecule is motionless in all its vibrational eigen-states, which also contradicts probabilistic prediction of quantum mechanics. In this paper, we point out that the quantum trajectory of a diatomic molecule completely consistent with quantum mechanics does exist and can be solved from the quantum Hamilton equations of motion derived in Part I, which is based on a complex-space formulation of fractal spacetime [El Naschie MS. A review of E-Infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals 2004;19:209–36; El Naschie MS. E-Infinity theory – some recent results and new interpretations. Chaos, Solitons & Fractals 2006;29:845–853; El Naschie MS. The concepts of E-infinity. An elementary introduction to the cantorian-fractal theory of quantum physics. Chaos, Solitons & Fractals 2004;22:495–511; El Naschie MS. SU(5) grand unification in a transfinite form. Chaos, Solitons & Fractals 2007;32:370–374; Nottale L. Fractal space-time and microphysics: towards a theory of scale relativity. Singapore: World Scientific; 1993; Ord G. Fractal space time and the statistical mechanics of random works. Chaos, Soiltons & Fractals 1996;7:821–843] approach to quantum mechanics. The fine-structure internuclear potentials obtained in Part I will be exploited here to derive the eigen-trajectories corresponding to each vibrational substate and to find the scattering trajectories under molecular dissociation. Quantum trajectories computed from the real spectroscopic data for several diatomic molecules will be demonstrated and compared.

Complex dynamics in diatomic molecules. Part I: Fine structure of internuclear potential

The current understanding of internuclear potential of diatomic molecules is limited to electronic states. In this paper, we point out that every electronic-state internuclear potential is actually accompanied by a fine structure, which characterizes the detailed internuclear potential for each vibrational substate belonging to the same electronic state. This fine structure, which governs the bond length, the force constant, the vibration frequency, and the quantum motion for each vibrational state, is obtained by extending Bohm’s quantum potential [Bohm D. A suggested interpretation of the quantum theory in terms of hidden variable. Phys Rev 1952;85:166–79] to complex domain. It is shown that the fine structure of the internuclear potential can be determined exactly by the vibrational wavefunctions so that its predictions about the internuclear forces (Part I) and the vibrational nuclear quantum motion (Part II) are fully consistent with the Max Born’s probability interpretation of the vibrational wavefunctions, and are in line with El Naschie’s E-infinity [El Naschie MS. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals 2004;19:209–36; El Naschie MS. E-infinity theory – some recent results and new interpretations. Chaos, Solitons & Fractals 2006;29:845–53; El Naschie MS. The concepts of E-infinity. An elementary introduction to the Cantorian-fractal theory of quantum physics. Chaos, Solitons & Fractals 2004;22:495–511], Nottale’s scale relativity [Nottale L. Fractal space-time and microphysics: Towards a theory of scale relativity. Singapore: World Scientific; 1993], and Ord’s random walk [Ord G. Fractal space time and the statistical mechanics of random works. Chaos, Soiltons & Fractals 1996;7:821–43] approaches to quantum mechanics.

The effect of modified dispersion relations on the thermodynamics of black-body radiation

In the study of loop quantum gravity and of models based on noncommutative geometry, there has been strong interest in some candidate modifications of the energy-momentum dispersion relation. In this paper we consider the effects of modified dispersion relation (MDR) on the thermodynamics of black-body radiation. We find a generalized Planck distribution and then apply it to find generalized Stefan–Boltzmann and generalized Wien’s law. As a consequence, we study the effects of these modifications on the entropy and specific heat of black-body radiation. We investigate also the relation between our findings and the results of E-infinity theory by considering distribution and temperature of cosmic microwave background radiation.

Random a-adic groups and random net fractals

Based on random a-adic groups, this paper investigates the relationship between the existence conditions of a positive flow in a random network and the estimation of the Hausdorff dimension of a proper random net fractal. Subsequently we describe some particular random fractals for which our results can be applied. Finally the Mauldin and Williams theorem is shown to be very important example for a random Cantor set with application in physics as shown in E-infinity theory.

A short review of the Higgs boson mass and E-infinity theory

Abstract Ever since Peter Higgs formulated the Higgs proposal in 1964, the search for the Higgs boson is one of the most important tasks in high-energy physics. The aim of the present short review is to summarise an important previous work on the calculation of the mass of the Higgs boson. Different mass formulas are pointed out and compared with each other.

