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Light Cone (x = ct)XctX'ct'Event (X, ct)

Live Telemetry & Summary

Observe the skewing of axes. The angle of skew between the primed axes $(X', ct')$ and the unprimed axes $(X, ct)$ depends on the relative frame velocity $v$. Notice that the 45-degree light cone boundaries stay perfectly centered between both sets of coordinates!

S Frame Coordinates:x = 2.00 m, t = 1.50 s
S' Frame Coordinates:x' = 1.443 m, t' = 0.577 s
Lorentz Factor (γ):1.1547x

Variable Adjuster

Frame Velocity (v/c)0.5c
-0.90.9
Event X Position2m
-44
Event T Time1.5s
-44

Lorentz Coordinate Transform

LRTZ

Lorentz Transformations describe how coordinates (x, t) of an event in reference frame S map to coordinates (x', t') in frame S' moving at speed v. In a Minkowski Spacetime Diagram, this transformation causes the spatial and temporal axes to rotate/skew toward each other, keeping the speed of light (45-degree angle) invariant.

x′=γ(x−vt),t′=γ(t−vxc2)x' = \gamma(x - vt), \quad t' = \gamma\left(t - \frac{vx}{c^2}\right)

Whiteboard Solver Steps

Step 1

Lorentz Factor (γ)

The relativity coefficient relates coordinates in S and S'.

γ=11−(v/c)2=11−(0.500)2=1.1547\gamma = \frac{1}{\sqrt{1 - (v/c)^2}} = \frac{1}{\sqrt{1 - (0.500)^2}} = 1.1547
Step 2

Lorentz Coordinate Transformations

These equations project spatial and temporal coordinates from the stationary frame S to the moving frame S'.

x′=γ(x−vt),t′=γ(t−vxc2)x' = \gamma(x - vt), \quad t' = \gamma\left(t - \frac{vx}{c^2}\right)
Step 3

Event Coordinates in S'

The coordinates of the event in the moving reference frame.

x′=1.155(2.00−(0.50⋅1.50))=1.443,t′=1.155(1.50−(0.50⋅2.00))=0.577x' = 1.155(2.00 - (0.50 \cdot 1.50)) = 1.443, \quad t' = 1.155(1.50 - (0.50 \cdot 2.00)) = 0.577