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Spacetime is a certain 4-d space (or 4-d manifold, to use Riemann's term for space). It's the 4-d continuum we live in. Spacetime is the intended model of the general theory of relativity. This requires it to be a differentiable space in which certain geometrical objects obey the covariant field equations of general relativity, and in which physical objects obey the equations of motion of the theory. The metaphysical question of whether spacetime is a substantial object or a relationship among events, or neither, is taken up in the discussion of the relational theory of time. Regardless of how that question is answered, spacetime is more fundamental in science than either space or time alone. Einstein's general theory of relativity (1915) assumes that spacetime is fundamental, with space and time being two distinct sub-spaces of it.
Spacetime is a continuum in which we can define points and straight lines. However, these points and lines do not satisfy the principles of Euclidean geometry. Einstein's principal equation in his general theory of relativity implies that the curvature of the geometry of spacetime is directly proportional to the density of mass in the spacetime. The equation can be interpreted as implying that matter causes curvature in the spacetime geometry, or vice versa. The region of spacetime at the center of a black hole develops infinitely large curvature. Curvature of spacetime is a curvature of its space part, not its time part. Mass doesn't cause time to curve.
Regions of spacetime are frequently pictured with a Minkowski diagram using a rectangular coordinate system. The vertical 'time' axis is the product of time and the speed of light so that world lines of light rays leaving the origin make a forty-five degree angle with any space axis. The Minkowski diagram applies to a particular observer who experiences the event that occurs at the point indicated by the diagram's origin. In a Minkowski diagram, an ideally small physical particle is not represented as occupying a point of spacetime but as occupying a line containing all the spacetime points at which it exists. The line is called the "world line" of the particle. If two world lines intersect, then the two particles have collided. A person's world line is composed of the world lines of the person's component particles. Inertial motion corresponds to straight world lines, and accelerated motion corresponds to curved world lines.
Although relativity theory assumes that spacetime is fundamental, there have been serious attempts over the last few decades to construct theories of physics in which spacetime is not fundamental but is a product of more basic entities such as superstrings. The primary aim of these new theories is to unify relativity with quantum theory, but so far these theories have not stood up to any empirical observations or experiments that could show them to be superior to the presently accepted theories. So, spacetime remains fundamental.
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