Given that Pioneer fooled around in the Solar System for a while, making flybys of Jupiter and Saturn, our calculation should be a bit different. 1992 is a useful lower bound, which we arrived at by calculating what would happen if Pioneer took a straight path out into interstellar space. In fact, it flew by Saturn in September 1979. A bit of trigonometry tells me that if it left Saturn in a straight line tangent to that planet’s orbit, it would probably reach the critical distance some time between ’95 and ’97, depending on Earth’s own position in its orbit. This rough map seems to suggest that it did take that approximate path, but it’s hardly accurate. If Pioneer skirted closer to the sun again, inside Saturn’s orbit on it’s way out then the critical distance comes later, but if it veered away harder then it comes earlier.
I had typed my calculations up, but I lost them just now when I accidentally pressed the back button. Hell’s bells and buckets of blood.
Anyway, basically what this tells us is that Quirrel probably has at least a few years of grace before Pioneer gets too far away, if that is in fact what’s going on. I think there’s a fair likelihood that this theory is correct, but given what I’ve said here, I don’t think the timing of the Pioneer’s critical distance should be counted as strong evidence in favour of that.
Thanks for the calculations… I had a rough guess that 6 light-hours was reached some time in the 90s, but didn’t know enough about the flight-path to check this.
I believe that the 6 light-hour limit only makes sense as a theory if Quirrell is going to hit it in this school-year (and it explains why it is impossible for him to continue as a teacher next year). If he’s still got a few years grace it doesn’t work so well, and I suspect that Eliezer would have done a detailed calculation if he was relying on this theory, rather than a rough-and-ready / linear interpolation calculation.
However, I still like the idea of Quirrell being hoisted by his own genius petard (and by his hatred of science, since if he’d bothered to study it, rather than just using it, he might have avoided that mistake).
However, I still like the idea of Quirrell being hoisted by his own genius petard (and by his hatred of science, since if he’d bothered to study it, rather than just using it, he might have avoided that mistake).
How’s he supposed to know that the Horcrux connection craps out at six light-hours? Presumably he’s the first to have a Horcrux anywhere but Earth.
(weighing, Minerva knew, the possibility that he might want to go back more than two hours from this instant; for you couldn’t send information further back in time than six hours, not through any chain of Time-Turners)
If information cannot travel back more than six hours, and a “soul” (stored on a Horcrux) is information (as Quirrell describes it), then it is a reasonable guess that the soul cannot travel over a spatial separation of more than 6 light-hours. Further than that, and it seems the soul parts must fall out of synch, though exactly what happens then is anyone’s guess. Does Quirrell die? Are there two separate Quirrells, one stranded permanently on Pioneer, and the other on Earth? Can the one on Earth be killed, even if the one on Pioneer is never destroyed?
If information cannot travel back more than six hours
This does seem to be a constraint that exclusively affects the time-turners. Otherwise prophesies wouldn’t be possible. It also seems like it’s an artificial rule rather than a deep law of magic because after the Stanford Prison experiment, Bones tells Dumbledore that she has information from four hours in the future and asks whether he’d like to know it. That there is relevant information from four hours in the future is information from the future—she would not have said that if it were otherwise, so it seems there must be exemptions of that kind.
Alternative hypothesis: prophesies are jive, and Eliezer didn’t think of the other thing.
Bones tells Dumbledore that she has information from four hours in the future and asks whether he’d like to know it. That there is relevant information from four hours in the future is information from the future—she would not have said that if it were otherwise, so it seems there must be exemptions of that kind.
That’s information to a careful logical thinker. There’s a lot of evidence that magic to a large extent acts as a naive person might expect reality to act. Broomsticks and the bag of holding are both examples of this.
If information cannot travel back more than six hours, and a “soul” (stored on a Horcrux) is information (as Quirrell describes it), then it is a reasonable guess that the soul cannot travel over a spatial separation of more than 6 light-hours.
I see Eliezer has responded in a way which kills my theory stone cold. (Though it was dead anyway if the 6 light-hour separation by Pioneer wasn’t reached in 1992.)
But basically what I was thinking was this. Consider any two space-time points x and y. Either they have a time-like separation, or a space-like separation or a null separation. If they have a space-like separation then there is a particular inertial reference-frame in which they are only separated in space, not in time. If the spatial separation in that frame is > 6 light-hours, then information cannot travel from x to y. (Or, if you want to think of it in terms of a causal graph, and Pearl’s intervention calculus, then every intervention to the graph at x will leave events at y unaltered.)
