In relativity, space and time are both dimensions. So instead of 3 dimensions of space moving through time, we have 4 dimensions: 3 dimensions of time and 1 dimension of time. Time behaves exactly like another dimension of space.
So, in principle, yes, space and time can behave independently. Space and time are a bit like the “stage” on which physics events happen. But in general relativity, physics also affects the stage: mass will stretch and warp it through gravity.
Time has a geometry, because all dimensions have a geometry. Each dimension is like a piece of string. You could lay the string out straight, and this would be a flat geometry. Or you can curve it back on itself, and it will have a curved geometry. When you have 4 dimensions, there’s a lot of room for a really complex geometry.
We think the Universe is curved, a bit like a “donut” shape. But every object with a mass slightly bends the space and time around it too. That means time seems to slow down around heavy objects, and other objects are drawn towards them: this is Gravity.
I hope that’s slightly clear! These are really difficult concepts to understand, and really tough to explain too!
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