Ok, my head hurts, what is going on with Quirrell?
was performed on a moving planet
Of course. This suggests that the spell uses something as a reference. If it’s the caster, then casting Aresto Momentum on a tree while riding the TGV will cause the tree to suddenly start moving at a few hundred km/s. If it’s the planet, casting it on an object inside the train will have the same effect. Wizards might not use fast vehicles a lot, but even the Hogwarts train and the flying brooms are fast enough to be very dangerous with heavy objects.
(That said, I don’t think there are any examples, in canon or MoR, of the spell being used for anything other than falling objects. If it only does that, then it’s much less dangerous in normal life, especially in a society without high-speed elevators, and it makes a bit more sense, though the name is even sillier.)
You could probably make Arresto Momentum relatively safe by having it choose between the caster's frame of reference and the earth's (at the caster's position) based on whichever results in the spell doing less work. It's still dangerous, obviously casting it on someone else's moving vehicle would be a bad move, but it avoids making anything go "zoom" in a privileged frame of reference.
Broom-spells are cast long before the rider gets on.
Yes, you’re right, the analogy was not correct. But my point is that it appears that the broom spell does what’s intuitive, and the transfiguration spell apparently does not.
think if nobody warned about the dangers of transfiguration there wouldn't be any issues?
No, in MoRverse at least people would die. But that’s my point, it’s weird that you need dire warnings that transfiguration doesn’t work as you might expect, but pretty much every other spell we’ve seen does not require such warnings, even if very powerful (e.g., time-turners; note that Harry was terrified, and Minerva acted less concerned than if she gave him a bike).
shallow expectations don't seem to have much of an effect on transfiguration
Exactly. Why do they seem to have an effect in other cases?
For example, a teleport spell will also have to compensate for the difference in velocity between the departure and destination. But the shallow expectation is that you’ll arrive stationary, and it works as you expect. Also, it takes with you whatever you’re wearing, even in a pocket, and presumably even if you don’t know you have it on you, but doesn’t take the carpet you’re standing on (and so do time-turners).
Aresto Momentum itself looks very safe on first view, and nobody warns about, say, casting it while inside a moving vehicle (depending on what it actually means, which if you think hard about it is not very clear, it should be very dangerous to cast it on objects inside or outside the vehicle).
Time turners don’t drop you in outer space. Brooms partly ignore inertia. Tooth-growing charms don’t break your jaw. Accio doesn’t seem to kill people or destroy property, even if you summon an object from very far away, and doesn’t work on buildings. Fold-space objects have limited capacity, but one can enter a space-folding trunk while holding a space-folding pouch without needing to think about the possible consequences. Floo powder protects you not only from the burning, but also from suffocation and CO poisoning (you keep your head in the fire to use it for communication).
Even accidents are somewhat intuitive: an extra cat hair in Polyjuice can give you cat attributes instead of blowing up or not working at all. Varying pronunciation varies the kind of bats you can summon, but all variations are benign (e.g., it makes green-glowing bats instead of X-ray–glowing bats).
It’s not obvious why the same does not happen with transfiguration. (One might expect that if you break the transfigured object, the original might be broken, but movement of molecules in what appears to be a solid is not intuitive.)
What’s even weirder is that if you think even deeper about it, it should be much worse. For example, if you transform something into a liquid, the original should probably disintegrate completely. But Minerva’s desk looks normal, even though almost 10% of the pig (the blood) is completely shuffled. (Also, if you can make a pig, and you can transfigure a person (dangerously), you should be able to transfigure a dozen stones into a dozen copies of yourself. The copies are doomed, of course, but it’s still weird nobody ever made a temporary army of themselves.)
Arresto Momentum itself looks very safe on first view, and nobody warns about, say, casting it while inside a moving vehicle
Every single casting of Arresto Momentum ever was performed on a moving planet, which resulted in no issues. It's possible that casting from inside of a moving vehicle to outside of it might result in problems, but I strongly doubt that it'll do anything which would seem bizarre from the caster's frame of reference.
