I understand why the warping of spacetime affects moving objects, but why would it affect stationary ones if it even does? Would two completely stationary objects not move closer together because they aren't moving in space therefore wouldn't start bending space towards each other? And if they do, why would they move towards each other? If there's no movement, then there would be no movement to bend towards the other object.
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$\begingroup$ It can also make them move apart. It depends on the type of warping. $\endgroup$– GhosterCommented Mar 24 at 0:31
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$\begingroup$ there is no such thing as a stationary object versus a moving object in relativity. $\endgroup$– JEBCommented Mar 24 at 2:59
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2 Answers
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Would two completely stationary objects not move closer together because they aren't moving in space therefore wouldn't start bending space towards each other?
No. Spacetime has four dimensions. All objects are moving forward in time. Spacetime curvature involves all four dimensions, including time. To put it colloquially, around a massive static body, the time direction is "curved radially inward", so that temporal velocity is rotated into a inward spatial velocity and this is what is observed as gravitational attraction.
In addition, objects do not "start bending" space toward each other. Mass and energy always curve spacetime. The movement of objects change according to curvature, which in turn changes according to their movement. It's a dynamical process.
answered Mar 24 at 0:32
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$\begingroup$ Thanks, that makes sense. Is there an answer to why it would move? $\endgroup$ Commented Mar 24 at 0:34
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$\begingroup$ Rather than thinking of objects as moving forward in time, it is clearer (and more faithful to the physics) to simply understand them as being extended in a time direction. So, for example, a point in 3D space is a line in 4D spacetime. Those lines tend to follow spacetime curvature for the simple reason that they are "locally straight" (in the absence of nongravitational influence). $\endgroup$– StenCommented Mar 24 at 3:01
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$\begingroup$ @HunterSherring By definition. Points in spacetime are events (i.e. a specific position and instant in time). And objects don't exist for just a single instant in time. You may know from special relativity that all objects move through spacetime with speed $c$ regardless of their spatial velocity. This remains true in GR. $\endgroup$ Commented Mar 24 at 12:43
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$\begingroup$ @safesphere Yes, but I wasn't talking about dilation/contraction. I believe that the time curvature is much more significant (at least in the Newtonian limit, where the velocities are slow such that only the 00 component matters) due to the factors of $c$. $\endgroup$ Commented Apr 8 at 10:37
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$\begingroup$ @safesphere In any case, I have reworded that sentence. $\endgroup$ Commented Apr 8 at 10:44
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Warping of space-time is only a figurative way to express some mathematical equations. Even the familiar Newtonian gravity can be viewed in this geometric fashion: $$\mathbf F = \frac{-GMm\mathbf{\hat r}}{r^2}$$ If only gravity acts on the mass: $$m\mathbf a = \frac{-GMm\mathbf{\hat r}}{r^2} \implies \frac{ d^2\mathbf r}{dt^2} = \frac{-GM\mathbf{\hat r}}{r^2}\implies \frac{ d^2\mathbf r}{dt^2} + \frac{GM\mathbf{\hat r}}{r^2} = 0$$ This last expression can be interpreted by differential geometry as a geodesic equation in a curved space-time.
answered Mar 24 at 1:06