Spacetime Curvature: What Does it Mean?

[Demiwing]

Hi, anyone know what they mean by spacetime is curved and its warped. Thanks in advance

 

[cincirob]

We grow up thinking time and space are separate things. This is because the situations where the fact that they are involved are not obvious. It is easy to understand how the shape of objects can be described by assigning x,y,z coordinates to their shape. If you have an object made of rubber and you bend it, the coordinates you asigned to the points on the object get warped. For instance' straight lines will no longer be straight.

It has been shown that, in reality, you must define objects with four coordinates, x,y,z,t where t is time. The most obvious connection between space and time is velocity, v. So, like x,y,t coordinates can be warped, so can x,y,z,t coordinates.

The reason this warping is not easily seen, is that many of the effects are a function of velocity. And, the effect is very small for the kinds of velocities we are familiar with. For instance you have probably read about time dilation effects on this forum. This is the fact that a clock moving relative to you will be running slower than your own clock. The slowing is described by the formula

(rate of moving clock) = (rate of your clock)[(1-(v/c)^2)^.5] where v is the relative velocity and c is the speed of light. Since c = 300,000 km/sec, the function in the brackets is very close to 1 unless v is very large.

Finally, the other thing that warps spacetime is gravity (gravity is acceleration which relates it to velocity). Mass, such as the mass of the Earth warps spacetime and this is noticable as the acceleration we call gravity. Humans didn't notice this feature of mass for a long time because it is very weak. If you put two objects on a table they don't slide together as a result of their respective masses. Actually very careful experiments can measure the tiny forces that occur between small objects but you wouldn't normally notice it.

It is also the case that the warpage of space by gravity causes straight lines to become curved. It has been shown that light passing the sun is deflected. Most will say the light is "bent". It's more accurate to say the light is following geodesics in x,y,x,t spacetime which are "straint lines" in that space.

 

[selfAdjoint]

Hi, anyone know what they mean by spacetime is curved and its warped. Thanks in advance

It means that simple geometric facts become slightly noneuclidean in the presence of energy-momentum, so that for example the angles of a triangle don't sum to 180^o and the area of a circle is not $$\pi r^2$$. And the amount by which these things differ from the euclidean value varies from point to point. Many people can accept this, which is quite accurate, where they can't accept curving 4-D spacetime.