Incidentally, this formulation implies the rule that “information can’t go back in time more than 6 hours” and implies it in any inertial reference frame. For if information could travel from x to a point z, more than 6 hours in the past of x (but at the same place) in some reference frame, then it could be sent further along a future-pointing null vector from z to y (by an ordinary light-beam), where y is > 6 light-hours from x in the same reference frame. So the restriction of “no spatial jumps > 6 light-hours” neatly implies “no temporal jumps back > 6 hours”.
Basically, this looks something like the Minkowski interval formulation: there is no privileged reference frame, just a new constant of nature (i.e. whatever 6 light-hours translates to in Planck lengths).
But basically what I was thinking was this. Consider any two space-time points x and y. Either they have a time-like separation, or a space-like separation or a null separation. If they have a space-like separation then there is a particular inertial reference-frame in which they are only separated in space, not in time. If the spatial separation in that frame is > 6 light-hours, then information cannot travel from x to y. (Or, if you want to think of it in terms of a causal graph, and Pearl’s intervention calculus, then every intervention to the graph at x will leave events at y unaltered.)
The problem is that points that 6 light-hours away from X have points more than 6 light-hours away from X in their future light cone.
So the issue here is that we might have three points x, y and z, where x and y have a space-like separation, y and z have a time-like or null separation (which is future pointing from y to z) and x and z have a space-like separation. Further, d(x,y) < 6 (measured in light hours), but d(x,z) > 6.
If so, then the principle I described would prevent information passing from x to z. So it either prevents information transmission from x to y; or if a Time-Turner has already been used to get info from x to y, prevents the further transmission from y to z. The last would be a very interesting effect, because either there is no communication attempt from y to z at all, or the usual communication methods—like light-beams—are attempted, but fail for some reason.
Alternatively, suppose the principle I described is wrong, and info can move from x back in time to x’, then forward to y, then to z by the usual physical means. Then I believe we can make d(x,z) arbitrarily large and this opens up some even more exciting possibilities.
Consider a two-dimensional example, with one space and one time co-ordinate—space first then time. Fix a particular inertial reference frame. Point x is (0,0), point x’ is (0, -delta) i.e. a tiny bit in the past of x. Point y is (delta, 0) i.e. a tiny bit spatially separated from x, and then point z is (delta+t, t) i.e. t hours in the future from y along a light beam through x’ and y.
Then d(x,z) = Sqrt( (delta+t)^2 - t^2 ) = Sqrt(2 x delta x t + delta^2) which of course grows without limit as t gets arbitrarily large. And there is some reference frame in which x and z are that distance apart spatially. So now here’s a neat trick. Imagine that Harry wants to send a message to the Andromeda galaxy, but without it taking two millions years to arrive. Let’s say that x is the Earth now, and z is somewhere in Andromeda which is approximately “now” in the Earth’s reference frame, and in cosmological terms (e.g. at z, measurements of the temperature of the background radiation and the Hubble constant are the same as at x). Then Harry finds a suitable alternative reference frame in which to pick the points x’ and y, uses a Time Turner to send a message from x to x’, then uses ordinary light to send it through y to z. Instant magical faster-than-light signalling out to any distance! And indeed faster-than-light space travel as well, provided he can transfigure rockets that travel at near-light speed...
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.
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.
… 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?)
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
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.
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.
Unless MoR is going to include an explanation of how magic is implemented in terms of known (or new and deeper) laws of physics, Harry might as well not be made of atoms. After all, modern technology conveniently doesn’t work near magic so we can’t investigate the matter...
Which should Harry believe at this point: that the Ultimate Law is better described as fundamentally Muggle physics with a Source of Magic built on top; or that the Ultimate Law is an alien, magical, human-intuition-confirming system where someone once cast a big spell that specified the Muggle laws of physics? Hell, if the existence of magic is actively erased from the minds of Muggles, maybe we shouldn’t put too much trust in the Muggle evidence for the natural evolution of humans, or for the age of the world.
You could put something sorta like a Time Turner in MWI. But I don’t see any way to do it that would reliably result in consistent time-loops, as opposed to people observing different results in their second pass than they remember from the first.
You sure can! It’s a bit hard on the complexity, but probably less so than spontaneous collapse.
there are a bunch of different versions, the most obvious (but not only) class consists of proceeding the simulation as if time travel didn’t exist then pruning paradoxical branches retroactively. There’s tweaks and hacks needed to figure out how that actually works with interference, and to fix the problem of any branch where time travel is invented at all losing all it’s measure in effect acting as a probability pump preventing it, but you’re smarter than me and can probably work out better versions.
