# Proposition: Time Dilation, Lorentz Factor

Let $$\mathcal I_1$$ and $$\mathcal I_2$$ be two inertial frames of reference moving relatively to each other with the constant speed $$v$$ obeying the inequation $$0\le v < c$$, where $$c$$ denotes the constant speed of light1. If an observer inside the reference frame $$\mathcal I_1$$ measures the time $$t_1$$ elapsed in $$\mathcal I_1$$ and compares it to the time $$t_2$$ elapsed he observes in the inertial frame of reference $$\mathcal I_2$$, then both times elapsed will show a difference called time dilation, which is given by the formula

$t_1=t_2\cdot \gamma.$

The factor $\gamma:=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}},\quad\quad (0\le v < c)$

is called the Lorentz factor2.

Proofs: 1 Explanations: 1

Explanations: 1

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### References

#### Bibliography

1. WeingĂ¤rtner, Andreas: "Spezielle RelativitĂ¤tstheorie - ganz einfach", Books On Demand, 2016

#### Footnotes

1. If both inertial frames of reference are in a vacuum, this speed equals $$c=299\,792\,458~m/s.$$

2. Named so after Hendrik Antoon Lorentz (1853 - 1928).