Event Ordering and the Light Cone

Source

Collection: Wiki SR simulations — converted to the global shell design.
Concept: Whether a Lorentz boost can reverse the time order (flip the sign of Δt′) of two events depends entirely on their separation: it can for a spacelike pair, never for a timelike pair.
Serves: The student places a second event on a Minkowski diagram (c = 1) and changes the observer's frame with the boost slider — relabelling the ct′/x′ axes — to see Δt′ slide through zero and reverse only when the interval (Δs)² = Δt² − Δx² is negative (spacelike).
Inquiry: Can switching inertial frames reverse the order of two events? Always, never, or only for some pairs? What distinguishes those pairs?
Misconception: That ordering is either always reversible (A) or always absolute (B), rather than being controlled by the invariant interval's sign (light-cone structure).

Pedagogy principles applied

ID	Principle	How it shows up here
H1	Misconception is structural, not a text card	The "always reversible" and "never reversible" errors are the wrong prediction choices A and B; each rebuttal appears only if that choice is picked.
J	Invariant panels are scoped to invariance sims	This sim's lesson IS the invariant interval, so the (Δs)² = Δt²−Δx² readout is shown and colour-coded timelike/spacelike/lightlike.
A2	Fewest objects	Opens with only the light cone and one reference event; the student places a single second event — no vestigial counters.
C	Every number earns its place	Δt′, (Δs)², and the critical boost β = Δt/Δx are each read or predicted by a step; the interval's sign is the whole point.
Physics honesty	No false animation of β	The boost is a static slider — dragging it relabels the ct′/x′ axes (a frame change), rather than auto-sweeping β as if the frame were accelerating.

Event Ordering

Speed

Spacetime diagramc = 1 · primed axes = the boosted observer's frame

timelike region (inside cone) spacelike region (outside cone) ct′ axis x′ axis (line of simultaneity, t′ = 0)

Guided Inquiry

1 · Predict

Can switching to a different inertial frame (a Lorentz boost) reverse the time order of two events — flip the sign of Δt′?

2 · Place an event

Click anywhere on the diagram to drop a second event (the origin is the reference event). Drop it well inside the yellow light cone first — a timelike separation. The sidebar readouts light up.

3 · Boost the timelike pair

Drag the Boost v/c slider. Watch Δt′ in the readouts. For this timelike event, does Δt′ ever reach zero or change sign?

4 · Now a spacelike pair

Drag the event outside the light cone (into the red region), then use Find simultaneous frame (Δt′ = 0). What happens to the order as you push the boost past that value?

5 · Resolve

The invariant (Δs)² = Δt² − Δx² decides everything. > 0 (timelike): order protected. < 0 (spacelike): order reversible. = 0 (lightlike): the boundary. A boost is not motion — it relabels the axes to a new observer's frame. Open ∑ Formal for the algebra, or drag the event around to explore. Hit Finish to tuck this away.

Controls

▾

Click on the diagram to place a second event first.

Boost of viewing frame v/c = β 0.000

−0.99+0.99

Live readouts

▾

Δt′—

(Δs)² = Δt²−Δx²—

separation—

Lorentz boost (c = 1)

Lorentz factor

Invariant interval

Frame with Δt′ = 0

The primed axes scissor toward the 45° light line — they skew, they do not rigidly rotate. Skew angle from the unprimed axes is arctan(β); the rapidity is φ = atanh(β). Making Δt′ = 0 requires v = c²Δt/Δx, hence β = cΔt/Δx; with c = 1 this is simply β = Δt/Δx, which only has |β| < 1 when the pair is spacelike.