If the inertial mass of a spell is greater than its gravitational mass, it would appear that the spell doesn’t react to gravity as much as it should. It is also possible that spells work a bit like brooms.
Gravity doesn’t work that way. Something not reacting to gravity under general relativity is like something stopping under special relativity (or even Galilean invariance). However, considering that there’s a spell that does just that, this doesn’t mean much.
I hereby declare Arresto Momentum to match the velocity of a small mass to the velocity of some much larger mass that the wizard thinks is a reference frame.
Does that mean Harry can’t use it (becuse there is no universal reference frame) or he can use it in all sorts of munchkiny ways (I stop the car … relative to the moon!)
Now I come to think, he would probably just conclude it uses Earth as a reference frame, just as broomsticks use Aristotelian physics and transfiguration uses form/substance duality.
You can’t use Arresto Momentum for that; you need a much more massive object as a reference, but your reference frame only contains massless objects. I guess you could say that massless objects have much larger mass than other massless objects, and use Arresto Momentum to make photons go in arbitrary directions with negligible losses.
If you can make a surface cast a long-lasting Arresto Momentum, you have a near-perfect mirror for all wavelengths from radio to gamma and all angles. That would be useful. (Of course you can also make the light slower if you wish, but the fun you can have with arbitrary refractive indices with no wavelength dependence and no absorption is redundant here.)
Also, if we figure out the necessary ratio of masses at given magical energy, we can use the spell to measure mass. Assuming your aim is precise enough to Arresto Momentum a neutrino, anyway.
So what would it do with a wizard who had truly internalized the principle of relativity, and who understood that there was no privileged reference frame? Could he use it to de facto impart an arbitrary velocity to an arbitrary object?
impart an arbitrary velocity to an arbitrary object?
You can equalize velocity of a given small object with that of the caster’s reference frame. The excess momentum is transferred to the Earth (or potentially another massive body, though there is no proof that magic works outside the Earth’s atmosphere, which incidentally means that the Pioneercrux may have decayed). This way there is no preferred reference frame.
Of course there’s no proof, but I don’t think it’s really possible, if only for literary reasons, that the Sphere of Stars spell is just a fancy hologram. I think we can take that as fairly strong evidence it’s working as intended.
So “arbitrary” might be a bit strong, but what’s to prevent him from using the Moon or the Sun as a reference frame? Or even the Earth as a whole, instead of the local part? Even imparting a relative 1000 mph to an object near the equator would be pretty powerful.
Just saying that if the spell is designed to work relative to the rest frame, then no amount of relativistic internalizing will change how it works. Of course it is possible in the HPMOR universe to design new spells, and a competent Wizard with a good grasp of invariance in physics might be able to create a new spell, Attache Momentum.
You are right, he did phrase it this way, which makes this spell unreasonably easy to munchkin. He would have probably thought harder about it were he a DM of an actual DD game.
It seems like a hack of the rules on the level of partial transfiguration. Also, if you house-rule that it requires “magical energy” in proportion to the delta-momentum, it shouldn’t be too overpowered.
Actually, Eliezer has stated that he deliberately inserts impossible details in all his stories because he’s disturbed by the notion that they might be simulated somewhere. I wouldn’t expect it to affect the plot, though.
Didn’t he say that he mentioned the time-turner because it disproves the simulation hypothesis? It would also guarantee that nobody would simulate it.
He seems to have figured out how to simulate it later, but that requires simulating everything, and there’s no guarantee that there will even be a reality with a stable time loop, unless you have the infinite number of realities necessary to allow connectedness, in which case you can’t possibly simulate all the possibilities.
Actually, there is a guarantee that there will be a stable time loop. Look up the Novicov Consistency Principal some time. And I think that was to stop people speculating that magic was being provided by the Matrix Lords, although sadly it doesn’t. I was referring to the corridor tiled with pentagons (although it never actually says they were regular pentagons) and the spiral staircase that lifts you by rotating.
The Novicov Consistency Principal relies on the Kakutani fixed-point theorem, which relies on convexness, which implies connectedness, which implies an infinite number of realities.
I admit I’ve never seen a proof of the Novikov Consistency Principle. I know that’s how I’d prove something like that, and I know I could easily come up with a case of time travel with no possible stable time loop of I’m given a discrete space, a non-compact space, etc.
Sorry, I cannot find a link, but feel free to ask what does not make sense. As for the stable time loop, I’m not sure that it is always possible to find, given that you apparently want to fix both initial and final conditions of a hyperbolic PDE, unless I misunderstand what is involved in constructing such a loop.
But if you had done such arduous research as, say, reading the Wikipedia page for the NCP, you would see that a sum over histories using only non-paradoxical timelines apparently works. Not that I really understand that in more than a superficial way, but it sure as hell sounds like an answer to your point.
There are only guaranteed to be non-paradoxical timelines if you have an infinite number of realities, which is what I was saying from the beginning.
You could look for all the timelines that are within delta of being a paradox. I think the shadowing theorem guarantees that, for small enough delta, this is epsilon-close to a non-paradoxical history. I don’t think it tells you what delta is, and I don’t think it’s guaranteed that every non-paradoxical history will be shadowed. This would mean that you’re not randomly picking the choice of history. More importantly, it might be that none of the non-paradoxical histories are shadowed, and you’ll have no idea what to look at.
