whabbear

Janus, thank you so much! Your answers and accompanying descriptions were right on!

Physicists: I'm struggling with some issues stemming from jointly considering General Relativity and Einstein's Equivalency Principle. Consider, first, two objects occupying two distinct frames of reference: An apple hanging from a tree on the Earth’s surface, and a geostationary satellite far (but directly) above the apple. Both objects have a clock affixed to them. There is no relative motion between the two: Measure the distance between them at any time, and the distance measurement would not vary. Yet, if the clock aboard the geosynchronous satellite and a clock affixed to the apple try to measure the duration of any arbitrary event in the vicinity of the apple, they won’t agree. The clock affixed to the apple will record a shorter duration for the event than the clock affixed to the satellite, because the curvature of spacetime is different in the apple's frame of reference than in the satellite's frame of reference. Now, consider two identical spacecraft located adjacent to each other somewhere out in space, each one containing a clock. Initially, the two spacecraft start out in the same reference frame, as they are motionless relative to each other. If an event happens inside one of the spacecraft, both clocks will record the same duration for it. However, if one of the pair then fires up its engines and starts to accelerate away from the other, time dilation effects will occur, and the clocks onboard the two spacecraft will no longer record equal durations for events occurring in their twin. First question: Is the time dilation that accompanies the fact that there's now time dilation between the two spacecraft due entirely to the fact that there is now relative motion between them (as opposed to the fact that the relative motion is of an accelerating form), and is therefore a phenomenon of Special Relativity, rather than General Relativity? Now suppose, as a thought experiment, one of the twin spacecraft fires up its engines, but can't actually move relative to the inert spacecraft because the active vehicle is butting up against some “immovable object” (meaning that, in some sense, the active spacecraft is experiencing a force “trying” to accelerate it, even though the immovable object prevents it from actually moving). Is the fact that there's a force being applied to the active spacecraft sufficient to induce a local spacetime curvature, and hence, despite the fact that there is no relative motion between the two spacecraft, time dilation effects kick in? If the answer to my second question is "No", then it seems to me that there's a fundamental limitation to the Equivalency Principle. The apple on the Earth's surface is constantly "trying" to follow its shortest path through gravity-induced curved spacetime, but is prevented from doing so by the stronger force that keeps it attached to the apple tree. If this countervailing force is removed, say by a strong wind the severs the apple from the tree, the apple immediately begins to accelerate toward the Earth's surface with dynamics that are equivalent to the dynamics of an unimpeded accelerating spacecraft. But before that, while the apple is still connected to the tree, the mere "attempt to accelerate" manifests itself in the form of a time dilation effect. Again, would the same be true for the two spacecraft in my thought experiment?