spacetime

Spacetime is three-dimensional space also with time as a fourth dimension. For an event, such as snapping your fingers in your living room, its position in space might be described by distances from the floor and two walls, and its time by the time on the clock, i.e., four numbers.

Relativity's spacetime has a quality not imagined before; its spacetime has four dimensions, but the time dimensions of the two objects with some relative motion are at an angle to each other within the spacetime, and some of what is space to one person can be some of what is time to another. (The effect is too slight for us to notice in daily life, but with extreme speeds, it becomes significant.)

Minkowski space is a particular mathematical model of spacetime which fits very well with the Lorentz transformation used in the equations of special relativity. It treats time as a dimension along an axis of imaginary numbers, i.e., real numbers multiplied by i, which is the square root of minus one. Minkowski spacetime's advantage is that measuring distances using the Pythagorean theorem naturally extend to time: whereas a distance across a plane is √(x²+y²) for coordinates across the plane, spacetime "distances" (spacetime intervals, such as between two events at different times) are √(d²-t²) for d as the distance between the events and t as time expressed as (c × our concept of time). This can be expressed as the normal Pythagorean-theorem form √(d²+t²) if t includes i (i × c × our concept of time).

Special relativity models a (4D) spacetime that is like Euclidean space extended to include a fourth dimension, but it specifically does not fix the time and space we experience to fixed axes of its four dimensions: there is an angle between the time axes of a pair objects that are moving relative to each other, and similarly for their corresponding space axes. General relativity additionally models space and spacetime as non-Euclidean, i.e., with curvature. Its effects are also too small for us to perceive in everyday life.