Can’t you have mixed states that are stable or at least self-consistent? Something like there’s a 50% chance you go back and kill your grandfather and there’s then a 50% chance you don’t exist? I seem to remember David Deutsch discussing something similar at one point.
You can if nearby Everett branches reinforce each other and ‘bleed over’ into each other. Then you wind up with a bifurcation diagram, with each path’s “weight” based on the number of other paths that are close/similar enough to reinforce it, and some paths can converge into the internal appearance of a stable time loop.
It may be better to put it like this: “if there are many worlds, then time travel would generally create loops across worlds; it does not force consistency within a single world”.
However, if the Source of Magic is careful how it sets up the loops, it can force a consistent outcome, or at least force one of the consistent outcomes to become much more probable than any inconsistent outcome (one which loops between worlds). In particular this still allows any NP problem, or indeed any PSPACE problem, to be solved in polynomial time using tricks like Harry’s factorisation attempt (though perhaps with a small probability of failure). See Scott Aaranson’s wonderful lecture here.
So the fact that Harry always observes a consistent single-world loop doesn’t by itself imply a single world interpretation, or any non-computability. It simply means that the Source of Magic is a PSPACE oracle!
I think a simulation (Y) is a process of mimicking something else (X). In which case we should not observe in Y something (Z) that couldn’t happen in X.
So maybe we should rather say that Y is a game with otherwise X-like rules, but additional rules that allow Z, rather than calling it simulation. Or at least I think if “simulation” Y is not an accurate simulation of X, we should use some explicit qualifier to indicate its non-accuracy.
Could this constraint apply in other ways? Suppose magic is the result of something that responds to the wishes of witches, as suggested at one point. If that something is Earth-based, perhaps a wizard on an outbound spacecraft would stop being able to do magic when he reaches 6 light-hours out. An interesting experiment.
Harry might be able to realistically do an experiment similar to this as a first year if there is a magic spell that lets you communicate with an object. He could use a spell to accelerate that object to a very high speed and then check in on it as it approaches the 6 light-hour point.
I know. Gastogh made the 1992 calculation. I was making the point that although Gastogh calculated Pioneer to have reached the critical distance of six light-hours in 1992, and you pointed out that Taboo Tradeoffs was happening in 1992, we shouldn’t take this coincidence as evidence in favour of the theory that communication between horcruxes and their master is limited to light speed, and that this is somehow related to time turners. I don’t necessarily think either of you support such a theory, for that matter, nor am I making any argument for or against that theory itself.
April 1992.
Given that Pioneer fooled around in the Solar System for a while, making flybys of Jupiter and Saturn, our calculation should be a bit different. 1992 is a useful lower bound, which we arrived at by calculating what would happen if Pioneer took a straight path out into interstellar space. In fact, it flew by Saturn in September 1979. A bit of trigonometry tells me that if it left Saturn in a straight line tangent to that planet’s orbit, it would probably reach the critical distance some time between ’95 and ’97, depending on Earth’s own position in its orbit. This rough map seems to suggest that it did take that approximate path, but it’s hardly accurate. If Pioneer skirted closer to the sun again, inside Saturn’s orbit on it’s way out then the critical distance comes later, but if it veered away harder then it comes earlier.
I had typed my calculations up, but I lost them just now when I accidentally pressed the back button. Hell’s bells and buckets of blood.
Anyway, basically what this tells us is that Quirrel probably has at least a few years of grace before Pioneer gets too far away, if that is in fact what’s going on. I think there’s a fair likelihood that this theory is correct, but given what I’ve said here, I don’t think the timing of the Pioneer’s critical distance should be counted as strong evidence in favour of that.
Thanks for the calculations… I had a rough guess that 6 light-hours was reached some time in the 90s, but didn’t know enough about the flight-path to check this.
I believe that the 6 light-hour limit only makes sense as a theory if Quirrell is going to hit it in this school-year (and it explains why it is impossible for him to continue as a teacher next year). If he’s still got a few years grace it doesn’t work so well, and I suspect that Eliezer would have done a detailed calculation if he was relying on this theory, rather than a rough-and-ready / linear interpolation calculation.
However, I still like the idea of Quirrell being hoisted by his own genius petard (and by his hatred of science, since if he’d bothered to study it, rather than just using it, he might have avoided that mistake).
How’s he supposed to know that the Horcrux connection craps out at six light-hours? Presumably he’s the first to have a Horcrux anywhere but Earth.
