Spacelike order reverses
NOT A NOVELTY CLAIM. This is a machine-checked formalisation, checked by the Lean 4 kernel and resting on no axiom beyond propext and Quot.sound. It is dated and citable. Prior art, where it exists, is cited below. No discovery is claimed.
FOR A SPACELIKE SEPARATION THERE IS A FRAME BELOW c IN WHICH THE ORDER REVERSES — exhibited: with 0 < t < x, the boost β = (2t+1)/(2x) sends Δt to −x.
Proposition
(t x : Int) (ht : 0 < t) (hx : t < x) : belowC (2*t+1) (2*x) ∧ boostT (2*t+1) (2*x) t x = -xProof
By refine ⟨⟨by omega, by omega, by omega⟩, ?_⟩ in spacetime.lean. Checked by the Lean kernel: it rests on Quot.sound and propext and on no other 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--spacelike_order_reverses
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 boost preserves the interval
- 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 simultaneous
- Velocity addition below c