Why does Space-Time curve and more importantly, why and how does Space and Time come together to form a “fabric”?
In: Physics
Short answer? SpaceTime curves in the presence of mass. How does it form a “fabric?’ The fabric is a loose analogy.
The concrete example is of a piece of paper. The paper is “2D”, but you could curve it into 3D. It would be a curved surface in 3D. The distance squared on the paper would be spatial x^2 + y^2. If you followed your pencil in a straight line on the flat paper, then curved it, you would notice the straight line has a different trajectory.
In General Relativity, the piece of paper is space time. Curvature is defined in the presence of mass which consequentially causes gravity. On this surface we travel in straight lines along the curvature in the absence of forces.
The distance squared on this surface includes what we think of as time (time is just a special spatial dimension). The distance squared, s^2 = x^2 + y^2 + z^2 – c^2 t^2. Notice the minus sign. c is the speed of light and speed times time is distance, so it works out.
Objects in free fall on curved surfaces follow straight lines. For a flat piece of paper this is a straight line. For the surface of a sphere, this is a great circle (a circle whose center is at the center of the sphere).
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