From Chapter 61:
If information cannot travel back more than six hours, and a “soul” (stored on a Horcrux) is information (as Quirrell describes it), then it is a reasonable guess that the soul cannot travel over a spatial separation of more than 6 light-hours. Further than that, and it seems the soul parts must fall out of synch, though exactly what happens then is anyone’s guess. Does Quirrell die? Are there two separate Quirrells, one stranded permanently on Pioneer, and the other on Earth? Can the one on Earth be killed, even if the one on Pioneer is never destroyed?
This does seem to be a constraint that exclusively affects the time-turners. Otherwise prophesies wouldn’t be possible. It also seems like it’s an artificial rule rather than a deep law of magic because after the Stanford Prison experiment, Bones tells Dumbledore that she has information from four hours in the future and asks whether he’d like to know it. That there is relevant information from four hours in the future is information from the future—she would not have said that if it were otherwise, so it seems there must be exemptions of that kind.
Alternative hypothesis: prophesies are jive, and Eliezer didn’t think of the other thing.
That’s information to a careful logical thinker. There’s a lot of evidence that magic to a large extent acts as a naive person might expect reality to act. Broomsticks and the bag of holding are both examples of this.
More then 6 hours in what reference frame?
Returning to this thread after a few months...
I see Eliezer has responded in a way which kills my theory stone cold. (Though it was dead anyway if the 6 light-hour separation by Pioneer wasn’t reached in 1992.)
But basically what I was thinking was this. Consider any two space-time points x and y. Either they have a time-like separation, or a space-like separation or a null separation. If they have a space-like separation then there is a particular inertial reference-frame in which they are only separated in space, not in time. If the spatial separation in that frame is > 6 light-hours, then information cannot travel from x to y. (Or, if you want to think of it in terms of a causal graph, and Pearl’s intervention calculus, then every intervention to the graph at x will leave events at y unaltered.)
Incidentally, this formulation implies the rule that “information can’t go back in time more than 6 hours” and implies it in any inertial reference frame. For if information could travel from x to a point z, more than 6 hours in the past of x (but at the same place) in some reference frame, then it could be sent further along a future-pointing null vector from z to y (by an ordinary light-beam), where y is > 6 light-hours from x in the same reference frame. So the restriction of “no spatial jumps > 6 light-hours” neatly implies “no temporal jumps back > 6 hours”.
Basically, this looks something like the Minkowski interval formulation: there is no privileged reference frame, just a new constant of nature (i.e. whatever 6 light-hours translates to in Planck lengths).
The problem is that points that 6 light-hours away from X have points more than 6 light-hours away from X in their future light cone.
So the issue here is that we might have three points x, y and z, where x and y have a space-like separation, y and z have a time-like or null separation (which is future pointing from y to z) and x and z have a space-like separation. Further, d(x,y) < 6 (measured in light hours), but d(x,z) > 6.
If so, then the principle I described would prevent information passing from x to z. So it either prevents information transmission from x to y; or if a Time-Turner has already been used to get info from x to y, prevents the further transmission from y to z. The last would be a very interesting effect, because either there is no communication attempt from y to z at all, or the usual communication methods—like light-beams—are attempted, but fail for some reason.
Alternatively, suppose the principle I described is wrong, and info can move from x back in time to x’, then forward to y, then to z by the usual physical means. Then I believe we can make d(x,z) arbitrarily large and this opens up some even more exciting possibilities.
Consider a two-dimensional example, with one space and one time co-ordinate—space first then time. Fix a particular inertial reference frame. Point x is (0,0), point x’ is (0, -delta) i.e. a tiny bit in the past of x. Point y is (delta, 0) i.e. a tiny bit spatially separated from x, and then point z is (delta+t, t) i.e. t hours in the future from y along a light beam through x’ and y.
Then d(x,z) = Sqrt( (delta+t)^2 - t^2 ) = Sqrt(2 x delta x t + delta^2) which of course grows without limit as t gets arbitrarily large. And there is some reference frame in which x and z are that distance apart spatially. So now here’s a neat trick. Imagine that Harry wants to send a message to the Andromeda galaxy, but without it taking two millions years to arrive. Let’s say that x is the Earth now, and z is somewhere in Andromeda which is approximately “now” in the Earth’s reference frame, and in cosmological terms (e.g. at z, measurements of the temperature of the background radiation and the Hubble constant are the same as at x). Then Harry finds a suitable alternative reference frame in which to pick the points x’ and y, uses a Time Turner to send a message from x to x’, then uses ordinary light to send it through y to z. Instant magical faster-than-light signalling out to any distance! And indeed faster-than-light space travel as well, provided he can transfigure rockets that travel at near-light speed...
