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rocurley comments on Harry Potter and the Methods of Rationality discussion thread, part 16, chapter 85 - Less Wrong
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More then 6 hours in what reference frame?
Why the heck is this being voted down? It's a perfectly valid question! You could have some Minkowskian interval that Time Turners can't go further back than, and it would make sense in terms of Special Relativity, but there's no obvious analogy for a maximum spacelike separation being built into the laws of magic.
I may be willing to put Time Turners in my fic - I may even be willing to swallow the single-world interpretation of QM which that necessarily implies - but even I'm not going to give magic a privileged reference frame, or talk like "hours" are an intrinsically meaningful measure. Special Relativity is... I mean... it's over the local properties of the variables on which everything else is built, it's the stuff that the fabric of reality is locally made of. It's like having Harry not be made of atoms.
If you're not willing to have a privileged reference frame, how do time turners know where to go?
(Especially thorny is that the surface of the earth accelerates upwards relative to inertial reference frames; if you stay in your inertial reference frame played backwards through time, you don't lose the earth in space, but you do oscillate through it like a mass on a spring. I personally think this is a really cool way for time travel to work, but it's clearly not how time turners do).
If Time Turners went backwards in intervals of 81 minutes, instead of an hour, that'd fit with the "you fell to the center of the earth and oscillated back" method of inertial time travel.
The time turner remembers its worldline and jumps back along it, in a perfectly relativistically invariant way.
That's perfectly well defined, but you also wind up inside yourself 6 hours ago, which is an issue.
That's not your original objection! Also, my model (elsewhere in this thread) defines time-turners as world-splitters, which avoids the time loops.
I'm not saying it's my original objection, it's a new one. It's addressed by having them be world splitters, but I didn't know you had posted about that elsewhere.
Could you re-explain this?
I don't even konw what search for in google so that I undestand it: special relativity?
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.
Imagine you're on a merry-go round. You could calculate physics as if you and the merry-go-round were rotating, and that will be fine. Alternatively, you could pretend you're not rotating (choosing a non-inertial reference frame). However, if you want physics to still work, you have to introduce centrifugal and coriolis forces to make everything work out properly (this is the force you feel "pushing" you out to the edge).
Now in general relativity, inertial reference frames are those that are in free fall. An example of an inertial reference frame would be an orbiting satellite. Note that there is no gravity in an inertial reference frame like a satellite. Now, you can pretend that standing on the surface of the earth is an inertial reference frame (ignoring totally the rotation for now), but to make everything work out properly, you need to introduce a new force accelerating you downward: gravity.
Thanks!
General Relativity, actually. You could also look for "gravity as a fictitious force".
Yeah, I guess one future key ability will be know how keywords use to solve a problem. Using the google, of course.
... and that's why TTs only go back in increments of one hour :D
More seriously, 'tis magic. It works how the person who made it expected it to work, if Harry is correct, whether that's Aristotelian acceleration or just our intuitions about how "moving backwards in time" should look.
(Maybe it simulates a "marker" sitting in your position as the timeline is rewound. What happens if you travel to somewhere a wall was just built?)