When is there a repulsive force

We hope that our theoretical prediction about decreasing acceleration of the Universe can be verified by observations. It is logical to suppose that the found mechanism of the repulsive force may be applied to a model of the expanding universe. This may imply that big bang and accelerated expansion of the Universe is not related to current processes in the Universe but to a relic repulsive gravitational force or to a configuration of space—time that originates in the previous cycle of the Universe when at the last stage of a collapse the intensive generation of gravitational waves resulted in sharp decrease of the gravitational mass of the Universe and may be in avoiding a singularity.

This process generated a powerful repulsive force that transformed big crunch into big bang. At the early stage of big bang the repulsive acceleration was extremely high see the dropping branches of the curves 1 and 2 in Fig. Because the repulsive acceleration decreases with time, the current Universe expands with lower acceleration see the gently sloping parts of curve 3 in Fig. The proposed metric with the varying gravitational mass of a system may be used for the development of a cosmological model that explains the current expansion of the Universe without assumptions of new fields and particles.

Such a cosmological model may allow an explanation of the anisotropy of movement of galaxies discovered by Kashlinsky et al. Abbot B. Bamba K. Nojiri S. Odintsov S.

B Banks T. Fischler W. Buchert T. Classical Quantum Gravity 32 Chandrasekhar S. Google Scholar. Google Preview. Eddington A. Einstein A. Gorkavyi N. BAAS 35 Green S. Wald R. D 87 Grishchuk L.

Guth A. D 23 Hilbert D. Nachrichten von der Gesellschaft der Wissenschaften zu Gottingen 24S Hoyle F. MNRAS Joyce A. Lombriser L. Schmidt F. Kashlinsky A. Atrio-Barandela F. Kocevski D. Ebeling H. ApJ Kutschera M. Landau L. Lifshitz E. The Classical Theory of Fields, Vol. McGruder Ch. D 25 McVittie G. Misner Ch. Thorne K. Wheeler J. Perlmutter S. And for decades, mathematicians have been trying to pin down the exact magnitude of the repulsion in this setting.

In a proof posted online in late December , Vesselin Dimitrov of the University of Toronto finally did it. The problem Dimitrov solved, known as the Schinzel-Zassenhaus conjecture, is about the geometry of values of polynomials. It also provides new insight into the laws that numbers seem to obey. A polynomial has as many roots as its degree, or the value of its largest exponent. Mathematicians want to know how the roots of a polynomial relate to each other.

For example, when graphed, the roots of some polynomials fall exactly on the vertices of regular polygons — they stand apart by an exact geometric length. Mathematicians are interested in finding other, more subtle geometric relationships between roots. Can you get any patterns, or are the patterns somewhat restricted?

The problem that Dimitrov solved involves the roots of a particularly important family of expressions called the cyclotomic polynomials. Unlike the periodic table, however, the list of cyclotomic polynomials goes on forever. The roots of cyclotomic polynomials follow a very special geometric pattern. To see it, start with the empty complex plane, in which the x -axis plots real numbers and the y -axis plots imaginary ones.

Then inscribe a circle with a radius of 1 around the origin. This is the unit circle. The roots of cyclotomic polynomials all lie on this circle. But most polynomials are non-cyclotomic, and their roots are not roots of unity. This is the case with almost any combination of coefficients, variables and exponents you could come up with.

In , Andrzej Schinzel and Hans Zassenhaus predicted that the geometry of the roots of cyclotomic and non-cyclotomic polynomials differs in a very specific way. Take any non-cyclotomic polynomial whose first coefficient is 1 and graph its roots.

Our theoretical framework is based on Embodied Learning theory by relating conceptual learning to bodily experiences. The study uses qualitative and quantitative methods with 21 high school chemistry students in a pretest—intervention—posttest design. During a 40 minute activity with the ELI-Chem simulation, students were prompted to discover the underlying forces of bonding and relate them to energy changes. Findings show that learning with the ELI-Chem simulation supports students in gaining the knowledge elements that are required to build the dynamic force-based mental model of chemical bonding, and to conceptualize chemical energy as due to forces.

Finally, the design principles of the ELI-Chem environment are discussed. Zohar and S. Levy, Chem. To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page.

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