Mathematical Physics

   

The Velocity-Wavelength Right Triangles Unit Circles Standard Clock and the Twin Paradox

Authors: Claude Michael Cassano

Using energy and momentum definitions: E=(m_0)c²/sqrt(1-v²/c²) and p=(m_0)v/sqrt(1-v²/c²)their frequencies and wavelengths may be shown as reciprocal transformations: f=c/λ_{c} , λ=c/f_{c} yielding the generally referred to: (λ_{c)}(f_{c})=v=v_{g} group velocity ; and λf=(c/f_{c})(c/λ_{c))=c²/((λ_{c)}(f_{c}))=c²/v=v_{p} phase velocity and yields the right triangles: ((((m_0)c)/h)λ_{c})²(v/c)²=1 and [((((m_0)v)/h))λ]²(v/c)²=1 represent wavelength-velocity right triangles with unit hypotenuses (radii of unit circles) As unit circles, the time rate of change of the angle of these wavelength-velocity right triangles may be considered a standard clock of a relativistic reference frame. Analysis may be made for any planets in a solar system; and similarly for binary star/planet/moon system(s) and also for bodies within rotating galaxies. Using this standard relativistic clock the effects of acceleration concerning the twin paradox may be calculated.

Comments: 6 Pages.

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[v1] 2023-06-17 01:19:43

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