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Author Topic: relativity  (Read 627 times)

abikman

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relativity
« on: August 15, 2016, 11:47:29 PM »
Hello!
According to general relativity space is curved by the presence of mass, and therefore obejcts "fall" geometrically through curved lines, right?
If there is no real force of gravity according to this, why would objects move at all? So what if it's curved? What forces them to move?
Thanks!

particleman

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Re: relativity
« Reply #1 on: March 18, 2017, 04:36:44 PM »
Dear abikman,
Lets rephrase that to "why does the curvature of spacetime produced by a massive object make things fall down".
First imagine a lattice in a flat spacetime: just a grid of lines in 3 dimensions.
Then try to imagine the flat-spacetime lattice in 4 dimensions: three space dimensions and one time dimension. So now there are lines through time that do not change spacial location. An object following one of these lines through time would appear to just stay at one location and not move. It stands still with no forces on it.

Now put a mass in the middle of this lattice. The time-lines now bend inwards towards the center of the planet, like light rays being bent inwards by a lens. So now an object with no forces on it, doing it's geometric best to stand still propagates through time by moving towards the center of the planet. Stuff falls because falling is what standing still looks like in a bent 4D geometry.
The momentum 4-vector (-Energy, X-momentum, Y-momentum, Z-momentum) of the object keeps constant  length, but rotates as the object propagates along the time line. And because of that minus in front of Energy, that rotation looks like both kinetic energy and momentum of the object increasing as it falls.

These bent lines that I'm talking about are properly called "geodesics" which means the straightest lines that can be imagined on a curved surface--the shortest path between two points. So for, example, lines of longitude on a globe are geodesics (but not lines of latitude). Geodesics on a sphere are great circles. Planes crossing the atlantic fly far north because that's the shortest path, following great circle geodesics between destinations.