First, imagine yourself in a spaceship far away from any gravitational sources. If your rockets are off, objects inside the ship left at rest relative to it will stay at rest. In this situation, your ship is in an inertial reference frame, so called because in it the law of inertia is valid. (By contrast, if your rockets are on, objects left at rest will start accelerating towards the back wall, unless there is some countervailing force acting on them).
Now imagine your spaceship close to Earth, within its gravitational field. What is an inertial frame now? Not the situation of the ship at rest relative to Earth: in this situation, objects will accelerate (“fall”, as we usually say) towards the bottom of the ship. The ship is in an inertial frame only if it is freely falling towards Earth[1], like an elevator when the cable breaks: then, objects left at rest inside it will stay at rest relative to it absent countervailing forces (because they will be “falling” at the same universal rate g = 9.8 m/s^2).
So a frame accelerating towards Earth with g is an inertial frame. If we abstract away all other forces that will come into play when the ship crashes hitting the Earth and think only of the effects of gravity (which is what determines the inertial frames, according to GR), the freely falling trajectory would continue straight through Earth, emerge at the other side, reach a maximum altitude, fall again, and so on like a mass on spring. Thus the frame that follows Earth in its trajectory through space while oscillating back and forth through it is an inertial frame.
[1] IActually, it could also be shooting up from Earth but decelerating (to fall eventually), or be in a stable orbit around it. All these situations have the key property that objects at rest relative to the ship tend to stay at rest relative to it.
Really thank you, Alejandro1, you clarified the “inertial reference” point.
Going a little bit beyond, what the heck the gravity has to do with time turners and time travel?
My knowledge is pretty restrict in this area (almost zero), so if you can’t answer this in a simple way [1]; just saying “go study X” will work fine,too, if that’s the case.
[1] As Feynman says, if you want to explain something complicated for someone, you can rephrase or use analogies as long as the person has an (or a few) equivalent model of that topic in their reality. So, if the topic requires some model that I don’t own by not knowing lots of relativity, just point that out so that I can study and not lose good threads like this in the future. Thanks.
So, in this fic, you time travel and you wind up in the “same place” as you started. The concept of “same place”, however, is actually really complicated. The earth is spinning and orbiting the sun, which is itself orbiting the center of the galaxy, which is in turn....
My first intuition was that, if you traveled in time, you would wind up floating in space. However, it’s not at all obvious that a reference frame where the sun is stationary is better than any other, which is how I got to using your current stationary inertial reference frame: it’s the only one that’s unique from all the other possible ones, and yields the behavior above.
First, imagine yourself in a spaceship far away from any gravitational sources. If your rockets are off, objects inside the ship left at rest relative to it will stay at rest. In this situation, your ship is in an inertial reference frame, so called because in it the law of inertia is valid. (By contrast, if your rockets are on, objects left at rest will start accelerating towards the back wall, unless there is some countervailing force acting on them).
Now imagine your spaceship close to Earth, within its gravitational field. What is an inertial frame now? Not the situation of the ship at rest relative to Earth: in this situation, objects will accelerate (“fall”, as we usually say) towards the bottom of the ship. The ship is in an inertial frame only if it is freely falling towards Earth[1], like an elevator when the cable breaks: then, objects left at rest inside it will stay at rest relative to it absent countervailing forces (because they will be “falling” at the same universal rate g = 9.8 m/s^2).
So a frame accelerating towards Earth with g is an inertial frame. If we abstract away all other forces that will come into play when the ship crashes hitting the Earth and think only of the effects of gravity (which is what determines the inertial frames, according to GR), the freely falling trajectory would continue straight through Earth, emerge at the other side, reach a maximum altitude, fall again, and so on like a mass on spring. Thus the frame that follows Earth in its trajectory through space while oscillating back and forth through it is an inertial frame.
[1] IActually, it could also be shooting up from Earth but decelerating (to fall eventually), or be in a stable orbit around it. All these situations have the key property that objects at rest relative to the ship tend to stay at rest relative to it.
Really thank you, Alejandro1, you clarified the “inertial reference” point.
Going a little bit beyond, what the heck the gravity has to do with time turners and time travel? My knowledge is pretty restrict in this area (almost zero), so if you can’t answer this in a simple way [1]; just saying “go study X” will work fine,too, if that’s the case.
[1] As Feynman says, if you want to explain something complicated for someone, you can rephrase or use analogies as long as the person has an (or a few) equivalent model of that topic in their reality. So, if the topic requires some model that I don’t own by not knowing lots of relativity, just point that out so that I can study and not lose good threads like this in the future. Thanks.
So, in this fic, you time travel and you wind up in the “same place” as you started. The concept of “same place”, however, is actually really complicated. The earth is spinning and orbiting the sun, which is itself orbiting the center of the galaxy, which is in turn....
My first intuition was that, if you traveled in time, you would wind up floating in space. However, it’s not at all obvious that a reference frame where the sun is stationary is better than any other, which is how I got to using your current stationary inertial reference frame: it’s the only one that’s unique from all the other possible ones, and yields the behavior above.
I got it! wow, it feels great ;) thanks again.