There is another point which wasn't discussed much, but does trouble me : the "outpouring of magic" that happened in chapter 89 when Hermione died.
It's the first time we heard about anything like that happening after a wizard death. It's not canon. It wasn't hinted to before, like Dumbledore didn't speak about it in "pretending to be wise", when he tries to convince Harry souls exist. Harry didn't feel it when his parents were killed. Harry didn't feel it when Rita Skeeter is killed by Quirrell. That's a lot of evidence pointing to it not being the common thing that happens when someone dies.
And yet, Harry doesn't ask any question about it, he doesn't try to know if it happens rarely (and then in which circumstances ?) or frequently, or if it's even an entirely new phenomena, it doesn't ask around if it could be faked, ...
Some possibles explanations :
It's the Source of Magic recording the brain state of person when it dies, allowing for resurrection before. But then, why no hint about it before ? Why Harry didn't feel it for Rita ?
It's the Source of Magic recording the brain state of person when it dies, but the Source of Magic didn't use to do it. Harry had to hack the Source of Magic to implement it. And he had to cleverly use Time Turners so he could hack it before Hermione's death.
Someone made an Horcrux of Hermione, and it's the Horcrux that gives the feeling.
It doesn't occur usually, but it does occur because of a bond between Hermione and Harry, be it just "love magic" or be it with Hermione being bound to House Potter.
This is purely faked (either memory-charm, or a fake feeling) by either Dumbledore or Quirrell (maybe using a Time Turner) to try to convince Harry that Hermione is really dead so he doesn't do any folly to try to save her (but then, it seemed to fail).
I don't think Rita Skeeter is good evidence. It would not do for Quirrell to have Harry notice an unexpected, strange burst of magic when he's trying to quietly kill someone; Quirrell would have found a way to suppress it, if it had existed. (It's also possible that her Animagi transformation suppressed the effect.) The absence of the burst of magic in Harry's parents' deaths, on the other hand, has led me to an inverse suspicion to yours...
Of course, he will have problems once someone starts trailing him.
It is notoriously difficult to trail someone who is wearing the True Cloak of Invisibility, with added anti-detection charms because apparently the Deathly Hallow just wasn't enough.
Harry seems to think of puberty as purely binary. It's not; it's a gradual process. I don't know what deficiency in Harry's education led him to think this way, but it fumbles all of his thoughts about puberty.
Harry almost seems to be reasoning as follows:
Puberty doesn't work that way.
Or, Harry is summarizing a wide variety of observations on the topic of puberty in a pithy and relatively un-embarrassing fashion. We don't know Harry's actual basis for claiming that he hasn't yet begun puberty, but his comments on the subject are just a little too flippant to be the complete truth.
It occurs to me that I've seen very little mention of one major dangling plot thread: The Interdict of Merlin. Bypassing the interdict may get Harry sufficient power, without necessarily getting at 'the source of magic' or becoming omnipotent.
There's some precedent for this: partial transfiguration, patronus 2.0, and acorn brewing were all made possible by understanding something others did not. It's possible that the Interdict is something similar, and that Harry will be able to understand his way through it.
This mechanism appears to have been used in other of Eliezer's works as well, for example the "Jeffreyssai" stories in the Sequences.
The problem is that "bypassing the Interdict" is not, on its own, useful; it's only valuable if Harry happens to have written notes on powerful magic spells that are censored by the Interdict. Apparently, there's a loophole allowing Interdict-restricted material to exist (wizards can keep notes for themselves, implied by chapter 23), but it seems unlikely that Harry would be able to get ahold of much of it. (Possible exception: Bacon's diary? Quirrell didn't think Bacon found much of interest, but he could be wrong.)
