Length Contraction

L=L01β2L = L_0 \sqrt{1 - \beta^{2}}

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Length contraction is time dilation seen from the other chair. The muon racing toward the ground says its clock is fine — instead, the 15 km of atmosphere ahead has contracted to 1.5 km, an easy trip in 2.2 μs. Both descriptions predict identical outcomes; relativity lets each observer keep their own self-consistent story. Only the dimension along the motion shrinks — a passing sphere stays a sphere in silhouette, just squashed in depth.

Length Contraction
L=L01β2L = L_0 \sqrt{1 - \beta^{2}}
Where
  • LL= Contracted length
  • L0L_0= Rest length
  • β\beta= Speed ratio v/c
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