4DSpacetime

4DSpacetime is the four-dimensional continuum that unifies three spatial dimensions with one temporal dimension into a single geometric structure. In special relativity it is modeled as flat Minkowski space, with coordinates x^μ = (ct, x, y, z). The spacetime interval between events is ds^2 = c^2 dt^2 − dx^2 − dy^2 − dz^2; this quantity is invariant under Lorentz transformations and determines causal relations: timelike intervals allow sub-light-speed influence, lightlike intervals lie on the light cone, and spacelike intervals cannot influence each other.

In general relativity spacetime is curved by matter and energy; the geometry is described by the metric tensor g_{μν}(x). Distances and angles are obtained from ds^2 = g_{μν} dx^μ dx^ν. Free-falling particles follow geodesics, and proper time is defined by dτ^2 = ds^2/c^2 for timelike paths. The Einstein field equations G_{μν} = 8πG/c^4 T_{μν} relate curvature to energy–momentum content.

Historically, Hermann Minkowski introduced spacetime in 1908 as a geometric setting for special relativity, and Einstein extended the concept to general relativity in 1915. The framework provides a common language for motion, causality, and gravity. Experimental confirmations include time dilation, gravitational redshift, gravitational lensing, and the relativistic corrections used in satellite navigation.

In modern physics, 4DSpacetime underpins classical field theories, quantum field theory in curved spacetime, and cosmology, illustrating the inseparability of space and time in forming physical laws.