section_path: Physical properties/Spacetime
section_name: Spacetime
paragraph_text: Spacetime
  
  Modern physics regards events as being organized into spacetime. This idea originated with the special theory of relativity, which predicts that if one observer sees two events happening in different places at the same time, a second observer who is moving relative to the first will see those events happening at different times. The two observers will disagree on the time T {\displaystyle T} between the events, and they will disagree about the distance D {\displaystyle D} separating the events, but they will agree on the speed of light c {\displaystyle c}, and they will measure the same value for the combination c 2 T 2 − D 2 {\displaystyle c^{2}T^{2}-D^{2}}. The square root of the absolute value of this quantity is called the interval between the two events. The interval expresses how widely separated events are, not just in space or in time, but in the combined setting of spacetime.
  
  The special theory of relativity cannot account for gravity. Its successor, the general theory of relativity, explains gravity by recognizing that spacetime is not fixed but instead dynamical. In general relativity, gravitational force is reimagined as curvature of spacetime. A curved path like an orbit is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by John Archibald Wheeler that has become proverbial among physicists summarizes the theory: "Spacetime tells matter how to move; matter tells spacetime how to curve", and therefore there is no point in considering one without the other. The Newtonian theory of gravity is a good approximation to the predictions of general relativity when gravitational effects are weak and objects are moving slowly compared to the speed of light.
  
  The relation between matter distribution and spacetime curvature is given by the Einstein field equations, which require tensor calculus to express. The universe appears to be a smooth spacetime continuum consisting of three spatial dimensions and one temporal (time) dimension. Therefore, an event in the spacetime of the physical universe can be identified by a set of four coordinates: (x, y, z, t). On average, space is observed to be very nearly flat (with a curvature close to zero), meaning that Euclidean geometry is empirically true with high accuracy throughout most of the universe. Spacetime also appears to have a simply connected topology, in analogy with a sphere, at least on the length scale of the observable universe. However, present observations cannot exclude the possibilities that the universe has more dimensions (which is postulated by theories such as the string theory) and that its spacetime may have a multiply connected global topology, in analogy with the cylindrical or toroidal topologies of two-dimensional spaces.