Sin-Tan Rosetta Elliptical Sinh-Tanh Rosetta PerSpace-PerTime Physical Terms Compton Scattering Space-Space Basic Coordinates Coordinates & Per-Coordinates

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Rapidity = ρ =

Aberration angle = σ =

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Listing of Modern Physics material form 2012
Hit return after selecting one

Units	--- Unit 1 Unit 2 Unit 3
Lectures
Papers & Talks	--- What's the Matter with Mass? Harvard 2010 Molecular Eigensolution Symmetry Analysis and Fine Structure - Int.J.MolSci 1.4.13 Molecules and Molecular Spectroscopy - UAF 2013 Relativity and Quantum Theory by Ruler and Compass - SRQM"

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Time Sense: Time evolves

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u/c = β21 =

u/c = β31 =

x =    ct =    τ=

x' =    ct' =    τ'=

x'' =    ct'' =    τ''=

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\begin{array}{*{10}{|c|c|cc|cc|cc|c|}} \hline {time} & \color{red}{b_{RED}^{Doppler}} & {\frac{{\color{green}{V_{group}}}}{c}}&{\frac{{\color{green}{\upsilon _{group}}}}{{\color{green}{\upsilon _A}}}} & {\frac{{\color{blue}{\tau _{phase}}}}{{\color{blue}{\tau _A}}}}&{\frac{{\color{blue}{\upsilon _{phase}}}}{{\color{blue}{\upsilon _A}}}} & {\frac{{\color{green}{\tau _{group}}}}{{\color{green}{\tau _A}}}}&{\frac{{\color{blue}{V_{phase}}}}{c}} & \color{blue}{\color{darkorchid}b_{BLUE}^\color{darkorchid}{Doppler}} \\ \hline {space} & {\frac{1}{\color{blue}{\color{darkorchid}b_{BLUE}^\color{darkorchid}{Doppler}}}} & {\frac{c}{{\color{blue}{V_{phase}}}}}&{\frac{{\color{blue}{\kappa _{phase}}}}{{\color{blue}{\kappa _A}}}} & {\frac{{\color{green}{\lambda _{group}}}}{{\color{green}{\lambda _A}}}}&{\frac{{\color{green}{\kappa _{group}}}}{{\color{green}{\kappa _A}}}} & {\frac{{\color{blue}{\lambda _{phase}}}}{{\color{blue}{\lambda _A}}}}&{\frac{c}{{\color{green}{V_{group}}}}} & {\frac{1}{\color{red}{b_{RED}^{Doppler}}}} \\ \hline {_{{\text{ }}\rho }^{rapidity}} & {\color{red}{e^{ - \rho }}} & \color{green}{\tanh \rho }&{\sinh \rho } & {\operatorname{sech} \rho }&{\cosh \rho } & {{\text{csch}}\rho }&\color{blue}{\coth \rho } & \color{darkorchid}{{e^{ + \rho }}} \\ \hline {_{\beta = 3/5}^{value\,for}} & {\frac{1}{\color{red}2}{\kern 1pt} \negthickspace= \negthickspace\color{red}{0.5}} & \color{green}{\frac{3}{5}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace0.6}&{\frac{3}{4}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace0.75} & {\frac{4}{5}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace0.80}&{\frac{5}{4}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace1.25} & {\frac{4}{3}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace1.33}&\color{blue}{\frac{5}{3}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace\color{blue}{1.67}} & {\frac{\color{darkorchid}2}{1}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace\color{darkorchid}{2.0}} \\ \hline \end{array}

