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
The space around you is flat. If you make a triangle out of three straight things, laser beams are popular, the angles between the sides add to 180˚.
If you imagine a giant triangle made of string with one point at the north pole and two points on the equator, the angles will sum to more than that because the two equator points are 90˚ angles and the angle at the pole pushes the sum over 180˚. This occurs because the strings are not straight, they follow the surface of a curved planet.
When you go near a very massive object, the laser beams will react to the curved space and give a result equivalent to the string triangle.
The time dimension is more complex, an effect we call Relativity, but at speeds measured in fractions of the speed of light (ultra high speeds) the length and clock speed of objects is different when measured from different points moving at high speed relative to the object.
In ELI5 terms, a sheet of paper is flat, a globe is closed, and a frying pan is open. If you can conceive of those notions in 3+1 dimensions, you understand spacetime curvature
[Here](https://www.youtube.com/watch?v=MTY1Kje0yLg) is a good visualization of curvature. Spacetime is a like a sheet of textile and the mass of object will curve it which will change their trajectory.
Obviously it’s a analogy and it can be hard to really understand for people. It’s not something you can see or touch, it’s outside of the human experience.
You, as a being capable of visualizing 3 dimensions, can look at a curved sheet and see where how it curves downwards within a 3-dimensional space. However if you were a 2-dimensional being and you lived within that sheet, then you would only perceive it as “flat” as you moved “straight” across it. You would perceive yourself as continuing to move straight even as you moved down the curved section – because your perception of reality simply wouldn’t include any such concept as “up” or “down”.
The *concept* is that our 3-dimensional space can likewise be curved when viewed from a hypothetical outside view by a being capable of visualizing 4 physical dimensions. The only possible way for *us* to visualize it is to liken it to a two-dimensional example, though. We experience those curves as gravity, and we visualize them as being “pulled” and going “straight” towards the other object, but that hypothetical 4-dimensional observer would see us moving along a curve.
Condition for understanding curved spacetime is that you first understand special relativity properly. If you don’t then take a step back and leave general relativity alone until you have caught up.
Once you have done that try this [https://www.youtube.com/watch?v=xodtfM1r9FA&list=PLu7cY2CPiRjVY-VaUZ69bXHZr5QslKbzo&index=1](https://www.youtube.com/watch?v=wUucK7BF-oc&list=PLsPUh22kYmNAmjsHke4pd8S9z6m_hVRur)
and this [https://www.youtube.com/watch?v=UfThVvBWZxM](https://www.youtube.com/watch?v=UfThVvBWZxM)
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…
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