What is the meaning of 'space is curved' ?

Answer 1

Do not listen to educated responses above.

The meaning is very simple:
if you have two satellites starting from the same point and in opposite directions, they will travel along 'straight lines'

-> in flat space-time they will fly further and further away from each other
-> in curved space-time they will orbit arond the earth and collide at opposite point. This latter scenario happens in real world and means that space-time is curved. Simple.

Compare:

if two ants begin walking from the same point in opposite direction on flat plane, they will move further and further away and will never meet.

if two ants begin walking from the same point in opposite direction on the globe, they will circumnavigate the globe and meet at opposite point. Because the surface of the globe is not flat, it is curved.

Answer 2

Ones upon the time there was Euclid( 325 -265BC ) and he put a collection of work in geometry that was accepted as the absolute foundation of mathematics. The basic idea of two parallel lines that never intercept is the pivoting concept of our discussion.

Gauss(1777-1855)) had interesting ideas about curved spaces and when Riemann(1826-1866) ) defined the mathematics expressing these ideas Gauss was overjoyed. We know this mathematic as Riemann Geometry.

In Riemann space two parallel lines intercept. The entire two-dimensional infinite Euclidean space can be curved into a sphere (3-D if you will). So finally I’ll employ the explanations that were eloquently brought forward by distinguished Alexander, and others before him, that two parallel straight lines starting anywhere on the north pole of that sphere will meet or intercept each other on the south pole.

So what are the interesting conclusions we may draw?
1.A three dimensional surface of a sphere can be mapped into an infinite two dimensional space. A good practical example is a flat map of our Earth.
2.A four-dimensional space-time can be visualized in three dimensions.
That leads us into the world of physics or General Relativity.
According to Newton Euclidean geometry is fine however Einstein went a bit further explaining gravitation phenomena, where Riemann’s Geometry of curved spaces apparently became an important tool.

Answer 3

Actually, the correct terminology is that spacetime is curved. Spacetime is a four dimensional continum in which our Universe resides. According to Relativity, anything with mass would cause spacetime around that object to be warped, or curved. A good way of thinking aobut this is to image spacetime as a rubber sheet. Now place a ball on this rubber sheet and you will the ball creating a dent on the rubber sheet. This is an anology to the bending of spacetime.

Also, the general shapd of the spacetime contium is not flat. It is actually curved (think of it like the surface of the Earth. Locally it is flat but overall it is curved).

Answer 4

It has been proven that gravity can bend light. Actually the light is still traveling in a straight line but the space that the light travels through is curved.