Construct the endpoint events that actually measure length

1. Define events, frames and conserved quantities

A rod length in a frame is the distance between its endpoints measured simultaneously in that frame. The proper length L0 uses the rod’s rest frame S′. A laboratory S sees the rod move at +β, so its simultaneous endpoint events are not the same pair as the rod-frame simultaneous events.

Choose the left event at the common origin and the right laboratory event at Δt=0. Transforming gives Δx′=γΔx and Δt′=−γβΔx. The right endpoint has fixed rest position L0, so Δx=L0/γ and Δt′=−βL0. The rest spatial coordinate still spans the full rod, but the rest times differ.

Instead transform a pair selected with Δt′=0 and Δx′=L0. The laboratory obtains Δx=γL0 and Δt=γβL0. This larger spatial separation does not contradict contraction: those endpoint readings were not simultaneous in the laboratory and are not a laboratory length measurement.

Length contraction is a relation between different simultaneity slices, not an assertion that a moving material has been mechanically compressed in its own rest frame. This ideal inertial rod model does not specify how the rod accelerated, how stress propagates or how an image would appear after different light-travel times.

2. Reconstruct the original case

With L0=4 and β=0.6, γ=1.25 and laboratory simultaneous length is 3.2. That laboratory pair has rest-frame time difference −2.4 and spatial difference 4. The rest-simultaneous pair instead transforms to laboratory differences (Δt,Δx)=(3,5).

3. Predict and investigate

Which difference in event selection explains 3.2 and 5 without treating either calculation as an algebra mistake?

Construct both endpoint pairs, transform each explicitly and label which frame imposes simultaneity. Reject any purported length that uses different endpoint times in the measuring frame.

Primary mechanism context. Checked 31 October 2026. Original derivations, records and diagrams; no physical apparatus operation or actual independent clock/particle measurement is claimed. Retain first reasoning and public-feedback exposure in the course evidence workspace when registered.