Spacetime Interval Simulator - DP Physics A5 Relativity

Spacetime Diagram

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Click and drag to create spacetime intervals. Click existing events to select them. Use controls to adjust reference frame velocity.

Reference Frame

Velocity (v/c): 0.00

Events & Intervals

Event Position (x): 0.0

Event Time (ct): 0.0

Physics Examples

Spacetime Interval

$$\Delta s^2 = c^2\Delta t^2 - \Delta x^2$$

Select two events to calculate interval

Lorentz Transformation

$$t' = \gamma\left(t - \frac{vx}{c^2}\right)$$ $$x' = \gamma(x - vt)$$

$\gamma = $ 1.000

Spacetime Interval Theory

The spacetime interval is invariant under Lorentz transformations:

$$\Delta s^2 = c^2\Delta t^2 - \Delta x^2 = \text{invariant}$$

This means all observers measure the same spacetime interval between two events, regardless of their relative motion.

Timelike: $\Delta s^2 > 0$ (events can be causally connected)
Spacelike: $\Delta s^2 < 0$ (events cannot be causally connected)
Lightlike: $\Delta s^2 = 0$ (events connected by light signal)

Reading Spacetime Diagrams

Axes:

Vertical axis: time (ct)
Horizontal axis: position (x)
Light rays travel at 45° angles

Moving Reference Frames:

Time axis rotates toward light cone
Space axis rotates toward light cone
Simultaneity changes between frames

DP Physics Examples

Twin Paradox: Shows how proper time differs from coordinate time. The traveling twin ages less due to time dilation during acceleration phases.

Simultaneity: Events simultaneous in one frame are not simultaneous in another. The relativity of simultaneity depends on the relative velocity between frames.

Length Contraction: A rod's length appears contracted when measured in a frame where it's moving. The proper length is measured in the rod's rest frame.

Time Dilation: Moving clocks run slower. The proper time (τ) is always less than the coordinate time (t) by a factor of γ.

Key formulas for FE2025:

$$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$ $$\Delta\tau = \frac{\Delta t}{\gamma} \text{ (proper time)}$$ $$L_0 = \gamma L \text{ (proper length)}$$ $$\Delta s^2 = c^2\Delta t^2 - \Delta x^2 \text{ (invariant)}$$