spacetime: suppose you are floating in the middle of space, and i pass you at near the speed of light. we will disagree on long a second is, and we’ll disagree on how long a meter is. however, we will always agree on how fast light travels (in meters per second). it seems strange to those of us who crawl around the universe at infitesimal fractions of the speed of light, but it’s a fact of the universe that’s been borne out time and time again by experiment. distances in time and distances in space dilate in an equal an opposite way that leaves distances in space-time constant regardless of inertial frame (ie how fast we’re travelling relative to each other). it’s natural for physicists to consider space and time together like this so they can describe the laws of nature in a way that don’t privilege any inertial frame. from my perspective it is I that am floating in space and you are passing me at the speed of light.
curvature of spacetime: imagine you and I were two-dimensional beings living on a sphere. locally, space looks flat: if I draw a triangle, its angles add up to 180 just like Euclid said they would. however if I draw a REALLY BIG triangle, like one that goes from Panama to the North Pole to Africa, I find that in fact I make a triangle that has three right angles in it! this clues me in to the real nature of reality, that I live on a curved surface, despite the fact that I, as a 2D being, am not able to physically point into the third dimension. curved spacetime is basically the same concept, except with one more dimension. locally, space looks flat and I can refer to points as orthogonal x, y, z coordinates, but at large scales, particularly around massive objects, I can see that space is not flat, but it is bending in a way that can at least be mathematically described as “3D space being bent around another dimension which we are unable to point into”.
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