Sunday, June 19, 2016

spacetime - How to explain space-time curvature in two minutes?



How would you explain what is the curvature of space-time in a short period of time like 2 minutes to non experience people?



Answer




Imagine space-time as a flat sheet of elastic fabric. Put a grapefruit on it, and it will sag and form a depression around the grapefruit. Now try to roll a marble straight across the fabric. If it passes near the grapefruit, it will start rolling into the depression. If the marble is rolling fast enough, it will begin to circle the grapefruit before falling into it. But if the marble is going really fast, it will turn into the depression and then will continue to roll through it and up the other side, although its trajectory will have been bent. Here is a diagram: http://theory.uwinnipeg.ca/users/gabor/black_holes/slide5.html


This is what happens to objects and even to light moving through space around a massive gravitating body. Flat space doesn't interfere with trajectories, but curved space does.


Time changes along with space in the presence of massive gravitating bodies. Notice as the marble circles the grapefruit, it speeds up and circles faster as it gets closer to the bottom of the depression. In the same way, clocks run faster as they fall deeper into a gravity field.


Curved space-time alters trajectories of objects and of light in the presence of gravitating bodies, and it speeds up clocks as they fall into gravity fields.


Caveat: This analogy is not the real story. But it may help, if not taken too literally. Here are two critiques of the elastic fabric analogy. Also see rob's answer, a profound and eloquent way to conceive of curvature.


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