Muggles' Guide to Harry Potter/Magic/Underage Sorcery

Overview
The Decree for the Reasonable Restriction of Underage Sorcery is a law that limits the magic that underage wizards are allowed to use. The apparent intent is to keep young, untutored wizards from running amok with their wands and causing consternation among the Muggles.

Extended Description
Our first introduction to this statute is the note given to every student at the close of each school year; Harry first receives his at the end of Harry Potter and the Philosopher's Stone. Fred and George comment they always hope the note will be forgotten one year, but it never is. While not mentioning the rule by name, the note informs students they are forbidden to perform magic outside of school until they come of age.

Harry first runs afoul of this law in Harry Potter and the Chamber of Secrets when Dobby uses a Hover Charm to destroy a dessert in the Dursleys' kitchen. Evidently, the Ministry assumes Harry performed the magic, because a letter is sent by one Mafalda Hopkirk warning him not do that again.

When Harry accidentally inflates his Aunt Marge, he is deathly afraid that, having violated this Statute, he may now be expelled from Hogwarts (and probably the wizarding world). He decides his only recourse is to become a fugitive, but as he is approaching Diagon Alley to retrieve his money, he is intercepted by Cornelius Fudge, the Minister for Magic. Fudge inexplicably dismisses the inflating incident.

When Harry uses the Patronus charm to protect Dudley from Dementors, he is once again told that he has violated this Decree, and his wand will be destroyed. This results, eventually, in a hearing, at which it is determined that Harry was justified in using magic to defend himself and a Muggle bystander against a magical threat.

While escaping from a horde of Death Eaters at the beginning of Harry Potter and the Deathly Hallows, Harry uses a large amount of defensive magic, despite still being underage when this happens. The Ministry of Magic does not seem to be aware of this, and does not deliver a reprimand to Harry because of it.

Finally, Harry is overjoyed when, on his seventeenth birthday, he is free to use any magic he chooses without hindrance.

Analysis
In Harry Potter and the Deathly Hallows, we learn that the technique that is used to determine whether a Wizarding child has performed magic is called the Trace. This apparently will detect a child using magic by triggering some alert within the Ministry. Apparently, in order to be sensitive enough to register the child using small spells, it also detects other magic being used nearby. We are told that in Wizarding households, it is the parents' responsibility to monitor their child using magic, as adults using magic near him may trigger the Trace accidentally; Muggle-born wizards, however, are directly monitored by the Ministry, as it is assumed that the only magic that can occur near them is their own. This is presumably why Dobby's Hover Charm was attributed to Harry.

One must wonder, though, about the Trace's accuracy. There is no apparent notice when Aunt Marge's glass magically shatters, or the cabinet under the stairs magically unlocks as Harry leaves Privet Drive. There is no apparent notice when magic occurs in Harry's vicinity when he stays at the Burrow, Grimmauld Place, or in Diagon Alley. There is no notice of the magic occurring in his vicinity when he is being visited by Arthur Weasley, the Advance Guard, or Professor Dumbledore at Privet Drive, or when Hagrid is taking him off the island and back to shore in the first book. Additionally, the Trace did not trigger when Harry was casting spells to try and revive Dumbledore in the cavern, or Apparate him back to Hogwarts, in Harry Potter and the Half-Blood Prince, or when he was using defensive magic against Death Eaters in Harry Potter and the Deathly Hallows. If we assume that the Trace can detect an adult wizard, and damp its responses accordingly, then the only unexplained situations are the shattering wineglass and the opening cupboard during Aunt Marge's stay at Privet Drive, and possibly the summoning of the Knight Bus. Those, along with Aunt Marge's inflation, might have been lumped together and forgiven by Cornelius Fudge. The defensive magic use against Death Eaters may be something of an anomaly; Hagrid presumably had been reinstated as a legal wizard by that time, so his close proximity to Harry might have damped the Trace's response, but we suspect, due to the Trace not triggering when Hagrid returned himself and Harry to the shore in the first book, that Hagrid was detected as an adult wizard by the Trace even if his use of magic had supposedly been proscribed. The presence of other, mature wizards, namely the attacking Death Eaters, might also have served to quiet the Trace in the later instance. It is also possible that Rufus Scrimgeour may be trying to cover up the scale of the Death Eater attack, so as to not reveal how powerful Voldemort has become.