Do random samples until you find enough, then. It wouldn’t be perfect, but it should be close enough that you wouldn’t notice with enough computing power, right?
I can think of ways to simulate those quite easily. It does involve cheating with the environment, but not really cheating with any minds. Mostly the same kinds of tricks mentioned in Eliezers “that’d it take to make me belive 2+2=3” article.
Like, for example, deforming the tiling pattern constantly so that it was always the right type of angles and side lengths where the eyes were looking, and stopping the motion detection from going of on those changes. Or have the stairs tile exactly, just snap people on them up in exact increments of tiles, and again doing clever things with the way motion is detected in the eye.
The pentagons are doable, if you’re willing to cheat, but the spiral staircase is harder; spiral staircases appear to lift things but actually don’t. What would an optical illusion that was true be like? How do you build Penrose steps in 3d?
Probably, but these are not mutually exclusive. If Dumbledore is right, the set of rules that the HPMOR world runs on are the laws of Narrative Causality.
Appearances
Harry Potter and the Prisoner of Azkaban (First mentioned)
Harry Potter and the Prisoner of Azkaban (film) (First identified as Aresto Momentum)
It looks to me like they established that there is a spell that does that, but it wasn’t named until the movie. I suppose without the name there’s no real evidence that it doesn’t just accelerate the subject in any way the caster pleases.
In any case, in the MoR verse, the brooms act in a manner that involves some sort of rest state. Also, as of Eliezer’s reply to this post, that spell canonically exists in the MoR verse.
Well, it’s the name that actually tells us it’s “arresting momentum” and not, I don’t know, stopping him getting too close to the ground or some sort of anti-gravity spell. The scene is in the book, but the spell itself is not.
(The wiki treats the films a canon when they don’t actually contradict the books, instead of a separate canon like most sane people would. They do the same for everything, in fact, from videogames to trading cards, although they draw the line at fanfiction.)
If the inertial mass of a spell is greater than its gravitational mass, it would appear that the spell doesn’t react to gravity as much as it should. It is also possible that spells work a bit like brooms.
Gravity doesn’t work that way. Something not reacting to gravity under general relativity is like something stopping under special relativity (or even Galilean invariance). However, considering that there’s a spell that does just that, this doesn’t mean much.
I hereby declare Arresto Momentum to match the velocity of a small mass to the velocity of some much larger mass that the wizard thinks is a reference frame.
Does that mean Harry can’t use it (becuse there is no universal reference frame) or he can use it in all sorts of munchkiny ways (I stop the car … relative to the moon!)
Well, for one thing, he’s not powerful enough to cast it period, but if he were, I expect it would only work on near / nearest masses.
That requires original research, like partial transfiguration.
That’s what I had in mind, yes.
Original research is dangerous. This original research in particular seems dangerous.
Now I come to think, he would probably just conclude it uses Earth as a reference frame, just as broomsticks use Aristotelian physics and transfiguration uses form/substance duality.
http://en.wikipedia.org/wiki/The_Billiard_Ball
You can’t use Arresto Momentum for that; you need a much more massive object as a reference, but your reference frame only contains massless objects. I guess you could say that massless objects have much larger mass than other massless objects, and use Arresto Momentum to make photons go in arbitrary directions with negligible losses.
If you can make a surface cast a long-lasting Arresto Momentum, you have a near-perfect mirror for all wavelengths from radio to gamma and all angles. That would be useful. (Of course you can also make the light slower if you wish, but the fun you can have with arbitrary refractive indices with no wavelength dependence and no absorption is redundant here.)
Also, if we figure out the necessary ratio of masses at given magical energy, we can use the spell to measure mass. Assuming your aim is precise enough to Arresto Momentum a neutrino, anyway.
So what would it do with a wizard who had truly internalized the principle of relativity, and who understood that there was no privileged reference frame? Could he use it to de facto impart an arbitrary velocity to an arbitrary object?
You can equalize velocity of a given small object with that of the caster’s reference frame. The excess momentum is transferred to the Earth (or potentially another massive body, though there is no proof that magic works outside the Earth’s atmosphere, which incidentally means that the Pioneercrux may have decayed). This way there is no preferred reference frame.
Of course there’s no proof, but I don’t think it’s really possible, if only for literary reasons, that the Sphere of Stars spell is just a fancy hologram. I think we can take that as fairly strong evidence it’s working as intended.
What is it then? A signal sent from the pioneer horcrux?
So “arbitrary” might be a bit strong, but what’s to prevent him from using the Moon or the Sun as a reference frame? Or even the Earth as a whole, instead of the local part? Even imparting a relative 1000 mph to an object near the equator would be pretty powerful.
“the caster’s rest frame” is relativistically invariant.
But he didn’t say “the caster’s reference frame”, he said “some much larger mass that the wizard thinks is a reference frame”.
Just saying that if the spell is designed to work relative to the rest frame, then no amount of relativistic internalizing will change how it works. Of course it is possible in the HPMOR universe to design new spells, and a competent Wizard with a good grasp of invariance in physics might be able to create a new spell, Attache Momentum.
