As the tittle says, I am constantly hearing about spacetime, which I sort of get (it’s a 4D space, with 3 spatial and 1 temporal axis) and curvature, which I do not get. What is curved in spacetime? When we say geodesics, what are they representing? I am getting the feeling that it is something like the spatiotemporal distance between two events that is being modified, but what does it mean in physical terms? Is it even physical, since two observers can disagree in almost everything, except the order of casually linked events?
Or I am thinking it too much, and it’s only a model of interpreting observation that only approximates complex reality up to a point?
In: 5
Curvature is like the curvature of a surface. Imagine a flat sheet of paper it works like flat space-time. Imagine a ball the ball’s surface had curvature too. Curvature changes how straight lines look. In general we call a straight line on a curved surface a geodesic. When there are no forces acting on you, your worldline is a geodesic. Curvature changes where the geodesics go in terms of spacial coordinates. So in curved space-time in order to stay in one place you mustn’t follow a geodesic. Without curvature so in flat space-time to stay in one place you must follow one.
The thing is we don’t really have a good grip on curved surfaces abow 2D, visually. But the math scales up. Curvature in 4D works just as well. The key idea is intrinsic curvature. Intrinsic curvature is curvature that you can measure from within. If you are living on the surface of a sphere you can do experiments that tell you the surface is curved. Intrinsic curvature changes the rules of geometry locally. Like on a sphere you draw a triangle and the angels add up to more than 180°.
There is no intrinsic curvature in 1D. In 1D geometry a line and a circle work the same. From 2D on surfaces have intrinsic curvature changing their geometric properties. You can mathematically create a 3D surface and work out how different curvature types change the geometry on or more like in that surface and that can be expended to 4D, 5D…
Latest Answers