Author Topic: Curvature of Spacetime  (Read 1621 times)

Offline Grawk1

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Curvature of Spacetime
« on: May 12, 2013, 03:00:01 AM »
I was just re-listening to your (excellent as always) "Dark Equivalence" episode about Schwarzschild geometry. When you describe spacetime as a rubber sheet being warped and gravity curving the paths of objects because straight lines aren't straight anymore, I realise that I don't understand the analogy at a basic level: I understand that the concept of a straight line breaks down in non-euclidean geometry, but this doesn't explain to me why velocity matters.

If you and I stand on either side of the equator, face directly east and walk in a straight line our paths will seem parallel at first, but they will cross eventually because of the way a straight line acts on a curved surface, but the distance we travel before we cross stays the same regardless of how fast we move. In a gravity field, my path depends on the speed that i travel through the field. Can you resolve this?

Offline bn

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Re: Curvature of Spacetime
« Reply #1 on: May 12, 2013, 11:19:36 AM »
good question. and it's true. everything you say is true.

the difference is that our trajectories (which get tweaked by curvature) aren't in space, they're in spacetime.

Imagine an ant and a motorbike. both of them travel the length of a 1 km road. the motorbike goes quickly, and the ant goes slowly.

In space, they travelled the same trajectory.

in spaceTIME, they do not. they might have started at the same place and time, but the motorbike ended up at the end of the road in 5 minutes, and it took the ant 5 days to arrive at the same place. You can draw their trajectories on a piece of paper if you want: label the vertical axis "time" and the horizontal axis "space". they travel the same distance, but it takes less time for the motorbike to cross it, so the motorbike's spacetime trajectory will be steeper than the ant's.
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Offline Grawk1

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Re: Curvature of Spacetime
« Reply #2 on: October 09, 2013, 09:13:37 AM »
I forgot to thank you before, that was a great explanation - it really clarified the fundamental misunderstanding I had about the whole concept!