The reference frame of the Heart of Magic, naturally.
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.
… 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?)
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.
Unless MoR is going to include an explanation of how magic is implemented in terms of known (or new and deeper) laws of physics, Harry might as well not be made of atoms. After all, modern technology conveniently doesn’t work near magic so we can’t investigate the matter...
Which should Harry believe at this point: that the Ultimate Law is better described as fundamentally Muggle physics with a Source of Magic built on top; or that the Ultimate Law is an alien, magical, human-intuition-confirming system where someone once cast a big spell that specified the Muggle laws of physics? Hell, if the existence of magic is actively erased from the minds of Muggles, maybe we shouldn’t put too much trust in the Muggle evidence for the natural evolution of humans, or for the age of the world.
I might be missing something obvious, but I don’t think it implies single world quantum mechanics. It certainly makes it messier thou.
You could put something sorta like a Time Turner in MWI. But I don’t see any way to do it that would reliably result in consistent time-loops, as opposed to people observing different results in their second pass than they remember from the first.
You can’t have a “stable time loop” without a single future.
You sure can! It’s a bit hard on the complexity, but probably less so than spontaneous collapse.
there are a bunch of different versions, the most obvious (but not only) class consists of proceeding the simulation as if time travel didn’t exist then pruning paradoxical branches retroactively. There’s tweaks and hacks needed to figure out how that actually works with interference, and to fix the problem of any branch where time travel is invented at all losing all it’s measure in effect acting as a probability pump preventing it, but you’re smarter than me and can probably work out better versions.
Just think about it for 5 minutes. ;p
Can’t you have mixed states that are stable or at least self-consistent? Something like there’s a 50% chance you go back and kill your grandfather and there’s then a 50% chance you don’t exist? I seem to remember David Deutsch discussing something similar at one point.
Yes, but that’s not a “stable time loop” as portrayed in either cannon or MoR.
You can if nearby Everett branches reinforce each other and ‘bleed over’ into each other. Then you wind up with a bifurcation diagram, with each path’s “weight” based on the number of other paths that are close/similar enough to reinforce it, and some paths can converge into the internal appearance of a stable time loop.
It may be better to put it like this: “if there are many worlds, then time travel would generally create loops across worlds; it does not force consistency within a single world”.
However, if the Source of Magic is careful how it sets up the loops, it can force a consistent outcome, or at least force one of the consistent outcomes to become much more probable than any inconsistent outcome (one which loops between worlds). In particular this still allows any NP problem, or indeed any PSPACE problem, to be solved in polynomial time using tricks like Harry’s factorisation attempt (though perhaps with a small probability of failure). See Scott Aaranson’s wonderful lecture here.
So the fact that Harry always observes a consistent single-world loop doesn’t by itself imply a single world interpretation, or any non-computability. It simply means that the Source of Magic is a PSPACE oracle!
As soon as I saw the stable time loop in HPMOR, I thought, “Oh, they’re all in a simulation.”
I think a simulation (Y) is a process of mimicking something else (X). In which case we should not observe in Y something (Z) that couldn’t happen in X.
So maybe we should rather say that Y is a game with otherwise X-like rules, but additional rules that allow Z, rather than calling it simulation. Or at least I think if “simulation” Y is not an accurate simulation of X, we should use some explicit qualifier to indicate its non-accuracy.
Could this constraint apply in other ways? Suppose magic is the result of something that responds to the wishes of witches, as suggested at one point. If that something is Earth-based, perhaps a wizard on an outbound spacecraft would stop being able to do magic when he reaches 6 light-hours out. An interesting experiment.
Harry might be able to realistically do an experiment similar to this as a first year if there is a magic spell that lets you communicate with an object. He could use a spell to accelerate that object to a very high speed and then check in on it as it approaches the 6 light-hour point.
Idea: Dumbledore says
Maybe the Pioneercrux is dragging the shade-part into space.
...I meant April 1992 is when Taboo Tradeoffs happens.
I know. Gastogh made the 1992 calculation. I was making the point that although Gastogh calculated Pioneer to have reached the critical distance of six light-hours in 1992, and you pointed out that Taboo Tradeoffs was happening in 1992, we shouldn’t take this coincidence as evidence in favour of the theory that communication between horcruxes and their master is limited to light speed, and that this is somehow related to time turners. I don’t necessarily think either of you support such a theory, for that matter, nor am I making any argument for or against that theory itself.