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I'm always trying to find underlying principles, like that the force is always directed toward a (locally) lower potential energy and alot of stuff like that.

Recently I've begun to gain some layman understanding of GR and it seems that things move toward states in which time flows slower.

Is this generally true? And if so, is there some sense in which forces like the E&M-force brings particles to a state of slower moving time? I can't really think of anything obvious but maybe some of you guys have some ideas/have thought about this kind of stuff already...

ctsmd
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I'm always trying to find underlying principles, like that the force is always directed toward a lower potential energy and alot of stuff like that.

Recently I've begun to gain some layman understanding of GR and it seems that things move toward states in which time flows slower.

Those two statements may be equivalent, depending on the case.

First off, consider what makes time "flow slower". It is the presence of energy (for reasonable definitions thereof). So what you're really seeing is that energy is concentrating.

That energy can be concentrated should not be surprising - gravity exists. There is some circularity there, gravity-energy-gravity, but not so much.

But one has to consider things like the photons streaming out from the sun. They are doing precisely the opposite of what you suggest, they are leaving the area of "slow flow".