And I’m just saying, the way Eliezer phrased it above, there’s no singular reference frame—any suitable mass will do.
You are right, he did phrase it this way, which makes this spell unreasonably easy to munchkin. He would have probably thought harder about it were he a DM of an actual DD game.
It seems like a hack of the rules on the level of partial transfiguration. Also, if you house-rule that it requires “magical energy” in proportion to the delta-momentum, it shouldn’t be too overpowered.
Magic works like the author of the story wants it to work.
I think it’s safe to say that the HPMOR universe still runs on some sort of rules, even if they’re not the usual ones Einstein taught us.
Actually, Eliezer has stated that he deliberately inserts impossible details in all his stories because he’s disturbed by the notion that they might be simulated somewhere. I wouldn’t expect it to affect the plot, though.
Didn’t he say that he mentioned the time-turner because it disproves the simulation hypothesis? It would also guarantee that nobody would simulate it.
He seems to have figured out how to simulate it later, but that requires simulating everything, and there’s no guarantee that there will even be a reality with a stable time loop, unless you have the infinite number of realities necessary to allow connectedness, in which case you can’t possibly simulate all the possibilities.
Actually, there is a guarantee that there will be a stable time loop. Look up the Novicov Consistency Principal some time. And I think that was to stop people speculating that magic was being provided by the Matrix Lords, although sadly it doesn’t. I was referring to the corridor tiled with pentagons (although it never actually says they were regular pentagons) and the spiral staircase that lifts you by rotating.
The Novicov Consistency Principal relies on the Kakutani fixed-point theorem, which relies on convexness, which implies connectedness, which implies an infinite number of realities.
It does not.
I admit I’ve never seen a proof of the Novikov Consistency Principle. I know that’s how I’d prove something like that, and I know I could easily come up with a case of time travel with no possible stable time loop of I’m given a discrete space, a non-compact space, etc.
What does it rely on?
Solely on the uniqueness of the metric in GR.
Do you have a link to a better explanation?
Also, can you explain how this could be used to find a stable time loop?
Sorry, I cannot find a link, but feel free to ask what does not make sense. As for the stable time loop, I’m not sure that it is always possible to find, given that you apparently want to fix both initial and final conditions of a hyperbolic PDE, unless I misunderstand what is involved in constructing such a loop.
Couldn’t it be approximated?
The theorem doesn’t tell you how to find a fixed point. It only tells you that one exists.
But if you had done such arduous research as, say, reading the Wikipedia page for the NCP, you would see that a sum over histories using only non-paradoxical timelines apparently works. Not that I really understand that in more than a superficial way, but it sure as hell sounds like an answer to your point.
There are only guaranteed to be non-paradoxical timelines if you have an infinite number of realities, which is what I was saying from the beginning.
You could look for all the timelines that are within delta of being a paradox. I think the shadowing theorem guarantees that, for small enough delta, this is epsilon-close to a non-paradoxical history. I don’t think it tells you what delta is, and I don’t think it’s guaranteed that every non-paradoxical history will be shadowed. This would mean that you’re not randomly picking the choice of history. More importantly, it might be that none of the non-paradoxical histories are shadowed, and you’ll have no idea what to look at.
Do random samples until you find enough, then. It wouldn’t be perfect, but it should be close enough that you wouldn’t notice with enough computing power, right?
I can think of ways to simulate those quite easily. It does involve cheating with the environment, but not really cheating with any minds. Mostly the same kinds of tricks mentioned in Eliezers “that’d it take to make me belive 2+2=3” article.
Like, for example, deforming the tiling pattern constantly so that it was always the right type of angles and side lengths where the eyes were looking, and stopping the motion detection from going of on those changes. Or have the stairs tile exactly, just snap people on them up in exact increments of tiles, and again doing clever things with the way motion is detected in the eye.
The pentagons are doable, if you’re willing to cheat, but the spiral staircase is harder; spiral staircases appear to lift things but actually don’t. What would an optical illusion that was true be like? How do you build Penrose steps in 3d?
Inception sort of almost pulled it of.
Nah, that scene only works from the right angle.
Probably, but these are not mutually exclusive. If Dumbledore is right, the set of rules that the HPMOR world runs on are the laws of Narrative Causality.
You know that spell was invented for the film, right?
According to the wiki:
It looks to me like they established that there is a spell that does that, but it wasn’t named until the movie. I suppose without the name there’s no real evidence that it doesn’t just accelerate the subject in any way the caster pleases.
In any case, in the MoR verse, the brooms act in a manner that involves some sort of rest state. Also, as of Eliezer’s reply to this post, that spell canonically exists in the MoR verse.
Well, it’s the name that actually tells us it’s “arresting momentum” and not, I don’t know, stopping him getting too close to the ground or some sort of anti-gravity spell. The scene is in the book, but the spell itself is not.
(The wiki treats the films a canon when they don’t actually contradict the books, instead of a separate canon like most sane people would. They do the same for everything, in fact, from videogames to trading cards, although they draw the line at fanfiction.)