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MichaelHoward comments on Striving to Accept - Less Wrong
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Even better: due to relativity, realize that if you're only considering the earth/sun system and not paying attention to other planets, you can go ahead and choose either one as your reference frame (traditionally, you pick the one you're in). So the sun really is quickly orbiting a stationary Earth.
"the sun goes around the Earth quickly while rotating slowly" and "the Earth is rotating quickly while orbiting the sun slowly" express the same sentiment.
EDIT: Okay, you got me - you can't rotate an inertial frame, and 'fictitious forces' would be detectable differently in each of those examples. But I stand by my first point.
Don't they both just move in straight lines through curved space-time, or is that just another way of percieving the math?
Like Camelot, "it's only a model".
Yes, that's another way of looking at it. More or less intuitive depending on the application.