Magnitude of Lorentz-Fitzgerald Contraction

Theorem

Let $B$ be a body moving in an inertial frame of reference $\FF_1$.

Let an observer $O$ be in a different inertial frame of reference $\FF_2$.

Let $v$ be the magnitude of the relative velocity of $\FF_1$ with respect to $\FF_2$.

Let $l$ be the length of $B$ in the direction of the relative velocity of $\FF_1$ with respect to $\FF_2$.

Let $l'$ be the length of $B$ in the direction of the relative velocity of $\FF_1$ with respect to $\FF_2$ as measured by $O$.

Then:

$l' = l \sqrt {1 − \dfrac {v^2} {c^2} }$

where $c$ denotes the speed of light.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Lorentz-Fitzgerald contraction
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Lorentz-Fitzgerald contraction