\begin{array}{*{10}{|c|c|cc|cc|cc|c|}} \hline {time} & \color{red}{b_{RED}^{Doppler}} & {\frac{{\color{green}{V_{group}}}}{c}}&{\frac{{\color{green}{\upsilon _{group}}}}{{\color{green}{\upsilon _A}}}} & {\frac{{\color{blue}{\tau _{phase}}}}{{\color{blue}{\tau _A}}}}&{\frac{{\color{blue}{\upsilon _{phase}}}}{{\color{blue}{\upsilon _A}}}} & {\frac{{\color{green}{\tau _{group}}}}{{\color{green}{\tau _A}}}}&{\frac{{\color{blue}{V_{phase}}}}{c}} & \color{blue}{\color{darkorchid}b_{BLUE}^\color{darkorchid}{Doppler}} \\ \hline {space} & {\frac{1}{\color{blue}{\color{darkorchid}b_{BLUE}^\color{darkorchid}{Doppler}}}} & {\frac{c}{{\color{blue}{V_{phase}}}}}&{\frac{{\color{blue}{\kappa _{phase}}}}{{\color{blue}{\kappa _A}}}} & {\frac{{\color{green}{\lambda _{group}}}}{{\color{green}{\lambda _A}}}}&{\frac{{\color{green}{\kappa _{group}}}}{{\color{green}{\kappa _A}}}} & {\frac{{\color{blue}{\lambda _{phase}}}}{{\color{blue}{\lambda _A}}}}&{\frac{c}{{\color{green}{V_{group}}}}} & {\frac{1}{\color{red}{b_{RED}^{Doppler}}}} \\ \hline {_{{\text{ }}\rho }^{rapidity}} & {\color{red}{e^{ - \rho }}} & \color{green}{\tanh \rho }&{\sinh \rho } & {\operatorname{sech} \rho }&{\cosh \rho } & {{\text{csch}}\rho }&\color{blue}{\coth \rho } & \color{darkorchid}{{e^{ + \rho }}} \\ \hline {_{{\text{ }}angle{\text{ }}\sigma }^{stellar{\text{ }}\forall }} & {1{\kern 1pt} /{\kern 1pt} \color{darkorchid}{e^{ + \rho }}} & \color{green}{\sin \sigma }&{\tan \sigma } & {\cos \sigma }&{\sec \sigma } & {\cot \sigma }&\color{blue}{{\text{csc}}\sigma } & {1{\kern 1pt} /{\kern 1pt} \color{red}{e^{ - \rho }}} \\ \hline {\beta {\kern 1pt} \equiv {\kern 1pt} \frac{u}{c}} & {\sqrt {\frac{{1{\kern 1pt} - \beta }}{{1{\kern 1pt} + \beta }}} } & {\frac{\beta }{1}}&{\frac{1}{{\sqrt {{\beta ^{ - 2}} - {\kern 1pt} 1} }}} & {\frac{{\sqrt {1{\kern 1pt} - {\beta ^2}} }}{1}}&{\frac{1}{{\sqrt {{1-\beta ^2} } }}} & {\frac{{\sqrt {{\beta ^{ - 2}} - {\kern 1pt} 1} }}{1}}&{\frac{1}{\beta }} & {\sqrt {\frac{{1{\kern 1pt} + \beta }}{{1{\kern 1pt} - \beta }}} } \\ \hline {_{\beta = 3/5}^{value\,for}} & {\frac{1}{\color{red}2}{\kern 1pt} \negthickspace= \negthickspace\color{red}{0.5}} & \color{green}{\frac{3}{5}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace0.6}&{\frac{3}{4}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace0.75} & {\frac{4}{5}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace0.80}&{\frac{5}{4}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace1.25} & {\frac{4}{3}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace1.33}&\color{blue}{\frac{5}{3}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace\color{blue}{1.67}} & {\frac{\color{darkorchid}2}{1}{\kern 1pt} \negthickspace= {\kern 1pt} \negthickspace\color{darkorchid}{2.0}} \\ \hline \end{array}

