How can the Lorentz factor $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ be understood? what What does that mean? - forFor example, what is the reason for the second power/roots and square root?, why Why not $\frac{1}{1-\frac{v}{c}}$?, or what would happen if it took that would be the caseform?. Can you point me to other physicphysical laws that make use of the $\sqrt{1-r^2}$ so as to "translate" it.
Let $T_0$ be the local period and $L_0$ the local length
- Light-clock moves $\bot$ light $\rightarrow$ $T=\frac{T_0}{\sqrt{1-\frac{v^2}{c^2}}}$
- Light-clock moves $\parallel$ light $\rightarrow$ $T=\frac{2L}{c(1-\frac{v^2}{c^2})}$$T=\frac{2L}{c\left(1-\frac{v^2}{c^2}\right)}$
Referring to 1, How could photons not miss the mirror?
Q: How could I understand the Lorentz factor formula intuitively, or what is your concept of it?