# Time dilation derived from first principles vs. “width contraction”

Wikipedia describes the usual derivation of time dilation with a moving light clock:

In this and similar derivations nothing is ever said about a possible "width contraction" and why it does not happen. In principle, the clock would not run slower, if it would undergo sufficient width contraction from $$L$$ to $$L'=\alpha L$$ with $$\alpha<1$$ such that the path $$D=\sqrt{(1/2 v\Delta t')^2 + L'^2}$$ is again equal to $$L$$.

Can width contraction be ruled out theoretically or does it need measurement and observation?

• The length contraction will be only along the direction of relative motion. – UKH Apr 14 at 7:00

• @Harald As to symmetry of movement, surely the following is required: If frame B is moving wrt A with velocity $v$, then A is moving wrt B with velocity $-v$. This is no independent axiom and is frequently taken for obvious. It derives from space and time homogeneity and space isotropy - axioms anyway necessary for founding SR. The proof however isn't exactly trivial, AFAIK. – Elio Fabri Apr 15 at 13:18