A rod one light-year long, made as stiff as physics allows, floats at rest in front of you. You shove your end forward by one meter. When does the far end move — and if the answer were “immediately,” could you use the rod to send messages faster than light?
Solution
Tens of thousands of years later — and no.
A perfectly rigid body is a Newtonian fiction. Your shove propagates down the rod as a compression wave at the material’s sound speed, , and relativistic causality caps every signal — elastic waves included — at . Stiffness is not a loophole: the elastic moduli enter the stress-energy tensor, and a material with would have to violate the causal structure of the field equations that govern it. For diamond, , so the far end of a light-year rod answers your shove roughly years later.
The deeper point is that relativity does not merely forbid building a rigid rod; it forbids defining one that can be commanded from one end. The strongest notion of rigidity the theory admits — Born rigidity, constant proper distance between neighboring pieces — is so restrictive (this is the Herglotz–Noether theorem) that a Born-rigid body has essentially no independent degrees of freedom left to push.
Deeper in the notebook: 01. Timelike, Null and Spacelike Separation; the Causal Order · 03. Tachyons and the Limits of Causality (signpost) · 03. Bell’s Spaceship Paradox and Born Rigidity