Covered by the official notes: spring constant parallel to the boost (PDF p. 13; handwritten p. 8).[ref]
Covered by the official notes: spring constant orthogonal to the boost (PDF p. 13; handwritten p. 8).[ref]
The orientation-dependent results in the official notes show that the measured spring constant is not a Lorentz scalar. A Lorentz transformation changes both the simultaneous extension and the measured three-force; their ratio depends on the orientation. This does not make the spring intrinsically anisotropic in its own rest frame, or require a preferred inertial frame. It is a quasistatic effective stiffness comparison between frames; an extended real spring also has finite internal signal speeds.

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