E-infinity as a fiber bundle and its thermodynamics

This paper presents a novel approach for the investigation of fractals. Using parameters of fractal organization we introduce generalized Gibbs statistic and apply it for the development of thermodynamics of fractals. Our generalization is based on a fractal generation function that produces a representation for particular states of fractal space–time. All considerations are embedded into the framework of E-infinity theory viewed as a fiber bundle. Nevertheless El Naschie’s space–time represents a particular case of undistorted fractal state which corresponds to the equilibrium state of fractal space–time in our theory. Related topics of thermodynamics of fractals are discussed.

Hadron mass, Regge pole model and E-infinity theory

With the use of Regge pole model and E-infinity theory, we have calculated the masses of the excited states in hadrons, and obtained the nice agreement with experiments. We have shown the Regge–Chew–Frautschi diagrams and discussed some properties of excited states in hadrons. We have also classified the masses of elementary particles according to the mass formula m k = b ℓ n ( k ) ( 〈 m π 〉 ) ℓ ( ϕ ) n δ k , which we have used in this paper.

Twenty-six dimensional polytope and high energy spacetime physics

Abstract We give the exact geometrical shape and study the combinatorial properties of higher dimensional polytopes for the dimensions from n = 4 to n = 12 as well n = 26 relevant to Heterotic, M and F superstring theories. Connections to E-infinity theory and the holographic principles are also discussed.

The two-slit gedanken experiment in E-infinity theory

Abstract The paper draws some fundamental and methodological relations that must be taken into account in order to apply E-infinity theory for investigations of the dynamical problems of the multi-scaled phenomena.

Nano-effects, quantum-like properties in electrospun nanofibers

Abstract Electrospun nanofiber technology bridges the gap between deterministic laws (Newton mechanics) and probabilistic laws (quantum mechanics). Our research reveals that fascinating phenomena arise when the diameter of the electrospun nanofibers is less than 100 nm. The nano-effect has been demonstrated for unusual strength, high surface energy, surface reactivity, high thermal and electric conductivity. Dragline silk is made of many nano-fibers with diameter of about 20 nm, thus it can make full use of nano-effects. It is a challenge to developing technologies capable of preparing for nanofibers within 100 nm. Vibration-melt-electrospinning is uniquely qualified to address this challenge. The flexibility and adaptation provided by the method have made the method a strong candidate for producing nanofibers on such a scale. The application of Sirofil technology to strengthen nanofibers is also addressed, E-infinity theory is emphasized as a challenging theory for nano-scale technology and science.

The mass spectrum of heavier hadrons and E-infinity theory

Abstract With the use of quark model and E-infinity theory, we have calculated the mass of heavier hadrons, such as decuplet baryons and nonet vector mesons, and obtained the nice agreement with experiments. We have also investigated the sum rules among hadron masses, and obtained the good agreement with experiments. We have discussed the mass of heavier particles, such as Higgs bosons, by using the Mahmoud mass formula. We have also classified the mass of elementary particles according to the extended mass formula of Mahmoud m k = b n ( k ) 〈 m π 〉 ( N SM ) n δ k , which we have used in this paper (n = 0).

Feigenbaum scenario for turbulence and Cantorian E-infinity theory of high energy particle physics

Abstract The work draws some fundamental connections between Feigenbaum’s golden mean renormalization group and scenario for turbulence on the one side and high energy particle physics on the other side. The analysis which is based on the natural and obvious connections between the Fibonacci-like geometrical growth rate of e (∞) spacetime and Feigenbaum’s renormalization gives vital information to basic questions not only of quantum geometry, but also of quantum field theory.

Golden mean relevance for chaos inhibition in a system of two coupled modified van der Pol oscillators

In this work, we present a novel evidence of the importance of the golden mean criticality of a system of oscillators in agreement with El Naschie’s E-infinity theory. We focus on chaos inhibition in a system of two coupled modified van der Pol oscillators. Depending on the coupling between the two oscillators, the system shows chaotic behavior for different ranges of the coupling parameter. Chaos suppression, as a transition from irregular behavior to a periodical one, is induced by perturbing the system with a harmonic signal with amplitude considerably lower than the value which causes entrainment. The frequency of the perturbation is related to the main frequencies in the spectrum of the freely running system (without perturbation) by the golden mean. We demonstrate that this effect is also obtained for a perturbation with frequency such that the ratio of half the frequency of the first main component in the freely running chaotic spectrum over the frequency of the perturbation is very close (five digits coincidence) to the golden mean. This result is shown to hold for arbitrary values of the coupling parameter in the various ranges of chaotic dynamics of the free running system.

Shrinkage of body size of small insects: A possible link to global warming?

Abstract The increase of global mean surface temperature leads to the increase of metabolic rate. This might lead to an unexpected threat from the small insect world. Global warming shrinks cell size, shorten lifespan, and accelerate evolution. The present note speculates on possible connections between allometry and E-infinity theory.