the most incredible spell in "Half-Blood Prince"

Early on in "Harry Potter and the Half-Blood Prince", the wizard Dumbledore enters a room which is in disarray - items wrecked and disorganized, walls and ceiling missing pieces - and waggles his trusty magic wand. Everything is restored, repaired, and repositioned back to what appears to be the original state of the room. (It trounces Mary Poppins' finger-snap trick.)

This has to be a contender for the most incredible spell in the entire movie. Illumination on demand, movement controlled from a distance, and fire-throwing are great and all, but aren't that fantastic, relatively speaking, from the standpoint of the current level of technological progress. The rollback of the room is more astounding because it reduces entropy without expending energy. Maxwell's demon, thy name is Dumbledore (and you have our condolences).

There's no physical obstacle to roughly accomplishing part of the effect of this Entropy Reversal Spell. Sure, if an automobile crashed into my living room (just posit that I exist in a sitcom and the probability shoots way up!), I or more likely a contracted team of workers could remove the rubble and rebuild the wall to an approximation of its former glory. The energy (and currency) to do so would far exceed zero even apart from questions of efficiency, so reducing the entropy level here would merely increase the entropy level somewhere else.

Instant home repair would still be inferior to the Entropy Reversal Spell, though. To exactly reverse the breaking of a solid or the spill of a liquid first requires the retrieval of all the involved atoms and molecules then the restoration of the orientations and interactions between. Assuming nanotechnology or another technique is up to the task, one of its necessary inputs is an information representation of all those mutual orientations and interactions. Unfortunately, this is a clear case of combinatorial explosion, with the accompanying space and time problems inherent to the data processing. (It'd be a good opportunity to try out your quantum computer.)

Of course, the possible uses for the Entropy Reversal Spell extend far beyond perfect housekeeping. For instance, imagine that an engine - a Carnot heat engine, say - converts a temperature change into usable work. Then, at the tail end of each cycle through the casting of the magic of entropy reversal, the atoms could be restored without energy cost from the less-useful low-temperature state back to the handier high-temperature state. Presto! No more fuel necessary for all time and no harmful emissions, either.

But perpetual motion machines are still thinking too small. Consider the general notion of reversibility. Rolling a pen across my cubicle counter is quite reversible without trouble; just tap it with a finger to move it a few inches then tap it with a different finger to move it back. Putting the pen back on the counter after it falls on the floor takes more work and energy, both because it's a longer distance and because it's working against gravitational force (yeah, yeah, call me lazy for complaining). When the pen falls it moves from a higher (potential) energy state to a lower - the entropy increases and it's more work to reverse. Generally, the greater the entropy change of any occurrence, the harder it is (more work and energy) to reverse, and in any case the reversal ends up increasing overall entropy and energy loss still more because the reversal's energy-efficiency isn't perfect. In contrast, with an Entropy Reversal Spell, entropy isn't a factor anymore and theoretically any occurrence can be reversed without significant penalty. Feeling older all the time? Reverse it and forget about it. Father Time can suck it!

Although entropy reversal is a nifty feat when one can manage it, teleportation should at least get an honorable mention. Yet it's not quite as awe-inspiring since all one needs to do is somehow get all the information describing the object, transfer it elsewhere, and use the information to reproduce the original. Note that you'll need to get your hands on a Heisenberg compensator (find the details online).

Oh yes, I am a nerd.