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Progress in Physics : The Journal on Advanced Studies in Theoretical and Experimental Physics, Including Related Themes from Mathematics, Volume 2

By: Florentin Smarandache

...pon a misunderstanding of the signifcance of the coordinate radius r. This quantity is neither a coordinate nor a radius in the gravitational feld and... ...its distance from the “origin”. It is this distance which is the important quantity, not the coordinate. It is simply the case that on (1), in the usu... ...etheless, the distance from the designated “origin” is still the important quantity, not the coordinate. It is therefore clear that the designation of... ...vitational feld only the circumference χ of a great circle is a measurable quantity, from whichR c andR p 6 S J. Crothers. On the Geometry of the Gene... ...9) is independent of ther-parameter entirely. Since only χ is a measurable quantity in the gravitational feld, (19) constitutes the correct solution f... ...om now on we shall use the Gaussian system of units; in this system a is a dimensionless quantity equal to 1 16π ”. According to §27 of The Classical ...

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Progress in Physics : The Journal on Advanced Studies in Theoretical and Experimental Physics, Including Related Themes from Mathematics

By: Florentin Smarandache

...uce that in a constant curvature space Z=6c 2 K. Equating this to the same quantity in an arbitrary curvature space, we obtain a correlation between t... ...nometric invariants [1, 2], takes the form ds 2 =c 2 dτ 2 −dσ 2 . Here the quantity dτ = 1− w c 2 dt− 1 c 2 v i dx i is an interval of physical ob... ...imensional observable velocity of the particle. Sods is: (1) a substantial quantity underv<c; (2) a zero quantity under v=c; (3) an imaginary quantity... ...interpreted as the maximal string tension whenL P is the Planck scale. The quantity g(τ) is the proper four-acceleration of a particle of mass m in th... ...sion (or maximal Force)b= 1 L 2 P is a true physical invar- iant universal quantity. Also we notice that the Phase-space areas, or cells, in units of ... ...ons and with different signatures. The line element dS as defned in (4) is dimensionless. Alternatively, one can defne [8, 9] the line element whose d...

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