I'm trying to understand the concept of the space-time continuum and it's effect on time dilation but am having difficulty with parts of it. To me there seems to be two separate components to time dilation...
Space-time is warped by mass (the stronger the gravitational field the slower time goes).
Time dilation at relativistic speeds (the faster you go the slower time goes).
I understand that space-time is effected by mass and this makes sense. But are we talking about the same warping of space-time when travelling at relativistic speeds (e.g. is the warping proportional to the speed)?
Specifically my confusion arises if we consider a spaceship travelling at say 50% the speed of light. Time dilation will have some effect here and time will travel slower on the spaceship. That is fine but is that due to space-time? E.g.
- Is space-time warped around the spaceship?
- Is it dragged along with the spaceship as it moves?
- What is the boundary? Is there time dilation within the spaceship which instantly changes to zero time dilation at the outside boundary of the spaceship or is there a gradient from outside to inside?
- If we consider a move complex shaped spaceship that is rotating (say a hexagonal mesh sphere with hollow inside) it seems impossible that space-time could be dragged along by this as it would be cutting its way through space-time or making a swirling mess of it.
I find it hard to understand how space-time can 'follow' a moving spaceship through space. It seems that #1 & #2 above are two separate things (e.g. both aren't caused by space-time). Is this correct? Or is space-time dragged along with a moving spaceship?
Note: I understand that the spaceship has mass and this will warp space-time to a small degree (and cause a tiny amount of time dilation) but am more interested in the time dilation caused by the spaceships speed (and the relationship between the speed, time dilation and space-time).