RaumZeitIntervall

RaumZeitIntervall is the term for the separation between two events in the four-dimensional spacetime framework of special relativity. It describes a single invariant quantity that combines spatial and temporal separations and remains unchanged under Lorentz transformations, making it a fundamental tool for understanding causality and clock synchronization.

In the common convention with the spacetime metric ds^2 = c^2 dt^2 − dx^2 − dy^2 − dz^2, the spacetime interval between events with coordinates (t1, x1, y1, z1) and (t2, x2, y2, z2) is s^2 = c^2 Δt^2 − Δx^2 − Δy^2 − Δz^2. Depending on the sign of s^2, intervals are categorized as timelike (s^2 > 0), lightlike or null (s^2 = 0), or spacelike (s^2 < 0). The categorization determines possible causal relationships: timelike intervals permit signals and causal influence, null intervals correspond to light signals, and spacelike intervals cannot be connected by any signal traveling at or below the speed of light.

The interval relates to other quantities: for timelike intervals, the proper time Δτ between events satisfies s = c Δτ; for spacelike intervals, the proper distance is related to √(−s^2). In general relativity, the concept extends locally via ds^2 = g_{μν} dx^μ dx^ν, with invariance preserved under coordinate changes but modified by spacetime curvature on larger scales.

RaumZeitIntervall underpins the causal structure of spacetime, the geometry of worldlines, and practical calculations in physics, including particle dynamics, relativistic kinematics, and technologies such as GPS that require relativistic corrections.