Related: since Muggle physics can apparently contribute to powerful magics (see: partial transfiguration) would the Interdict apply if Harry ever wrote a physics book? What would the Interdict do if a Muggle happened to accidentally write (presumably as fiction) the details of a powerful magic spell? Can Muggles read Interdict-restricted works?
Many people seem to suggest time-turner tricks for Harry to hide Hermione body. But that raises a few issues to me :
Do we have any evidence for or against the fact that the Hogwarts wards, or more generally a spell that Dumbledore could cast, would inform him of the usage of time-turner inside Hogwarts ? There is mention of "anti-time-loop ward", could there be "time-loop detecting wards" ?
Dumbledore didn't seem to check if Harry used his time-turner or not, and he didn't even ask him if he did. That's suspicious. It seems surprising that Dumbledore goes to great length to do a careful check of Harry's belonging, despite the social cost of doing so, and yet, not a single mention of the time-turner. Not even casually like the portkey. From an "outsider" point of view, it points to the fact Harry used it. Or at least, it would from many authors, but such a "oh well the NPC just didn't think about that major plot device" hand-waving doesn't seem at all to be Eliezer's way of doing things.
Time-Turners are in frequent and authorized use by a fair number of students, as well as Dumbledore himself and possibly other staff members. Any such ward would be constantly triggering, for no particularly important reason. Even if one exists, I can't imagine that Dumbledore pays much attention to it.
Dumbledore is only looking for Hermione. There's no reason for him to be much interested in Harry's magical devices, beyond proving that they aren't Hermione. The portkey was only mentioned because it was a part of Dumbledore's body search; the Time-Turner, presumably, wasn't on his body.
Note that Harry has no legitimate way to know what an Inferius is.
Also, I highly doubt that Hermione is in the ring - it's just too awkward, it risks detection, if it gets detransfigured in a critical situation then suddenly he has to lug Hermione's body around while fighting off Voldemort or something.
It's far more likely to be an anonymous brick, marked with, oh, let's say a stylized helium atom, that he placed in plain sight somewhere. Shame he doesn't know about the Room of Requirement, or he could've used the Room of Lost Things...
Inferi appear to be common knowledge; they're cited in casual contexts in chapters 70 and 78, by Lavender Brown and the narrator respectively.
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A few weeks ago I began reading the visual novel Umineko no Naku Koro ni, partially because I enjoyed the Higurashi anime and partially because Tuxedage said it was a mindfuck; I'm up to 3 of 8, and it's becoming clear that this VN is going to take a while, to say the least. (I've never read any visual novels before, so I was not sure what to expect.)
The cramped window and tedium of having to constantly hit the spacebar to advance lines aside (I wish I could just tell it 'my reading speed is 400WPM, please advance at that rate automatically except for dialogue'; visual novels seem to have the worst of both worlds of novels & anime, where they show as little information as a screen of an anime yet still force you to choose your own pacing without interaction being as easy as a novel where you read an entire page before needing to take any physical action), I'm enjoying it. It's an interesting mystery setup, I was able to beat the protagonist to some of the solutions which gratifies my ego, and recently it showed off the best use ever of Hempel's Raven which pleased the heck out of me.
On the downside, I happened to read ANN's review of the second volume of the manga and apparently the author Ryukishi07 remarks that most readers will be convinced that it's all supernatural and inexplicable (implying that it'll turn out to be like Higurashi, with naturalistic explanations for all the events) - which makes me angry since in the dozens of hours I've spent reading this, I was pretty sure that we were being shown all the events from third-person omniscient perspective, and one of the narrative rules of third-person omniscient is that you don't lie to the reader, and we see plenty of supernatural events from this perspective.
EDIT: final thoughts in my review
Just so you're aware, it's fairly easy to dump the script files from Umineko if you'd prefer to read it that way. There's also an auto mode, which is irritatingly slow, and a skip mode, which I used to skim through the art after reading the script file.
You might prefer the story of the Higurashi visual novels to the anime, and the English release has a configurable (and pleasantly fast) auto mode.