However, it is also true that the Ministry does not seem to be aware of Harry's use of magic before he turns eleven and gets his wand. In the first chapters of Harry Potter and the Philosopher's Stone, Harry unknowingly shrinks a horrible sweater down to doll-size so that he won't have to wear it, flies to a rooftop to avoid a beating from Dudley and his gang, regrows his hair overnight, and makes the glass vanish from a snake's cage. However, there are no warnings issued by the Ministry during this time. Possibly the Trace is only activated when the child reaches the age of 11 and is assumed to be consciously able to direct his or her magic. Could the law also prevent selling or giving wands to children under the age of 11?

This still leaves issues with the Trace remaining quiescent when the Twins and Ron are in Arthur's flying car, when Harry joins them, and when Harry and Ron are flying the car to Hogwarts. Certainly the car is a magical artifact, and so the Trace should be active, but none of the underage wizards involved in that escapade receive warnings. Another writer, in another series (Randall Garrett, in the Lord Darcy series), has drawn a distinction between active and passive magic, saying that possessing or using a charmed object is significantly different than actively creating a new spell. It is probably necessary that this same distinction be built into the Trace, as the number of charmed objects in the ordinary Wizarding household that would be used by a child is quite extensive — an infant banging on a self-stirring cauldron with a spoon, for instance, could be considered someone using a magical object. If this distinction was not made by the Trace itself, the Ministry would be overwhelmed with reports of magical objects being used by underage wizards.

Questions

 * 1) How old do Wizarding children have to be in order to legally use magic outside of school?

Greater Picture
As a side light, we note that Harry's being able to do magic at will after his seventeenth birthday proves nothing about whether the Trace has ended ("been broken"). At the time, Harry is in Ron's room, in close company with a wizard who is of age (Ron). In such a situation, as we have noted above, the Trace does not respond to use of magic in the vicinity.

As both Ron and Hermione are of age before Harry, even if the Trace had remained in place, it quite possibly would have remained quiescent as long as Harry remained in their company. So the fact that it had not triggered a warning from the Ministry on Harry's use of magic in the Burrow on his birthday is not a clear indication that it had ceased to exist. As it turns out, there is no point at which Harry was completely out of the company of nominally-mature wizards until after the retreat to Grimmauld Place. Once they have settled there, Harry does Apparate out to the approaches to the Ministry as the Trio plan their break-in. This is the first point in the story where Harry is performing magic at a distance from mature wizards. We believe that this surveillance of the Ministry continues through much of August, starting after Mundungus is brought back to Grimmauld Place, possibly a week after Harry's birthday. So while we cannot be certain exactly when the Trace is broken, it is reasonably certain that it occurred no later than early August, and that it is likely that it occurred as expected on Harry's birthday.

This is worth mentioning because a plot point hinges on it. The Trio leave The Burrow as the news of the fall of the Ministry reaches there, and are then attacked by Death Eaters in a café on the Tottenham Court Road. After the Death Eater attack, Harry wonders if they might have located the Trio by means of the Trace. Ron dismisses that, saying the Trace could not have been re-established since it had broken the day before, as Harry had not been approached by any Ministry wizards in the meanwhile. Despite Ron's assurances, readers may wonder if the Trace could still be active, given that Harry had not been out of the company of mature wizards when doing magic. It will turn out that the mechanism by which they had been discovered was their use of Voldemort's name; Voldemort had placed a taboo on his name, so that Death Eaters could be sent to destroy anyone who dared to speak it. Harry's raising the possibility of the Trace still being active obscures this possibility, until it is revealed by Ron after Christmas.