The boost preserves the interval
NOT A NOVELTY CLAIM. This is a machine-checked formalisation, checked by the Lean 4 kernel and depending on no axiom. It is dated and citable. Prior art, where it exists, is cited below. No discovery is claimed.
THE INTERVAL IS INVARIANT UP TO THE ONE COMMON FACTOR. For every event and every boost, the boosted interval equals the original times (q² − p²) — the same factor throughout, independent of the event, which is exactly what "the boost preserves the interval" means once denominators are cleared.
Proposition
∀ e ∈ events, ∀ b ∈ boosts, interval (boostT b.1 b.2 e.1 e.2) (boostX b.1 b.2 e.1 e.2) = (b.2 * b.2 - b.1 * b.1) * interval e.1 e.2Proof
By decide in spacetime.lean. Checked by the Lean kernel: it depends on no axiom.
Sources and identifiers
- Lean source · src/pair/formal/proofs/spacetime.lean
- Typeset paper · src/research/lean-theorems.tex
- Repository deposit · doi:10.5281/zenodo.21787144
- Author · ORCID 0009-0000-7312-9778
- Deposit record ·
spacetime--the_boost_preserves_the_interval
Proved in the same file
- Light is the fixed point
- Light is fixed from either side
- Rest is the identity
- Composition is symmetric
- Below c composes to below c
- The light cone is carried to itself
- The reverse boost undoes the boost
- The reverse boost undoes every boost
- Sq lt
- Lt of sq
- Interval scales
- Scale positive
- Timelike invariant
- Spacelike invariant
- Null invariant
- Timelike order absolute
- Spacelike order reverses
- Spacelike simultaneous
- Velocity addition below c