\begin{array}{*{10}{|c|c|cc|cc|cc|c|}} \hline {group} & \color{red}{b_{RED}^{Doppler}} & {\frac{{\color{green}{V_{group}}}}{c}}&{\frac{{\color{green}{\upsilon _{group}}}}{{\color{green}{\upsilon _A}}}} & {\frac{{\color{blue}{\tau _{phase}}}}{{\color{blue}{\tau _A}}}}&{\frac{{\color{blue}{\upsilon _{phase}}}}{{\color{blue}{\upsilon _A}}}} & {\frac{{\color{green}{\tau _{group}}}}{{\color{green}{\tau _A}}}}&{\frac{{\color{blue}{V_{phase}}}}{c}} & \color{blue}{\color{darkorchid}b_{BLUE}^\color{darkorchid}{Doppler}} \\ \hline {phase} & {\frac{1}{\color{blue}{\color{darkorchid}b_{BLUE}^\color{darkorchid}{Doppler}}}} & {\frac{c}{{\color{blue}{V_{phase}}}}}&{\frac{{\color{blue}{\kappa _{phase}}}}{{\color{blue}{\kappa _A}}}} & {\frac{{\color{green}{\lambda _{group}}}}{{\color{green}{\lambda _A}}}}&{\frac{{\color{green}{\kappa _{group}}}}{{\color{green}{\kappa _A}}}} & {\frac{{\color{blue}{\lambda _{phase}}}}{{\color{blue}{\lambda _A}}}}&{\frac{c}{{\color{green}{V_{group}}}}} & {\frac{1}{\color{red}{b_{RED}^{Doppler}}}} \\ \hline {rapidity\\ \rho = {\rm{tStrRap}}} & {\color{red}{e^{ - \rho }}} & \color{green}{\tanh \rho }&{\sinh \rho } & {\operatorname{sech} \rho }&{\cosh \rho } & {{\text{csch}}\rho }&\color{blue}{\coth \rho } & \color{darkorchid}{{e^{ + \rho }}} \\ \hline {stellar{\text{ }}aberration\\ \sigma = {\rm{tStrSig}}} & {1{\kern 1pt} /{\kern 1pt} \color{darkorchid}{e^{ + \rho }}} & \color{green}{\sin \sigma }&{\tan \sigma } & {\cos \sigma }&{\sec \sigma } & {\cot \sigma }&\color{blue}{{\text{csc}}\sigma } & {1{\kern 1pt} /{\kern 1pt} \color{red}{e^{ - \rho }}} \\ \hline {velocity{\text{ }}(rescaled{\text{ }}by{\text{ }}c)\\ \beta = {\rm{tStrVel}}} & {\sqrt {\frac{{1{\kern 1pt} - \beta }}{{1{\kern 1pt} + \beta }}} } & {\frac{\beta }{1}}&{\frac{1}{{\sqrt {{\beta ^{ - 2}} - {\kern 1pt} 1} }}} & {\frac{{\sqrt {1{\kern 1pt} - {\beta ^2}} }}{1}}&{\frac{1}{{\sqrt {{1-\beta ^2} } }}} & {\frac{{\sqrt {{\beta ^{ - 2}} - {\kern 1pt} 1} }}{1}}&{\frac{1}{\beta }} & {\sqrt {\frac{{1{\kern 1pt} + \beta }}{{1{\kern 1pt} - \beta }}} } \\ \hline {effects} & {\color{red}{b_{RED}^{Doppler}}} & {{\rm{Relativity }}\\ {\rm{parameter}}} & {Lorentz\\ \rm{off - diagonal}\\ \rm{asimultaneity}} & {Lorentz\\ \rm{contraction}} & {Einstein\\ \rm{time\:dilation}} & {\rm{Inverse\\ \:asimultaneity}} & {\color{blue}{V_{phase}}} & \color{blue}{\color{darkorchid}b_{BLUE}^\color{darkorchid}{Doppler}} \\ \hline {functions} & {\frac{1}{\color{blue}{\color{darkorchid}b_{BLUE}^\color{darkorchid}{Doppler}}}} & {V_{group}= c\,{\rm{tanh}}\rho} & {momentum\\ \rm{cp=Mc2sinh\rho}} & {-Lagrangian\\ \rm{L}} & {Hamiltonian\\ \rm{H=Mc2=:\\rm{cosh}\:\rho}} & {DeBroglie\\ \lambda=(1/Mc)\:\rm{csch}\:\rho} & {\color{blue}{V_{phase}}{\\=c\:\rm{coth}\:\rho}} & {\frac{1}{\color{red}{b_{RED}^{Doppler}}}} \\ \hline

\begin{array}{*{10}{|c|c|cc|cc|cc|c|}} \hline {time} & \color{red}{b_{RED}^{Doppler}} & {\frac{{\color{green}{V_{group}}}}{c}}&{\frac{{\color{green}{\upsilon _{group}}}}{{\color{green}{\upsilon _A}}}} & {\frac{{\color{blue}{\tau _{phase}}}}{{\color{blue}{\tau _A}}}}&{\frac{{\color{blue}{\upsilon _{phase}}}}{{\color{blue}{\upsilon _A}}}} & {\frac{{\color{green}{\tau _{group}}}}{{\color{green}{\tau _A}}}}&{\frac{{\color{blue}{V_{phase}}}}{c}} & \color{blue}{\color{darkorchid}b_{BLUE}^\color{darkorchid}{Doppler}} \\ \hline {space} & {\frac{1}{\color{blue}{\color{darkorchid}b_{BLUE}^\color{darkorchid}{Doppler}}}} & {\frac{c}{{\color{blue}{V_{phase}}}}}&{\frac{{\color{blue}{\kappa _{phase}}}}{{\color{blue}{\kappa _A}}}} & {\frac{{\color{green}{\lambda _{group}}}}{{\color{green}{\lambda _A}}}}&{\frac{{\color{green}{\kappa _{group}}}}{{\color{green}{\kappa _A}}}} & {\frac{{\color{blue}{\lambda _{phase}}}}{{\color{blue}{\lambda _A}}}}&{\frac{c}{{\color{green}{V_{group}}}}} & {\frac{1}{\color{red}{b_{RED}^{Doppler}}}} \\ \hline {_{{\text{ }}\rho }^{rapidity}} & {\color{red}{e^{ - \rho }}} & \color{green}{\tanh \rho }&{\sinh \rho } & {\operatorname{sech} \rho }&{\cosh \rho } & {{\text{csch}}\rho }&\color{blue}{\coth \rho } & \color{darkorchid}{{e^{ + \rho }}} \\ \hline

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