On Einstein´s theory of curved spacetime.

[svenraun]

Now if you view the cosmos from the side like imagine all planets horizontally they say spacetime is curved in a way like heavy sphere objects lying on a trampoline. What happens to the spacetime above the middle of the objects really, it seems like according to this space can push only on one side of the large objects. But it seems its pushing all around. And what if you can't view the scholarsystem horizontally but vertically, how do you then judge the curvature of space. Like it doesn't work the other way around. Taking the pi and viewing the higgs field around a planet even when its not a circular curvature doesn't matter, there should be a slight difference in gravity in some point on the planet, i mean exactly where pi becomes infinite. So the curvature should be actually a perfect sphere while the Earth for example is falling through space. Depends which point you are observing. Anyone familiar with this ?

 

[VantagePoint72]

There is no such thing as viewing "the cosmos from the side", "vertically", or from any other outside-looking-in direction. The trampoline analogy is just that—an analogy (and not a very good one). We are inside spacetime. We measure its curvature by looking at how free falling (inertial) test bodies behave. In flat spacetime, the separation between two inertial particles changes linearly with time. In curved spacetime, this is not true in general, and the extent to which it fails to be true is a measure of local curvature.

 

[Janus]

The trampoline example is just an analogy. In it, all of 3 dimensional space exists along the surface of the trampoline. Another way to look at it is it reduces all of space to two dimensions and use the third dimension to show the curve. This is done this way because we have no way of depicting 3 dimensions curved through a fourth dimension.

And even if we could, it would still be an analogy. Space-time curvature doe not actually require a 4th spatial dimension. It really is the result of non-Euclidean geometry.

 

[DimReg]

Now if you view the cosmos from the side like imagine all planets horizontally they say spacetime is curved in a way like heavy sphere objects lying on a trampoline. What happens to the spacetime above the middle of the objects really, it seems like according to this space can push only on one side of the large objects. But it seems its pushing all around. And what if you can't view the scholarsystem horizontally but vertically, how do you then judge the curvature of space. Like it doesn't work the other way around. Taking the pi and viewing the higgs field around a planet even when its not a circular curvature doesn't matter, there should be a slight difference in gravity in some point on the planet, i mean exactly where pi becomes infinite. So the curvature should be actually a perfect sphere while the Earth for example is falling through space. Depends which point you are observing. Anyone familiar with this ?

Probably the best way to grasp "curvature" of space-time is to use the mathematical definition of curvature. Basically, if you move a tangent vector along a closed path in a curved space, trying not to change it's orientation, it won't return to it's original orientation (notice that the tangent vector has to be tangent to the space). You can try it with the surface of a sphere: start with a vector pointing north at the equator. Then move it across the equator to the other side of the sphere. Now move it north to the north pole, and then continue in that direction until you reach the original point. If you did it correctly, the resulting vector should be pointing towards the south pole now. All of this can be done without considering the sphere as something living in 3 dimensions.

This is also the effect of the gravitational field. This curvature makes "geodesics", or paths of shortest distance, more complicated than just straight lines, and these "geodesics" are what particles follow. This is how gravity "pulls" things: they don't follow straight lines, which since Newton we associate with particles moving without forces applying to them.